Thermalizing Stochastic Programs

2026-08-02

AI Summary

This work proposes the first compiler framework enabling end-to-end mapping of general stochastic programs to thermodynamic sampling hardware. Addressing the challenge of efficiently compiling stochastic programs—expressed as directed factor graphs or parameterized random circuits—onto native energy-based model (EBM) hardware, the approach integrates context-aware pattern matching with a trajectory-level REINFORCE post-training strategy. This combination substantially reduces compilation error and enhances approximation fidelity. Empirical evaluation demonstrates the framework’s effectiveness and generality across diverse applications, including financial market simulation, ecological probabilistic modeling, Gibbs sampling for non-native EBMs, and Bayesian design of Gaussian random circuits, thereby establishing a viable pathway toward energy-efficient stochastic computing.

Abstract

We present a set of tools for mapping general stochastic programs to thermodynamic hardware designed for energy-efficient stochastic sampling. Given a target stochastic program expressed as a Directed Factor Graph (DFG) of stochastic channels, or equivalently as a Parametrized Stochastic Circuit (PSC), we first introduce a method to approximately compile each factor in the DFG to an Energy-Based Model (EBM) that is native to the hardware. We then analyze how the error of the compiled DFG accumulates from the per-factor errors, and introduce two training refinements, context matching and trajectory-level REINFORCE post-training, which can reduce the residual error left by training each factor in isolation. The \texttt{thermalizers} framework takes a stochastic program expressed in the \texttt{torx} library and replaces its factors with thermodynamic kernels implemented and sampled using the \texttt{thrml} library. We demonstrate it on several example applications, including a market simulator that learns the joint day-to-day dynamics of a panel of financial time series from recorded market history alone, a probabilistic model from mathematical ecology, Gibbs sampling of an EBM the hardware cannot natively express, and a sequential Bayesian design loop over a Gaussian stochastic circuit.

Problem

• stochastic programs
• thermodynamic hardware
• energy-based models
• stochastic sampling
• Directed Factor Graph

Innovation

• Thermalizing Stochastic Programs
• Energy-Based Models
• Directed Factor Graphs
• Stochastic Circuit Compilation
• Hardware-Aware Sampling