Applied Science, Faculty of
Electrical and Computer Engineering, Department of
DSpace
UBCV
Wang, Dan
Doctor of Philosophy - PhD
University of British Columbia
Neural networks (NNs) have reached remarkable performance in computer vision. However, numerous parameters and complex structures make NNs opaque to humans. The failure to comprehend NNs may raise serious issues in real-world applications. My research aims to explore the NN interpretability in diverse visual tasks from post-hoc explanation and intrinsic interpretability perspectives. Convolutional neural networks (CNNs) have outperformed humans in image classification. However, the logic of network decisions remains a puzzle. As such, we propose concept-harmonized hierarchical inference, a post-hoc explanation framework, to explain the decision-making process of CNNs. Firstly, we interpret layered feature representations of NNs with hierarchical visual semantics. Then we explain the NN feature learning as a bottom-up decision logic from low to high semantic levels in which a deep-layer decision is decomposed as a sequence of shallow-layer sub-decisions. With the evolution of virtual reality, researchers are focusing increasingly on inverse rendering: reconstructing a 3D scene from multi-view 2D images. In this field, NNs achieved superior performance in novel view synthesis and 3D reconstruction. For both tasks, learning a 3D representation from input views is the key process where prior methods separately designed a CNN-based single-view feature extraction and a pooling-based multi-view fusion. This incoherent design damages their intrinsic interpretability and performance. Therefore, we aim to design coherent, interpretable NNs that can adequately exploit knowledge of relationships from data. For novel view synthesis, we propose a unified Transformer-based neural radiance field (TransNeRF) conditioned on source views to learn a generic 3D-scene representation. TransNeRF explores deep relationships between the target-rendering view and source views. TransNeRF also improves intrinsic interpretability by enhancing the shape and appearance consistency of a 3D scene. In experiments, TransNeRF outperforms prior neural rendering methods, and the interpretation results are consistent with human perception. We reformulate 3D reconstruction as a sequence-to-sequence prediction and propose an end-to-end Transformer-based framework (EVolT). EVolT jointly explores multi-level associations between input views and the output volume-based 3D representation within our encoder-decoder structure. EVolT achieves state-of-the-art accuracy in multi-view reconstruction with fewer parameters (70% fewer) than prior methods. Experimental results also suggest the strong scaling capability of EVolT.
Exploring Neural Network Interpretability in VisualUnderstandingbyDan WangB.Sc, Beihang University, 2014M.Sc, Beihang University, 2017A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Electrical and Computer Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)April 2023© Dan Wang, 2023The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:Exploring Neural Network Interpretability in Visual Understandingsubmitted by Dan Wang in partial fulfillment of the requirements for the degree ofDoctor of Philosophy in Electrical and Computer Engineering.Examining Committee:Z. Jane Wang, Professor, Electrical and Computer Engineering, UBCSupervisorSeptimiu Salcudean, Professor, Electrical and Computer Engineering, UBCCo-SupervisorRabab Ward, Professor, Electrical and Computer Engineering, UBCSupervisory Committee MemberPanos Nasiopoulos, Professor, Electrical and Computer Engineering, UBCUniversity ExaminerMatı´as Salibia´n-Barrera, Professor, Statistics, UBCUniversity ExamineriiAbstractNeural networks (NNs) have reached remarkable performance in computer vision.However, numerous parameters and complex structures make NNs opaque to hu-mans. The failure to comprehend NNs may raise serious issues in real-world ap-plications. My research aims to explore the NN interpretability in diverse visualtasks from post-hoc explanation and intrinsic interpretability perspectives.Convolutional neural networks (CNNs) have outperformed humans in imageclassification. However, the logic of network decisions remains a puzzle. Assuch, we propose concept-harmonized hierarchical inference, a post-hoc expla-nation framework, to explain the decision-making process of CNNs. Firstly, weinterpret layered feature representations of NNs with hierarchical visual seman-tics. Then we explain the NN feature learning as a bottom-up decision logic fromlow to high semantic levels in which a deep-layer decision is decomposed as asequence of shallow-layer sub-decisions.With the evolution of virtual reality, researchers are focusing increasingly oninverse rendering: reconstructing a 3D scene from multi-view 2D images. In thisfield, NNs achieved superior performance in novel view synthesis and 3D recon-struction. For both tasks, learning a 3D representation from input views is the keyprocess where prior methods separately designed a CNN-based single-view featureextraction and a pooling-based multi-view fusion. This incoherent design damagestheir intrinsic interpretability and performance. Therefore, we aim to design coher-ent, interpretable NNs that can adequately exploit knowledge of relationships fromdata.For novel view synthesis, we propose a unified Transformer-based neural ra-diance field (TransNeRF) conditioned on source views to learn a generic 3D-iiiscene representation. TransNeRF explores deep relationships between the target-rendering view and source views. TransNeRF also improves intrinsic interpretabil-ity by enhancing the shape and appearance consistency of a 3D scene. In experi-ments, TransNeRF outperforms prior neural rendering methods, and the interpre-tation results are consistent with human perception.We reformulate 3D reconstruction as a sequence-to-sequence prediction andpropose an end-to-end Transformer-based framework (EVolT). EVolT jointly ex-plores multi-level associations between input views and the output volume-based3D representation within our encoder-decoder structure. EVolT achieves state-of-the-art accuracy in multi-view reconstruction with fewer parameters (70% fewer)than prior methods. Experimental results also suggest the strong scaling capabilityof EVolT.ivLay SummaryNeural networks (NNs) remain opaque to humans despite their tremendous suc-cess in diverse visual tasks. My research is focused on the exploration of NN in-terpretability in various visual tasks from post-hoc explanation and intrinsic inter-pretability perspectives. To comprehend the network decision logic in image clas-sification, we propose a post-hoc explanation framework that explains the decision-making of NNs as a hierarchical inference of visual concepts. To improve the in-trinsic interpretability of NNs in inverse rendering, we propose novel frameworksfor novel view synthesis and 3D object reconstruction, respectively. For novel viewsynthesis, we propose a unified Transformer-based neural radiance field. Its intrin-sic interpretability is improved because the unified structure facilitates exploringdeep relationships between the target-rendering view and source views. For 3Dreconstruction, we propose an end-to-end Transformer-based framework. The in-trinsic interpretability is boosted because of the joint exploration of multi-levelassociations between input views and the output volume-based 3D representation.vPrefaceThis dissertation is composed based on several manuscripts. These manuscriptshave been modified to present a consistent dissertation. The manuscripts are pri-marily drafted by the candidate, with helpful revisions and valuable commentsfrom Professor Z. Jane Wang, and Professor Tim Salcudean.Chapter 2 is based on the following manuscript:• D. Wang, X. Cui, X. Chen, R. Ward, and Z. Wang, “Interpreting Bottom-UpDecision-Making of CNNs via Hierarchical Inference,” IEEE Transactions onImage Processing, vol. 30, pp. 6701-6714, 2021.Dan Wang formulated the problem, designed the proposed model and algo-rithm, implemented them, and wrote the paper. Xinrui Cui analyzed partial ex-periment results. Professor Wang and Professor Ward provided valuable technicalfeedback throughout the formulation of the method and helped polish the paper.Chapter 3 is based on the following manuscript:• D. Wang, X. Cui, S. Salcudean, and Z. Wang, “Interpretable Transformer-basedNeural Radiance Fields for Generalizable Novel View Synthesis,” under review.Dan Wang developed the idea for this research, formulated the model and al-gorithm, conducted experiments, and wrote the paper. Xinrui Cui is responsiblefor conducting partial experiments and analyzing the results. Professor Wang andProfessor Salcudean helped with the paper organization and provided valuable sug-gestions for experiment content.Chapter 4 is based on the following manuscript:• D. Wang, X. Cui, X. Chen, Z. Zou, T. Shi, S. Salcudean, Z. Wang, and R.Ward, “Multi-View 3D Reconstruction With Transformers,” Proceedings of theviIEEE/CVF International Conference on Computer Vision (ICCV), accepted asan ”Oral” paper, pp. 5722-5731, 2021.Dan Wang formulated the problem, derived the algorithm, proposed the model,and wrote the paper. Xinrui Cui provided useful comments and suggestions on theimplementation of the experiments. Professor Wang, Professor Salcudean, andProfessor Ward, Zhengxia Zou, provided insightful technical and editorial feed-back throughout the paper’s writing.viiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . xixAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Model interpretability . . . . . . . . . . . . . . . . . . . 21.1.2 Why is interpretability important? . . . . . . . . . . . . . 31.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.1 Neural networks . . . . . . . . . . . . . . . . . . . . . . 41.2.2 Interpretability of neural networks . . . . . . . . . . . . . 91.2.3 Visual analysis . . . . . . . . . . . . . . . . . . . . . . . 121.3 Challenges, Objectives, and Contributions . . . . . . . . . . . . . 17viii1.3.1 Work 1: Interpreting bottom-up decision-making of CNNsvia hierarchical inference . . . . . . . . . . . . . . . . . . 211.3.2 Work 2: Interpretable transformer-based neural radiancefields for generalizable novel view synthesis . . . . . . . . 221.3.3 Work 3: Interpretable and generalizable multi-view 3D re-construction . . . . . . . . . . . . . . . . . . . . . . . . . 251.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 Interpreting Bottom-up Decision-Making of CNNs via HierarchicalInference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.2.1 Concept harmonizing in the feature space . . . . . . . . . 342.2.2 Concept-harmonized hierarchical inference (CHAIN) . . . 352.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.3.1 Experimental setting . . . . . . . . . . . . . . . . . . . . 442.3.2 Instance-level CHAIN interpretation . . . . . . . . . . . . 462.3.3 Class-level CHAIN interpretation . . . . . . . . . . . . . 542.3.4 Influence of a shallower-layer concept on a deeper-layerconcept . . . . . . . . . . . . . . . . . . . . . . . . . . . 612.3.5 Inference distance of concepts in CHAIN interpretation . . 672.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743 Interpretable Transformer-based Neural Radiance Fields for Gen-eralizable Novel View Synthesis . . . . . . . . . . . . . . . . . . . . . 753.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 793.2.1 Framework . . . . . . . . . . . . . . . . . . . . . . . . . 793.2.2 Density decoder in surrounding-view space . . . . . . . . 823.2.3 Density decoder in ray-cast space . . . . . . . . . . . . . 833.2.4 Color decoder in surrounding-view space . . . . . . . . . 843.2.5 Color decoder in ray-cast space . . . . . . . . . . . . . . 853.2.6 TransNeRF interpretability . . . . . . . . . . . . . . . . . 85ix3.2.7 Rendering and training . . . . . . . . . . . . . . . . . . . 883.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893.3.1 Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . 903.3.2 Network details . . . . . . . . . . . . . . . . . . . . . . . 913.3.3 Training details . . . . . . . . . . . . . . . . . . . . . . . 923.3.4 Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . 923.3.5 Baselines . . . . . . . . . . . . . . . . . . . . . . . . . . 923.3.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 933.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1034 Interpretable and Generalizable Multi-view 3D Reconstruction . . . 1064.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1064.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1104.2.1 Divergence-enhanced 2D-view encoder . . . . . . . . . . 1114.2.2 3D-volume decoder . . . . . . . . . . . . . . . . . . . . . 1124.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1154.3.1 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . 1154.3.2 Evaluation metrics . . . . . . . . . . . . . . . . . . . . . 1154.3.3 Implementation details . . . . . . . . . . . . . . . . . . . 1174.3.4 Multi-view 3D object reconstruction . . . . . . . . . . . . 1204.3.5 View divergence . . . . . . . . . . . . . . . . . . . . . . 1224.3.6 Ablation study . . . . . . . . . . . . . . . . . . . . . . . 1364.3.7 Interpretability of EVolT . . . . . . . . . . . . . . . . . . 1374.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1375 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . 1405.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1405.1.1 Interpreting bottom-up decision-making of CNNs via hier-archical inference . . . . . . . . . . . . . . . . . . . . . . 1415.1.2 Interpretable transformer-based neural radiance fields forgeneralizable novel view synthesis . . . . . . . . . . . . . 1425.1.3 Interpretable and generalizable multi-view 3D reconstruction1435.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143x5.2.1 3D object reconstruction with hierarchical disentangled fea-ture attributes . . . . . . . . . . . . . . . . . . . . . . . . 1445.2.2 3D object shape editing via interpretable semantics . . . . 145Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146xiList of TablesTable 2.1 The mAP of semantic levels at different layers in ResNet18. . . 54Table 2.2 Influence of object-level concepts on the scene-level house con-cept. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Table 2.3 Influence of part-level concepts on the object-level house concept. 64Table 2.4 Influence of object-level concepts on the scene-level house con-cept for intra-class images. . . . . . . . . . . . . . . . . . . . 71Table 3.1 Quantitative comparisons of methods (PixelNeRF, MVSNeRF,IBRNet, and the proposed TransNeRF) for the scene-agnosticsetting on the realistic synthetic dataset. . . . . . . . . . . . . 93Table 3.2 Quantitative comparisons of methods (PixelNeRF, MVSNeRF,IBRNet, and the proposed TransNeRF) for the scene-agnosticsetting on the real forward-facing dataset. . . . . . . . . . . . 94Table 3.3 Quantitative comparisons of methods (PixelNeRF, MVSNeRF,IBRNet, and the proposed TransNeRF) for the per-scene fine-tuning setting on the realistic synthetic dataset. . . . . . . . . . 98Table 3.4 Quantitative comparisons of methods (PixelNeRF, MVSNeRF,IBRNet, and the proposed TransNeRF) for the per-scene fine-tuning setting on the real forward-facing dataset. . . . . . . . 99Table 4.1 Parameter sizes and pre-trained CNNs for the initial 2D-viewembeddings in competing methods. . . . . . . . . . . . . . . . 114xiiTable 4.2 Comparison of 24-views reconstruction on ShapeNet using In-tersection over Union (IOU) and F-Score. The best score foreach category is in bold. . . . . . . . . . . . . . . . . . . . . . 114Table 4.3 Comparison of multi-view reconstruction on ShapeNet usingIoU and F-Score. The best score for each view number is inbold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115xiiiList of FiguresFigure 1.1 A black-box deep learning model for image classification. . . 2Figure 1.2 The multi-layer perceptron network architecture. . . . . . . . 5Figure 1.3 The convolution layer in CNN. . . . . . . . . . . . . . . . . . 7Figure 1.4 The Transformer model architecture. . . . . . . . . . . . . . . 8Figure 1.5 Image classification for cat and tiger. . . . . . . . . . . . . . 11Figure 1.6 Novel view synthesis from multiple images. . . . . . . . . . 13Figure 1.7 3D representations. . . . . . . . . . . . . . . . . . . . . . . 13Figure 1.8 3D reconstruction from multiple images. . . . . . . . . . . . 16Figure 1.9 Challenges, objectives, and contributions. . . . . . . . . . . . 20Figure 1.10 Difficult real-world scenarios of novel view synthesis wherethere may be significant differences between the source viewsand the novel rendering view. . . . . . . . . . . . . . . . . . 24Figure 1.11 Comparisons of CNN-based methods (3D-R2N2 [10], AttSets[84], Pix2Vox/A [81], Pix2Vox++/A [82]) and the proposedTransformer-based methods. . . . . . . . . . . . . . . . . . . 26Figure 2.1 Illustration of the CHAIN interpretation. CHAIN providesboth instance-level and class-level interpretations to explainthe network decision-making process. . . . . . . . . . . . . . 31Figure 2.2 Scope of interpretation for different methods (CAM [90], Grad-CAM [61], TCAV [33], Network Dissection [94] and FLOWIN[13], and CHAIN). . . . . . . . . . . . . . . . . . . . . . . . 32Figure 2.3 The workflow of CHAIN interpretation. . . . . . . . . . . . 33Figure 2.4 Illustration of the hierarchical inference model. . . . . . . . . 37xivFigure 2.5 Instance-level CHAIN interpretation for images from farm andhouse classes. . . . . . . . . . . . . . . . . . . . . . . . . . . 47Figure 2.6 Instance-level CHAIN interpretation for images from orchardand pasture classes. . . . . . . . . . . . . . . . . . . . . . . . 48Figure 2.7 Instance-level CHAIN interpretation for images of a house witha swimming pool. . . . . . . . . . . . . . . . . . . . . . . . . 49Figure 2.8 Instance-level CHAIN interpretation for House-class imagesin which a house is enclosed the hedge. . . . . . . . . . . . . 50Figure 2.9 Instance-level CHAIN interpretation for House-class imagesin which a house is by the roadside. . . . . . . . . . . . . . . 51Figure 2.10 Average mAP values of semantic concepts at different layersof ResNet18. . . . . . . . . . . . . . . . . . . . . . . . . . . 55Figure 2.11 CHAIN interpretation for images from aeroplane and pottedplant classes in PASCAL VOC dataset. . . . . . . . . . . . . 56Figure 2.12 CHAIN interpretation for images from dog and car classes inPASCAL VOC dataset. . . . . . . . . . . . . . . . . . . . . . 57Figure 2.13 Comparison of interpretation methods (GradCAM [61], FLOWIN[13], CHAIN). . . . . . . . . . . . . . . . . . . . . . . . . . 58Figure 2.14 Comparison of interpretation methods (GradCAM [61], FLOWIN[13], CHAIN). . . . . . . . . . . . . . . . . . . . . . . . . . 59Figure 2.15 Class-level CHAIN interpretation for the house class. (Top)House images with three types of surroundings, i.e. curb, hedge,and swimming pool. (Middle) Sunburst charts of images withdifferent surroundings. (Bottom) CHAIN interpretation dia-gram for the house-class images. . . . . . . . . . . . . . . . 60Figure 2.16 Comparison of CHAIN interpretation in ResNet18. Contribu-tion weights α and occurrence numbers of object-level con-cepts to scene-level concepts are compared. . . . . . . . . . . 62Figure 2.17 Comparison of CHAIN interpretation in ResNet50. Contribu-tion weights α and occurrence numbers of object-level con-cepts to scene-level concepts are compared. . . . . . . . . . . 63Figure 2.18 The importance of shallower-layer concepts to a deeper-layerconcept. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66xvFigure 2.19 The influence of enhancing object-level concepts on the scene-level house concept for intra-class images. . . . . . . . . . . . 67Figure 2.20 Intra-class inference distance of a scene-level concept. The topchart plots the inference weights of the house concept (scenelevel) for three image sets (houses with curb, hedge, and swim-ming pool) in the 3D Principal Components Analysis (PCA)space. The bottom table shows their inference distances. . . . 68Figure 2.21 Intra-class inference distance of object-level concepts. The topchart plots the inference weights of three object concepts (curb,hedge, and swimming pool) for their corresponding image sets(houses with curb, hedge, and swimming pool) in the 3D PCAspace. The bottom table shows their inference distances. . . . 69Figure 2.22 Intra-class inference distance of an object-level concept. Thetop chart plots the inference weights of the house concept (ob-ject level) for three image sets (houses with curb, hedge, andswimming pool) in the 3D-PCA space. The bottom table showstheir inference distances. . . . . . . . . . . . . . . . . . . . . 70Figure 2.23 Inter-class inference distance of concepts for the orchard andthe house classes. The top row shows samples for two classes.The right chart (in the middle) plots the inference weights ofthe scene concepts for four image sets in the 3D-PCA space.The left table (in the middle) shows their inference distancesof scene-level concepts. Similarly, the bottom row shows theinference distances of object-level concepts. . . . . . . . . . . 73Figure 3.1 The intrinsic interpretability of TransNeRF in both the surrounding-view space and the ray-cast space when rendering a 3D pointalong the query ray. . . . . . . . . . . . . . . . . . . . . . . . 78Figure 3.2 Workflow of the proposed TransNeRF. . . . . . . . . . . . . 80Figure 3.3 Qualitative results (PixelNeRF, MVSNeRF, IBRNet and ourTransNeRF) for the fern scene under the scene-agnostic setting. 96Figure 3.4 Qualitative results (PixelNeRF, MVSNeRF, IBRNet, and ourTransNeRF) for the trex scene under the scene-agnostic setting. 97xviFigure 3.5 Qualitative results (PixelNeRF, MVSNeRF, IBRNet, and ourTransNeRF) for the fern scene under the per-scene finetuningsetting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100Figure 3.6 Qualitative results (PixelNeRF, MVSNeRF, IBRNet, and ourTransNeRF) for the trex scene under the per-scene finetuningsetting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Figure 3.7 Qualitative results (IBRNet and our TransNeRF) for the hot-dog scene under the per-scene finetuning setting. At the bot-tom, we also show the source-view sets S1 and S4 with theyellow frame. . . . . . . . . . . . . . . . . . . . . . . . . . . 102Figure 3.8 Interpretation results of fine-tuned TransNeRF for a renderingchair-scene view (a) based on source-view set S4 (b). For thetarget red-frame location in (a), (c) and (d) display attentionof source views to the target location for rendering the querydensity and color, respectively; (e) depicts the density attention(green) and color attention (orange) among 3D points along thetarget-viewing ray for rendering the query 3D point (index 83). 104Figure 3.9 Interpretation results of fine-tuned TransNeRF for the chairscene based on view set S1. (a) Source views (the target loca-tion for interpretation is highlighted via a red frame in an en-larged blue region); (b) density attention among source views;(c) color attention among source views; (d) density attentionand color attention among 3D points along the target-viewingray. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105Figure 4.1 Illustration of EVolT for Multi-view 3D Object Reconstruction. 109Figure 4.2 The proposed view-divergence enhancing function in EVolT. . 110Figure 4.3 Qualitative 3D object reconstruction results on ShapeNet basedon different number of input 2D-view chair images. . . . . . . 118Figure 4.4 Qualitative 3D object reconstruction results on ShapeNet basedon different number of input 2D-view monitor images. . . . . 119Figure 4.5 Effect of the view-divergence enhancing function on 3D recon-struction results. . . . . . . . . . . . . . . . . . . . . . . . . 121xviiFigure 4.6 Multi-view attention-matrix visualization in VolT and EVolT. . 121Figure 4.7 Divergence among multi-view representations in VolT and EVolT.122Figure 4.8 Qualitative reconstruction results of competing methods forthe bench. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123Figure 4.9 Qualitative reconstruction results of competing methods forthe aeroplane. . . . . . . . . . . . . . . . . . . . . . . . . . . 124Figure 4.10 Qualitative reconstruction results of competing methods forthe sofa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Figure 4.11 Qualitative reconstruction results of competing methods forthe table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126Figure 4.12 Qualitative reconstruction results of competing methods forthe lamp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Figure 4.13 Qualitative reconstruction results of competing methods forthe chair. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128Figure 4.14 Qualitative reconstruction results of competing methods forthe aeroplane. . . . . . . . . . . . . . . . . . . . . . . . . . . 129Figure 4.15 Qualitative reconstruction results of competing methods forthe display. . . . . . . . . . . . . . . . . . . . . . . . . . . . 130Figure 4.16 Qualitative reconstruction results of competing methods forthe chair. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Figure 4.17 Qualitative reconstruction results of competing methods forthe sofa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132Figure 4.18 Qualitative reconstruction results of competing methods forthe aeroplane. . . . . . . . . . . . . . . . . . . . . . . . . . . 133Figure 4.19 Qualitative reconstruction results of competing methods forthe bench. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134Figure 4.20 Kernel density estimation of D value in different attention lay-ers for VolT and EVolT. . . . . . . . . . . . . . . . . . . . . . 135Figure 4.21 EVolT interpretations. The blue cube indicates the queryingposition. Columns 2-5 show the top 4 critical views for thecorresponding cubes. . . . . . . . . . . . . . . . . . . . . . . 138Figure 4.22 EVolT interpretations. Columns 2-5 show the top 4 criticalviews for the corresponding object parts. . . . . . . . . . . . 139xviiiList of AbbreviationsAI Artificial IntelligenceBERT Bidirectional Encoder Representations from TransformersCAM Class Activation MappingCHIP Channel-wise Disentangled InterpretationCNN Convolutional Neural NetworkCHAIN Concept-harmonized Hierarchical InferenceDL Deep LearningFFN Feed Forward NetworkGPT Generative Pre-trained TransformerILSVRC ImageNet Large Scale Visual Recognition ChallengexixIOU Intersection over UnionKDE Kernel Density EstimationLPIPS Learned Perceptual Image Patch SimilarityMAD Mean Absolute DeviationML Machine LearningMLP Multi-Layer PerceptronNERF Neural Radiance FieldOMP Orthogonal Matching PursuitPASCAL Pattern Analysis, Statistical Modelling and Computational LearningPCA Principal Components AnalysisPSNR Peak Signal-to-Noise RatioRELU Rectified Linear UnitRNN Recurrent Neural NetworkxxSFM Structure from MotionSLAM Simultaneous Localization and MappingSSIM Structural Similarity Index MeasureVOC Visual Object ClassesxxiAcknowledgmentsI want to express my deepest appreciation to my supervisor, Professor Z. JaneWang, and co-supervisor, Professor Tim Salcudean, for their supervision duringmy Ph.D. period. Their invaluable insights have been essential in developing thisdissertation. I appreciate their consideration in providing me the opportunity to tryvarious ideas.My sincere thanks also go to Professor Rabab Ward for serving as my commit-tee member and for her valuable and constructive comments. I would like to thankmy labmates for the insightful discussions during my Ph.D. study. I also wouldlike to thank UBC for its financial support through the International Doctoral Fel-lowship.Last but not least, I would like to express my gratitude to my family for theirunconditional support. This accomplishment is as much yours as it is mine.xxiiChapter 1IntroductionNothing is inanimate; what is the rest is our interpretation.— Dejan Stojanovic1.1 MotivationIn the last decade, Deep Learning (DL) techniques have achieved great success ina variety of computer vision tasks, such as image classification [25], objection de-tection [35], semantic segmentation [62], novel view synthesis [63], and 3D objectreconstruction [83], etc. For instance, Florence, a new computer vision founda-tion model, achieves new state-of-the-art performance on 44 representative visionand vision-language benchmarks [86]. With these achievements, the applicationof DL is becoming more promising and extensive. Currently, DL has become anindispensable component for diverse applications, such as autonomous vehicles,healthcare, entertainment, language translation, etc.For DL models, a stack of layers jointly implements a complex nonlinear map-ping from the input to the output. The learning ability increases as the networkstructure becomes deeper and wider. Currently, a majority of prevalent DL net-works comprise dozens or hundreds of layers with learnable parameters. Con-sequently, numerous parameters and complex network structures make a neuralnetwork a black-box model.The inability of humans to understand DL models could raise serious problems.1Figure 1.1: A black-box deep learning model for image classification.As shown in Fig. 1.1, the Convolutional Neural Network (CNN) only predicts theclass of an input image as a bird without providing extra information for practi-tioners. The lack of interpretation of neural networks could impair the deploymentof their applications since end users may not trust their predictions. Therefore, theconcern of DL interpretability draws increasing attention among practitioners. Totackle this challenge, researchers explore and analyze the interpretability of deepneural networks.1.1.1 Model interpretabilityInterpretability is a difficult concept to define mathematically. In 2017, Millerprovided a non-mathematical definition, stating that interpretability is the extent towhich a human can comprehend the reason behind a decision. Hence, a model withhigher interpretability allows for better human understanding of its decisions. Cur-rently, researchers mainly explore model interpretability in two directions: post-hoc explanation and intrinsic interpretability.• Post-hoc explanation focuses on explaining predictions of a trained modelby providing human-friendly causal attribution or critical features.• Intrinsic interpretability aims to construct models with logical structuresand components that effectively explore and harness the relationships present2in data. It involves incorporating task-specific knowledge or logic into mod-els to improve their generality and robustness.Most traditional machine learning models are designed based on human knowl-edge, which indicates these models themselves are interpretable, such as decisiontrees. Interpretability is implicitly incorporated in the design of these traditionalmodels, rather than being explicitly represented.In contrast, the dominant approach for interpreting deep learning networks iscurrently post-hoc explanation, due to the uninterpretable multilayer-perceptron-based network structure. However, the current post-hoc interpretation methodscannot fully explain the reasoning behind deep networks. Meanwhile, Improvingthe transparency of deep neural networks remains an open challenge.In general, both post-hoc explanation and intrinsic interpretation have theirstrengths and weaknesses, and the choice between them depends on the specificrequirements of the application and the objectives of users. Post-hoc explanationis often preferred in applications where high accuracy is more important to hu-mans. Intrinsically interpretable neural networks are preferred in situations whereunderstanding the mechanics of neural networks is important.Currently, there are two challenges for interpretability studies of deep neuralnetworks from both post-hoc explanation and intrinsic interpretability:1. Post-hoc explanation: how to build a post-hoc interpretation to explain theinternal network logic in a human-friendly way?2. Intrinsic interpretability: how to design a network with a logical structurethat better collaborates with knowledge and information contained in data toimprove intrinsic interpretability, robustness, and generality?Accordingly, this thesis aims to solve these unmet challenges of the inter-pretability study for deep neural networks on visual analysis tasks, i.e., image clas-sification and 3D rendering.1.1.2 Why is interpretability important?Visual perception is a major source of learning and interpretation for humans. Deepneural networks, trained on large datasets, have demonstrated exceptional perfor-3mance in visual understanding. Without using radar, Tesla developed Model 3 andModel Y vehicles equipped with a camera-based Autopilot system. The systemuses cameras and neural network processing for Autopilot, Enhanced Autopilot,and Full-Self Driving. However, the black-box nature of deep networks raises con-cerns about their trustworthiness and their suitability for certain applications.The interpretability of neural networks is important because of the followingreasons:1. In real applications, customers need the interpretation of model decisions tobuild trust in models. For example, in healthcare patients need explanationsof why the diagnosis is made from Machine Learning (ML) models.2. Model interpretability can help end users understand how the decision ismade and further assist in debugging the problems which may involve. Forinstance, in mortgage applications, loan brokers need to know the key at-tributes considered by ML models to evaluate the financial risks and correctpotential mistakes.3. With good interpretability, we can enhance the machine learning model’srobustness and fairness to ensure that predictions are unbiased to under-represented groups and robust against small changes in the input.1.2 Related Work1.2.1 Neural networksIn the past decades, a series of neural networks have been proposed to make break-throughs in diverse research fields. Representative neural network types involvemulti-layer perceptrons, convolutional neural networks, and transformers, etc.Before a detailed description of representative neural networks, I will brieflyexplain some terms included in my dissertation.• Channel: a channel refers to a feature map in CNNs. In CNNs, a featuremap is a 2D matrix generated by applying a convolutional filter to the inputimage or the feature map output of the previous layers. It provides insightinto the internal representations of CNNs for a specific input.4Figure 1.2: The multi-layer perceptron network architecture.• Visual concepts: visual concepts are pixel-level dense annotations of im-ages that are interpretable to humans. In the dissertation, the visual con-cepts include discrete objects (e.g., car, person, grass, sky), object parts (e.g.,leaves, roof, shutter), materials (e.g., wood, skin, foliage), and colors (e.g.,red, blue).• Shallow layers and deep layers: A layer is a structure in the architecture ofa deep learning model. Typically, a deep learning model is composed ofmultiple layers. Each layer takes information from the previous layers andthen passes information to the next layer. In the dissertation, shallow layersrefer to layers that are close to the input of a neural network, and deep layersrefer to layers that are close to the output of a neural network.Multi-layer perceptronsA multi-layer perceptron (MLP) is a fully connected class of neural network, asshown in 1.2. It is fully connected since every node is connected to every neuron5in the layer below. An MLP consists of at least three layers of nodes: an inputlayer, a hidden layer, and an output layer. Each node, except for the input nodes,is a neuron that employs a nonlinear activation function. Its multiple layers andnon-linear activation enable it to distinguish data that is not linearly separable.MLPs are useful in a variety of domains, including complex classification, machinetranslation, and speech recognition.Convolutional neural networksConvolutional neural networks, a specific class of neural networks, substitute themathematical operation known as convolution for general matrix multiplicationin at least one of its layers. A convolutional neural network also consists of aninput layer, hidden layers, and an output layer. In contrast to MLP, a convolutionalneural network includes convolution layers in its hidden layers. The convolutionoperation generates a feature map as the convolution kernel moves across the inputmatrix for the layer, which in turn contributes to the input of the next layer, asshown in Fig. 1.3. Following the convolution layer are other layers like poolinglayers, fully connected layers, and normalization layers. In the areas of semanticparsing, paraphrase detection, and image and video recognition, convolution neuralnetworks exhibit very promising results.There have been numerous CNNs proposed so far. Here, we give a succinctoverview of the CNNs involved in this dissertation. We take into account the fol-lowing architectures: VGG16 [64] and ResNet50 [25].VGG16: VGG16 is a convolutional neural network proposed by Simonyan andZisserman from the University of Oxford [64]. The model achieves 92.7% top-5test accuracy in ImageNet, which is a dataset of over 14 million images belongingto 1000 classes. In VGG16, convolutional filters with a relatively small receptivefield 3× 3 are utilized, and an input image is processed through a stack of theselayers. The convolution stride is fixed to 1 pixel, and the spatial pooling is carriedout by five max-pooling layers. A stack of convolutional layers is followed by threefully-connected layers. The final layer is the soft-max layer. All hidden layersare equipped with the Rectified Linear Unit (RELU) as the nonlinear activationfunction. In total, there are 16 weight layers in the VGG16 network.6Figure 1.3: The convolution layer in CNN.ResNet50: ResNet, short for Residual Networks, is a representative neuralnetwork used as a backbone for diverse computer vision tasks. He et al. from Mi-crosoft Research Asia first introduce this cutting-edge neural network. ResNet washighly successful, as evidenced by the fact that its ensemble took first place at theImageNet Large Scale Visual Recognition Challenge (ILSVRC) 2015 classificationcompetition with a mere 3.57% error. Additionally, it won the 2015 ILSVRC &COCO contests for ImageNet detection, ImageNet localization, COCO detection,and COCO segmentation. The residual blocks are used in ResNet to boost modelprecision. The concept of “skip connections”, which lies at the core of the residualblocks, is the strength of ResNet. These skip connections operate in two differ-ent ways. First, they resolve the problem of the vanishing gradient by creating adifferent shortcut for the gradient to pass through. Second, they give the modelthe ability to learn an identity function, which ensures that the higher layers of themodel do not perform any worse than the lower layers. ResNet has many variantsthat have different numbers of layers. Resnet50 is used to denote the variant thatcan work with 50 neural network layers.7Figure 1.4: The Transformer model architecture.8TransformersTransformers were introduced in 2017 by Google Brain and are used primarily inthe fields of natural language processing [3] and computer vision [5, 8, 16]. Themain contribution of Transformers is utilizing the self-attention mechanism to ex-plore the dependence within input tokens and learn a global feature representation.Unlike Recurrent Neural Network (RNN), Transformers process the entire input allat once. This allows for more parallelization than RNNs and therefore reduces train-ing times. Based on the additional parallelization for training, larger datasets can betrained, such as Bidirectional Encoder Representations from Transformers (BERT)and Generative Pre-trained Transformer (GPT).The original Transformer model utilizes an encoder-decoder architecture, asshown in Fig. 1.4. The encoder is made up of encoding layers that process theinput iteratively, while the decoder is made up of decoding layers that process theencoder’s output successively. The function of each encoder layer is to generateencodings that contain information about which parts of the inputs are relevant toeach other. The encodings are passed to the next encoder layer as inputs. Specif-ically, each encoder has two main components: a self-attention mechanism and afeed-forward neural network. The self-attention mechanism takes the input encod-ings provided by the prior encoder and evaluates their interrelationships to produceoutput encodings. Each output encoding is then processed independently by thefeed-forward neural network. These output encodings are then passed to the nextencoder as its input, as well as to the decoders. Each decoder layer takes all theencodings and uses their incorporated contextual information to generate an out-put sequence. Specifically, each decoder consists of three main components, aself-attention mechanism, an encoder-decoder attention mechanism, and a feed-forward neural network. The decoder functions similarly to the encoder. The addi-tional encoder-decoder attention mechanism is used to draw relevant informationfrom the encodings generated by the encoders.1.2.2 Interpretability of neural networksInterpretation techniques have been applied to diverse practical problems, and nu-merous meanings have been attached to the term “interpretability”. In this section,9we will review the related work of model interpretability in our research field.Input-based network interpretationThis direction explains CNNs by learning critical input regions to a particular net-work prediction. Some methods utilize the perturbation mechanism in which crit-ical input regions are obtained by perturbing different input regions and observingthe variation of the prediction [11, 19, 58, 87]. Zeiler et al. [87] slide a regular gridas the perturbation patch over an image to find an important square region for theprediction. LIME [58] uses super-pixels as perturbation patches and calculates theimportance of each super-pixel via local linear regression. Wagner et al. [75] opti-mize a perturbed version of an input image to highlight the evidence in the imagefor a specific prediction. These methods map from the output space to the inputspace. However, such visual interpretations are only in the input space and do notexplain the internal network mechanism.Feature-based network interpretationAnother interpretation direction is based on network features. Some approachesuse visualization to understand network features. Guided Backpropagation [67]and Deconvolution [87] visualize the image pattern which can obtain the largest ac-tivation of a particular network unit. Olah et al. [48] give a reliable tool to visualizenetwork units with high quality in different layers. However, these methods onlyprovide a general interpretation, which means they cannot explain a specific net-work decision for a given input. In comparison, Class Activation Mapping (CAM)[90], and Grad-CAM [61] provide the class-discriminative interpretation of a spe-cific network decision by visualizing the linear combination of features. Never-theless, these approaches are not suited for fine-grained interpretation. Also, theirinterpretations are not as effective for shallow layers as those for the last layer.To tackle the challenge, Channel-wise Disentangled Interpretation (CHIP) distillsclass-discriminative network units from shallow to deep layers to interpret networkfeatures [12].10Figure 1.5: Image classification for cat and tiger.Concept-based network interpretationResearchers propose the concept-based interpretation to interpret network featuresas semantic concepts [33]. In [1], network features are interpreted as visual con-cepts by evaluating the overlap between a concept annotation and the saliency re-gion of a network feature. However, it is a one-to-one alignment and does notconsider the one-to-many situation. In comparison, Zhang et al. [88] develop amethod to learn an explanatory graph that automatically disentangles object partsfrom each unit without any part annotations. Zhou et al. [93] propose to representthe target image prediction as a linear combination of different concepts. In [93],the prediction and candidate concepts need to be represented utilizing networkunits from the same layer. However, studies show that different semantic-levelconcepts match network units at different layers. Therefore, for concept represen-tations in the last convolutional layer, low semantic-level concepts may not be asactive as high semantic-level concepts. Meanwhile, these methods do not explainthe layer structure for the network decision-making process.111.2.3 Visual analysisImage classificationAlthough the task of classifying images is instinctive to humans, it is much morechallenging for an automated system. Image classification refers to the task ofassigning a label or class to an entire image, as shown in Fig. 1.5. It is expectedthat images belong to only one class. Image classification can be considered thefundamental problem in computer vision. It forms the basis for other computervision problems.Image classification techniques are mainly divided into unsupervised and su-pervised image classification methods.The unsupervised image classification technique refers to a fully automatedmethod that does not leverage training data. This means that without the need forhuman intervention, machine learning algorithms are utilized to evaluate and clus-ter unlabeled datasets by identifying hidden patterns or data groups. Two popularalgorithms used for unsupervised image classification are “K-means” and “ISO-DATA”.Supervised image classification methods use previously classified samples (groundtruth) to train the classifier and subsequently classify unknown data. Currently, themost popular technique is deep learning. In comparison to the conventional com-puter vision approach in early image processing, deep learning requires only theknowledge of engineering of a machine learning tool. It does not need specificmachine vision expertise to create handcrafted features.3D rendering for novel view synthesisThe goal of novel view synthesis is to reconstruct unseen views of a scene fromits observed multiple images, as shown in Fig. 1.6. For this task, solutions canbe separated into three categories: novel view rendering by image-based represen-tation, discrete 3D shape-based representation, and implicit continuous 3D spatialcoordinate-based representation.Image-based representation. The image-representation-based approaches lever-age GAN models and auto-encoders [23] to learn a global embedding from multi-12Figure 1.6: Novel view synthesis from multiple images.Figure 1.7: 3D representations.view images and render an unseen view given its camera parameters. However,these image-representation-based models are limited by the lack of understandingof the underlying 3D shape representation. In contrast, the two 3D-representation-based types reconstruct novel views by exploiting multi-view consistent 3D shaperepresentation.13Discrete 3D shape-based representation. For novel view synthesis, the dis-crete 3D-shape representation involves point cloud [55], [28], mesh surface [22,45], voxel grid [76, 83], [72] approaches, as shown in Fig. 1.7. The point-cloud-based representation [55] reconstructed from multi-view images is typically sparse,making it difficult to infer the missing information. The mesh-based representation[22, 45] requires a template mesh with fixed topology and rigid texture parameter-izations for the category-specific shape. In complex real-world scenes, it is chal-lenging to fulfill this requirement. The volume-based representation [76, 83] caneasily leverage CNNs to obtain predicted voxel grids. Nevertheless, it causes dis-cretization artifacts from low-resolution voxel grids and limits its resolution-scaleability with computational and memory constraints.Implicit continuous 3D spatial coordinate-based representation. Recently,another promising branch implicitly represents geometric and appearance infor-mation of a 3D point in a scene as a function of its continuous spatial coordinates.Therefore this implicit continuous 3D shape representation has the potential torender higher-resolution complicated geometry and appearance of scenes withoutstoring an entire scene representation. In this direction, research work modelingoccupancy fields [21, 42] or signed distance functions [29, 52] requires ground-truth 3D information for supervision, limiting its real-world applications. To relaxthis requirement, researchers [47, 66] leverage differential rendering functions toallow 2D images as only supervision information for 3D representation. However,these models are unable to fully exploit the advantage of the implicit continuousrepresentation, which limits it to simple geometric and appearance scenarios.Neural radiance field scene representation. More recently, the impressiveneural radiance fields (NeRF) [44] have shown a solid ability to synthesize novelviews by representing continuous scenes as 5D radiance fields in MLPs. Neverthe-less, NeRF optimizes each scene representation independently, not exploring theshared information amongst scenes and being time-consuming. To solve this, re-searchers proposed models, such as PixelNeRF [85], MVSNeRF [7], IBRNet [78],which receives as conditional inputs multiple observer views to learn a generalneural radiance field. Following the design principle of divide-and-conquer, theyhave two separate components: a CNN feature extractor for a single image and anMLP as a NeRF network. For a single-view stereo, in these models, CNNs map an14image to a feature grid, and MLPs map a query 5D coordinate and its correspond-ing CNN feature to a single volume density and view-dependent RGB color. For amulti-view stereo, since CNN and MLP are unable to process an arbitrary numberof input views, they first process the coordinates and corresponding features in eachview coordinate frame independently and obtain an image-conditioned intermedi-ate representation for each view. Next, they use an auxiliary pooling-based modelto aggregate these intermediate representations across the views within the NeRFnetwork. In the 3D understanding, multiple views provide additional informationabout the scene.Multi-view 3D reconstructionMulti-view 3D object reconstruction has long been a research hot spot in bothcomputer vision and computer graphics, as shown in Fig. 1.8. For 3D object re-construction, there are different 3D representations, i.e., coordinate-based implicitrepresentation [6, 44, 66], voxel- [65, 81] and mesh-based [77] representations.Traditional methods [20, 49] of this field are typically designed based on hand-crafted geometric features. Some representatives of early methods like Structurefrom Motion (SFM) [49], Simultaneous Localization and Mapping (SLAM)) [20]can produce 3D reconstruction with satisfactory quality. However, they typicallycapture multiple images of the same object using well-calibrated cameras, whichis not practical in some situations. Recently, CNN-based approaches, without re-quiring complex camera calibration, have gained increasing attention in 3D recon-struction [10, 32] and have shown promising results.In CNN-based methods, a 2D-CNN single-view encoder, a 3D-CNN single-view decoder, and a multi-view fusion model are usually separately designed for3D reconstruction. Among them, the fusion model plays a central role in the in-tegration of multi-view feature information. Previous multi-view fusion methodscan be roughly grouped into three categories, i.e., pooling-based fusion, learn-able weighted-sum fusion, and RNN-based fusion. The pooling-based fusion onlylearns partial information of multiple views and ignores the view associations[26, 54]. The learnable weighted-sum fusion models are introduced to resolve theseproblems [82, 84]. The RNN-based fusion methods [10, 32] can learn effective15Figure 1.8: 3D reconstruction from multiple images.16view-to-view relations but are computationally expensive and permutation-variant[74].1.3 Challenges, Objectives, and ContributionsComputer scientists have been thinking about how to let the computer obtain vi-sual perception since the first instant photo was taken 75 years ago with a Polaroidcamera. Artificial intelligence research in the area of computer vision trains ma-chines to explore and understand visual data. To achieve it, there are two essentialelements: first, the camera works like our eyes, rapidly capturing the 3D world in arealistic 2D digital image; second, machine learning algorithms are like our brains,having the ability to interpret the surrounding environment through photos.In 1943, Warren McCulloch and Walter Pitts first proposed the neural networkand then developed the first true multilayered neural network in 1975. Neuralnetworks can cluster and categorize digital images from cameras and videos, andidentify hidden patterns and connections in raw data.In their early stages, the networks were adopted into classification problems,i.e., typed or handwritten text recognition as the first commercial usage, whichcan help the blind translate written text. After that, image classification becamea fundamental task to classify an image into a specific category. Today, ArtificialIntelligence (AI) researchers have started paying more and more attention to inverserendering: reconstructing a 3D scene from a collection of 2D images that were shotfrom different perspectives. From 2D to 3D, this technology helps us advance tothe next stage: virtual reality is the use of computer technology to create simulatedenvironments, placing the user inside a three-dimensional experience. Instead ofviewing a 2D screen in front of them, users are immersed in and interact with 3Dworlds.Despite these promising visions, the implementation of neural networks hasbeen dogged by their black-box nature, which renders them inappropriate for es-tablishing trust. Neural networks are defined as computing techniques with inter-connected nodes that operate similarly to the neurons in our brains. Nevertheless,over time, researchers began to veer away from a biologically based approach infavor of employing neural networks to fit particular tasks. This thesis is focused on17the following challenges and objectives for image classification and inverse render-ing tasks from both post-hoc explanation and intrinsic interpretability perspectives:1. Image classification is the computer vision task of identifying what an im-age represents. Although CNNs have already surpassed human levels of ac-curacy, we still do not fully understand the fundamental logic of the net-work’s decision-making process. By contrast, we humans have an inter-pretable knowledge-based logic for recognizing an object in an image.• Challenge 1. For human visual recognition, logic is built based on hi-erarchical visual concepts. The first challenge is how to explain featurerepresentations in CNNs based on visual concepts.• Our objective 1 is to develop a post-hoc explanation model that canlearn the representation relationships between network features fromshallow to deep layers and visual concepts from low to high semanticlevels.• Challenge 2. In human bottom-up logic, a decision can be hierarchi-cally deduced from sub-decisions. The second challenge is how tointerpret a specific network decision-making process as a hierarchicalinference.• Our objective 2 is to design a post-hoc explanation model which caninterpret the bottom-up decision-making process of CNNs via hierar-chical inference of semantic concepts from low to high levels.2. Novel view synthesis is concerned with rendering unseen views of a 3Dscene given a set of observed views. 3D reconstruction is the constructionof three-dimensional models from a collection of images. And learning 3Drepresentation from multi-view images is the essential process for both 3Dreconstruction and novel view synthesis.• Challenge 1 Prior CNN-based techniques for learning 3D represen-tation from multiple views use the divide-and-conquer design princi-ple, where it is typical to use a CNN to extract features from a sin-gle view and a multi-view fusion to aggregate the multi-view features18into 3D representations. Despite the two modules’ close relationship,each module is designed and examined independently. This incoherentframework design makes previous methods inefficient at integratingmulti-view features as 3D representation.• Objective 1 is to build a reasonable network framework with functionalmodules to competently learn and decode deep information from mul-tiple images into a 3D representation simultaneously.• Challenge 2 Exploring and learning complex relationships among mul-tiple views is crucial for a better 3D understanding. For previous meth-ods, the relationships between views are infrequently investigated dur-ing the CNN feature extraction stage, considering each view image sep-arately. It becomes challenging for previous approaches in scenarioswhere: the number of input images is large for 3D reconstruction; thesource views are captured at considerably different camera poses fromthe target view for novel view synthesis.• Objective 2 is to design neural networks with better intrinsic inter-pretability for exploring the complex relationships among multiple viewsand to subsequently improve the robustness and generalizability ofmodels for tackling these challenging scenarios.In the following subsections, we will describe in detail the proposed work and itscontributions, and the framework is shown in Fig. 1.9.19Figure 1.9: Challenges, objectives, and contributions.201.3.1 Work 1: Interpreting bottom-up decision-making of CNNs viahierarchical inferenceConvolutional neural networks (CNNs) have been effectively employed in a varietyof visual applications, including image processing [30], object detection [51], andclassification [25]. With the great success of CNNs, the interpretation of theirinternal network mechanisms has become increasingly critical, while the networkdecision-making logic is still an open issue. In the bottom-up hierarchical logic ofneuroscience, the decision-making process can be deduced from a series of sub-decision-making processes from low to high levels.Inspired by this, we propose the Concept-harmonized Hierarchical Inference(CHAIN) interpretation scheme in Chapter 2. In CHAIN, a network decision-making process from shallow to deep layers is interpreted by a hierarchical back-ward inference based on visual concepts from high to low semantic levels. Firstly,we learned a general hierarchical visual-concept representation in CNN layeredfeature space by the concept harmonizing model on a large concept dataset. Sec-ondly, for interpreting a specific network decision-making process, we conduct theconcept-harmonized hierarchical inference backward from the highest to the lowestsemantic level. Specifically, the network learning for a target concept at a deeperlayer is disassembled into that for concepts at shallower layers. Finally, a specificnetwork decision-making process is explained as a form of concept-harmonizedhierarchical inference, which is intuitively comparable to the bottom-up hierarchi-cal visual recognition way. Quantitative and qualitative experiments demonstratethe effectiveness of the proposed CHAIN at both instance and class levels.The main contributions are as follows:• In the CHAIN interpretation, we explain net features in a layered structurewith visual concepts in a hierarchical structure. Specifically, we build theconcept harmonizing model to learn the network feature representation forvisual concepts in a depth-stratified way (from deep to shallow layers).• In the CHAIN interpretation, the net-feature learning from shallow to deeplayers is interpreted as a hierarchical logical process of decision-makingfrom low to high levels. Through the hierarchical inference model, the netlearning for a deep-layer concept is inferred from shallow-layer features.21Based on the previous models, the concept-harmonized hierarchical infer-ence model can hierarchically deduce a deep-layer concept into shallow-layer concepts.• At the instance level, CHAIN provides the concept-harmonized hierarchicalinference of a net decision, which is an understandable logic for the networkdecision-making process from deep to shallow layers. Moreover, at the classlevel, CHAIN can explain net decisions for a class.• We analyze qualitatively and quantitatively the CHAIN interpretation forintra-class and inter-class net decisions.1.3.2 Work 2: Interpretable transformer-based neural radiancefields for generalizable novel view synthesisNovel view synthesis is a long-standing open problem concerned with the render-ing of unseen views of a 3D scene given a set of observed views [24, 41, 44, 56].The essence of novel view synthesis is to explore and learn a view-consistent 3Dscene representation from a sparse set of input views. However, the current Multi-Layer Perceptron (MLP)-based Neural Radiance Field (NERF) requires an auxiliarypooling-based operation to fuse source-view information and is unable to receiveobserved views with arbitrary numbers directly. As a result, complex relationshipsbetween source views and the target rendering view are missed. Both an MLP-based NeRF module and a Pooling-based multi-view fusion are present in theseearlier NeRFs. Even though there is an inherent relationship between these mod-ules, the overall structure is disconnected because each module is created and stud-ied separately. The intrinsic interpretability is harmed by this inconsistent frame-work design. Additionally, current methods process each 3D point separately anddisregard the local consistency of a scene representation based on a radiance field.These restrictions also affect how well they perform in difficult real-world scenar-ios where there may be significant differences between the source views and thenovel rendering view, as shown in Fig 1.10. In Fig 1.10, the complex radiance fieldscene representation function is shown with yellow/gray background. Given thecamera pose (rotation and translation) with respect to a world coordinate system,we can calculate the difference between each source view (the green and blue dots)22and the target rendering view (the red one). The green ones are source views withsmall differences from the target one, which are distributed close to the target onein a 3D scene representation space, making it possible to approximate their relationby a linear function. However, for source views (blue ones) with less similarity tothe target view, their association is more complex and cannot be approximated wellby a linear model.To tackle this unmet need, we propose a unified Transformer-based NeRF(TransNeRF) to learn a generic neural radiance field conditioned on observed viewsfor novel view synthesis. In contrast to previous research, which used two inde-pendent working processes of pooling-based fusion and MLP-based rendering, ourframework unifies source-view fusion and target-view rendering processes via anend-to-end Transformer-based network. As a result, TransNeRF enables the inves-tigation of deep relationships between the target-rendering view and source viewsthat were previously neglected by pooling-based fusion and fragmented render-ing procedures. TransNeRF also improves intrinsic interpretability by enhancingthe shape and appearance consistency of a 3D scene in both the surrounding-viewspace and the ray-cast space. For a query rendering 3D-point, TransNeRF consid-ers both its projected 2D pixels from the surrounding source views and its adjacent3D points along the query ray, and simultaneously decodes this knowledge into thequery 3D-point representation. Experiments show that TransNeRF outperformsstate-of-the-art image-based neural rendering methods in both scene-agnostic andper-scene finetuning scenarios, especially when there is a considerable disparitybetween source views and rendering views. The interpretation experiment indi-cates that the intrinsic interpretability of TransNeRF is consistent with our humanperception. Our code will be made publicly available.Our contributions can be summarized as follows:• We introduce TransNeRF, a unified Transformer-based architecture, to modela general neural radiance field from observed views for novel view synthesis,improving its inherent interpretability. Previous MLP-based NeRFs need anauxiliary pooling model to aggregate multi-view information when dealingwith an arbitrary number of observed source views.• TransNeRF, utilizing the attention mechanism, integrates information of the23Figure 1.10: Difficult real-world scenarios of novel view synthesis wherethere may be significant differences between the source views and thenovel rendering view.projected 2D pixels in the surrounding source views and the neighboring 3Dpoints along the query ray when rendering the density and radiance color ofa query 3D point. It gives our model a better understanding of the shape andappearance consistency in a local neural radiance field.• TransNeRF can explore complicated relationships between observed viewsand the rendering view and fuses the learned high-level multi-view informa-tion into coordinate-based 3D scene representation by our attention layers.• Experiments demonstrate that in both scene-agnostic and per-scene finetun-ing experimental settings, TransNeRF achieves more realistic rendering re-sults than previous state-of-the-art methods, especially when source views24are captured at camera poses with a considerable difference to the camerapose of the rendering view.• Using its attention layers, TransNeRF can explain how a query renderingprocess works. The inherent interpretability of TransNeRF is congruent withhuman perception, according to the accompanying studies.1.3.3 Work 3: Interpretable and generalizable multi-view 3DreconstructionLearning 3D object representation from multi-view images is a fundamental andchallenging problem in 3D modeling, virtual reality, and computer animation. Re-cently, deep CNN-based methods have so far achieved state-of-the-art results inmulti-view 3D object reconstruction. Despite the considerable progress, the twocore modules of these methods - view feature extraction and multi-view fusion,are usually investigated separately, and the relations among multiple input viewsare rarely explored. Previous approaches are ineffective in integrating multi-viewfeatures as 3D representation, especially when the number of input views is signif-icant, due to the incoherent framework design.Inspired by the recent great success in Transformer models, we reformulatethe multi-view 3D reconstruction as a sequence-to-sequence prediction problemand propose a framework named 3D Volume Transformer. Unlike previous CNN-based methods using a separate design, we unify the feature extraction and viewfusion in a single Transformer network. The natural advantage of our design liesin the exploration of view-to-view relationships using self-attention among mul-tiple unordered inputs. Our method outperforms the state-of-the-art method formulti-view 3D reconstruction on the ShapeNet dataset with a small parameter size.Figure 1.11 gives a comparison between the proposed transformer-based 3D re-construction methods and existing CNN-based methods from the perspective ofcomponents and structure.The contributions can be summarized as follows:• Learn explicitly the “2D-view × 2D-view”, “3D-volume × 3D-volume”,and “2D-view × 3D-volume” relationships by attention mechanism for 3Dreconstruction.25Figure 1.11: Comparisons of CNN-based methods (3D-R2N2 [10], AttSets[84], Pix2Vox/A [81], Pix2Vox++/A [82]) and the proposedTransformer-based methods.• Unify the feature extraction and multi-view fusion by attention layers inour Transformer-based framework, which can learn important informationin both view and spatial domains to explore a more comprehensive 3D rep-resentation.• Explore the effect of divergence decay for the multi-view information inTransformer deeper layers to 3D reconstruction and reduce it by the pro-posed view-divergence enhancing function.• Reach a new state-of-the-art multi-view 3D reconstruction on ShapeNet, us-ing only 30% of the parameters used by more recent CNN-based techniques.26• Have better scaling capability on the number of input views.1.4 Thesis OutlineThis thesis introduces three interpretation approaches to explain and understandnetworks. Specifically, the remaining chapters in this thesis are organized as fol-lows:In Chapter 2, we propose the Concept-harmonized HierArchical INference(CHAIN) interpretation scheme. It can interpret the bottom-up decision processof CNNs via hierarchical inference of semantic concepts. We propose three mod-els sequentially, i.e., the concept-harmonizing model, the hierarchical inferencemodel, and the concept-harmonized hierarchical inference model. Firstly, in theconcept harmonizing model, visual concepts from high to low semantic levels arealigned with net units from deep to shallow layers. Secondly, in the hierarchicalinference model, the concept in a deep layer is disassembled into units in shallowlayers. Finally, in the concept-harmonized hierarchical inference model, a deep-layer concept is inferred from its shallow-layer concepts. After several rounds, theconcept-harmonized hierarchical inference is conducted backward from the highestto the lowest semantic level. As a form of concept-harmonized hierarchical infer-ence that is analogous to human decision-making, the net decision-making processis finally explained. Meanwhile, the net layer structure for feature learning can beexplained based on hierarchical visual concepts. Both quantitative and qualitativeexperiments show the suggested CHAIN’s efficacy at the instance and class levels.In Chapter 3, we propose an interpretable Transformer-based NeRF (TransNeRF)to learn a generic neural radiance field conditioned on observed-view images forthe novel view synthesis task. By contrast, existing MLP-based NeRFs are not ableto directly receive observed views with an arbitrary number and require an auxiliarypooling-based operation to fuse source-view information, resulting in the missingof complicated relationships between source views and the target rendering view.Furthermore, current approaches process each 3D point individually and ignore thelocal consistency of a radiance field scene representation. These limitations poten-tially can reduce their performance in challenging real-world applications wherelarge differences between source views and a novel rendering view may exist.27To address these challenges, our TransNeRF utilizes the attention mechanism tonaturally decode deep associations of an arbitrary number of source views into acoordinate-based scene representation. Local consistency of shape and appearanceare considered in the ray-cast space and the surrounding-view space within a uni-fied Transformer network. Experiments demonstrate that our TransNeRF, trainedon a wide variety of scenes, can achieve better performance in comparison to state-of-the-art image-based neural rendering methods in both scene-agnostic and per-scene finetuning scenarios especially when there is a considerable gap betweensource views and a rendering view.In Chapter 4, we propose an interpretable and generalizable Transformer-based3D-Volume framework to explore the potential of the self-attention-based Trans-former model for multi-view 3D object reconstruction. In contrast to earlier CNN-based techniques that used separate two-step designs, we combine feature extrac-tion and view fusion into a single Transformer network and reframe the 3D recon-struction as a “sequence-to-sequence” prediction problem. The proposed techniqueexamines multi-level relationships and associations between the 2D input viewsand 3D output volume within our encoder-decoder Transformer structure simulta-neously and intuitively. We examine the issue of “diversity decay” in the suggestedframework and propose a view-diversity-increasing operation in our self-attentionlayers to mitigate it. With only 30% of the parameters used by more recent CNN-based algorithms, our technique provides a new state-of-the-art for multi-view 3Dreconstruction on ShapeNet. Additionally, our approach exhibits an improved abil-ity to scale when there are more input views.28Chapter 2Interpreting Bottom-upDecision-Making of CNNs viaHierarchical InferenceThe success of Convolutional Neural Networks (CNNs) has made it increasinglycrucial to comprehend their internal working mechanism. Despite this, the decision-making logic of CNNs remains a subject of discussion. In this chapter, we presenta new interpretation method to interpret the decision-making process of CNNs forimage classification, drawing inspiration from the bottom-up hierarchical logic inneuroscience. As a method to assess the interpretability of pre-trained neural net-works, this interpretation scheme views the network’s decision-making process asa hierarchical inference of human-comprehensible visual concepts.2.1 IntroductionConvolutional Neural Networks (CNNs) have proven successful in a variety oftasks, including image classification [25], object detection [51], and image recon-struction [30]. Despite their achievements, the lack of understanding of their inter-nal mechanisms limits further progress in their application [70]. In recent years,interpreting neural networks has become an area of growing research interest, withmultiple approaches proposed. Visual interpretation is one of the most widely stud-29ied directions in this field.Previous visual interpretation methods have primarily centred around visualiz-ing internal layers and deciphering their patterns [48]. Recently, researchers haveattempted to explain CNNs by incorporating human-interpretable visual concepts[33, 93]. For example, Kim et al. presented a method for learning the concept rep-resentation within an internal CNN layer by mapping visual concepts to networkunits [33]. However, these concept-based interpretation methods primarily aim toexplain internal layer features through concepts, but do not address the network’sdecision-making process from shallow to deep layers. Interpreting the network’sdecision-making process remains an unresolved issue.Neuroscientists have found that hierarchical decisions are formed in the visualcortex [37]. To explore human visual recognition, neuroscientists have proposeddifferent mechanisms including bottom-up hierarchy, integrative hierarchies, andparallel processing [17]. The bottom-up hierarchy is viewed as a visual recognitionprocess in which information is processed sequentially with increasing complexi-ties [27, 39, 59]. At the early vision stage, the basic features of an image, such ascolor and texture, are determined. Then, basic features are combined into recog-nizable object groups at the middle vision stage. High-level vision is the stage thatunderstands the scene.In the decision-making process of neural networks, features from low to highsemantic levels are learned from shallow to deep layers in CNNs [48]. Therefore,inspired by the bottom-up hierarchy in neuroscience, we intend to explore the net-work decision-making process in a similar way. To achieve it, we need to addressthe following issues:• For human visual recognition, logic is built based on hierarchical visual con-cepts. The first issue is how to explain feature representations in CNNs based onhierarchical visual concepts.• In human bottom-up logic, a decision can be hierarchically deduced from sub-decisions [37]. The second issue is how to interpret a specific network decision-making process as a hierarchical inference.To tackle the first challenge, the concept harmonizing model is applied to in-terpret network features from shallow to deep layers by utilizing visual concepts30Figure 2.1: Illustration of the CHAIN interpretation. CHAIN provides bothinstance-level and class-level interpretations to explain the networkdecision-making process.31Figure 2.2: Scope of interpretation for different methods (CAM [90], Grad-CAM [61], TCAV [33], Network Dissection [94] and FLOWIN [13],and CHAIN).that range from low to high semantic levels. To address the second challenge, wepropose the Concept-harmonized HierArchical INference (CHAIN) interpretationmethod to explain the network decision-making process. As shown in Fig. 2.1,given a specific network decision-making process, CHAIN can infer a concept ina deeper layer backward to concepts in a shallower layer. Fig. 2.2 shows the scopeof interpretation for different interpretation methods. Existing representative meth-ods interpret networks from different angles. In comparison, the proposed CHAINprovides a more comprehensive interpretation.The main contributions of this work are as follows:• We propose the CHAIN interpretation method to explain the network decision-making process for a specific instance. The proposed method interprets thebottom-up decision-making process of CNNs via hierarchical inference ofsemantic concepts from low to high levels.• To interpret the CNN logic inference from shallow to deep layers, CHAINdecomposes a deep-layer concept as a sparse combination of shallow-layerconcepts.• We use CHAIN to provide qualitative and quantitative interpretations tointra-class and inter-class network decisions at the class level.2.2 MethodologyOur work interprets neural networks in a hierarchical inference way analogous tothe bottom-up hierarchy in Neuroscience. In section 2.2.1, we first build a concept32Figure 2.3: The workflow of CHAIN interpretation.harmonizing model to explore the relationships between CNN units and semanticconcepts hierarchically, as shown in Phase A of Fig. 2.3. The model is trainedon the Broden dataset [1] and works as the pre-stage of our CHAIN interpretationframework. Based on the Broden dataset, the concept harmonizing model can learnreliable concept representations in the feature space. To this end, we build a linkbetween the semantic-stratified structure for visual concepts and the layer-stratifiedstructure in neural networks.Subsequently, in section 2.2.2, we propose the CHAIN model to interpret aspecific network decision-making process, as shown in Phase B of Fig. 2.3. Specif-ically, we first infer the target scene concept in the output layer backward as objectones in the shallower layer. Each critical object concept is continuously deducedinto part concepts and so on. At the instance level, a network decision-makingprocess can be interpreted as the concept-harmonized hierarchical inference fromscene to color semantic levels.The inference process from a deeper layer to a shallower layer includes two33steps. Firstly, in the hierarchical inference model (section 2.2.2), the target con-cept in a deeper layer is decomposed into critical network features in a shallowerlayer, as shown in Step B1 of Fig. 2.3. Secondly, in the concept-harmonized infer-ence model (section 10), the deeper-layer concept is further expressed as a sparserepresentation of shallower-layer concepts, as shown in Step B2 of Fig. 2.3.For the interpretation of network decisions for images from the same class, webuild the class-level CHAIN interpretation by selecting common concepts amonginstance-level CHAIN interpretations for different images in the same category. InCHAIN, a network decision-making process is interpreted as the concept-harmonizedhierarchical inference from high to low semantic levels.2.2.1 Concept harmonizing in the feature spaceIn recent works [33, 94], researchers disentangled the meaning of CNN features(units) as visual semantic concepts. By quantifying the alignment of unit-conceptpairs, they explored the expression ability of CNN features in different layers forvisual concepts at different semantic levels. Experiments demonstrated that fora network trained on a specific image dataset, the latent representation of hiddenunits for each concept is on a regular basis rather than a random basis [33, 94]. Ex-periments on different CNNs also showed that CNN features in a deeper layer learnhigher semantic visual concepts. It indicates that the concept representation in thefeature space has a regular hierarchical pattern [33, 94]. Therefore, it is reasonableto set the correspondence between CNN layers and visual concepts through theconcept harmonizing model.Here, we learn concept representations in the feature space. Specifically, visualconcepts from low to high semantic levels are aligned with network units fromshallow to deep layers, as shown in Phase A of Fig. 2.3.Visual conceptsBased on the Broden dataset [1], we utilize visual concepts at five semanticlevels, i.e., color, material, part, object, and scene. Network features in five layersare selected to align with concepts from low to high semantic levels. The selectedfive-level visual concepts are all labeled at the pixel level except scene-level ones.Training dataset for the concept harmonizing model34For the c′-th concept in the l-th layer, we design a concept harmonizing func-tion glc′(·)mapping from feature spaceA l to concept-score spaceYc′ . For an imageX, yc′(X) is the binary concept label where each value represents the absence (0)or presence (1) of the c′-th concept. During the training of glc′(·), an image pixelX(i, j) containing the target concept is the positive sample and its concept-score isyc′(X)(i, j) = 1. Other image pixels are negative samples. Training samples of a tar-get concept are fed into the network to obtain features in the corresponding layer.The concept harmonizing model glc′(·) is optimized viaargminglc′1N(i, j)N(i, j)∑(i, j)[glc′(Fl(X)(i, j))− yc′(X)(i, j)]2(2.1)where the network function Fl maps from image spaceX to feature space A l .Similar to [33], we utilize a linear model as the concept harmonizing model toalign units with visual concepts. On top of [33], we further interpret CNNs basedon the semantic-stratified visual concepts obtained by the concept harmonizingmodel.Harmonizing weights of units for a visual conceptThe concept harmonizing function is defined asglc′(Fl(X)(i, j)) = vlc′Fl(X)(i, j) (2.2)where Fl(X)(i, j) ∈ RI×1 is feature in the l-th layer and I is the number of units.Units in the l-th layer are harmonized with the c′-th concept by the harmonizingweight vlc′ = [vl,1c′ vl,2c′ · · ·vl,ic′ · · ·vl,Ic′ ], where vl,ic′ is the harmonizing weight of the i-thunit.Similarly, we calculate concept harmonizing functions for concepts in differentlayers. We can learn optimal concept harmonizing functions G= {glc′}l,c′ for visualconcepts at different semantic levels.2.2.2 Concept-harmonized hierarchical inference (CHAIN)On top of the optimal concept harmonizing functions G= {glc′}l,c′ , we propose theCHAIN framework to interpret the network decision-making process of an input35image.For an input image, CHAIN explains the network decision-making processas a concept-harmonized hierarchical inference from shallow to deep layers. Asshown in Step B1 and B2 of Fig. 2.3, CHAIN includes two steps, the hierarchicalinference model and the concept-harmonized inference model.Firstly, a concept in a deeper layer is decomposed into critical features in ashallower layer. Secondly, these critical shallower-layer features are representedby concepts harmonized in the layer. Accordingly, we can represent a concept in adeeper layer as a sparse representation of concepts in a shallower layer.Hierarchical InferenceThe hierarchical inference function is designed to approximate the network infer-ence process from a shallow layer to a deep layer for the target concept. It isoptimized as a local linear regression problem based on the network perturbation,as shown in Fig. 2.4.As shown in Fig. 2.4(a), the network inference from a shallow layer to a deeplayer for the target concept is highly nonlinear. The idea of local linear regressionis that if the network inference function has sufficient smoothness, then it will looklinear in local regions, as shown in Fig. 2.4(b). It is based on locally fitting aline rather than a constant. The network function Fl can be expressed as Fl(X) =fl( fl−1(· · ·( f1(X)) · · ·)), where fl is the function in the l-th layer.Inspired by the network perturbation [12], the hierarchical inference model islearned by analyzing the variation of the concept representation in a deeper layerafter randomly switching off shallower-layer units, as shown in Fig. 2.4(c). Theunit-wise perturbed vector is denoted as a binary vector e. The l-th layer is per-turbed by e = [e1 e2 · · ·ei · · ·eI] in which each item controls the state of the corre-sponding unit in the l-th layer. The i-th unit is turned off if ei is zero.By selecting elements of e as 1 uniformly at random, we collect samples in thelocal region to approximate the network inference function for a specific instancevia the local linear regression method, as shown in Fig. 2.4(b). The underlyingprinciple is that the concept in a deeper layer would drop dramatically if its im-portant shallower-layer units are blocked. For the c-th concept in the (l + 1)-th36Figure 2.4: Illustration of the hierarchical inference model.layer, its hierarchical inference function hlc(·) maps from feature space A l in thel-th layer to concept-harmonizing space G l+1c , as shown in Fig. 2.4(d).To infer the c-th concept in the (l+1)-th layer backward to features in the l-thlayer for a given image X, we formulate the hierarchical inference model asargminhlcEe[L (hlc(A˘l),gl+1c ( fl+1(A˘l)))]+ψ(hlc) (2.3)where a unit-wise perturbed feature in l-th layer is denoted as A˘l = e⊗Fl(X) and⊗ is a broadcasted outer product. During the optimization of Eq. (2.3), e is gen-erated by selecting its elements as 1 uniformly at random. We obtain {en}Nn=1 by37generating N perturbed vector samples.Inference weights of shallow-layer units to a concept in a deep layerFor the c-th concept in the (l+1)-th layer, its hierarchical inference function ishlc(A˘l) =wlc ∗ A˘l , where ∗ is a 1×1 convolutional operation. The inference weightvector is wlc = [wl,1c wl,2c · · ·wl,ic · · ·wl,Ic ], where wl,ic denotes the importance of the i-thunit in the l-th layer to the c-th concept in the (l+ 1)-th layer. In the hierarchicalinference function, feature A˘l in the l-th layer is resized to the spatial dimension offeature fl+1(A˘l) in the (l+1)-th layer.In Eq. (2.3), the first term is the loss functionL (hlc(A˘l),gl+1c ( fl+1(A˘l)))=12r(e)‖hlc(e⊗Fl(X))−gl+1c ( fl+1(e⊗Fl(X)))‖2F(2.4)where r(e) is the proximity measure between a binary vector e and the all-onevector 1. Specifically, it is defined asr(e) = exp(− 1σ2‖e−1‖22) (2.5)The second term of Eq. (2.3) is the sparse regularization termψ(hlc) = λ‖wlc‖1.λ is the regularization parameter. To make the hierarchical inference model simpleenough to be interpretable, the sparsity of inference weights measures the com-plexity of the interpretation model.Hierarchical inference algorithmTo optimize Eq. (2.3), we design a hierarchical inference algorithm by adoptingthe alternating iteration rule. Specifically, to infer the c-th concept in the (l+1)-thlayer from features in the l-th layer for an image X, we formulate the hierarchicalinference model asargminwlc∑e12r(e)‖wlc ∗ (e⊗Al)−gl+1c ( fl+1(e⊗Al))‖2F+λ‖wlc‖1(2.6)38The optimization of Eq. (2.6) can be rewritten asargminwlc∑n∑(i, j)12r(en)[wlc(en al(i, j))T−gl+1c ( fl+1(en al(i, j)))]2+λ‖wlc‖1(2.7)where is the Hadamard product and al(i, j) ∈ R1×I . In the l-th layer, feature at(i, j) location is Al(i, j) = al(i, j).The optimization problem can be converted into the equivalent formulationarg minwlc,m∑n∑(i, j)12r(en)[wlc(en al(i, j))T−gl+1c ( fl+1(en al(i, j)))]2+λ‖m‖1subject to wlc = m(2.8)The augmented Lagrangian for the above problem isarg minwlc,m,s12∑n ∑(i, j)r(en)[wlc(en al(i, j))T−gl+1c ( fl+1(en al(i, j)))]2+λ‖m‖1+ sT (wlc−m)+ρ2‖wlc−m‖22(2.9)The equation can be rewritten asarg minwlc,m,u12∑n ∑(i, j)r(en)[wlc(en al(i, j))T−gl+1c ( fl+1(e al(i, j)))]2+λ‖m‖1+ρ2‖wlc−m−u‖22(2.10)whereu≡− 1ρs (2.11)Through a careful choice of the new variable, the initial problem is convertedinto a simple problem. Given that the optimization is considered over the variable39wlc, the optimization function can be reduced towlc← argminwlc12∑n ∑(i, j)r(en)[wlc(en al(i, j))T−gl+1c ( fl+1(e al(i, j)))]2+ρ2‖wlc−m−u‖22(2.12)The solution is(wlc)k+1←(∑n∑(i, j)r(en)gl+1c ( fl+1(en al(i, j)))(en al(i, j))+ρmk+ρuk)(∑n∑(i, j)r(en)(en al(i, j))T (en al(i, j))+ρI)−1(2.13)To calculate m, the optimization problem to be solved ism← argminmλ‖m‖1+ ρ2 ‖wlc−m−u‖22 (2.14)The solution ismk+1← so f t((wlc)k+1−uk,λρ) (2.15)Lagrange multipliers update touk+1← uk− ((wlc)k+1−mk+1) (2.16)By optimizing Eq. (2.6), we get the optimal inference weight wlc of the l-thlayer units to concept c in the (l+1)-th layer. The pseudocode of the hierarchicalinference algorithm is shown in Algorithm 1.Concept-harmonized InferenceA deeper-layer concept can be represented as a sparse combination of concepts ina shallower layer. To infer the c-th concept in the (l + 1)-th layer from conceptsin the l-th layer for a given image X, the concept-harmonized inference model is40Algorithm 1: Pseudocode of the Hierarchical Inference AlgorithmInput: a network FL = fL( fL−1(· · ·( f1(X)) · · ·)) being interpreted; animage X being interpreted; the being-inferred concept setS l+1 inthe (l+1)-th layer; the optimal concept harmonizing functions{gl+1c }c for visual concepts inS l+1; the perturbed vector dataset{en}Nn=1.Output: the optimal inference weight wlc of shallower-layer (the l-thlayer) units to the concept c in a deeper layer (the (l+1)-thlayer).1 Initialization: set k = 0, m0, u0, λ > 0;2 For a given image X, to infer the concept c ∈S l+1 in the (l+1)-thlayer, the hierarchical inference optimization is:argminwlc ∑e12 r(e)‖wlc ∗ (e⊗Al)−gl+1c ( fl+1(e⊗Al))‖2F +λ‖wlc‖1 (inEq. (2.6));3 repeat4 1: (wlc)k+1← (∑n∑(i, j) r(en)gl+1c ( fl+1(en al(i, j)))(en al(i, j))+ρmk5 +ρuk)(∑n∑(i, j) r(en)(en al(i, j))T (en al(i, j))+ρI)−1 (in Eq.(2.13));6 2: mk+1← so f t((wlc)k+1−uk, λρ ) (in Eq. (2.15));7 3: update Lagrange multipliers: uk+1← uk− ((wlc)k+1−mk+1) (inEq. (2.16));8 4: update iteration: k← k+1;9 until stopping criterion is satisfied;10 Return: the optimal inference weight wlc;optimized byargminαc‖Vlα c− (wlc)T‖22+‖α c‖0 (2.17)where Vl = [vl1;vl2; · · · ;vlc′ ; · · · ;vlC′ ]T is the harmonizing weights of a concept set inthe l-th layer.Contribution weights of shallow-layer concepts to a deep-layer conceptThe contribution weight vector of concepts in the l-th layer to the c-th conceptin the (l + 1)-th layer is defined as α c = [α1c α2c · · ·αc′c · · ·αC′c ]T . Specifically, αc′cis the contribution of the c′-th concept in the l-th layer to the c-th concept in the(l+1)-th layer.Based on the contribution weights, the high-level concept is inferred from low-41level concepts. Here, we use Orthogonal Matching Pursuit (OMP) algorithm [4] toobtain α c. The selected inference concept set is denoted as C l+1c which containscritical concepts in the l-th layer for the concept c in the (l+1)-th layer. The stopcondition in OMP is ‖∑c′∈C l+1c Vlc′α c′c − (wlc)T‖22 ≤ 0.1‖wlc‖22.Similarly, the concept-harmonized inference for other critical concepts in the(l+1)-th layer is also optimized. In the process, we denoteS l =⋃c∈S l+1 C l+1c asthe concept set being inferred in the l-th layer. Subsequently, the optimization ofthe concept-harmonized inference model is conducted to infer concepts in the l-thlayer.Finally, a network decision-making process is interpreted as the hierarchicalinference of concepts. For a network decision, CHAIN interpretation learns itsoptimal inference concept set C = {C l+1c }l,c. Meanwhile, we can quantitativelyanalyze the CHAIN interpretation for a network decision. The pseudocode of theCHAIN interpretation is shown in Algorithm 2.For the inference of part-level concepts, we only care about the most importantmaterial-level concept. It is also applied to the inference from the material-levelconcept to the color-level concept. Therefore, in the concept-harmonized inferencemodel Eq. (2.17), the sparsity of α c is set as 1 to select the most critical shallow-layer concept for the target deep-layer concept.It also can be achieved by utilizing the directional-derivative of concept. Theconcept directional-derivative of the function gl+1c ( fl+1(·)) along the concept di-rection vlc′ at the Al is∇vlc′gl+1c ( fl+1(Al))= limδ→0gl+1c ( fl+1(Al +vlc′ ∗δ ))−gl+1c ( fl+1(Al))δ=∂gl+1c ( fl+1(Al))∂Al·vlc′(2.18)where vlc′ is the direction of the c′-th concept at the l-th layer (shallow layer) featurespace. gl+1c (·) is concept harmonizing function for the c-th concept in the (l+1)-thlayer.In mathematics, the directional-derivative of concept represents the instanta-42Algorithm 2: Pseudocode of the CHAIN InterpretationInput: a network FL = fL( fL−1(· · ·( f1(X)) · · ·)) being interpreted; animage X being interpreted; the concept harmonizing functions{gl+1c }l,c for visual concepts;Output: for a network decision, the optimal inference concept setC = {C l+1c }l,c;1 Initialization: the being-inferred concept setS L in the L-th layer andS l = /0(l < L); the inference concept set C l+1c = /0 for the concept c inthe (l+1)-th layer; l = L−1;2 repeat3 for each concept c ∈S l+1 do4 hlc← argminhlc Ee[L (hlc(A˘l),gl+1c ( fl+1(A˘l)))]+ψ(hlc). (in Eq.(2.3));5 α c← argminαc ‖Vlα c− (wlc)T‖22+‖α c‖0. (in Eq. (2.17));6 S l =S l⋃C l+1c7 return the optimal inference concept set C l+1c for the concept c inthe (l+1)-th layer8 end for return the being-inferred concept setS l in the l-th layer9 update iteration: l← l−110 until the CHAIN interpretation is optimized from the deepest to shallowestlayer;11 return the optimal inference concept set C = {C l+1c }l,c for a networkdecision being interpreted.neous rate of change of the function gl+1c ( fl+1(·)), moving through Al with a ve-locity specified by vlc′ . In the hierarchical inference model, it is assumed that∂gl+1c ( fl+1(Al))∂Al≈ ∂hlc(Al)∂Al= wlc (2.19)Therefore, the concept directional-derivative is rewritten as∇vlc′gl+1c ( fl+1(Al))≈ wlc ·vlc′ (2.20)which is also the contribution weight of the c′-th concept in the l-th layer to thec-th concept in the (l+1)-th layer.Therefore, we can obtain the most critical concept in the l-th layer to the c-th43concept in the (l+1)-th layer by optimizingargmaxc′∇vlc′gl+1c ( fl+1(Al)) (2.21)The optimal solution for the shallow-layer concept in Eq. (2.21) is the same asthat in Eq. (2.17) when the sparsity of α c is set to 1. It means that the optimizationbased on the concept directional-derivative can be viewed as a special case of theconcept-harmonized inference model in Eq. (2.17).2.3 ExperimentsExperiments are conducted to analyze qualitatively and quantitatively the perfor-mance of the proposed interpretation model. Experimental setting and quantitativeanalysis metrics are described in section 2.3.1. In section 2.3.2, we provide theinstance-level CHAIN interpretation. In section 2.3.3, the CHAIN interpretation isapplied to explain network predictions at the class level. In section 2.3.4, we studythe influence of a shallower-layer concept on a deeper-layer concept in CHAINinterpretation by manipulating the shallower-layer concept in the feature space. Insection 2.3.5, networks can be further understood by the intra-class and inter-classinference distance of concepts in CHAIN.2.3.1 Experimental settingResNets on the Places365 scene classification datasetCHAIN interpretation is applied to explain ResNet-18 and ResNet-50 [25] thatare pre-trained on the Places365 scene classification dataset [92]. In the conceptharmonizing model, we use five layers (i.e., the output, layer4, layer3, layer2, andlayer1) to align with five semantic level concepts (scene, object, part, material, andcolor).Concept harmonizing datasetIn the concept harmonizing model, the Broden dataset is utilized as the conceptdataset. Broden dataset contains a hierarchical level of labeled visual-concept44samples. Concept annotations are at the pixel level except for the scene annota-tion which is at the image level. The five semantic level concepts are from theADE20K [91], Pascal-Part [9], and OpenSurfaces datasets [2].Influence scoreThe CHAIN interpretation distills critical concepts in a shallower layer for a con-cept in a deeper layer. Therefore, we manipulate network features by enhancingor weakening a shallower-layer concept to examine its influence on a deeper-layerconcept.The influence of enhancing concept c′ in the l-th layer on concept c in the(l+1)-th layer for pixel (i, j) is4(concept l+1c ;concept lc′)+def=gl+1c ( fl+1(Al +vlc′ ∗δ )(i, j))−gl+1c ( fl+1(Al)(i, j))(2.22)where Al ∈ RW×H×I is network features and I is the number of units. For the c′-th concept in the l-th layer, its harmonizing weight is vlc′ = [vl,1c′ vl,2c′ · · ·vl,ic′ · · ·vl,Ic′ ],which can also be regarded as a concept direction in the feature space of the l-thlayer. Unit influence rate is denoted as δ ∈ RW×H×I .The influence of weakening concept c′ in the l-th layer on concept c in the(l+1)-th layer for pixel (i, j) is4(concept l+1c ;concept lc′)−def=gl+1c ( fl+1(Al−vlc′ ∗δ )(i, j))−gl+1c ( fl+1(Al)(i, j))(2.23)For a deeper-layer concept l+1c , its important shallower-layer conceptlc′ is as-sumed to have positive value for4(concept l+1c ;concept lc′)+, and negative value for4(concept l+1c ;concept lc′)−. In contrast, its unimportant shallower-layer concept lc′is assumed to have non-positive value for 4(concept l+1c ;concept lc′)+, and non-negative value for4(concept l+1c ;concept lc′)−. In section 2.3.4, we evaluate CHAINinterpretation by the influence score.45Inference distanceThe hierarchical inference model obtains critical features in a shallower layer fora concept in a deeper layer. Therefore, we define the inference distance to quan-titatively analyze the inference of concepts on intra-class and inter-class networkdecisions in section 2.3.5.Inference distance of concept c for image set s is defined as the averageEuclidean distance of inference weights for images in the image set s, which isdenoted asdist(conceptc,sets)def=1Ni∑i‖wconceptcsets,i − w¯conceptcsets ‖2(2.24)where the center of inference distance w¯conceptcsets isw¯conceptcsetsdef=1Ni∑iwconceptcsets,i (2.25)Here, wconceptcsets,i is the inference weight vector of shallower-layer units to the c-th concept in the deeper layer for the i-th image in the image set s. Ni is the numberof images in set s.Inference distance between concept c for image set s and concept c′ forimage set s′ is obtained bydist(conceptc,sets;conceptc′ ,sets′)def=‖w¯conceptcsets − w¯conceptc′sets′ ‖2(2.26)2.3.2 Instance-level CHAIN interpretationFor illustration, we use CHAIN to explain network predictions of four randomlyselected images from different classes. ResNet-18 accurately predicts their sceneclasses.Fig. 2.5 and Fig. 2.6 show the instance-level CHAIN interpretation for imagesfrom four classes (i.e., farm, orchard, house, and pasture). For a specific network46Figure 2.5: Instance-level CHAIN interpretation for images from farm andhouse classes.47Figure 2.6: Instance-level CHAIN interpretation for images from orchard andpasture classes.decision, CHAIN shows the hierarchical concept inference to explain the networkdecision-making process. For example, in the bottom of Fig. 2.6, the CHAIN inter-pretation shows that the pasture scene prediction is inferred from the horse, grass,and fence concepts. Moreover, the object-level horse concept is inferred from thepart-level torso concept that is deduced from the material-level skin concept. Fi-nally, the horse concept can be hierarchically inferred from the orange concept.House images with three surroundings are selected to analyze the CHAIN in-48Figure 2.7: Instance-level CHAIN interpretation for images of a house witha swimming pool.49Figure 2.8: Instance-level CHAIN interpretation for House-class images inwhich a house is enclosed the hedge.50Figure 2.9: Instance-level CHAIN interpretation for House-class images inwhich a house is by the roadside.51terpretation within a class for ResNet-18. Due to the space limit, we randomlychoose two instances to show results for each type.Fig. 2.7 shows instance-level CHAIN interpretations for two house imageswith swimming pools. CHAIN interpretations include house and swimming poolconcepts at the object level. The left image also contains a hedge region that doesnot exist in the right image. The house roof can be observed clearly in the rightimage compared with that in the left image. It means CHAIN interpretation ex-plains the difference in network feature learning for different images with swim-ming pools.For the subsequent backward inference, the swimming pool is inferred from thewater concept for both images. In the left image, the inference of the object-levelhouse concept includes a bush which does not exist in the right image.Fig. 2.8 is an instance-level CHAIN interpretation for two house images withhedges. CHAIN can distill the difference and similarities in the network featurelearning as the concept interpretation for different images. For example, the houseand hedge object concepts are shared in the CHAIN interpretation for both images.The roof and chimney only exist in the left image.Fig. 2.9 shows instance-level CHAIN interpretation for two house images withroadside. The object-level house concept is the common interpretation for houseimages with different surroundings. The swimming pool, hedge, and curb conceptsare unique interpretations of the corresponding house surroundings. Therefore,CHAIN can interpret the difference and similarities of network feature learning forimages within a class.Meanwhile, CHAIN provides visualization for concepts at each semantic level.The visualization of concepts in the CHAIN interpretation can localize the corre-sponding image regions, which validates the effectiveness of concept representa-tions and interprets the network feature learning for visual concepts.To demonstrate that CHAIN is applicable to different classification tasks, wealso conduct CHAIN interpretation experiments on object classification based onthe Pattern Analysis, Statistical Modelling and Computational Learning (PASCAL)Visual Object Classes (VOC) dataset.For PASCAL VOC classification, we need to obtain its global concept repre-sentation in ResNet18 feature space by our concept harmonizing model as the pre-52stage of CHAIN. The concept harmonizing model is also trained on the Brodendataset, which contains the object, part, material, and color concept annotationsfor PASCAL VOC object classes.To further examine the correspondence between the hidden CNN layers and theconcepts, we evaluate the representational abilities of different layers for differentsemantic-level concepts by mAP value, as shown in Fig. 2.10 and Tab. 2.1.Fig. 2.10 shows average mAP values of different semantic levels at differentlayers of ResNet18. Tab. 2.1 further lists mAPs of five example concepts from eachsemantic level. Tab. 2.1 also shows the average mAP for each semantic level on theBroden dataset. Based on Fig. 2.10 and Tab. 2.1, part-, material-, and color-levelare aligned to layer3, layer2, and layer1 of ResNet18. It demonstrates that a highernetwork depth promotes the emergence of visual concepts with a higher semanticlevel, which is also found in related works. Therefore, in the concept harmonizingmodel, we align a semantic level to the layer with the maximal mAP.CHAIN is then used to interpret the network decision. Fig. 2.11 and Fig. 2.12show CHAIN results for object classification on the PASCAL VOC dataset. Forexample, the “dog” prediction is deduced from “leg”, “muzzle”, and “eye” part-level concepts. Each part-level concept can be traced back to the material level andcolor level. For instance, the “leg” part is deduced from the “fur” material, whichis then deduced from the “grey” color.Fig. 2.13 and Fig. 2.14 show interpretation results of different methods in-cluding GradCAM [61], FLOWIN [13], and the proposed CHAIN. Fig. 2.13 andFig. 2.14 are only used to compare the scope of interpretation among differentmethods qualitatively. In [61] and [13], GradCAM and FLOWIN results are basedon VGG16. In Fig. 2.13 and Fig. 2.14, GradCAM and FLOWIN can give an in-terpretation of a network decision. GradCAM localizes important image regionsat different layers for a network decision. However, GradCAM cannot providesemantic interpretation, and the interpretation results become less reasonable inshallower layers. FLOWIN visualizes important units to a network decision ateach layer but cannot align them to interpretable concepts. In comparison, the pro-posed CHAIN explains a network decision by providing the hierarchical conceptinference at different layers.53Table 2.1: The mAP of semantic levels at different layers in ResNet18.mAP concept layer 4 layer 3 layer 2 layer 1parthair 0.235 0.962 0.858 0.706wheel 0.220 0.958 0.729 0.554muzzle 0.520 0.949 0.669 0.547ear 0.790 0.946 0.721 0.548eye 0.805 0.939 0.918 0.619avg. on all parts 0.614 0.800 0.742 0.460materialpainted 0.601 0.769 0.947 0.820sky 0.954 0.820 0.909 0.380carpet 0.443 0.867 0.897 0.465fabric 0.824 0.771 0.896 0.769wood 0.847 0.795 0.892 0.731avg. on all materials 0.609 0.685 0.694 0.496colorblack 0.509 0.935 0.905 0.989orange 0.572 0.830 0.820 0.958brown 0.540 0.483 0.468 0.953white 0.661 0.888 0.888 0.953grey 0.370 0.647 0.579 0.940avg. on all colors 0.684 0.794 0.794 0.9042.3.3 Class-level CHAIN interpretationIn this experiment, we give the intra-class and inter-class CHAIN interpretations.Specifically, in section 2.3.3, house images with different surroundings are selectedfor the intra-class analysis. In section 2.3.3, three scene classes are chosen for theinter-class CHAIN interpretation for different networks.Intra-class CHAIN interpretationFor the house scene class, the class-level interpretation is analyzed by house im-ages with three typical surroundings (i.e., curb, hedge, and swimming pool). Werandomly choose twenty house images for each surrounding as the correspondingimage set to explain their ResNet-18 predictions.Fig. 2.15 displays the CHAIN interpretation for the house class. The top rowshows house image examples with the three surroundings. Sunburst charts for im-ages with three surroundings are in the middle. The innermost circle of a sunburst54Figure 2.10: Average mAP values of semantic concepts at different layers ofResNet18.chart shows object-level concepts that are crucial to the house-scene prediction.The outer circle shows the lower-level concepts that are important to concepts inthe inner circle. The proportion of each visual concept in the innermost circle in-dicates its contribution to the network scene prediction. Similarly, the contributionof a part concept to its object concept is shown by its proportion in the outer cir-cle. In each sunburst chart, concepts at each level are sorted in descending orderof the contribution to their corresponding high-level concept. In the three sun-burst charts, the object-level house concept has the most significant contribution tothe house scene prediction. Meanwhile, hedge and swimming pool concepts ownthe second-largest contribution to the network prediction of house image sets withhedge and swimming pool, respectively. The curb concept also contributes a lot tothe house scene prediction of the house image set with the curb. Therefore, CHAINcan explain the intra-class network predictions by presenting common and uniqueconcepts for images within a class.55Figure 2.11: CHAIN interpretation for images from aeroplane and pottedplant classes in PASCAL VOC dataset.At the bottom of Fig. 2.15, we present the CHAIN interpretation diagram forthe house class in which the network output is inferred from the scene to the colorlevel. The fraction enclosed by the purple dashed line denotes the house-relatedconcepts shared by the three types of images. Fractions in yellow, green, andred dashed rectangles are the concepts for different surroundings. The diagram isconsistent with the observation of the three sunburst charts. For example, the hedgeconcept is inferred from the plant, then to the foliage, and finally to the green color.Meanwhile, the hedge concept is shared in the interpretation of house image setswith hedges and swimming pools. At the instance level, it is observed that manyimages in the image set with a swimming pool involve a hedge. Therefore, theCHAIN interpretation diagram is reasonable.56Figure 2.12: CHAIN interpretation for images from dog and car classes inPASCAL VOC dataset.57Figure 2.13: Comparison of interpretation methods (GradCAM [61],FLOWIN [13], CHAIN).58Figure 2.14: Comparison of interpretation methods (GradCAM [61],FLOWIN [13], CHAIN).59Figure 2.15: Class-level CHAIN interpretation for the house class. (Top)House images with three types of surroundings, i.e. curb, hedge, andswimming pool. (Middle) Sunburst charts of images with differentsurroundings. (Bottom) CHAIN interpretation diagram for the house-class images.60Inter-class CHAIN interpretation for different networksThis section analyzes inter-class CHAIN interpretation of three scene classes (Liv-ing room, Farm, and Pasture) for ResNet18 and ResNet50. We use all images in thePlaces365 validation dataset for each scene class to analyze the inter-class CHAINinterpretation.Results are shown in Fig. 2.16 and Fig. 2.17 for ResNet18 and ResNet50,respectively. In each bar chart, concepts with top contribution weights α are shownfor comparison. Meanwhile, the occurrence numbers of concepts are presented asyellow dots. Contribution weights α and occurrence numbers in ResNet50 aremore harmonized compared with those in ResNet18.In Fig. 2.16 and Fig. 2.17, CHAIN provides reasonable inferences for differentscene classes and networks. Besides, shallow-layer concepts that are important tothe specific deep-layer one vary in different networks. As shown in the first row ofFig. 2.16 and Fig. 2.17, the important shallow-layer concepts for the living roomare different between ResNet18 and ResNet50. They share a portion of importantconcepts for the scene living room, such as seat cushions, ottoman, coffee table,and vases. We observe similar results in CHAIN interpretation for other scenes. Itis reasonable because the decision-making process of different networks may notbe identical. By comparing CHAIN interpretation in different networks, we have abetter understanding of the internal mechanisms of networks.2.3.4 Influence of a shallower-layer concept on a deeper-layerconceptIn this experiment, we analyze the influence of a shallower-layer concept on adeeper-layer one in CHAIN interpretation by manipulating concepts in the featurespace, as described in section 2.3.1. We enhance or weaken a shallower-layerconcept in feature space to examine its influence on a deeper-layer concept. Houseimages with three types of surroundings are used to evaluate CHAIN interpretationon ResNet-18.61Figure 2.16: Comparison of CHAIN interpretation in ResNet18. Contribu-tion weights α and occurrence numbers of object-level concepts toscene-level concepts are compared.62Figure 2.17: Comparison of CHAIN interpretation in ResNet50. Contribu-tion weights α and occurrence numbers of object-level concepts toscene-level concepts are compared.63Table 2.2: Influence of object-level concepts on the scene-level house con-cept.Influence of object concepts in CHAIN on the scene househouse roof shutter curb chimney hedge palm swimming pool4+ 0.6209 0.4898 0.3390 0.1882 0.2991 0.2666 0.1667 0.05904− -0.6209 -0.4898 -0.3390 -0.1882 -0.2991 -0.2666 -0.1667 -0.0590Influence of unrelated object concepts on the scene houseice basket airplane book dog boat bicycle bed4+ -0.2502 -0.2231 -0.1953 -0.1763 -0.1653 -0.1562 -0.1520 -0.14604− 0.2502 0.2231 0.1953 0.1763 0.1653 0.1562 0.1520 0.1460Table 2.3: Influence of part-level concepts on the object-level house concept.Influence of part concepts in CHAIN on the object housedormer roof porch bush4+ 5.2879 4.9468 3.3671 3.71484− -7.6448 -6.4966 -4.8573 -4.9578Influence of unrelated part concepts on the object housetaillight crosswalk bumper sash4+ -1.9990 -1.8485 -1.7969 -1.67134− 0.4857 0.7345 0.4081 0.5885Influence of a shallower-layer concept on a deeper-layer concept at the classlevelTab. 2.2 shows the influence of object-level concepts in a shallower layer on thescene-level house concept in a deeper layer. The top is the influence of object-levelconcepts in CHAIN, while the bottom is the influence of unrelated object-levelconcepts randomly selected from the complementary set of object-level conceptsin CHAIN interpretation. Tab. 2.2 reveals that the manipulation of object-levelconcepts in CHAIN has a positive correlation with the scene-level house concept.Concretely, enhancing object concepts in CHAIN leads to an increase in the scene-level house concept. In comparison, the manipulation of unrelated concepts isinversely correlated with the scene-level house concept. It validates the efficacyof object-level concepts in CHAIN to the scene-level house concept. It is notedthat the scale of enhancing and weakening influences are the same owning to linearnetwork mapping functions (fully connected layer) from layer4 (object-level layer)64to the output (scene-level layer).Tab. 2.3 shows the influence of part-level concepts on the object-level houseconcept. The top is the influence of part-level concepts in CHAIN, while the bot-tom is the influence of randomly selected unrelated part-level concepts. Tab. 2.3validates that the manipulation of part-level concepts in CHAIN has a positive cor-relation with the object-level house concept. In comparison, unrelated part-levelconcepts are negatively correlated with the object-level house concept. The obser-vation is in accordance with that in Tab. 2.2.To further validate CHAIN, we compare the contribution weight α and the in-fluence 4+ of a shallower-layer concept to a deeper-layer concept in Fig. 2.18.It shows a shallower-layer concept with a higher contribution weight generallycomes with a more considerable enhancing influence. It also validates that thecontribution weight α and the influence 4+ reflect comparable results in mea-suring the importance of a shallower-layer concept to a deeper-layer concept. InCHAIN interpretation, a deeper-layer concept is inferred from a sparse combina-tion of shallow-layer concepts weighted by the contribution weights α . In contrast,influence4+ is computed independently for each shallower-layer concept. There-fore, contribution weight α is more reasonable.Influence of object-level concepts on the scene-level house concept forintra-class imagesThe influence of object-level concepts on the scene-level house concept for intra-class images is shown in Tab. 2.4. Bold numbers indicate the largest influences onscene-level house concept among three house image subsets. Fig. 2.19 shows theinfluence of enhancing object-level concepts on the scene-level house concept. InFig. 2.19, concepts of surroundings (curb, hedge, and swimming pool) impact themost on house images with corresponding surroundings.In Tab. 2.4, it is also observed that the swimming pool has a slightly negativeinfluence on house images with a curb. This observation is reasonable because theswimming pool barely appears when we look at a house on the street. However, inTab. 2.4, the curb has a weak positive influence on house images with a swimmingpool. The reason is that the edge of a swimming pool paved by marble tiles lookssimilar to a curb. This observation indicates that CHAIN interpretations for intra-65Figure 2.18: The importance of shallower-layer concepts to a deeper-layerconcept.66Figure 2.19: The influence of enhancing object-level concepts on the scene-level house concept for intra-class images.class images coincide with visual perception.2.3.5 Inference distance of concepts in CHAIN interpretationIn this section, we study the inference process of concepts for intra-class and inter-class network decisions based on the inference distance defined in section 2.3.1.Here, we apply CHAIN to explain the ResNet-18 decision-making process.Inference distance of concepts for the intra-class interpretationIn the experiment, house images with three types of surroundings are selected forevaluation.Fig. 2.20 depicts the intra-class CHAIN interpretation for the house class atthe scene level. The top plot shows the inference weights of the scene-level houseconcept for three image sets (houses with curb, hedge, and swimming pool) in the3D-PCA space. The bottom table shows their inference distances.67Figure 2.20: Intra-class inference distance of a scene-level concept. The topchart plots the inference weights of the house concept (scene level)for three image sets (houses with curb, hedge, and swimming pool) inthe 3D Principal Components Analysis (PCA) space. The bottom tableshows their inference distances.68Figure 2.21: Intra-class inference distance of object-level concepts. The topchart plots the inference weights of three object concepts (curb, hedge,and swimming pool) for their corresponding image sets (houses withcurb, hedge, and swimming pool) in the 3D PCA space. The bottomtable shows their inference distances.69Figure 2.22: Intra-class inference distance of an object-level concept. Thetop chart plots the inference weights of the house concept (object level)for three image sets (houses with curb, hedge, and swimming pool) inthe 3D-PCA space. The bottom table shows their inference distances.70Table 2.4: Influence of object-level concepts on the scene-level house conceptfor intra-class images.Influence of object concepts in CHAIN on the scene househouse roof shutter curb chimney hedge palm swimming poolhouse images with curb4+ 0.6960 0.5822 0.4080 0.2784 0.3601 0.2489 0.1321 -0.01184− -0.6960 -0.5822 -0.4080 -0.2784 -0.3601 -0.2489 -0.1321 0.0118house images with hedge4+ 0.6725 0.5091 0.3466 0.1844 0.3102 0.3643 0.1784 0.01384− -0.6725 -0.5091 -0.3466 -0.1844 -0.3102 -0.3643 -0.1784 -0.0138house images with swimming pool4+ 0.4943 0.3780 0.2624 0.1018 0.2269 0.1867 0.1895 0.17494− -0.4943 -0.3780 -0.2624 -0.1018 -0.2269 -0.1867 -0.1895 -0.1749Influence of unrelated object concepts on the scene houseice basket airplane book dog boat bicycle bedhouse images with curb4+ -0.3078 -0.2789 -0.2164 -0.1791 -0.1856 -0.1930 -0.1740 -0.15874− 0.3078 0.2789 0.2164 0.1791 0.1856 0.1930 0.1740 0.1587house images with hedge4+ -0.2584 -0.2493 -0.2145 -0.1995 -0.1856 -0.2176 -0.1616 -0.17614− 0.2584 0.2493 0.2145 0.1995 0.1856 0.2176 0.1616 0.1761house images with swimming pool4+ -0.1843 -0.1411 -0.1551 -0.1504 -0.1248 -0.0579 -0.1205 -0.10334− 0.1843 0.1411 0.1551 0.1504 0.1248 0.0579 0.1205 0.1033In the table of Fig. 2.20, bold numbers (0.1344 and 0.1115) are larger thanothers. For the top plot, red points can be easily separated from other points. Incomparison, green and blue points have some overlap. Therefore, at the scenelevel, the inference of the house concept for the swimming pool set is differentfrom those for the curb and hedge sets. In visual perception, house surroundingsin the swimming pool set also have a huge difference from those for the curb andhedge sets.Fig. 2.21 presents the intra-class CHAIN interpretation for the house class onthe object level. The top chart plots the inference weights of three object concepts(curb, hedge, and swimming pool) in their corresponding image sets (houses withcurb, hedge, and swimming pool) in the 3D-PCA space. The bottom table showstheir inference distances.In the top plot of Fig. 2.21, color points can be clustered into three groupsseparately. In the table, diagonal entries are smaller than the others. Therefore,71at the object level of the CHAIN interpretation, the inference of the three objectconcepts can be easily distinguished from each other.Fig. 2.22 shows the intra-class CHAIN interpretation for the house class on theobject level. The top chart plots the inference weights of the house concept (objectlevel) for three image sets (houses with curb, hedge, and swimming pool) in the3D-PCA space. The bottom table shows their inference distances.The top plot in Fig. 2.22 shows that color points mix with each other, whichis also testified by the right table. It means at the object level, inferences of thehouse concept for three image sets are similar. For the three image sets, the houseobject is similar despite the difference in their surroundings. In summary, CHAINinterpretation learns the similarity and variance within a class, which is consistentwith our visual understanding.Inference distance of concepts for the inter-class interpretationIn this experiment, orchard and house are utilized for the study of the inter-classinference distance of concepts in CHAIN interpretation.Fig. 2.23 shows the inter-class CHAIN interpretation for orchard and houseclasses. The top row shows samples from four image sets (orchard, houses withcurb, hedge, and swimming pool) for two classes. The right chart (in the middle)plots the inference weights of scene concepts for four image sets in the 3D-PCAspace. The left table (in the middle) shows their inference distances. Similarly, thebottom row shows the analysis of the object-level concepts.In the left two tables of Fig. 2.23, the bold entries are higher than the others.In the right two plots, data in red color can be easily separated from other data.At the scene level, the CHAIN interpretation of the scene-level orchard conceptis different from that of the scene-level house concept. Likewise, there is a largediscrepancy between the interpretation of the object-level house concept and thetree concept. Therefore, the inter-class difference between the orchard and thehouse is larger than the intra-class difference, which is also aligned with the visualperception of images. Therefore, CHAIN interpretation can be used for the inter-class investigation.72Figure 2.23: Inter-class inference distance of concepts for the orchard and thehouse classes. The top row shows samples for two classes. The rightchart (in the middle) plots the inference weights of the scene conceptsfor four image sets in the 3D-PCA space. The left table (in the middle)shows their inference distances of scene-level concepts. Similarly, thebottom row shows the inference distances of object-level concepts.732.4 ConclusionThe CHAIN interpretation is proposed to explain the network decision-makingprocess. Specifically, the CHAIN interpretation hierarchically reasons a networkdecision to be visual concepts from the high to the low level. Hierarchical vi-sual concepts also help explain the layer structure of the network. Except for theinstance-level interpretation, the CHAIN interpretation can also provide inferenceat the class level. Experiment results demonstrate that the proposed CHAIN modelcan provide reasonable interpretations at both intra-class and inter-class levels.74Chapter 3Interpretable Transformer-basedNeural Radiance Fields forGeneralizable Novel ViewSynthesisChapter 2 is focused on the post-hoc explanation for network predictions in im-age classification. Now let us turn our focus to intrinsic interpretability in inverserendering tasks. One inverse rendering task is novel view synthesis, which refersto synthesizing previously unseen views of a 3D scene from a collection of ob-served views. In this chapter, we propose a unified Transformer-based frameworkwith improved intrinsic interpretability to model a general neural radiance field fornovel view synthesis.3.1 IntroductionNovel view synthesis is a long-standing open problem concerned with the render-ing of unseen views of a 3D scene given a set of observed views [63]. It is a funda-mental and challenging task in 3D modeling [50, 57] and computer animation [36].The essence of novel view synthesis is exploring and learning a view-consistent3D scene representation from a sparse set of input views. The early work focused75on modeling 3D shapes by discrete geometric 3D representations, such as meshsurface [22, 45], point cloud [55] and voxel grid [76, 83]. Although explicit 3Dgeometry-based representations are intuitive, they are discrete and sparse, makingthem incapable of learning high-resolution renderings with sufficient quality forcomplex scenes.The recent promising work, implicit continuous 3D coordinate-based repre-sentation [21, 29, 42, 52], has shown to have the potential to reconstruct 3D sceneswith complicated geometry and appearance in high resolution. However, mostdiscrete [22, 45, 55, 76, 83] and continuous [21, 29, 42, 52] 3D representationsrequire ground-truth 3D geometry as supervision, which is difficult to achieve inreal-world scenes. Subsequently, research work [28, 47, 66, 72] re-visits this re-quirement by introducing differential approximation and rendering functions, andoptimizes the 3D representation only by multi-view images. However, these ap-proaches do not exploit the advantages of continuous 3D coordinate-based repre-sentation sufficiently and therefore only produce over-smoothed renderings.The more recent remarkable Neural Radiance Field (NeRF) models [34, 44,46, 53] introduce neural radiance field scene representations, which use multi-layerperceptrons (MLPs) to map a continuous 3D location and 2D viewing direction toits volume density and radiance color. Unlike previous models in implicit continu-ous representation, NeRF-based models can achieve high-quality novel view syn-thesis from observed images in complex scenes. However, these models need to op-timize a scene-specific 3D representation for each scene, which is time-consumingand does not learn the shared information among scenes. Subsequently, to learnprior knowledge in diverse scenes, researchers [71, 85] generalize the radiance fieldscene representation by receiving a pooling-based multi-view feature as a condi-tional input. These prior NeRFs contain three basic components: a CNN-basedsingle-view feature extraction, a pooling-based multi-view fusion, and an MLP-based NeRF module. Despite the intrinsic connection between these modules, eachmodule is designed and studied independently, making the overall framework dis-jointed. This incoherent framework design damages the intrinsic interpretabilityfrom the following aspects:• In the first module, extracting features of each source view separately over-76looks their relevancy in representing 3D scenes;• In the second module, pooling-based fusion cannot explore the complicatedrelationship among source views;• While the importance of an observed view describes its contribution to thequery rendering, the source-view importance in the second module is de-cided without considering the target rendering information;• Despite the pooling-based aggregated multi-view feature losing useful infor-mation, the third module renders the color and density from a single aggre-gated feature, ignoring intricate relationships between observed views andthe rendering view.Therefore, intrinsic interpretability is mainly restrained by the pooling-basedfusion and the MLP-based rendering, which should work together rather than sep-arately. The reason for this framework design is that previous NeRFs are builton MLPs that are incapable of receiving and processing an arbitrary number ofobserved views. Consequently, they need an auxiliary fusion model to aggregatemulti-view information, and pooling-based fusion provides such a straightforwardtechnique.This limitation also impairs the capability of NeRFs to learn a view-consistent3D scene representation from observed views, especially for the scenario wheresource views have a more complicated relationship with the target view, e.g. theobserved source views are captured at camera poses that are very different fromthe camera pose of the target view. When camera poses of source views are similarto the rendering view, source views and the target view are distributed in a localregion in 3D scene representation space, making it possible to approximate theirrelationship by a linear function as in previous work [71, 85]. However, as the dif-ference between observed views and the rendered view increases, the correlationbecomes more complicated, making it challenging for these approaches to syn-thesize a realistic novel view. In this scenario, existing MLP-based NeRFs, usingthe pooling-based function to fuse the multi-view, are insufficient to resolve thischallenge.77Figure 3.1: The intrinsic interpretability of TransNeRF in both thesurrounding-view space and the ray-cast space when rendering a 3Dpoint along the query ray.Therefore, the fundamental issue is how to free the intrinsic interpretability ofNeRFs from pooling-based fusion and MLP-based rendering. To tackle this unmetneed, we present TransNeRF, an end-to-end Transformer-based architecture thatunifies source-view fusion and target-view rendering processes. The learning pro-cess of TransNeRF is divided into two stages: the first works in the surrounding-view space, which includes the Density-ViewDecoder and Color-ViewDecoder;and the second works in the ray-cast space, which includes the Density-RayDecoderand Color-RayDecoder. The four sub-modules stated above are built by the Transformer-based network. By taking advantage of the attention mechanism, in the renderingprocess for a query 3D point, TransNeRF integrates information about its projected2D pixels at the surrounding source views in the first stage and its neighboring 3Dpoints along the query ray in the second stage, as shown in Fig 3.1. This design pro-vides our model with a comprehensive understanding of the shape and appearanceconsistency of a 3D scene in both the surrounding-view space and ray-cast space.Furthermore, the Transformer-based framework enables our rendering process to78learn in-depth and high-level complicated relationships between source views andthe rendering view, which is essential for novel view synthesis. As a result, theproposed TransNeRF has improved intrinsic interpretability and can learn a morecomprehensive general neural radiance field.Our contributions can be summarized as follows:• We propose a unified Transformer-based framework (TransNeRF) to learn ageneralizable neural radiance field rather than the disjointed Pooling-fusion+ MLP-rendering architecture in prior NeRFs for image-based rendering.• TransNeRF learns high-level correlations between observed and renderingviews and simultaneously integrates this intricate information into a neuralradiance field leveraging attention layers, strengthening its intrinsic inter-pretability.• TransNeRF exploits the geometry and appearance consistency of a neuralradiance field in both the surrounding-view space and the ray-cast space viaour Transformer network.• Experiments show that TransNeRF achieves more realistic rendering resultsthan state-of-the-art methods in both scene-agnostic and per-scene fine-tuningsettings, especially when source views are captured at camera poses that dif-fer significantly from the camera pose of the rendering view.• TransNeRF can explain a query rendering process by utilizing its atten-tion layers. The associated results show that the inherent interpretabilityof TransNeRF is consistent with human perception.3.2 Methodology3.2.1 FrameworkUnlike Neural Radiance Field (NeRF) [44] optimizing a scene-specific 3D repre-sentation, we propose TransNeRF to learn a generic radiance field representationfor novel scenes. Given captured multi-view images {Im}Mm=1 (M source views)79Figure 3.2: Workflow of the proposed TransNeRF.of diverse scenes and their camera parameters {Θm}Mm=1 (camera poses, intrinsicparameters and scene bounds), TransNeRF reconstructs a generic radiance field,denoted FTransNeRF, to learn the prior knowledge(σ ,c)← FTransNeRF((x,y,z),d;{Im,Θm}m) , (3.1)where (x,y,z) is a 3D point location, d denotes a unit-length direction of a viewingray and outputs are a differential volumetric density σ and a directional emittedcolor c.As shown in Fig. 3.2, the two stages of TransNeRF are as follows: the firststage in the surrounding-view space uses the Density-ViewDecoder and Color-ViewDecoder to integrate source-view information into the query density and colorrepresentation; the second stage in the ray-cast space employs the Density-RayDecoderand Color-RayDecoder to learn neighboring 3D points along the query ray.Our TransNeRF enhances intrinsic interpretability from the following as-pects:• In contrast to prior work that used separate fusion and rendering modules, thefirst stage of our framework unites source-view fusion and target-view ren-dering processes via our Transformer-based network. Here, the Transformer80attention of various source views for a query 3D point is used to learn thecontribution of source views to the rendering of the query 3D point.• In the first stage, our Transformer-based rendering (Density-ViewDecoderand Color-ViewDecoder) investigates deep relationships between the target-rendering view and source views, simultaneously decoding observed multi-view representations and target-rendering spatial information for a query 3Dpoint into density and color representations, whereas previous MLP-basedrendering requires an auxiliary pooling-based fusion to aggregate multiplefeatures for source views.• Self-attention layers in the Density-ViewDecoder learn source-view repre-sentations by considering global correlations among source views rather thanlearning each source view separately.• In contrast to prior work that handled each 3D point separately, the secondstage of our TransNeRF takes into account nearby 3D points on the target-viewing ray by using attention layers when rendering a query 3D point.To render a query 3D point on a target-viewing ray, TransNeRF receives asinputs its spatial location (x,y,z), viewing direction d and a set of source views{Im,Θm}m. The rendering procedure contains four steps: 1) For each observedsource view, we first extract its feature volume based on a pre-trained U-Net and re-trieve spatial-aligned 2D-pixel features for the query 3D point as its initial source-view features. Then, Density-ViewDecoder (Sec. 3.2.2) decodes the initial source-view features into the latent density representations of the query point. 2) Density-RayDecoder (Sec. 3.2.3) thereafter enhances the latent density representation byconsidering neighboring points along the target-viewing ray and outputs the den-sity for the query 3D point. 3) Given latent source-view features from Density-ViewDecoder and the query-point density representation from Density-RayDecoder,Color-ViewDecoder (Sec. 3.2.4) fuses them into the latent color representationfor the query point. 4) Similar to Density-RayDecoder, Color-RayDecoder (Sec.3.2.5) decodes the query color by integrating color information of 3D points alongthe target-viewing ray. Finally, we can obtain the density and directional color(σ ,c) for the query 3D point on a target-viewing ray.813.2.2 Density decoder in surrounding-view spaceWe first present our density decoder in surrounding-view space (Density-ViewDecoder)fusing source views into the latent density representation for a query 3D point.For each source view image, we first extract its feature volume by a pre-trainedview-shared U-Net. A query 3D point (x,y,z) is then projected into each source-view image Im by its camera projection matrix Θm to extract the correspondingRGB color {cmsrc}Mm=1 and feature vector {fmsrc}Mm=1 at the projected 2D pixel loca-tion through bilinear interpolation. In each source view, we also record its view-ing direction {dmsrc}Mm=1 for the projected 2D pixel from the source camera pose.And then based on this information, we obtain the initial source-view embeddings{xm0 }Mm=1 for source views, as in [78].For the query 3D point, Density-ViewDecoder receives the initial source-viewembeddings {xm0 }Mm=1 and the learnable query density embedding xσ0 as inputs X0.The Density-ViewDecoder can be formulated as follows:X0 = [xσ0 ;x10;x20; · · · ;xM0 ] , (3.2)X˜l = Norm(Density-ViAttn(Xl−1)+Xl−1) , (3.3)Xl = Norm(FFN(X˜l)+ X˜l) , (3.4)where l denotes the index of a basic block (l = 1, · · · ,L), “Norm” is the layernormalization function and “FFN” is a position-wise feed-forward network. At theL-th block, we can obtain XL = [xσL ;x1L;x2L; · · · ;xML ]. In the Density-ViewDecoder,we concatenate the embedding xσL and its 3D coordinate location (x,y,z) as theoutput density representation for the query 3D point.Density-view attention layers (Density-ViAttn) can explore deep relationshipsamong source views, defined as follows:Density-ViAttn(X) = MH-Attn(X,X,X) , (3.5)82where the multi-head attention function is defined as:MH-Attn(Q,K,V) = Cat(A1, · · · ,AH)W , (3.6)where Ah = Attention(Qh,Kh,Vh) ,Qh = QWqh;Kh = KWkh;Vh = VWvh .Here, Wqh,Wkh ∈ Rdk×dh ;Wvh ∈ Rdv×dh and W ∈ RHdh×dk are parameter matrices(H × dh = dk and dh is the feature dimension in each head). And the Attentionfunction is computed byAttention(Q,K,V) = softmax(QKT√dk)V ,where Q = [q1;q2; · · · ;qi; · · · ;qNq ] ,K = [k1;k2; · · · ;k j; · · · ;kNk ] ,V = [v1;v2; · · · ;v j; · · · ;vNk ] .(3.7)Here, Nq queries are stacked in Q ∈RNq×dk , a set of Nk key-value pairs are stackedin K ∈ RNk×dk and V ∈ RNk×dv , dk is used as a scalar for normalization. OurDensity-ViewDecoder is invariant to permutations of source views and can receivean arbitrary number of source views.3.2.3 Density decoder in ray-cast spaceThe density decoder in ray-cast space (Density-RayDecoder) decodes the densityinformation of the query 3D point by aggregating the density features of the neigh-boring 3D points along the target-view ray.For the query point and neighboring 2n points along the target-viewing ray, wedenote [σ i−n0 ; · · · ;σ i−10 ;σ i0;σ i+10 ; · · · ;σ i+n0 ] as their initial density representationsat the input end of the Density-RayDecoder, where the query point is denoted asqi and neighboring 2n points are {qi−n, · · · ,qi−1,qi+1, · · · ,qi+n}. Here, the initialdensity representation for each 3D point is computed via an FC layer based on theDensity-ViewDecoder output for the corresponding point (σ0 = FC(xσL (x,y,z)),where is the concatenation operation). Then positional encodings Epos are addedto density representations of neighboring 3D points to keep their position informa-83tion in the ray-cast space. Each positional encoding informs each point of its 3Dspatial location, which is computed by utilizing sine and cosine functions of dif-ferent frequencies in a similar way to [5]. The Density-RayDecoder is representedas:D0 = [σ i−n0 ; · · · ;σ i−10 ;σ i0;σ i+10 ; · · · ;σ i+n0 ]+Epos , (3.8)D˜l = Norm(Density-Attn(Dl−1)+Dl−1) , (3.9)Dl = Norm(FFN(D˜l)+ D˜l) , (3.10)where the density attention layer (Density-Attn) is computed as Density-Attn(D) =MH-Attn(D,D,D) fusing information of surrounding 3D points on the target-viewingray. At the end block, the Density-RayDecoder outputs the density representationσ iL of the query 3D point, and then we use an FC layer to project it to the densityvalue for the query point.3.2.4 Color decoder in surrounding-view spaceThe color decoder in surrounding-view space (Color-ViewDecoder) learns a querydirectional emitted color as a function of viewing direction, source-view represen-tations learned from Density-ViewDecoder, and the latent density representationfrom Density-RayDecoder.The Color-ViewDecoder can be formulated as follows:Y˜l = Norm(Color-ViAttn(Yl−1,Xsrc,Csrc)+Yl−1) , (3.11)Yl = Norm(FFN(Y˜l)+ Y˜l) . (3.12)In the color-view layer (Color-ViAttn), the initial query directional color embed-ding is represented as Y0 = FC(σ iL) dtgt , where σ iL is the latent density repre-sentation from Density-RayDecoder and dtgt is the target-viewing direction for thequery 3D point. The Color-ViAttn layer is calculated as:Color-ViAttn(Y,Xsrc,Csrc) = MH-Attn(Y,Xsrc,Csrc) , (3.13)where the value is Csrc = [γ(c1src);γ(c2src); · · · ;γ(cMsrc)] (γ(·) is the embedding func-84tion) and the key is Xsrc = [FC(x1L) d1src;FC(x2L) d2src; · · · ;FC(xML ) dMsrc] rep-resenting conditional source-view information. The output of Color-ViewDecoderycL is the latent color representation for the query 3D point.3.2.5 Color decoder in ray-cast spaceThe color decoder in ray-cast space (Color-RayDecoder) learns a query direc-tional emitted color by fusing color features of adjacent 3D points along the tar-get ray in color attention layers (Color-Attn(Z) = MH-Attn(Z,Z,Z)). The Color-RayDecoder can be formulated as follows:Z0 = [zi−n0 ; · · · ;zi−10 ;zi0;zi+10 ; · · · ;zi+n0 ]+Epos , (3.14)Z˜l = Norm(Color-Attn(Zl−1)+Zl−1) , (3.15)Zl = Norm(FFN(Z˜l)+ Z˜l) . (3.16)where the latent color representation ycL for the query 3D point is assigned to thecorresponding zi0 and likewise for adjacent 2n 3D-points in ray-cast space.Subsequently, after the Color-RayDecoder, we use an FC layer to project theoutput color embedding ziL to its output predicted color value. Then the predictedvolume density and directional color of each query point along a camera ray of thedesired virtual camera are put forward to the classical volume rendering. The im-plementation details of the network and training are described in the supplementarymaterial.3.2.6 TransNeRF interpretabilityThe proposed TransNeRF enhances the shape and appearance consistency in bothsurrounding-view space and ray-cast space by utilizing the attention mechanism,hence strengthening the inherent interpretability of our learned neural radiancefield. Specifically, when rendering the density and radiance color of a query 3Dpoint, TransNeRF, by attention layers, integrates information about the projected2D pixels from the surrounding source views (in the Density-ViewDecoder andColor-ViewDecoder) and the neighboring 3D points along the query ray (in theDensity-RayDecoder and Color-RayDecoder).85TransNeRF Interpretability in Surrounding-view SpaceThe intrinsic interpretability of TransNeRF in surrounding-view space is enhancedbecause its attention layers learn high-level relationships between observed viewsand the rendering view in the rendering process for a query 3D point. For atten-tion layers in surrounding-view space, the attention of different observed viewsfor a query 3D point is learned to represent the contributions of observed viewsin rendering the query 3D point. Based on that, TransNeRF can explain its ren-dering process in surrounding-view space by visualizing its attention layer in theDensity-ViewDecoder and Color-ViewDecoder.Mathematically, the attention function explores high-level relationships layer-by-layer between the query and key, as follows:softmax(QKT√dk)V=softmax(1√dkq1q2...qNq [kT1 ,kT2 , · · · ,kTNk ])v1v2...vNk=softmax(1√dkq1kT1 q1kT2 · · · q1kTNk....... . ....qNqkT1 qNqkT2 · · · qNqkTNk)v1...vNk=α1,1 α1,2 · · · α1,Nk....... . ....αNq,1 αNq,2 · · · αNq,Nkv1...vNk ,where αi, j =exp(qikTj )√dk∑Nkr=1 exp(qikTr ).(3.17)The attention-score αi, j, stored in softmax(QKT√dk), of a specific value v j is ob-tained by the match between the i-th query qi and the j-th key k j. The outputfor a query xi is computed by decoding the relationships between the query and86key-value embeddings, i.e. [x1;x2; · · · ;xi; · · · ;xNq ] = softmax(QKT√dk)V, wherexi =Nk∑j=1αi, jv j=Nk∑j=1exp(qikTj )√dk∑Nkr=1 exp(qikTr )v j .(3.18)In the rendering process of the Density-ViewDecoder and Color-ViewDecoder, at-tention layers learn the density and color representation for a query 3D point byintegrating features of its projected 2D pixels from the surrounding source views.Specifically, in the Density-ViewDecoder, the output query xσL of the density for aquery 3D point learns the relationships between the query density and source-viewembeddings, and attention scores of source views on the query density describethe importance of source views on rendering the density of the query 3D point.Similarly, for a query 3D point, Color-ViewDecoder explores the interconnectionsbetween the query color and source-view embeddings by attention scores and de-codes them into the color query output.For human perception in surrounding-view space, an observed view captur-ing a query 3D point contains meaningful information for rendering the query 3Dpoint and consequently contributes more than observed views that do not captureit. Accordingly, the importance of an observed view to a 3D-point rendering is pos-itively correlated with the visibility of the 3D point in the observed view. It meansthe important source view should be the one that captures the target 3D point whilethe trivial one does not. Therefore, we study intrinsic TransNeRF interpretabil-ity in surrounding-view space by evaluating whether the attention in the Density-ViewDecoder and Color-ViewDecoder is consistent with the above description ofhuman perception.TransNeRF Interpretability in Ray-cast SpaceThe intrinsic interpretability of TransNeRF is improved in ray-cast space during therendering of a query 3D point because attention layers take into account the 3D-scene consistency of adjacent 3D points on the target-viewing ray. In the Density-RayDecoder and Color-RayDecoder, the attention of adjoining 3D points to the87query 3D point is learned to represent the contributions of adjacent 3D points tothe query 3D point rendering in ray-cast space. Therefore, we can visualize itsattention layer in the Density-RayDecoder and Color-RayDecoder to illustrate itsrendering process in ray-cast space.During the rendering process in ray-cast space, the attention layers of theDensity-RayDecoder and Color-RayDecoder learn the density and color represen-tation of a query 3D point by integrating features of neighboring 3D points on thetarget-viewing ray. For the query 3D point, the Color-RayDecoder and Density-RayDecoder investigate the relationships between the query and adjacent 3D pointson the target-viewing ray by the attention function and decode them into the queryoutput of color and density, respectively. The attention function in Eq. (3.17) learnshow the density and color of a query 3D point correlate with adjacent 3D points onthe target-viewing ray.For 3D scene understanding, the shape and appearance consistency of a 3Dscene determine the density and color correlation of neighboring 3D points on thetarget-viewing ray. As a result, in a neural radiance field, neighboring 3D pointswith comparable features contribute more to rendering the query 3D point thanthose with less similar features. Based on the consistency in a 3D representation,the Density-RayDecoder and Color-RayDecoder should pay more attention to theneighboring 3D points with similar representations when rendering a query 3Dpoint in ray-cast space. We analyze intrinsic TransNeRF interpretability in ray-cast space to examine whether the attention in the Density-RayDecoder and Color-RayDecoder is in accord with the geometry consistency.3.2.7 Rendering and trainingAs in NeRF [44], classical volume rendering [31], a differentiable ray marchingrendering, is utilized to render a 2D image from our radiance field scene repre-sentation FTransNeRF. To calculate a pixel color at a rendered image, classical vol-ume rendering marches a ray via the pixel and accumulates radiance at sampled3D points along the ray. Specifically, the rendered color C(r) of the camera ray88r(t) = o+ td with near and far bounds [tn, t f ] is computed as:C(r) =∫ t ftnT (t)σ(r(t);Im,Θm)c(r(t),d;Im,Θm)dt , (3.19)where the function T (t) = exp(−∫ ttn σ(r(s);Im,Θm)ds) calculates the accumulatedtransmittance along the ray between depth bounds [tn, t].The rendering loss between the rendered and ground-truth pixel colors for allcamera rays of the target view with camera pose Θ isL = ∑r∈R(Θ)‖Cˆ(r)−C(r)‖22 , (3.20)where R(Θ) is the set of all camera rays of the desired virtual camera with poseΘ.Given a set of observed source views, the rendering lossL between the groundtruth and the prediction is minimized by optimizing FTransNeRF. Here, our TransNeRFis fully differentiable and can be trained end-to-end. After being trained on a largedataset containing diverse scenes, our TransNeRF effectively generalizes to unseenscenes even without per-scene finetuning. Accordingly, given the camera pose ofa query novel view of a scene and its multiple source views, our TransNeRF canrender the query novel view from the pre-trained general neural radiance field bycasting rays from the target camera center towards the 3D space using volume ren-dering in Eq. (3.19).Here, we present a generic Transformer-based NeRF framework with a highcapacity for modeling radiance field scene representation from observed sourceview images. Similar to MLP-based NeRFs, our framework can be easily extendedto advanced TransNeRF derivatives, e.g. from NeRF to NeRF-W [40] by addingappearance and transient variables as inputs to model uncertainty in the wild sce-narios. Here, we only focus on the vanilla TransNeRF and hope this work willserve as a blueprint for future work.3.3 ExperimentsThe proposed approach is evaluated in the following experimental settings:89• Scene-agnostic setting: we train a single scene-agnostic model on a largetraining dataset that includes various camera setups and scene types. We testits generalization ability to novel view synthesis of unseen scenes on all testscenes from the evaluation dataset;• Per-scene finetuning setting: our pre-trained scene-agnostic model can befinetuned on each test scene. We then evaluate each finetuned scene-specificmodel on its corresponding scene separately.The experiments are designed to examine whether our TransNeRF can effi-ciently learn a neural radiance field scene representation in scenarios where thedifference between source views and the target rendering view varies.3.3.1 DatasetsWe train and evaluate our method on a collection of several multi-view datasetscontaining both synthetic data and real data, as in IBRNet.• Real datasets for training include the Spaces dataset [18], RealEstate10K[95], and the handheld-cellphone-captured scene dataset. The Spaces dataset[18] has 100 scenes and each scene is collected with a 16-camera rig at 3to 10 rig positions. RealEstate10K [95], a large indoor-scene dataset, iscaptured from around 80K video clips with camera poses. The cellphone-captured scene dataset contains 95 real scenes (36 from LLFF [43] and 59from IBRNet [78]), where each scene consists of 20 to 60 forward-facingimages. COLMAP [60] is adopted to estimate camera poses, intrinsic pa-rameters, and scene bounds for real data as in [44].• Synthetic dataset for training is generated by IBRNet from Google ScannedObjects, which contains 1,030 models with a variety of view density rates.During training, we randomly sample M source views for each target view froma pool of m×M views where M is sampled uniformly at random from [8, 12] andm is from [1, 5], as in [78].• Real dataset for evaluation collects 8 complex real-world scenes capturedwith a handheld cellphone (5 from LLFF [43] and 3 from NeRF [44]). Each90scene consists of 20 to 62 forward-facing images with 1008× 756 pixels,and 1/8th of these is held out as the test set (7/8 for per-scene finetuning).• Synthetic dataset for evaluation, adopted from NeRF, includes 8 objectswith complicated geometry and realistic non-Lambertian materials whichare rendered at 800×800 pixels from viewpoints sampled either on the upperhemisphere or full sphere (100 views for per-scene finetuning and 200 viewsfor testing).Evaluation based on the difference between source views and the targetview. For the evaluation of a specific scene, target rendering views are from thetesting set of evaluation datasets, and the corresponding surrounding view set is inthe training set of evaluation datasets. In this evaluation, we sampled M = 10 viewsfrom the surrounding view set as source views to render a targeted view. Given thecamera pose (rotation and translation) with respect to a world coordinate system,we can calculate the difference between each source view and the target renderingview. Based on the calculation, the sampling procedure of source views is definedas follows: for each target rendering view, we first compute the differences be-tween the target-view camera pose and the surrounding-view camera poses usingEuclidean transformation matrices of camera poses, and then rank the surroundingviews according to the difference. Based on this difference ranking, we constructNs source-view sets ({Si}Nsi=1) of 10 views from the surrounding-view set to rendereach test view. For the real evaluation dataset, there are Ns = 3 sets, i.e. the top-10(S1), the middle-10 (S2), and the bottom-10 (S3) views; for the synthetic evalua-tion dataset, there are Ns = 4 sets which are the top-10 (S1), the middle-10 (S2), the3/4th-10 (S3), and the bottom-10 (S4) views, respectively. This sampling strategycan be used to compare methods in scenarios where the camera poses of sourceviews have diverse degrees of difference from the camera pose of the target view.3.3.2 Network detailsWe use a shared network to extract features of each source view; and the shared net-work is of a U-Net-like architecture, as in [78]. Our TransNeRF network containsfour sub-modules: Density-ViewDecoder, Density-RayDecoder, Color-ViewDecoder,and Color-RayDecoder, where the first two sub-modules and the last two are for91the density and color representations by considering surrounding source views andneighboring points along the target ray. The sub-modules (Sec. III-A, III-B, III-C,III-D) are adapted from the vanilla Transformer network, and each of them con-tains L=2 blocks. The first two sub-modules have H=4 heads for attention layersand d=32 dimensions for each token feature while the last two have H=5 heads andd=45 dimensions. The blocks for each sub-module are implemented as describedin the methodology section of the work.3.3.3 Training detailsDuring training, we adopt the hierarchical volume sampling strategy from NeRFto achieve more efficient sampling. For the hierarchical volume sampling, we con-struct a coarse TransNeRF and a fine TransNeRF with identical network architec-ture. At each optimization iteration, we randomly sample a batch of camera raysfrom the set of all pixels in the dataset (batch size = 2048 rays) and then sampleNc = 64 points at the coarse-scale and N f = 64 additional points at the fine-scalefor each ray. After rendering the color of each ray from both scale sets of samplesby the volume rendering, we can train the feature extraction network as well asthe coarse and fine TransNeRF simultaneously by minimizing the mean squarederror between ground-truth pixel colors and the rendered colors in coarse and finescales. Both the feature extraction network and the TransNeRF are optimized usingAdamW. The initial learning rates of the feature extraction network and TransNeRFare 10−3 and 5×10−4, respectively.3.3.4 MetricsFor novel view synthesis, we quantitatively evaluate the rendered image qualitybased on Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Mea-sure (SSIM) [79] (higher is better), and Learned Perceptual Image Patch Similar-ity (LPIPS) [89] (lower is better) by comparing with the ground truth.3.3.5 BaselinesWe compare the proposed method quantitatively and qualitatively with top-performinggeneric NeRF approaches (PixelNeRF [85], MVSNeRF [7], IBRNet [78]) that are92Table 3.1: Quantitative comparisons of methods (PixelNeRF, MVSNeRF,IBRNet, and the proposed TransNeRF) for the scene-agnostic setting onthe realistic synthetic dataset.Scene-agnostic setting on realistic synthetic datasetPSNR ↑ SSIM ↑ LPIPS ↓Scene Si PixelNeRF MVSNeRF IBRNet TransNeRF PixelNeRF MVSNeRF IBRNet TransNeRF PixelNeRF MVSNeRF IBRNet TransNeRFChairS1 21.21 23.50 28.55 29.06 0.890 0.910 0.942 0.954 0.135 0.108 0.066 0.055S2 16.98 19.38 24.93 25.79 0.784 0.811 0.854 0.903 0.240 0.224 0.173 0.135S3 15.76 18.37 24.12 25.17 0.712 0.745 0.798 0.870 0.298 0.267 0.206 0.164S4 14.51 17.21 23.12 24.85 0.612 0.647 0.714 0.823 0.387 0.338 0.259 0.194LegoS1 19.51 21.13 24.64 26.13 0.834 0.862 0.917 0.923 0.174 0.148 0.106 0.090S2 15.30 17.08 21.14 22.80 0.685 0.717 0.787 0.851 0.331 0.311 0.257 0.179S3 14.21 16.08 20.33 22.18 0.613 0.650 0.731 0.819 0.390 0.354 0.291 0.207S4 13.04 14.92 19.33 21.10 0.532 0.571 0.665 0.768 0.471 0.421 0.339 0.246ShipS1 21.31 21.79 22.92 24.57 0.803 0.808 0.825 0.836 0.267 0.256 0.227 0.211S2 17.04 17.69 19.37 21.25 0.650 0.658 0.689 0.725 0.443 0.438 0.397 0.305S3 15.98 16.69 18.56 20.64 0.577 0.591 0.633 0.693 0.503 0.480 0.431 0.333S4 14.83 15.59 17.63 19.34 0.481 0.497 0.552 0.637 0.599 0.565 0.495 0.370DrumsS1 17.60 18.74 21.28 21.99 0.771 0.807 0.893 0.902 0.184 0.164 0.113 0.105S2 13.85 15.14 18.21 18.69 0.642 0.683 0.782 0.802 0.321 0.312 0.252 0.201S3 12.72 14.16 17.40 18.49 0.570 0.616 0.725 0.770 0.383 0.354 0.285 0.230S4 11.53 12.99 16.40 18.18 0.480 0.528 0.652 0.724 0.474 0.434 0.346 0.254MicS1 26.51 27.28 28.93 29.32 0.929 0.938 0.951 0.968 0.071 0.062 0.045 0.033S2 22.64 23.61 25.80 26.09 0.852 0.864 0.891 0.914 0.165 0.165 0.135 0.135S3 21.46 22.60 24.99 25.85 0.779 0.797 0.835 0.881 0.226 0.207 0.169 0.164S4 20.53 21.61 24.15 25.65 0.686 0.706 0.758 0.816 0.295 0.265 0.207 0.197FicusS1 21.86 22.73 24.72 25.14 0.899 0.904 0.919 0.923 0.125 0.117 0.089 0.077S2 18.60 19.67 22.20 22.70 0.793 0.801 0.830 0.831 0.227 0.228 0.189 0.159S3 17.51 18.65 21.39 22.56 0.720 0.735 0.774 0.799 0.288 0.270 0.222 0.187S4 16.05 17.27 20.15 22.14 0.626 0.642 0.695 0.746 0.368 0.339 0.271 0.235MaterialsS1 19.47 19.93 20.98 22.67 0.828 0.847 0.895 0.903 0.195 0.174 0.124 0.110S2 14.41 14.91 16.48 19.15 0.654 0.683 0.739 0.807 0.357 0.348 0.288 0.198S3 13.15 13.92 15.66 18.54 0.581 0.615 0.683 0.774 0.420 0.390 0.322 0.227S4 11.89 12.66 14.58 16.25 0.486 0.521 0.603 0.729 0.514 0.472 0.386 0.267HotdogS1 22.14 24.70 30.45 32.70 0.902 0.919 0.958 0.968 0.135 0.115 0.066 0.054S2 17.20 20.02 26.29 28.82 0.797 0.817 0.871 0.904 0.275 0.259 0.198 0.149S3 16.22 18.99 25.48 28.20 0.724 0.750 0.814 0.871 0.332 0.301 0.232 0.178S4 14.98 17.79 24.43 26.27 0.636 0.662 0.740 0.825 0.410 0.365 0.276 0.216AveS1 21.20 22.47 25.31 26.45 0.857 0.874 0.913 0.922 0.161 0.143 0.104 0.092S2 17.00 18.44 21.80 23.16 0.732 0.755 0.805 0.842 0.295 0.286 0.236 0.183S3 15.88 17.43 20.99 22.70 0.660 0.687 0.749 0.810 0.355 0.328 0.270 0.211S4 14.67 16.25 19.97 21.72 0.567 0.597 0.672 0.758 0.440 0.400 0.322 0.248also designed to generalize the scene-specific NeRF representation to a scene-agnostic one by taking multi-view features as conditional inputs. In the evalua-tion, each comparing method trains a single set of model parameters on the sametraining dataset and tests generalizability for novel scenes on the same evaluationdataset described in Sec. 3.3.1. Furthermore, for a specific scene, we also evaluatecomparing methods in the per-scene finetuning experimental setting. All compar-ing approaches are implemented based on their released codes in the same trainingsetting.3.3.6 ResultsIn both the scene-agnostic setting (Sec. 3.3.6) and per-scene fine-tuning setting(Sec. 3.3.6), we evaluate the performance of different methods in scenarios wherethe source views belong to different source view sets {Si}Nsi=1 defined in Sec. 3.3.1.93Table 3.2: Quantitative comparisons of methods (PixelNeRF, MVSNeRF,IBRNet, and the proposed TransNeRF) for the scene-agnostic setting onthe real forward-facing dataset.Scene-agnostic setting on real forward-facing datasetPSNR ↑ SSIM ↑ LPIPS ↓Scene Si PixelNeRF MVSNeRF IBRNet TransNeRF PixelNeRF MVSNeRF IBRNet TransNeRF PixelNeRF MVSNeRF IBRNet TransNeRFFernS1 20.65 21.12 23.69 23.70 0.671 0.696 0.767 0.771 0.355 0.322 0.250 0.247S2 18.69 19.40 22.18 22.35 0.602 0.639 0.709 0.720 0.427 0.389 0.307 0.295S3 17.99 18.80 21.96 22.11 0.574 0.607 0.703 0.704 0.460 0.410 0.316 0.304TrexS1 18.63 19.24 23.83 23.84 0.705 0.722 0.849 0.850 0.392 0.377 0.239 0.237S2 16.03 16.88 21.68 21.85 0.633 0.660 0.788 0.797 0.467 0.448 0.299 0.287S3 13.80 15.18 19.94 20.51 0.561 0.611 0.737 0.764 0.544 0.516 0.352 0.328HornsS1 20.01 21.35 26.34 26.35 0.702 0.739 0.866 0.868 0.356 0.323 0.179 0.179S2 16.78 18.37 23.56 23.74 0.626 0.680 0.802 0.812 0.438 0.401 0.247 0.236S3 14.06 15.99 21.32 21.71 0.537 0.610 0.734 0.760 0.531 0.482 0.316 0.293FortressS1 22.37 24.31 29.97 29.98 0.719 0.732 0.879 0.880 0.327 0.287 0.155 0.152S2 20.14 22.36 28.19 28.40 0.683 0.701 0.853 0.862 0.368 0.325 0.180 0.170S3 15.15 17.97 23.68 24.36 0.560 0.595 0.751 0.767 0.498 0.446 0.287 0.267LeavesS1 15.56 16.37 20.30 20.31 0.513 0.561 0.722 0.724 0.418 0.378 0.228 0.226S2 13.07 14.23 18.26 18.54 0.395 0.456 0.615 0.627 0.529 0.484 0.324 0.309S3 11.20 12.73 16.87 17.39 0.303 0.394 0.544 0.578 0.607 0.550 0.378 0.355OrchidsS1 15.57 16.14 19.25 19.26 0.464 0.492 0.629 0.631 0.461 0.422 0.294 0.291S2 13.64 14.58 17.76 18.07 0.371 0.410 0.547 0.558 0.560 0.517 0.378 0.363S3 12.28 13.42 16.89 17.26 0.299 0.345 0.496 0.507 0.627 0.575 0.421 0.399RoomS1 21.52 22.74 29.70 29.71 0.820 0.835 0.941 0.944 0.318 0.293 0.155 0.153S2 17.81 19.43 26.45 26.78 0.775 0.788 0.907 0.916 0.379 0.352 0.202 0.191S3 13.71 15.64 22.83 23.33 0.699 0.738 0.852 0.870 0.479 0.442 0.278 0.259FlowerS1 17.84 19.46 26.61 26.63 0.614 0.663 0.854 0.858 0.414 0.376 0.165 0.157S2 14.21 16.23 23.43 23.76 0.524 0.580 0.775 0.787 0.507 0.464 0.243 0.229S3 10.28 11.97 19.15 19.85 0.374 0.446 0.646 0.662 0.662 0.607 0.374 0.336AveS1 19.02 20.09 24.96 24.97 0.651 0.680 0.813 0.816 0.380 0.347 0.208 0.205S2 16.30 17.68 22.69 22.94 0.576 0.614 0.749 0.760 0.459 0.422 0.273 0.260S3 13.56 15.21 20.33 20.81 0.489 0.543 0.683 0.701 0.551 0.504 0.340 0.318To render a testing view, each comparing approach receives as input the samesource-view set. We present both qualitative and quantitative results for evalua-tion. In Sec. 3.3.6, we provide the interpretation results of TransNeRF to evaluatewhether it is consistent with human perception. For each section, more results areprovided in the supplementary material.Scene-agnostic ExperimentsIn scene-agnostic experiments, we compare our TransNeRF with PixelNeRF [85],MVSNeRF [7] and IBRNet [78] on the real forward-facing dataset [43] and therealistic synthetic dataset.Tab. 3.1 and 3.2 show that the proposed TransNeRF outperforms comparingmethods on synthetic and real datasets under the scene-agnostic setting. For com-paring quantitative results in each evaluation metric, the best scores are in bold. Itshows that our method has better generalization ability to novel scenes though itis trained on datasets with noticeably different scenes and view distributions. Thesuperior generalization ability of our method is also reflected in qualitative results.94As shown in Fig. 3.3, we examine the performance of the comparing methods onrendering the same randomly-selected testing view based on different source-viewsets. In Fig. 3.3, the results of comparing approaches contain more obvious ar-tifacts than our approach and even completely fail in the S3 scenario, where thedifference between source views and the target rendering view is more consider-able than that in S1 and S2. As depicted in colored frames, the comparing methodscannot synthesize clean boundaries of fronds and recover thin structures (branchesand leaves besides fern).From the above qualitative results, we observe that there exists a gradual de-cline in the quality of the synthesized view when the difference between sourceviews and the target rendering view increases from S1 to S3. Similarly, in quan-titative results from S1 to S3, PSNR and SSIM values both decrease while LPIPSincreases for all comparing methods. It reveals that the more dissimilar the sourceviews are with respect to the target rendering view, the more difficult novel viewsynthesis becomes. The tables also indicate that the advantage of TransNeRF be-comes more significant than the comparing methods with the increase of the dif-ference between source views and the target rendering view. It demonstrates thatTransNeRF has a stronger capability to explore complicated relationships betweensource views and the target view and learn a better scene representation in chal-lenging scenarios. Fig. 3.4 shows qualitative comparisons for the trex scene undera scene-agnostic setting.Per-scene Finetuning ExperimentsIn the per-scene finetuning setting, each pre-trained model of comparing methodsis finetuned for each scene in the evaluation dataset.As shown in Tab. 3.3 and 3.4, TransNeRF outperforms other comparing meth-ods after per-scene finetuning. The best scores in each evaluation metric are inbold. Similar to scene-agnostic results, per-scene finetuning results further val-idate that TransNeRF can learn more satisfactory novel view rendering than thecomparing methods in different source-view settings. Meanwhile, the performancegap between TransNeRF and comparing methods becomes more extensive in con-trast with that in the scene-agnostic setting, indicating that per-scene finetuning can95Figure 3.3: Qualitative results (PixelNeRF, MVSNeRF, IBRNet and ourTransNeRF) for the fern scene under the scene-agnostic setting.further fulfill the potential of TransNeRF. Similar to quantitative results, Fig. 3.5illustrates that TransNeRF can achieve more realistic view synthesis results withfewer artifacts in comparison with other comparing approaches. Fig. 3.6 showsqualitative comparisons for the trex scene under the per-scene finetuning setting.In Fig. 3.7, TransNeRF is compared with IBRNet in four source-view sets(S1, S2, S3 and S4). Here, we randomly select a testing view from the hotdogscene as the rendering view. To show the difference between source view sets, we96Figure 3.4: Qualitative results (PixelNeRF, MVSNeRF, IBRNet, and ourTransNeRF) for the trex scene under the scene-agnostic setting.97Table 3.3: Quantitative comparisons of methods (PixelNeRF, MVSNeRF,IBRNet, and the proposed TransNeRF) for the per-scene fine-tuning set-ting on the realistic synthetic dataset.Per-scene finetuning setting on realistic synthetic datasetPSNR ↑ SSIM ↑ LPIPS ↓Scene Si PixelNeRF MVSNeRF IBRNet TransNeRF PixelNeRF MVSNeRF IBRNet TransNeRF PixelNeRF MVSNeRF IBRNet TransNeRFChairS1 23.95 29.48 32.62 33.49 0.910 0.950 0.972 0.989 0.114 0.071 0.044 0.038S2 19.84 25.54 29.06 30.45 0.820 0.870 0.896 0.942 0.205 0.156 0.123 0.096S3 18.93 24.78 28.35 30.21 0.764 0.817 0.852 0.911 0.244 0.192 0.153 0.118S4 17.90 23.80 27.48 29.84 0.683 0.738 0.780 0.868 0.300 0.241 0.190 0.143LegoS1 22.50 26.34 28.65 30.46 0.854 0.916 0.947 0.959 0.153 0.099 0.068 0.056S2 18.58 22.58 25.28 27.38 0.722 0.790 0.829 0.890 0.304 0.246 0.207 0.140S3 17.67 21.82 24.57 26.91 0.664 0.734 0.782 0.859 0.343 0.283 0.237 0.162S4 16.64 20.84 23.69 26.02 0.601 0.676 0.731 0.814 0.394 0.327 0.269 0.194ShipS1 24.22 25.33 26.83 28.90 0.823 0.838 0.855 0.870 0.246 0.216 0.188 0.177S2 20.34 21.61 23.49 25.84 0.688 0.707 0.733 0.763 0.416 0.381 0.346 0.265S3 19.45 20.85 22.80 25.15 0.631 0.653 0.687 0.731 0.454 0.418 0.376 0.287S4 18.48 19.94 21.98 24.26 0.551 0.578 0.619 0.680 0.523 0.479 0.425 0.317DrumsS1 20.27 22.96 25.20 26.32 0.791 0.861 0.922 0.935 0.164 0.116 0.076 0.053S2 16.67 19.53 22.15 23.27 0.677 0.757 0.823 0.840 0.302 0.248 0.202 0.161S3 15.96 18.96 21.64 23.22 0.622 0.705 0.779 0.808 0.341 0.284 0.232 0.183S4 14.93 17.98 20.76 23.11 0.551 0.637 0.718 0.767 0.404 0.339 0.276 0.201MicS1 29.39 31.65 32.77 33.64 0.949 0.970 0.981 0.983 0.050 0.039 0.033 0.027S2 25.84 28.26 29.76 30.68 0.889 0.914 0.934 0.952 0.124 0.109 0.095 0.084S3 25.11 27.67 29.24 30.66 0.831 0.860 0.887 0.921 0.156 0.138 0.118 0.114S4 24.24 26.85 28.51 30.57 0.756 0.790 0.824 0.861 0.202 0.177 0.145 0.139FicusS1 24.74 26.68 28.54 29.46 0.919 0.933 0.949 0.957 0.104 0.076 0.051 0.044S2 21.80 23.90 26.15 27.29 0.825 0.844 0.869 0.872 0.203 0.171 0.137 0.119S3 21.07 23.32 25.62 27.19 0.771 0.792 0.826 0.838 0.242 0.206 0.167 0.141S4 19.81 22.11 24.51 27.06 0.695 0.721 0.762 0.791 0.295 0.253 0.202 0.184MaterialsS1 22.27 23.32 24.98 26.99 0.848 0.889 0.925 0.938 0.174 0.130 0.098 0.077S2 17.27 18.49 20.54 23.74 0.688 0.740 0.781 0.845 0.325 0.275 0.237 0.158S3 16.44 17.80 19.90 22.95 0.633 0.686 0.735 0.814 0.364 0.310 0.267 0.181S4 15.33 16.73 18.94 21.18 0.556 0.612 0.669 0.774 0.432 0.371 0.316 0.216HotdogS1 25.14 30.58 34.54 37.03 0.922 0.948 0.973 0.986 0.114 0.077 0.048 0.041S2 20.90 26.51 30.85 33.40 0.850 0.881 0.915 0.943 0.226 0.185 0.147 0.110S3 19.56 25.32 29.71 32.54 0.792 0.826 0.867 0.910 0.264 0.220 0.177 0.132S4 18.49 24.30 28.79 31.19 0.719 0.758 0.806 0.869 0.314 0.262 0.207 0.164AveS1 24.06 27.04 29.27 30.79 0.877 0.913 0.940 0.952 0.140 0.103 0.076 0.064S2 20.15 23.30 25.91 27.76 0.770 0.813 0.847 0.881 0.263 0.221 0.187 0.142S3 19.27 22.56 25.23 27.35 0.714 0.759 0.802 0.849 0.301 0.256 0.216 0.165S4 18.23 21.57 24.33 26.65 0.639 0.689 0.739 0.803 0.358 0.306 0.254 0.195display overall source views in S1 and S4 at the bottom of Fig. 3.7. It is obviousthat the viewing angles of source views in S1 are closer to the rendering viewcompared with those in S4. In Fig. 3.7, the top two rows display the renderingviews of comparing methods based on four source-view sets. The artifacts in therendering views of IBRNet are perceptible in S2 and become more obvious in S3and S4. In contrast, the artifacts in rendering views of TransNeRF remain to a lowdegree in four source-view sets. Fig. 3.7 illustrates TransNeRF can obtain betterrendering results than IBRNet in diverse source-view sets, especially when there isa considerable difference between the source views and the rendering view.Analysis of Interpretability in TransNeRFBased on the attention mechanism, TransNeRF utilizes shape and appearance con-sistency in both surrounding-view space and ray-cast space, improving the intrin-98Table 3.4: Quantitative comparisons of methods (PixelNeRF, MVSNeRF,IBRNet, and the proposed TransNeRF) for the per-scene finetuning set-ting on the real forward-facing dataset.Per-scene fine-tuning setting on real forward-facing datasetPSNR ↑ SSIM ↑ LPIPS ↓Scene Si PixelNeRF MVSNeRF IBRNet TransNeRF PixelNeRF MVSNeRF IBRNet TransNeRF PixelNeRF MVSNeRF IBRNet TransNeRFFernS1 22.35 23.43 24.89 24.92 0.713 0.749 0.803 0.812 0.300 0.262 0.212 0.208S2 20.52 21.86 23.60 23.89 0.653 0.696 0.752 0.775 0.351 0.308 0.253 0.236S3 19.77 21.06 23.51 23.85 0.630 0.680 0.749 0.769 0.378 0.324 0.257 0.240TrexS1 20.33 23.21 26.43 26.47 0.747 0.817 0.896 0.900 0.338 0.271 0.202 0.198S2 17.74 20.87 24.38 24.68 0.684 0.759 0.843 0.864 0.394 0.323 0.248 0.235S3 15.76 19.20 23.07 23.76 0.622 0.705 0.801 0.841 0.455 0.375 0.287 0.268HornsS1 21.71 24.34 28.27 28.31 0.744 0.801 0.898 0.907 0.300 0.241 0.145 0.142S2 18.92 21.79 26.01 26.31 0.679 0.742 0.842 0.864 0.361 0.295 0.195 0.183S3 16.18 19.34 23.94 24.61 0.595 0.667 0.779 0.829 0.435 0.359 0.247 0.228FortressS1 24.07 26.94 30.99 31.05 0.761 0.822 0.894 0.901 0.272 0.216 0.143 0.139S2 22.51 25.60 29.96 30.27 0.738 0.804 0.881 0.896 0.295 0.235 0.155 0.144S3 17.94 21.30 26.05 26.72 0.625 0.698 0.787 0.830 0.400 0.330 0.238 0.217LeavesS1 17.26 19.22 21.65 21.69 0.555 0.637 0.773 0.776 0.363 0.283 0.189 0.186S2 14.78 16.97 19.70 19.99 0.432 0.523 0.659 0.691 0.450 0.364 0.267 0.256S3 12.80 15.33 18.39 19.10 0.351 0.447 0.598 0.634 0.512 0.415 0.305 0.284OrchidsS1 17.27 19.03 20.70 20.74 0.506 0.596 0.682 0.691 0.406 0.316 0.233 0.230S2 15.51 17.50 19.46 19.77 0.420 0.514 0.605 0.632 0.485 0.390 0.302 0.289S3 14.04 16.30 18.67 19.32 0.349 0.452 0.555 0.589 0.539 0.434 0.333 0.312RoomS1 23.22 27.59 32.03 32.08 0.862 0.904 0.955 0.960 0.263 0.205 0.140 0.137S2 19.95 24.56 29.30 29.59 0.828 0.875 0.930 0.947 0.304 0.243 0.172 0.160S3 16.56 21.42 26.58 27.20 0.766 0.820 0.888 0.920 0.378 0.306 0.222 0.203FlowerS1 19.54 22.77 27.89 27.93 0.656 0.740 0.872 0.878 0.359 0.284 0.148 0.145S2 16.27 19.74 25.15 25.45 0.567 0.657 0.792 0.818 0.429 0.348 0.209 0.196S3 12.24 15.00 20.79 21.46 0.414 0.512 0.659 0.721 0.565 0.473 0.322 0.299AveS1 20.72 23.32 26.61 26.65 0.693 0.758 0.847 0.853 0.325 0.260 0.177 0.173S2 18.28 21.11 24.69 24.99 0.625 0.696 0.788 0.811 0.384 0.313 0.225 0.212S3 15.66 18.62 22.62 23.25 0.544 0.623 0.727 0.767 0.458 0.377 0.276 0.256sic interpretability of our model. Here, we study the intrinsic interpretability ofTransNeRF to evaluate whether it is consistent with the description of human per-ception in Sec. 3.2.6.In surrounding-view space, we visualize the attention of different source viewsto a target 3D point to interpret its rendering in Density-ViewDecoder and Color-ViewDecoder. Similarly, in ray-cast space, the rendering process of Density-RayDecoderand Color-RayDecoder can be explored by visualizing the attention of surrounding3D points on the target-viewing ray to the target 3D point. Specifically, for a 2Dregion (a 5× 5 pixel region) in the rendering view, we first compute the averagedepth value of the corresponding viewing directions for the target pixels based onour learned neural radiance field. Then we retrieve the 3D point that is locatedthe closest to the average depth in the average viewing direction as the target-interpreted 3D point. For the target 3D point, we can explain its rendering processin both surrounding-view and ray-cast spaces by visualizing the corresponding at-tention layers in TransNeRF.To study the interpretability of TransNeRF, we provide interpretation to thesame testing view of a chair scene based on source-view sets S4 and S1 in Fig. 3.899Figure 3.5: Qualitative results (PixelNeRF, MVSNeRF, IBRNet, and ourTransNeRF) for the fern scene under the per-scene finetuning setting.and Fig. 3.9, respectively. Here, we randomly select a camera pose for renderingand the rendering results are obtained by the fine-tuned TransNeRF. The targetrendering view is shown in Fig. 3.8 (a) and the target location for interpretation arehighlighted via a red frame in an enlarged blue region. As depicted in Fig. 3.8 (b)and Fig. 3.9 (a), the difference between source views in S4 and the rendering viewis more significant than that between S1 and the rendering view. For our visualperception, the source views in each set are divided into two groups depending onwhether they capture the target location in the rendering view. In Fig. 3.8 (b) and100Figure 3.6: Qualitative results (PixelNeRF, MVSNeRF, IBRNet, and ourTransNeRF) for the trex scene under the per-scene finetuning setting.101Figure 3.7: Qualitative results (IBRNet and our TransNeRF) for the hotdogscene under the per-scene finetuning setting. At the bottom, we alsoshow the source-view sets S1 and S4 with the yellow frame.Fig. 3.9 (a), the top half, named “visible views”, are source views that capture thetarget location, and the bottom half, named “invisible views”, do not.For the target location within the red frame in Fig. 3.8 (a), Fig. 3.8 (c)and (d) display attention of source views to the target location for rendering thequery density and color in Density-ViewDecoder and Color-ViewDecoder, respec-tively. In Fig. 3.8 (c) and (d), attention of the visible source views in Fig. 3.8(b) are colored blue for clarity while that of the invisible source views are col-ored gray. Source views (85, 41, and 61) with high attention values are consistentwith those with the visible region of interest. It indicates that the attention layers102in Density-ViewDecoder and Color-ViewDecoder can learn the important sourceviews in the query rendering that meet human perception. Fig. 3.8 (e) depicts thedensity attention (green) and color attention (orange) among 3D points along thetarget-viewing ray for rendering the query 3D point in Density-RayDecoder andColor-RayDecoder. Here, the red index (83) denotes the retrieved 3D point for thetarget location within a red frame in the rendering view. As shown in Fig. 3.8(e), both density attention and color attention in Density-RayDecoder and Color-RayDecoder exist a crest near the query 3D point, which illustrates that TransNeRFin the ray-cast space takes into account the consistency of adjoining 3D points onthe target rendering ray when rendering the query 3D point.In Fig. 3.9, we give an interpretation for the same rendering view of the chairscene based on the source-view set S1. Fig. 3.9 (b) and (c) show density atten-tion and color attention to different source views for the identical red-box regionin the rendering view. Similarly, source views (2, 72, 28, and 95) with high at-tention values are consistent with those with the visible region of interest shownin Fig. 3.9 (a), suggesting that the attentions in Density-ViewDecoder and Color-ViewDecoder are in accordance with human perception. As with Fig. 3.8 (e), Fig.3.9 (d) demonstrates that Density-RayDecoder and Color-RayDecoder utilize theconsistency of 3D points on the target rendering ray for the query 3D-point render-ing.3.4 ConclusionWe propose a unified Transformer-based NeRF framework to learn a general neuralradiance field for novel view synthesis. The proposed framework can explore com-plex relationships between source views and the target rendering view. Meanwhile,the framework improves intrinsic interpretability by utilizing the shape and appear-ance consistency of 3D scenes. Experiments demonstrate that TransNeRF achievesstate-of-the-art performance on real and synthetic datasets in both scene-agnosticand per-scene finetuning settings. Experiments also indicate the interpretation ofTransNeRF is consistent with human perception.103Figure 3.8: Interpretation results of fine-tuned TransNeRF for a renderingchair-scene view (a) based on source-view set S4 (b). For the targetred-frame location in (a), (c) and (d) display attention of source viewsto the target location for rendering the query density and color, respec-tively; (e) depicts the density attention (green) and color attention (or-ange) among 3D points along the target-viewing ray for rendering thequery 3D point (index 83).104Figure 3.9: Interpretation results of fine-tuned TransNeRF for the chair scenebased on view set S1. (a) Source views (the target location for interpre-tation is highlighted via a red frame in an enlarged blue region); (b)density attention among source views; (c) color attention among sourceviews; (d) density attention and color attention among 3D points alongthe target-viewing ray.105Chapter 4Interpretable and GeneralizableMulti-view 3D ReconstructionChapter 3 explores the intrinsic interpretability of neural networks in novel viewsynthesis. In this chapter, we focus on multi-view 3D object reconstruction, an-other inverse rendering task. In this task, most existing methods comprise modulesthat are designed separately, which results in the insufficient exploitation of mul-tiple input views for 3D object reconstruction. Here, we propose a unified frame-work to simultaneously learn and decode deep information from multiple inputimages into the 3D representation, improving the intrinsic interpretability and 3Dreconstruction performance.4.1 IntroductionLearning 3D object representation from multi-view images is a fundamental andchallenging problem in 3D modeling, virtual reality, and computer animation. Re-cently, deep learning approaches have greatly promoted the research in multi-view3D reconstruction, where the deep convolutional neural network (CNN) based ap-proaches have so far achieved the state of the art results in this task [82, 84].To learn effective 3D representation from multiple input views, most recentCNN-based approaches follow the design principle of divide-and-conquer, wherea common practice is to introduce a CNN for single-view feature extraction and106multi-view fusion for integrating the features or reconstruction results from multi-ple views. Despite the strong connection between the two modules, their method-ology designs are investigated separately. Also, during the CNN feature extractionstage that processes each view image separately, the relations in different views arerarely explored. Although some recent approaches have introduced recurrent neu-ral network (RNN) to learn object relationships among different views [10, 32],such a design lacks computational efficiency, and the input views of the RNNmodel are permutation-sensitive [74], which is not compatible with a set of un-ordered input views. It is also shown in recent research that CNN-based recon-struction methods may suffer from the model scaling problem. For example, whenthe number of input views exceeds a particular scale (e.g., 4), the accuracy of meth-ods will be saturated, showing the difficulty of learning complementary knowledgefrom a large set of independent CNN feature extraction units [84].Considering the above challenges, we propose a new framework named “3DVolume Transformer” and explore the potential of the self-attention-based Trans-former model for the multi-view 3D object reconstruction task. We reformulatethe multi-view 3D reconstruction as a sequence-to-sequence prediction problemand unify the feature extraction and view fusion in a single Transformer network.On the one hand, in multi-view 3D reconstruction, we need to learn the underly-ing 3D representation by exploring the relationships among multiple input viewssince we can only see part of the 3D structure from a particular view. On the otherhand, in a Transformer model, the self-attention mechanism has recently shown itsgreat power in learning complex semantic abstractions within an arbitrary numberof input tokens [14, 69] and is naturally suitable for exploring the view-to-view re-lationships of a 3D object’s different semantic parts. Given all this, the structure ofTransformer [16, 73] becomes a natural and attractive solution for the multi-view3D reconstruction.Our Transformer-based framework contains a 2D-view Transformer encoderand a 3D-volume Transformer decoder, as presented in Figure 4.1. The 2D-viewTransformer encoder encodes and fuses multiple 2D-view information by explor-ing their “2D-view × 2D-view” relationships of different inputs. The 3D-volumeTransformer decoder decodes and fuses the multi-view features from the encoderand generates a 3D probabilistic voxel output for each spatial query token. The at-107tention layers in the decoder learn “2D-view × 3D-volume” relationships betweeneach of the output voxel grids and input views. Meanwhile, volume attention lay-ers in the decoder further learn “3D-volume × 3D-volume” relationships by ex-ploiting correlations among different 3D locations. By using the above unifieddesign, the “2D-view × 2D-view”, “3D-volume × 3D-volume”, and “2D-view ×3D-volume” relationships can be jointly explored by multiple attention layers inboth the encoder and decoder networks.Based on the above encoder-decoder Transformer structure design, we furtherinvestigate the “attention uniformity” problem in a Transformer model and pro-pose an effective solution for enhancing the effectiveness of a Transformer modelin the multi-view reconstruction task. In Transformers, self-attention possessesa solid inductive bias towards “token uniformity” [15], which encourages featurerepresentations of input tokens to converge. However, this convergence may fur-ther cause the problem of “attention uniformity” in deeper layers, which makes aTransformer model loses expressive power speedily with respect to network depth[15]. We show that this problem is particularly prominent in the multi-view 3Dreconstruction task and will limit the Transformer’s capability to explore and ab-stract multi-view associations at a deeper level. To tackle it, we further proposethe divergence-enhanced Transformer that can slow down the divergence decay inself-attention layers by enhancing the discrepancy of the embeddings from differ-ent views.The contributions can be summarized as follows:• We propose a brand new Transformer-based framework for multi-view 3Dobject reconstruction. Different from the previous CNN-based methods thatuse a separate design of feature extraction + view fusion, we unify these twostages into a single Transformer network and re-frame the 3D reconstructionas a “sequence-to-sequence” prediction problem.• The proposed method can jointly and naturally explore multi-level corre-spondence and associations between the 2D input views and 3D output vol-ume within our encoder-decoder Transformer structure.• We investigate the problem of “divergence decay” in the proposed frame-work and propose a view-divergence enhancing operation in our self-attention108Figure 4.1: Illustration of EVolT for Multi-view 3D Object Reconstruction.layers to avoid such degradation.• Our method achieves a new state-of-the-art for multi-view 3D reconstructionon ShapeNet with only 30% amount of parameters of recent CNN-basedmethods. Our method also shows better scaling capability on the number ofinput views.There are different 3D representations, i.e., coordinate-based implicit represen-tation [6, 66, 85], voxel- [65] and mesh-based [77] representations. In terms oflearning 3D representation, our method is voxel-based and trained across multi-scenes for 3D reconstruction instead of optimizing 3D scenes individually [65, 66,77]. Besides, our method is learned without requiring camera parameters, whilecoordinate-based implicit 3D representation methods are primarily for view syn-thesis and require camera parameters [44, 78, 85].109Figure 4.2: The proposed view-divergence enhancing function in EVolT.4.2 MethodologyThe proposed 3D volume Transformer model, as shown in Figure 4.1, consists of a2D-view encoder and a 3D-volume decoder. The inputs are multi-view images ofan object. The 2D-view encoder encodes the relevant information among differentviews via view attention layers. The 3D-volume decoder learns global correlationsof different spatial locations in volume attention layers and decodes the relation-ships between the view and spatial domains. In the decoder, we uniformly split the3D space into a set of tokens as inputs. The predicted volumes for each token arefinally stitched into the final 3D reconstruction as the output. The output containsoccupancy voxel predictions where each defines the object-occupancy probabilityin its voxel.In this work, we implement three different versions of method based on theproposed framework: Vanilla 3D Volume Transformer (VolT), Vanilla 3D Volume110Transformer+ (VolT+), and view-divergence-Enhanced 3D Volume Transformer(EVolT).• VolT: A baseline implementation of our method employing vanilla Trans-former model and using standard VGG16 [64] features as our initial viewembeddings.• VolT+: Using 2D-view embeddings obtained from an advanced pre-trainedCNN compared with VolT. We use it to testify the impact of 2D-view em-beddings on our Transformer-based framework for reconstruction.• EVolT: A full implementation of our method adopting the proposed view-divergence enhancing function and using standard VGG16 [64] for 2D-viewembeddings.Here, to obtain 2D-view initial embeddings, we use a pre-trained CNN sharedamong multiple views.4.2.1 Divergence-enhanced 2D-view encoderSuppose I = {I1,I2, · · · ,IM} denotes the multi-view image set of an object to bereconstructed. For each view Im, we first use a pre-trained view-shared CNN to ob-tain its initial view embedding xm ∈R1×d , where d is the feature dimension. Then,the 2D-view encoder takes in the initial view embeddings X0 = [x1;x2; · · · ;xM] ∈RM×d and refines the multi-view representations by exploring global relationshipsamong multiple views using a series of self-attention layers. Here, to keep per-mutation invariant for the view sequence, the positional encodings of a standardTransformer are removed. We build our divergence-enhanced 2D-view encoderbased on DETR [5] by stacking N = 6 basic blocks. Each basic block consists of amulti-head divergence-enhanced view attention layer (denoted as MH-DEAtt, Eq.(4.2)) and a position-wise Feed Forward Network (FFN), Eq. (4.3). The 2D-viewencoder is formulated as follows:X0 = [x1;x2; · · · ;xM], (4.1)X¯l = Norm(MH-DEAtt(Xl−1,X0)+Xl−1), (4.2)Xl = Norm(FFN(X¯l)+ X¯l), (4.3)111where “Norm” denotes layer normalization and l is the index of a basic block(l = 1, · · · ,L). The embeddings of the block L are used as the output of our 2D-view encoder.As shown in Figure 4.2, the scaled dot-product attention (denoted as Attn, Eq.(4.5)) aggregates the feature representations among multiple views by learningview-to-view relationships. In the meantime, we propose a view-divergence en-hancing function (DiView, Eq. (4.4)) to ease the discrepancy degradation of themulti-view representations in deeper layers. Specifically, DiView introduces skipconnections and concatenates the internal view features with the input view em-beddings in the feature dimension. The MH-DEAtt layer is defined as follows:MH-DEAtt(Xl−1,X0) = DiView(A,X0)Wview,whereA = cat(A1, · · · ,AH), (4.4)Ah = Attn(Qh,Kh,Vh).Here, “cat” denotes the concatenation operation and h is the number of heads inMH-DEAtt layer. Wview ∈ R(Hdk+d)×d denotes the parameter matrix of the lin-ear function, and dk is the feature dimension in each head. In the h-th head, Mqueries stacked in Qh ∈ RM×dk are projected from M view embeddings stacked inXl−1 with the parameter matrix WhQ ∈ Rd×dk (Qh = Xl−1WhQ). Similarly, the keysand values stacked in Kh ∈ RM×dk and Vh ∈ RM×dk are obtained with parametermatrices WhK ∈ Rd×dk ,WhV ∈ Rd×dk , respectively.Specifically, in the Attention function “Attn”, the output for a query is rep-resented as an attention-score weighted sum of the values. The Attn function isformulated asAttn(Q,K,V) = softmax(QKT√dk)V, (4.5)4.2.2 3D-volume decoderThe 3D-volume decoder learns the global correlation among different spatial loca-tions and explores the relationship between the view and spatial domains. Givenan object, we denote [y1;y2; · · · ;yN ] as a sequential learnable 3D-volume queries at112the input end of the decoder, where yn ∈ R1×d corresponds to the n-th 3D-volume.The 3D-volume embeddings, denoting a set of 3D sub-volumes for an object, areoptimized end-to-end together with the network parameters and shared across allpotential inputs (like object queries in [5]). These volume embeddings are notview-conditional variables but can provide a global prior for the dataset.Positional encodings Epos are added to 3D-volume embeddings to keep theposition information in the spatial domain. Each positional encoding informs eachsub-volume of its 3D spatial location in an object. It is calculated in a similar wayto [5] using sine and cosine functions of different frequencies. In the decoder, abasic block contains a volume attention layer, a view-volume attention layer, andan FFN. The decoder can be formulated as follows:Y0 = [y1;y2; · · · ;yN ]+Epos, (4.6)Y¯l = Norm(MH-VolAttn(Yl−1)+Yl−1), (4.7)Yˆl = Norm(MH-ViewVolAttn(Y¯l,XL)+ Y¯l), (4.8)Yl = Norm(FFN(Yˆl)+ Yˆl), (4.9)where MH-VolAttn (in Eq.(4.7)) and MH-ViewVolAttn (in Eq.(4.8)) denote themulti-head volume attention layer and the multi-head view-volume attention layer,respectively.In our decoder, the MH-VolAttn layer learns global dependencies among dif-ferent 3D volumes as follows:MH-VolAttn(Yl−1) = cat(A1, · · · ,AH)Wvol,where Ah = Attn(Yl−1WhQ,Yl−1WhK ,Yl−1WhV ). (4.10)The MH-ViewVolAttn layer integrates the relevant information across the view andspatial domains, and is calculated as follows:MH-ViewVolAttn(Y¯l,XL) = cat(A1, · · · ,AH)W,where Ah = Attn(Y¯lWhQ,XLWhK ,XLWhV ). (4.11)where Wvol ∈ RHdk×d and W ∈ RHdk×d are the parameter matrices of the corre-113Table 4.1: Parameter sizes and pre-trained CNNs for the initial 2D-view em-beddings in competing methods.Param.(M)Pretrained CNN used for2D-view embeddingsPix2Vox-A [81] 114.24 VGG16 [64]Pix2Vox++/A [82] 96.31 ResNet50 [25]VolT 28.63 VGG16 [64]VolT+ 96.76 2D-CNN+3D-DCNNEVolT 29.03 VGG16 [64]Table 4.2: Comparison of 24-views reconstruction on ShapeNet using Inter-section over Union (IOU) and F-Score. The best score for each categoryis in bold.24-views IoU 24-views F-Score@1%CategoryPix2-Vox-APix2-Vox++/AVolT VolT+ EVolTPix2-Vox-APix2-Vox++/AVolT VolT+ EVolTairplane 0.731 0.729 0.719 0.725 0.741 0.635 0.614 0.604 0.618 0.636bench 0.679 0.686 0.678 0.682 0.707 0.525 0.522 0.513 0.525 0.548cabinet 0.822 0.829 0.825 0.825 0.832 0.448 0.456 0.452 0.455 0.464car 0.880 0.883 0.884 0.885 0.894 0.598 0.598 0.604 0.609 0.624chair 0.620 0.647 0.645 0.641 0.681 0.318 0.341 0.339 0.340 0.373display 0.599 0.613 0.635 0.613 0.674 0.320 0.335 0.366 0.339 0.403lamp 0.475 0.493 0.478 0.481 0.520 0.335 0.351 0.320 0.338 0.366speaker 0.751 0.762 0.762 0.753 0.772 0.309 0.326 0.327 0.317 0.339rifle 0.676 0.686 0.663 0.693 0.711 0.615 0.624 0.597 0.634 0.653sofa 0.764 0.782 0.781 0.776 0.800 0.427 0.454 0.449 0.448 0.478table 0.644 0.666 0.649 0.658 0.675 0.398 0.419 0.407 0.418 0.431telephone 0.837 0.849 0.857 0.850 0.867 0.659 0.666 0.678 0.675 0.687watercraft 0.655 0.668 0.670 0.670 0.693 0.441 0.460 0.456 0.470 0.494Overall 0.706 0.720 0.714 0.716 0.738 0.462 0.473 0.468 0.475 0.497sponding linear functions.Finally, after the decoder block L, we use a linear function to project the em-beddings of each 3D volume to their 3D output space. Then the predicted 3Dvolumes are reshaped and grouped into the reconstruction output. We use binarycross-entropy between the voxel label and the output as our loss function.114Table 4.3: Comparison of multi-view reconstruction on ShapeNet using IoUand F-Score. The best score for each view number is in bold.F-Score@1% 24 23 22 21 20 18 16 14 12 8 6 43D-R2N2 [10] - - - - 0.383 - 0.382 - 0.382 0.383 - 0.378AttSets [84] - - - - 0.448 - 0.447 - 0.445 0.444 - 0.430Pix2Vox-A [81] 0.462 0.462 0.462 0.462 0.462 0.461 0.461 0.461 0.460 0.458 0.456 0.452Pix2Vox++/A [82] 0.473 - - - 0.462 - 0.461 - 0.460 0.459 - 0.457VolT 0.468 0.467 0.467 0.465 0.464 0.461 0.459 0.456 0.450 0.430 0.410 0.356VolT+ 0.475 0.475 0.474 0.474 0.474 0.473 0.472 0.471 0.469 0.464 0.460 0.451EVolT 0.497 0.496 0.495 0.494 0.492 0.489 0.486 0.481 0.475 0.448 0.423 0.358IoU3D-R2N2 [10] - - - - 0.636 - 0.636 - 0.636 0.635 - 0.625AttSets [84] 0.694 - - - 0.693 - 0.692 - 0.688 0.685 - 0.675Pix2Vox-A [81] 0.706 0.706 0.706 0.706 0.706 0.705 0.705 0.705 0.704 0.702 0.700 0.697Pix2Vox++/A [82] 0.720 - - - 0.719 - 0.718 - 0.717 0.715 - 0.708VolT 0.714 0.713 0.712 0.711 0.711 0.708 0.706 0.703 0.699 0.681 0.662 0.605VolT+ 0.716 0.716 0.716 0.715 0.715 0.714 0.714 0.713 0.711 0.707 0.704 0.695EVolT 0.738 0.738 0.737 0.735 0.735 0.732 0.729 0.726 0.720 0.698 0.675 0.6094.3 Experiments4.3.1 DatasetWe utilize the ShapeNet dataset [80] to evaluate the proposed methods and othercompared methods. We follow 3D-R2N2 [10] and use the same setting for a faircomparison. Specifically, we use a subset of ShapeNet, which consists of 13 cat-egories and 43,783 common 3D objects. For each 3D object, 24 2D images arerendered from different viewing angles circling the object. For each category, wefollow [82] and randomly split samples into 70% training, 10% validation, 20%test. Categories in training are the same as those in evaluation. During training, theinput-view number can be varied.4.3.2 Evaluation metricsIoUThe mean Intersection-over-Union (IoU) calculates the matching degree betweenpredicted 3D voxel grids and ground-truth grids. A higher IoU value means a better115reconstruction result. For each voxel grid, the IoU is defined as:IoU =∑(i, j,k) I(y(i, j,k)> t)I(y¯(i, j,k))∑(i, j,k) I[I(y(i, j,k)> t)+ I(y¯(i, j,k))], (4.12)where y(i, j,k) denotes the predicted occupancy probability, which is binarizedwith an optimal fixed voxelization-threshold t for compared methods. y¯(i, j,k) isthe ground truth at (i, j,k). I(·) is an indicator function.F-ScoreCompared with IoU, F-score [68] explicitly evaluates the distance between objectsurfaces, which is more interpretable. F-score is formally defined as the harmonicmean between precision P(d) and recall R(d) with a distance threshold d:F-Score(d) =2P(d)R(d)P(d)+R(d), (4.13)A higher F-score with a stringent distance threshold indicates a better reconstruc-tion result.In F-Score, P(d) estimates the reconstruction accuracy by counting the portionof reconstructed points lying within the distance d = 1% to the ground truth. R(d)quantifies the reconstruction completeness by counting the percentage of ground-truth points lying within the distance d to the reconstruction. These two metricsare defined as follows:P(d) =1|R| ∑r∈R[ming∈G‖r−g‖< d], (4.14)R(d) =1|G | ∑g∈G[minr∈R‖g− r‖< d]. (4.15)where [·] is the Iverson bracket. G is the ground-truth point set, and R is thereconstructed point set being evaluated. We apply F-Score with the same setting in[82].116Divergence measurement for multi-view representationsWe also define a metric to explore the convergence of multi-view representationsin different layers. Since the convergence has a positive correlation with the di-vergence decay of multi-view attentions, we utilize a similarity measure based onmulti-view attentions to evaluate the divergence-enhancing ability in our method.In each view attention layer, an attention-score matrix S = softmax(QKT√dk) con-tains view-to-view attention vectors. The m-th row of S, denoted as sm, is anattention-score vector where each element represents its attention weight to an-other view. For 3D reconstruction of a specific object, the Mean Absolute De-viation (MAD) measuring the similarity of multi-view attentions, is calculated asD = 1Nview ∑m ‖sm− s¯‖2, where s¯ = 1Nview ∑m sm. Here, a small D means a more con-siderable similarity and the convergence of multi-view representations.4.3.3 Implementation detailsWe set the batch size to 64 and the view image size to 224×224 for training. The3D spatial size of the voxelized output is set to 32×32×32. The VolT and its twovariants VolT+, and EVolT are trained by an AdamW optimizer [38] with a β1 of0.9 and a β2 of 0.999.Table 4.1 shows the parameter sizes and pre-trained CNNs for the initial viewembeddings used in different competing methods. Compared with Pix2Vox-Aand Pix2Vox++/A, the parameter size of EVolT is only around 30% of them. Toobtain the reported best results, Pix2Vox-A and Pix2Vox++/A both adopt an ad-ditional 3D-CNN-based refiner containing another 3D-CNN and 3D-DCNN. Incontrast, our proposed end-to-end methods do not need additional refiner and canalso achieve the best results. To testify the impact of 2D-view embeddings on ourTransformer-based framework, in VolT+, we apply an advanced CNN feature ex-traction model for 2D-view embeddings from the 2D-CNN and 3D-DCNN withoutthe last layer in Pix2Vox-A.117Figure 4.3: Qualitative 3D object reconstruction results on ShapeNet basedon different number of input 2D-view chair images.118Figure 4.4: Qualitative 3D object reconstruction results on ShapeNet basedon different number of input 2D-view monitor images.1194.3.4 Multi-view 3D object reconstructionQuantitative resultsHere, we show the quantitative results of compared methods on ShapeNet usingdifferent evaluation metrics. Table 4.2 shows the comparison of 24-view objectreconstruction on ShapeNet using IoU and F-Score metrics. The highest valuefor each category is highlighted in bold. This table shows that EVolT reaches thehighest IoU and F-score among the compared methods. VolT gets moderate resultsbetween Pix2Vox-A and Pix2Vox++/A. VolT+ works better than VolT because ituses better initial features. However, VolT+ still falls behind EVolT even EVolTis based on the plain VGG features. These observations indicate that the view-divergence enhancing function in EVolT plays an indispensable role in increasingits performance against the compared methods.Table 4.3 shows the multi-view object reconstruction results on ShapeNet. Thebest score for each number of views (column label) is highlighted in bold. This ta-ble shows that the performances of our methods increase appreciably as the numberof views increases. In comparison, other compared methods increase slightly whenthe view number enlarges. For example, the mean IoU of EVolT increases by 0.04from 8 views to 24 views, which is eight times the improvement of Pix2Vox++/A.This observation indicates that the proposed Transformer-based methods have bet-ter scaling ability and can learn a more comprehensive 3D representation with theincrease of view number. We can also see from this table that our proposed meth-ods get the best F-Score when the view number is larger than 6 and get the bestIoU when the view number is higher than 12.Qualitative resultsIn Figure 4.3 and Figure 4.4, we show the qualitative results of 3D object recon-struction of different methods on ShapeNet. In each object sample, we provideobject reconstruction results from different numbers of input views, i.e., 12 views,18 views, and 24 views. The first two rows of Figure 4.3 show the 12 input viewsof an object. The corresponding reconstruction results of competing methods areshown at the bottom. Similarly, the first three rows are the 18 input views corre-120Figure 4.5: Effect of the view-divergence enhancing function on 3D recon-struction results.Figure 4.6: Multi-view attention-matrix visualization in VolT and EVolT.sponding to the results at the bottom.Figure 4.3 and Figure 4.4 show that EVolT can obtain more accurate and com-plete 3D reconstruction against compared methods. For example, the EVolT resultsin the last column successfully recover chair legs and monitor stand while othermethods only show incomplete parts. More qualitative results are presented fromFigure 4.8 to Figure 4.19.121Figure 4.7: Divergence among multi-view representations in VolT andEVolT.4.3.5 View divergenceIn Figure 4.20, we plot the estimated probability density of the D value at differentattention layers for VolT and EVolT. We use Kernel Density Estimation (KDE) tocompute the probability density and explore the convergence of multi-view rep-resentations in different attention layers. A small D means a more considerableconvergence of multi-view representations.In each view attention layer, the probability density function pˆ(D) of D is esti-mated aspˆ(D) =1Nob jectNviewhNob ject∑iNview∑mK(Dim−Dh),where Dim = ‖sim−1NviewNview∑msim‖2.(4.16)where sim is the attention vector of the m-th view for the i-th object. The number ofrandom objects is set to Nob ject = 100. The input view number is set to Nview = 24.Here, we used the Gaussian kernel K(x) = 1√2pi exp(−x22 ). h is computed by therule of thumb of Scott.It is shown in Figure 4.20 that the density of EVolT has a much larger variancethan that of the VolT. Also, as the attention layers go deeper, the D value of theVolT gradually moves closer to 0 while the EVolT can still cover a larger range122Figure 4.8: Qualitative reconstruction results of competing methods for thebench.123Figure 4.9: Qualitative reconstruction results of competing methods for theaeroplane.124Figure 4.10: Qualitative reconstruction results of competing methods for thesofa.125Figure 4.11: Qualitative reconstruction results of competing methods for thetable.126Figure 4.12: Qualitative reconstruction results of competing methods for thelamp.127Figure 4.13: Qualitative reconstruction results of competing methods for thechair.128Figure 4.14: Qualitative reconstruction results of competing methods for theaeroplane.129Figure 4.15: Qualitative reconstruction results of competing methods for thedisplay.130Figure 4.16: Qualitative reconstruction results of competing methods for thechair.131Figure 4.17: Qualitative reconstruction results of competing methods for thesofa.132Figure 4.18: Qualitative reconstruction results of competing methods for theaeroplane.133Figure 4.19: Qualitative reconstruction results of competing methods for thebench.134Layer 1 Layer 2Layer 3 Layer 4Layer 5 Layer 6Figure 4.20: Kernel density estimation of D value in different attention layersfor VolT and EVolT.of D values. This indicates that the divergence enhancement function in EVolTcan effectively slow down the convergence degradation of multi-views in deeperlayers.1354.3.6 Ablation studyEffect on 3D reconstruction accuracyIn Figure 4.5, we quantitatively evaluate the influence of the view-divergence en-hancing function on 3D reconstruction results by comparing EVolT with VolT andPix2Vox-A. From Figure 4.5, we can observe that EVolT significantly outperformsVolT which achieves better results than Pix2Vox-A. This indicates the positive ef-fect of the view-divergence enhancing function on 3D reconstruction results.Effect on the view divergenceIn Figure 4.6, we visualize the view-to-view attention matrix in different layersby VolT and EVolT. We set the input view number to 24 in this experiment. Inthe attention matrix at each layer, the m-th row shows an attention vector whereeach element is the attention weight of the m-th view to another view. From thetop of Figure 4.6, we can observe that rows become more similar in a standardtransformer as the attention layers go deeper. As a comparison, in EVolT, we cansee the diversity of multi-view attention still keeps in deep layers, which meansthat the divergence enhancing function in EVolT can effectively slow down theconvergence degradation of multi-views in deeper layers.In Figure 4.7, the similarity measurement score D is also recorded to analyzethe convergence among multi-view representations in each layer. For 100 randomlychosen objects, we plot D in different layers displayed in Figure 4.7. A small Dsuggests a significant convergence among multi-view representations. As shownin Figure 4.7, the value of D obtained by VolT declines gradually with deepeningthe 2D-view encoder layer while the value of D of EVolT at the same layer keepshigher than that of VolT.The ablation studies indicate that the view-divergence enhancing function playsan essential role in improving the proposed EVolT performance and relieving theconvergence among multi-view representations in different layers.1364.3.7 Interpretability of EVolTIn this section, we further examine the interpretability of EVolT via post-hoc in-terpretation. For a specific cube of the reconstructed 3D object, we aim to figureout the critical input views for the cube. Here, we utilize the perturbation-basedinterpretation method to identify the critical views. The intuition is that the differ-ence between the reconstructed cube and the ground truth would increase if criticalviews are discarded. Fig. 4.21 and 4.22 show the interpretation results of recon-structed objects. As shown in Fig. 4.21, the querying cubes of the chair, sofa, anddisplay are highlighted in blue color. The corresponding top 4 critical input viewsare shown in the right columns. Similarly, Fig. 4.22 shows the corresponding top4 critical input views for different object parts. It is reasonable that the queryingcubes and object parts are all visible among the obtained critical input views.4.4 ConclusionThis work proposes a Transformer-based framework for multi-view 3D reconstruc-tion, which achieves state-of-the-art accuracy on ShapeNet with fewer parametersthan CNN-based methods. The proposed framework explores view and spatial do-main relationships for multi-view 3D reconstruction. We also explore the problemof divergence decay for the multi-view information in deeper layers and propose aview-divergence enhancing function to ease such a problem.137Figure 4.21: EVolT interpretations. The blue cube indicates the querying po-sition. Columns 2-5 show the top 4 critical views for the correspondingcubes.138Figure 4.22: EVolT interpretations. Columns 2-5 show the top 4 criticalviews for the corresponding object parts.139Chapter 5Conclusion and Future Work5.1 ConclusionDeep networks accomplish record performances and are at the center of currentadvancements in a number of applications due to the increase in training methodsand expanding training datasets. Despite these encouraging outcomes, neural net-work deployment has been hampered by their black-box nature, which makes themunsuitable for building trust.A stack of layers works together to produce a sophisticated nonlinear mappingfrom the input to the output for DL models. As the network structure developsdeeper and wider, the learning ability strengthens. Most widely used DL networkscurrently have dozens or hundreds of layers with learnable parameters. These deepnetworks are challenging to decipher due to their intricate nonlinear mapping andinability to be broken down into simple parts, despite their superior results. Inparticular, it might be difficult to comprehend how a trained deep network arrivesat a prediction.The incapacity of humans to comprehend deep networks might be a concernwhen they encroach on crucial areas like financial markets and healthcare. Becausethe results might be disastrous, it is not possible to anticipate deep networks in thesecrucial areas on the basis of blind trust. Because deep networks have a black-boxaspect, many practitioners are hesitant to employ them in practice. As a result,merely aiming for greater performance is no longer the main focus given the rapid140growth of DL in academia and industry.The interpretability of DL has drawn the attention of numerous researchersas a solution to this problem. In this thesis, we concentrate on the interpretabil-ity exploration of DL from both post-hoc explanation and intrinsic interpretabilityviewpoints. In Chapter 2, we propose a post-hoc explanation framework to ex-plain the decision-making of NNs as a hierarchical inference of visual concepts.In Chapter 3, we propose a unified Transformer-based neural radiance field fornovel view synthesis. The intrinsic interpretability of the proposed method is im-proved because the unified structure design facilitates exploring deep relationshipsbetween the target-rendering view and source views. In Chapter 4, we proposean end-to-end Transformer-based framework for 3D object reconstruction. The in-trinsic interpretability is also boosted because of the joint exploration of multi-levelassociations between input views and the output volume-based 3D representation.In summary, our work shows that the interpretability of neural networks can be ex-plored from post-hoc explanation and intrinsic interpretability perspectives basedon diverse forms, such as visual concepts, and attention. For different computervision tasks, it is critical to choose in advance the proper way to embody the inter-pretation in the network design process.We provide a summary of the thesis contributions and planned future works inthis chapter.5.1.1 Interpreting bottom-up decision-making of CNNs viahierarchical inferenceThe computer vision task of classifying an image is called image classification.While CNNs have already reached human levels of accuracy, we are still unsure ofthe core reasoning behind the network’s decision-making. In contrast, for recog-nizing an object in an image, we have comprehensible knowledge-based reasoning.The decision-making process in neuroscience can be determined from a num-ber of sub-decision-making processes ranging from low to high levels using bottom-up hierarchical logic. Inspired by this, we propose a post-hoc interpretation model(CHAIN) to explain the network decision-making process. In the CHAIN inter-pretation, we use visual concepts to interpret net features in a layered network.According to the CHAIN interpretation, the network’s feature learning from shal-141low to deep layers can be understood as a hierarchy of logical decision-makingthat proceeds from low to high levels. Specifically, a deeper concept is modeledby CHAIN as a sparse mixture of shallow concepts to decode the CNN logic in-ference from shallow to deep layers. Except for the instance-level interpretation,the CHAIN interpretation can also provide inference at the class level. Experi-ment results demonstrate that the proposed CHAIN model can provide reasonableinterpretations at both intra-class and inter-class levels.5.1.2 Interpretable transformer-based neural radiance fields forgeneralizable novel view synthesisA long-standing and difficult topic, novel view synthesis deals with rendering pre-viously unseen views of a 3D scene from a collection of observed views. Thepresent MLP-based NeRFs, however, are unable to receive observed views witharbitrary numbers directly and instead need to fuse source-view information us-ing an auxiliary pooling-based procedure. Complex connections between sourceviews and the destination rendering view are thus overlooked. These early NeRFscontain both an MLP-based NeRF module and a pooling-based multi-view fusion.Despite the fact that there is a natural connection between these modules, the over-all structure is fractured since each module is developed and learned individually.This uneven framework design hurts the inherent interpretability.To tackle this challenge, we propose a unified Transformer-based NeRF frame-work to learn a general neural radiance field for novel view synthesis. Our ap-proach unites source-view fusion and target-view rendering processes via an end-to-end Transformer-based network, in contrast to prior research, which employedtwo discrete working processes of pooling-based fusion and MLP-based rendering.Meanwhile, the proposed framework naturally utilizes the attention mechanism tointegrate information from the projected 2D pixels in the surrounding source viewsand the neighboring 3D points along the query ray. Our framework explores andfuses deep and complicated relationships between observed views and the render-ing view, which is ignored in the previous MLP-based NeRFs. Therefore, theframework improves intrinsic interpretability by utilizing the shape and appear-ance consistency of 3D scenes. Experiments demonstrate that TransNeRF achievesstate-of-the-art performance on real and synthetic datasets in both scene-agnostic142and per-scene finetuning settings. Experiments also indicate the interpretation ofTransNeRF is consistent with human perception.5.1.3 Interpretable and generalizable multi-view 3D reconstruction3D reconstruction is the task of constructing three-dimensional models from a setof images. Deep CNN-based approaches have recently achieved state-of-the-artmulti-view 3D object reconstruction outcomes. Despite significant progress, thetwo basic modules of these approaches - view feature extraction and multi-viewfusion - are normally researched individually, and the relationships between nu-merous input views are rarely investigated. Due to inconsistent framework design,previous techniques are poor in incorporating multi-view features as 3D represen-tation, especially when the number of input views is large.Learning a view-consistent 3D scene representation from a set of input viewsis the core goal of 3D reconstruction. To achieve it, we recast multi-view 3Dreconstruction as a sequence-to-sequence prediction issue and present a 3D Vol-ume Transformer-based framework. It unifies the feature extraction and multi-view fusion by attention layers in our Transformer-based framework. The proposedframework explores view and spatial domain relationships for multi-view 3D re-construction. We also explore the problem of divergence decay for the multi-viewinformation in deeper layers and propose a view-divergence enhancing functionto ease such a problem. Our work achieves a new state-of-the-art multi-view 3Dreconstruction on ShapeNet, utilizing just 30% of the parameters needed by morecurrent CNN-based algorithms, while also having improved scaling capabilities onthe number of input views.5.2 Future WorkExisting research work about the interpretability of neural networks is primarilyon 2D image-based computer vision tasks, such as image classification, image de-tection, image synthesis, etc. In contrast, the interpretability of neural networks on3D computer vision tasks is not adequately explored. As such, in future work, Iwill conduct research about network interpretability on 3D-related tasks to explorethe role of interpretation in different 3D tasks.1435.2.1 3D object reconstruction with hierarchical disentangled featureattributesIn computer vision, 3D object reconstruction refers to the process of capturing theshape and appearance of objects. Through 3D object reconstruction, we can deter-mine the profile of an object and know the information of any point on the profile.It is a crucial technology in a variety of fields, such as computer graphics, com-puter vision, virtual reality, medical imaging, etc. Currently, DL models have beenwidely used in 3D reconstruction and have achieved superior performance in di-verse tasks. Likewise, these DL models are opaque, which hinders the developmentof their ability and application fields. Therefore, I intend to dive into the researchdirection and utilize interpretability to enrich existing related work.Reconstruction of a 3D object from a 2D image is a challenging task sincethere is a big gap between 2D and 3D visual understanding. In most existing work,semantic features of the input images are extracted at first via an encoder, and a3D decoder is used to correctly reconstruct the semantic features in 3D space. Forthe task, the crucial point is how to correctly represent the semantic informationfrom images in the 3D space. Though it is feasible to encode semantic informationinto image features, it remains a challenge to interpret the semantic informationfrom the 2D domain to the 3D domain for accurate 3D reconstruction. Becausemost existing methods only use features to convey visual information which is notsufficient to guide 3D object reconstruction. Furthermore, semantic attributes areusually entangled with each other and thus cannot be fully exploited via featurechannels.Here, we intend to explore deeply the features extracted from the input im-age and decode more semantic attributes in order to provide more guidance to thereconstruction process. Therefore, we disentangle the semantic attributes directlyfrom image features and incorporate them into the reconstruction process to en-hance the reconstruction of specific semantic attributes. I plan to conduct the workbased on the ShapeNet dataset and do qualitative and quantitative experiments tovalidate the effectiveness of the work. Meanwhile, an ablation study will be ex-perimented with to examine the impact of different components of the proposednetwork.1445.2.2 3D object shape editing via interpretable semantics3D object shape editing is the process of modifying the shape of 3D objects. Byediting 3D objects, end users are able to obtain self-defined ones. It is significantin computer graphics, virtual reality, human-computer interaction, etc. Currently,a variety of DL models have been used in 3D object editing and have achievedremarkable performance. However, research about model interpretability in 3Dobject editing is not well explored. Therefore, I am interested in exploring the roleof interpretability in 3D object editing.Neural networks are able to achieve superior performance in 3D object editing,however, they are of low interpretability and end users do not know what neuralnetworks learn. It is partially because there is no control over what each latentrepresentation represents. Recently, there are a series of attempts to condition theembedding space on a particular semantic feature in the input space to allow moreregularized exploration. However, these conditions need to be defined before train-ing, thus restricting possible semantic combinations that can be investigated.To facilitate end users in understanding what neural networks learn and edit-ing the shape of 3D objects, we intend to propose a framework by utilizing inter-pretable semantics. In this work, I will use an auto-encoder as the backbone anduse the ShapeNet as the dataset. Meanwhile, I will selectively collect a series ofsmall datasets that each represents a semantic concept. Corresponding networkfeature representation for each concept will be extracted and then used in featureinterpolation to edit 3D objects. Moreover, different concepts can be blended intothe editing of a 3D object to achieve more complex modifications. In this work, Iintend to conduct experiments on feature interpolation to visualize the variation ofobject shapes.145Bibliography[1] D. Bau, B. Zhou, A. Khosla, A. Oliva, and A. Torralba. 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Thesis/Dissertation
eng
Electrical and Computer Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Wang, Z. Jane
Salcudean, Septimiu Edmund
Exploring neural network interpretability in visual understanding
Text