🤖 AI Summary
This work addresses the challenge of implementing probabilistic computations such as Bayesian inference in biochemical systems, where conventional chemical reaction networks (CRNs) are often prohibitively large for practical use. The authors introduce, for the first time, factor graph reduction theory into CRN design by uncovering the implicit factor graph structure embedded within the Napp–Adams compilation framework and applying graph reduction algorithms. This approach significantly compresses the network size while preserving the fixed points of belief propagation for key variables. By doing so, it overcomes a critical limitation of existing CRN simplification techniques, which are unable to handle probabilistic models, thereby enabling efficient and exact compression of probabilistic CRNs.
📝 Abstract
Programming adaptive behaviors at the cellular level is a long-standing goal that raises the question of how probabilistic computation can be implemented in biochemical systems. Chemical reaction networks (CRNs) provide such a substrate and have been shown to realize probabilistic models, including hidden Markov models and factor graphs, with dynamics reproducing Bayesian inference and belief propagation. However, encoding these algorithms typically requires prohibitively large reaction networks, and classical CRN reduction techniques do not directly apply. By recovering the factor graph structure encoded in Napp--Adams-compiled CRNs, we transport recent factor-graph reduction results to their chemical implementations, obtaining significantly smaller CRNs while preserving the belief-propagation fixed points on surviving variables.