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About this paper
Toby St Clere Smithe
Toby St Clere Smithe's PhD thesis from the University of Oxford establishes a compositional mathematical framework for the Bayesian brain, leveraging applied category theory to formalize active inference and predictive coding. It introduces novel concepts like Bayesian lenses and statistical games to rigorously model bidirectional information flow and approximate inference, demonstrating how these structures compose.
Key insights
- Bayesian updating can be rigorously proven to compose 'optically' using Bayesian lenses, revealing the inherent modularity of hierarchical Bayesian inference.
- Problems of statistical inference, such as relative entropy and free energy minimization, can be formalized as 'loss models' within a framework of statistical games, providing a compositional analysis of learning.
- Approximate inference doctrines, instantiated as functors, offer a precise mathematical explanation for how abstract statistical models map to concrete dynamical systems that implement predictive coding.
Summary by alphaXiv.
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