Title: Drift-Diffusion Matching: Embedding dynamics in latent manifolds of asymmetric neural networks

Abstract:

While recurrent neural networks (RNNs) serve as a theoretical basis for deciphering computation within biological neural circuits, traditional models like Hopfield’s associative memory depend on symmetric connectivity. This symmetry confines network dynamics to gradient-like flows, limiting their complexity. Conversely, the inherent asymmetry of biological networks enables a diverse array of time-dependent behaviors. In this study, we present a novel training framework called "drift-diffusion matching," designed to train continuous-time RNNs to represent arbitrary nonlinear stochastic differential equations (SDEs). This framework operates within a low-dimensional latent subspace, utilizing specific drift and diffusion coefficients.

By leveraging asymmetric connectivity, we demonstrate that RNNs can accurately embed both the drift and diffusion components of a given SDE. This capability extends to capturing nonlinear and nonequilibrium dynamics, including chaotic attractors. We apply this approach to build RNN models of stochastic systems that temporarily investigate multiple attractors. These transitions occur through two mechanisms: input-driven switching and autonomous shifts propelled by nonequilibrium currents. We interpret these behaviors as computational models for associative and sequential (episodic) memory.

To clarify how these dynamics are encoded, we propose decompositions of the RNN that account for its asymmetric connectivity and time-irreversibility. These findings broaden attractor neural network theory beyond equilibrium states, illustrating that asymmetric neural populations can execute a wide range of dynamical computations within low-dimensional manifolds. This work unifies concepts from associative memory, nonequilibrium statistical mechanics, and neural computation.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC