Sufficient conditions for offline reactivation in recurrent neural networks

TL;DR

A mathematical framework is developed that outlines sufficient conditions for the emergence of neural reactivation in circuits that encode features of smoothly varying stimuli and demonstrates mathematically that noisy recurrent networks optimized to track environmental state variables using change-based sensory information naturally develop denoising dynamics, which cause the network to revisit state configurations observed during periods of online activity.

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.

Figures (8)

• Figure 1: Reactivation in a spatial position estimation task. a) Schematic of task. b) Test metrics as a function of training batches for the place cell tuning mean squared error loss used during training (gray) and for the position decoding spatial distance error (black). c) Explained variance as a function of the number of principal components (PCs) in population activity space during task engagement (blue) and during quiescent noise-driven activity (red). d) Sample decoded outputs during active behavior. Circles indicate the initial location, triangles indicate the final location. e) Same as (d), but for decoded outputs during quiescence. f) Neural activity projected onto the first two PCs during the active phase. Color intensity measures the decoded output's distance from the center in space. g) Neural activity during the quiescent phase projected onto the same active PC axes as in (f). h) Two-dimensional kernel density estimate (KDE) plot measuring the probability of state-occupancy over 200 decoded output trajectories during active behavior. i-k) Same as (h), but for decoded outputs during quiescence (i), neural activity projected onto the first two PCs during the active phase (j), and during the quiescent phase (k). Error bars (b-c) indicate $\pm 1$ standard deviation over five networks.
• Figure 2: Biased behavioral sampling and distribution comparisons for spatial position estimation.a-b) Decoded positions for networks trained under biased behavioral trajectories for the active (a) and quiescent (b) phases. c-d) KDE plots for 200 decoded active (c) and quiescent (d) output trajectories. e) KL divergence (nats) between KDE estimates for active and quiescent phases. $\textrm{U}$ = unbiased uniform networks, $\textrm{B}$ = biased networks, $\mathcal{U}$ = the true uniform distribution, $\mathrm R$ = random networks, and the $\sigma$ superscript denotes noisy networks. Values are averaged over five networks. f) Box and whisker plots of the total variance (variance summed over output dimensions) of quiescent trajectories, averaged over 500 trajectories. Each plot (e-f) is for five trained networks.
• Figure 3: Reactivation in a head direction estimation task.a-b) Distribution of decoded head direction bearing angles during the active (a) and quiescent (b) phases. c-d) Neural network activity projected onto the first two active phase PCs for active (c) and quiescent (d) phase trajectories. Color bars indicate the decoded output head direction.
• Figure C.1: Spatial position estimation results without increased noise variance during quiescence.a-b) Decoded output trajectories during active (a) and quiescent (b) phases for a network trained on the unbiased task. c-d) Same as (a-b) but for a network trained on the biased task. e-f) KDE plots for 200 decoded active (e) and quiescent (f) output trajectories for the unbiased task. g-h) Same as (e-f) but for the biased task.
• Figure C.2: Spatial position estimation results for GRU networks.a-b) Decoded output trajectories during active (a) and quiescent (b) phases for a network trained on the unbiased task. c-d) Same as (a-b) but for a network trained on the biased task. e-f) KDE plots for 200 decoded active (e) and quiescent (f) output trajectories for the unbiased task. g-h) Same as (e-f) but for the biased task.