On the Dynamics of Coherent Memory Structures in Neural Fields

Justin M. Baker, Harris Hardiman-Mostow, Yuer Tang, Andrea L. Bertozzi

Keywords: deep learning, traveling waves, neural oscillators, mori-zwanzig formalism, projection operator formalism

TL;DR: We show that coupled dynamics between memory encoding and decoding give rise to emergent dynamical modes.

Abstract: Memory in biological neural networks is often supported by coherent spatiotemporal patterns, such as traveling waves and neural activity confined to low dimensional manifolds, which are captured at mesoscopic scales by continuum neural field models. Substantial progress has been made in mechanistically analyzing both biological and artificial neural network architectures. Recent works obtain interpretable latent states by imposing traveling waves or low-dimensional invariant manifolds, but typically do not provide data-driven explanations for when and why such structures emerge during task training. We develop a theoretical framework for studying latent dynamics based on the Mori-Zwanzig projection-operator formalism. Our approach casts memory as a family of time-dependent projections that reveal how coupled dynamics support memory encoding and decoding. We instantiate a neural-field-inspired architecture, and evaluate it on both long-range benchmarks and neuroscience applications involving EEG and ECoG prediction. Across these tasks, we observe robust long-range accuracy and interpretable memory modes in the learned latent dynamics.

Primary Area: applications to neuroscience & cognitive science

Submission Number: 21675