Neural Manifolds and Cognitive Consistency: A New Approach to Memory Consolidation in Artificial Systems
Phuong-Nam Nguyen
TL;DR
The paper addresses memory consolidation in artificial systems by unifying neural population dynamics, hippocampal SpWR-like replay, and cognitive consistency constraints within a low-dimensional manifold framework. It introduces a mathematical formalism where neural drift is captured on a manifold $\mathcal{M}$ and a balance energy $E_{\text{balance}}$ enforces coherent inter-neuronal interactions, with SpWR content weighted by balance-aware replay. Efficient algorithms for balance-energy computation and fast gradients are developed, and simulations show that cognition-inspired constraints improve interpretability and robustness while preserving performance. The approach aims to enable scalable neuromorphic architectures that harness structured replay and consistency principles for robust, adaptive learning in AI systems.
Abstract
We introduce a novel mathematical framework that unifies neural population dynamics, hippocampal sharp wave-ripple (SpWR) generation, and cognitive consistency constraints inspired by Heider's theory. Our model leverages low-dimensional manifold representations to capture structured neural drift and incorporates a balance energy function to enforce coherent synaptic interactions, effectively simulating the memory consolidation processes observed in biological systems. Simulation results demonstrate that our approach not only reproduces key features of SpWR events but also enhances network interpretability. This work paves the way for scalable neuromorphic architectures that bridge neuroscience and artificial intelligence, offering more robust and adaptive learning mechanisms for future intelligent systems.