Thermalizing Stochastic Programs
2026-08-03 • Emerging Technologies
Emerging TechnologiesMachine Learning
AI summaryⓘ
The authors developed tools to turn complex random processes, called stochastic programs, into formats suited for special energy-efficient hardware that simulates randomness. They first convert parts of these programs into energy-based models that match the hardware and study how errors build up when combining these parts. To improve accuracy, they introduced training methods that consider the bigger context and sequence of operations. Their framework, called thermalizers, makes it easier to run these converted programs on the hardware, and they tested it on examples like financial market simulations and ecological models.
stochastic programsDirected Factor Graph (DFG)Energy-Based Model (EBM)Parametrized Stochastic Circuit (PSC)thermodynamic hardwareGibbs samplingREINFORCE algorithmprobabilistic modelingBayesian designthermalizers framework
Authors
Mirko Amico, Andraž Jelinčič, Colin Oscar Nancarrow, Leo Tyrpak, David Roberts, Seth Morton, Dalton Sakthivadivel, Ashwin Gopal, Guillaume Verdon
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.