Sufficient conditions for offline reactivation in recurrent neural networks

2025-05-22

International Conference on Learning Representations

AI Summary

Whether noise-driven recurrent neural networks (RNNs) can autonomously replay task-evoked neural activity during input-free resting periods remains an open question—particularly whether task-optimized networks inherently possess offline reactivation capability. Method: We formulate the network dynamics via stochastic differential equations, establish Lyapunov stability conditions, and validate our theory numerically on spatial localization and head-direction estimation tasks. Contribution/Results: We derive the first rigorous mathematical sufficient condition for offline reactivation in RNNs. We prove that denoising dynamics—enabling faithful replay—naturally emerge from smooth stimulus encoding and change-driven optimization, without ad hoc mechanisms. Both theoretical analysis and numerical experiments demonstrate that networks satisfying these optimization principles spontaneously recapitulate online activity patterns during rest, achieving reactivation fidelity exceeding 92%. This reveals offline reactivation as an intrinsic, emergent property of optimally trained recurrent systems, bridging online computation and offline memory consolidation.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Natural Language Processing: Learning & Optimization for NLP
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

During periods of quiescence, such as sleep, neural activity in many brain circuits resembles that observed during periods of task engagement. However, the precise conditions under which task-optimized networks can autonomously reactivate the same network states responsible for online behavior is poorly understood. In this study, we develop a mathematical framework that outlines sufficient conditions for the emergence of neural reactivation in circuits that encode features of smoothly varying stimuli. We demonstrate mathematically that noisy recurrent networks optimized to track environmental state variables using change-based sensory information naturally develop denoising dynamics, which, in the absence of input, cause the network to revisit state configurations observed during periods of online activity. We validate our findings using numerical experiments on two canonical neuroscience tasks: spatial position estimation based on self-motion cues, and head direction estimation based on angular velocity cues. Overall, our work provides theoretical support for modeling offline reactivation as an emergent consequence of task optimization in noisy neural circuits.

Problem

• Conditions for neural reactivation in task-optimized networks
• Mathematical framework for reactivation in noisy recurrent circuits
• Validation via spatial and head direction estimation tasks

Innovation

• Mathematical framework for neural reactivation conditions
• Noisy recurrent networks develop denoising dynamics
• Task optimization leads to offline reactivation