# Learning and Inference in Sparse Coding Models with Langevin Dynamics

arXiv: https://arxiv.org/abs/2204.11150 · HTML: https://mlsanity.com/paper/2204.11150/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 54 references that are in the map.
- First posted on arXiv 23 Apr 2022.

## Builds on (most cited first, 5 of 5)

- [Underdamped Langevin MCMC: A non-asymptotic analysis](https://mlsanity.com/paper/1707.03663/) (2017)
- [High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithm](https://mlsanity.com/paper/1908.10859/) (2019)
- [Hamiltonian Monte Carlo Without Detailed Balance](https://mlsanity.com/paper/1409.5191/) (2014)
- [Effect of top-down connections in Hierarchical Sparse Coding](https://mlsanity.com/paper/2002.00892/) (2020)
- [Building fast Bayesian computing machines out of intentionally stochastic, digital parts](https://mlsanity.com/paper/1402.4914/) (2014)

## Built on by (most cited first, 2 of 2)

- [Divide-and-Conquer Predictive Coding: a structured Bayesian inference algorithm](https://mlsanity.com/paper/2408.05834/) (2024)
- [Active Inference in Hebbian Learning Networks](https://mlsanity.com/paper/2306.05053/) (2023)

## Abstract (arXiv)

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.