揭示了神经网络在离线时自发重演在线状态的数学条件。
Sufficient conditions for offline reactivation in recurrent neural networks
- 基于任务优化的噪声递归网络会自发产生去噪动力学。
- 无输入时，网络可重现在线活动中的状态配置。
- 适用于研究睡眠中大脑活动重演的理论模型。
在静息期（如睡眠），许多脑回路的神经活动与任务执行期相似。然而，任务优化网络在何种条件下能自主重演在线行为对应的状态仍不明确。本文构建了一个数学框架，推导出在编码连续变化刺激的神经回路中实现神经重激活的充分条件。数学证明表明，利用变化型感官信息追踪环境状态变量的噪声递归网络，会自然发展出去噪动力学；在无输入时，该动力学会促使网络重现在线活动期间观察到的状态配置。通过两个经典神经科学任务的数值实验验证：基于自身运动线索的空间位置估计，以及基于角速度线索的方向估计。研究结果为将离线重激活视为噪声神经回路任务优化的涌现现象提供了理论支持。
原文摘要 · Abstract (English)
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.
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