Circuit realization for thermodynamic Bayesian linear regression

Construct a CMOS-compatible analog circuit that realizes the thermodynamic Langevin sampler for Bayesian linear regression with pθ(θ) = N(μπ, Σπ) and p(y|θ) = N(Hθ, Σℓ), mapping Σπ, H, Σℓ, and y into circuit elements, and validate that the device samples from the exact posterior p(θ|y).

Background

The paper shows that the stochastic differential equation for Bayesian linear regression matches the dynamics of a previously proposed thermodynamic linear algebra device, suggesting feasibility. However, an explicit circuit for Bayesian linear regression is not provided.

In the conclusion, the authors explicitly list designing a circuit realization of this algorithm as an immediate extension and an open question, highlighting a practical path to hardware acceleration for widely used probabilistic models.