Message Passing Inference with Chemical Reaction Networks

Recent work on molecular programming has explored new possi bilities for computational abstractions with biomolecules, including log ic gates, neural networks, and linear systems. In the future such abstractions might en able nanoscale devices that can sense and control the world at a molecular scale. Jus t as in macroscale robotics, it is critical that such devices can learn about th eir environment and reason under uncertainty. At this small scale, systems are typi cally modeled as chemical reaction networks. In this work, we develop a procedure that can take arbitrary probabilistic graphical models, represented as factor gra phs over discrete random variables, and compile them into chemical reaction network s that implement inference. In particular, we show that marginalization based on s um-product message passing can be implemented in terms of reactions between che mical species whose concentrations represent probabilities. W e show algebrai cally that the steady state concentration of these species correspond to the marginal d istributions of the random variables in the graph and validate the results in simula tions.