Learning and Inference in Sparse Coding Models with Langevin Dynamics

TL;DR

This paper introduces a continuous-time Langevin dynamics approach for inference and learning in sparse coding models, leveraging natural stochasticity to efficiently sample posteriors and learn parameters without digital clocks.

Contribution

It proposes a novel dynamical system for inference and learning in sparse coding models using Langevin dynamics, enabling efficient posterior sampling and parameter updates.

Findings

Efficient sampling from the posterior in the L0 sparse regime.

Successful inference and learning demonstrated on synthetic and natural images.

Bypassing digital accumulators and global clocks in model updates.

Abstract

We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models - sampling the posterior distribution over latent variables - is proposed to be solved by harnessing natural sources of stochasticity inherent in electronic and neural systems. We demonstrate this idea for a sparse coding model by deriving a continuous-time equation for inferring its latent variables via Langevin dynamics. The model parameters are learned by simultaneously evolving according to another continuous-time equation, thus bypassing the need for digital accumulators or a global clock. Moreover we show that Langevin dynamics lead to an efficient procedure for sampling from the posterior distribution in the 'L0 sparse' regime, where latent variables are encouraged to be set to zero as opposed to having a small L1 norm. This allows the model to properly incorporate the notion of sparsity rather than having to resort to a relaxed version of sparsity to make optimization tractable. Simulations of the proposed dynamical system on both synthetic and natural image datasets demonstrate that the model is capable of probabilistically correct inference, enabling learning of the dictionary as well as parameters of the prior.