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Description

Differential and tangent categories have been applied to providing the semantics of differential programming languages. As interest in differential programming langauges continues to grow due to applications in machine learning, many differential programming languages are being extended with features for probabilistic programming and in some cases quantum programming. In this talk, we will investigate structures on top of differential and tangent categories that allow modelling probabilistically extended programming languages. To do this, we will develop some of the basics of functional analysis and distribution theory in the context of differential categories. We will also develop different approaches to encoding probabilistic computations in a differential language.