SyLVER: symbolic equation recovery from neural population recordings

Understanding neural computation requires population dynamics models that are predictive and interpretable. Sequential variational autoencoders (SVAEs) recover low-dimensional latent trajectories from high-dimensional recordings but their learned dynamics are challenging to interpret. Sparse regression methods such as SINDy yield interpretable closed-form equations but require the state to be directly observed. This introduces a central challenge when applying these methods when the underlying state is unobserved: a latent state must first be inferred by a separate model, and equations are then fit to those estimates which were inferred without any knowledge of the equation. To address this challenge we introduce Symbolic Latent Variable Equation Recovery (SyLVER), a sequential VAE whose transition drift is a sparse dictionary of candidate terms that provide a closed-form dynamics equation. Because inference is structured, the drift also drives the approximate posterior through the predict step of the filter, so the dynamics and the inference network share one latent coordinate system and are trained jointly using block optimization. The recovered equation is thus constrained by inference itself rather than regressed onto post-hoc state estimates. We evaluate on the Lorenz system, van der Pol oscillator, and the MC Maze reaching dataset, and demonstrate comparable latent inference, forecasting, and coefficient recovery against two established methods, XFADS and SINDy Autoencoder.