  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.
