What question did this study set out to answer?

The aim is to explore the relationship between the Backward Filtering Forward Guiding algorithm and category theory, specifically optics.

March 26, 2026Compositionality0 citationsOpen Access

Compositionality in algorithms for smoothing

MSMoritz Schauer FMFrank van der Meulen AWAndi Q. Wang

Key Points

The aim is to explore the relationship between the Backward Filtering Forward Guiding algorithm and category theory, specifically optics.
Connect BFFG algorithm with category theory concepts.
Demonstrate how forward and backward mappings create a functor.
Analyze implications in the context of Markov kernels and optics.
Establish a functorial connection between BFFG and optics.
Show that the mapping is lax monoidal when guiding kernels align with generative dynamics.

Abstract

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

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Cite This Study

Schauer et al. (Tue,) studied this question.

synapsesocial.com/papers/69c4ccebfdc3bde448918979 https://doi.org/https://doi.org/10.46298/compositionality-8-3

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