### Abstract

Recent work on molecular programming has explored new possibilities for computational abstractions with biomolecules, including logic gates, neural networks, and linear systems. In the future such abstractions might enable nanoscale devices that can sense and control the world at a molecular scale. Just as in macroscale robotics, it is critical that such devices can learn about their environment and reason under uncertainty. At this small scale, systems are typically modeled as chemical reaction networks. In this work, we develop a procedure that can take arbitrary probabilistic graphical models, represented as factor graphs over discrete random variables, and compile theminto chemical reaction networks that implement inference. In particular, we show that marginalization based on sum-product message passing can be implemented in terms of reactions between chemical species whose concentrations represent probabilities. We show algebraically that the steady state concentration of these species correspond to the marginal distributions of the random variables in the graph and validate the results in simulations. As with standard sum-product inference, this procedure yields exact results for tree-structured graphs, and approximate solutions for loopy graphs.

Original language | English (US) |
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Journal | Advances in Neural Information Processing Systems |

State | Published - Jan 1 2013 |

Externally published | Yes |

Event | 27th Annual Conference on Neural Information Processing Systems, NIPS 2013 - Lake Tahoe, NV, United States Duration: Dec 5 2013 → Dec 10 2013 |

### All Science Journal Classification (ASJC) codes

- Computer Networks and Communications
- Information Systems
- Signal Processing