Neural Langevin Dynamics: towards interpretable Neural Stochastic Differential Equations

TL;DR

This paper introduces a Langevin dynamics restriction to Neural Stochastic Differential Equations, enhancing interpretability and enabling analysis of latent states and energy landscapes in data.

Contribution

It proposes a novel approach to make NSDEs more interpretable by constraining them to Langevin dynamics and training as VAEs, facilitating analysis and visualization.

Findings

Energy landscape with identifiable minima corresponding to latent states

Unsupervised detection of data underlying states

Inference of state dwell times using learned SDEs

Abstract

Neural Stochastic Differential Equations (NSDE) have been trained as both Variational Autoencoders, and as GANs. However, the resulting Stochastic Differential Equations can be hard to interpret or analyse due to the generic nature of the drift and diffusion fields. By restricting our NSDE to be of the form of Langevin dynamics, and training it as a VAE, we obtain NSDEs that lend themselves to more elaborate analysis and to a wider range of visualisation techniques than a generic NSDE. More specifically, we obtain an energy landscape, the minima of which are in one-to-one correspondence with latent states underlying the used data. This not only allows us to detect states underlying the data dynamics in an unsupervised manner, but also to infer the distribution of time spent in each state according to the learned SDE. More in general, restricting an NSDE to Langevin dynamics enables the use of a large set of tools from computational molecular dynamics for the analysis of the obtained results.