Backward Filtering Forward Guiding (BFFG) is a bidirectional algorithm proposed in Mider et al. [2021] and studied more in depth in a general setting in Van der Meulen and Schauer [2022]. In category theory, optics have been proposed for modelling systems with bidirectional data flow. We connect BFFG with optics by demonstrating that the forward and backwards map together define a functor from a category of Markov kernels into a category of optics, which is furthermore lax monoidal in the case when the guiding kernels coincide with the generative dynamics

翻译：反向滤波正向引导（Backward Filtering Forward Guiding, BFFG）是一种双向算法，由Mider等人[2021]提出，并在Van der Meulen与Schauer[2022]中对其一般性设定进行了更深入的研究。在范畴论中，光学（optics）已被提出用于建模具有双向数据流的系统。我们通过证明前向映射与后向映射共同定义了一个从马尔可夫核范畴到光学范畴的函子，将BFFG与光学联系起来；当引导核与生成动力学一致时，该函子进一步具有松弛幺半群（lax monoidal）性质。