Compositional Active Inference I: Bayesian Lenses. Statistical Games

通过统计博弈纤维化实现的近似推断

Approximate Inference via Fibrations of Statistical Games

本研究将近似推断系统刻画为统计博弈2-纤维化的损失模型，引入复制-复合与共参数化贝叶斯透镜等概念，揭示其组合结构与光学复合性质。

Bayesian Updates Compose Optically

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may ask whether composing the inversions of the component processes gives the same belief update as the inversion of the whole. We answer this question affirmatively, showing that the relevant compositional structure is precisely that of the lens pattern, and that we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a corresponding fibred category. We define a general notion …

贝叶斯大脑组合式解释的数学基础

Mathematical Foundations for a Compositional Account of the Bayesian Brain

该研究运用应用范畴论工具，提出贝叶斯透镜与统计博弈纤维化等概念，将开放动力系统形式化为多项式函子余代数，构建函子解释预测编码神经回路的双向结构，为贝叶斯大脑的组合式解释提供数学基础。

Compositional Active Inference II: Polynomial Dynamics. Approximate Inference Doctrines

We develop the compositional theory of active inference by introducing activity, functorially relating statistical games to the dynamical systems which play them, using the new notion of approximate inference doctrine. In order to exhibit such functors, we first develop the necessary theory of dynamical systems, using a generalization of the language of polynomial functors to supply compositional interfaces of the required types: with the resulting polynomially indexed categories of coalgebras, we construct monoidal bicategories of differential and dynamical ``hierarchical inference systems'',…

AutoBayes：广义变分推断的组合框架

AutoBayes: A Compositional Framework for Generalized Variational Inference

本文提出AutoBayes组合框架，统一广义变分推断，利用链式法则构建和优化模型，并展示其在经典示例中的扩展潜力。