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Sufficient conditions for offline reactivation in recurrent neural networks
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Derives sufficient conditions under which noisy continuous-time RNNs trained to track change-based state variables develop denoising dynamics that make quiescent (input-free) activity sample the same distribution as active-phase activity, validated on spatial position and head direction estimation.
Problem
Understanding when task-optimized recurrent networks autonomously reactivate the same states used during online behavior in the absence of input (e.g., during sleep), which prior work has modeled mainly via generative training or hand-built attractors.
Approach
Shows that greedy optimal dynamics for noisy path-integrating RNNs decompose into a denoising term (score function of the state distribution) plus a change-based integration term; with zero input and doubled noise, these dynamics become Langevin sampling of the active-phase distribution, so quiescent activity reproduces waking state statistics.
Key results
- In the spatial task, active and quiescent output KDEs closely match, with unbiased quiescent outputs almost as close to unbiased active outputs as a true uniform distribution by KL divergence.
- Biasing the training behavior (ring-shaped drift) produced a matching bias in quiescent reactivation, with biased-to-biased KL close to the within-phase comparison.
- Networks trained without noise showed less variable quiescent trajectories (lower steady-state total variance) than noisy-trained networks, indicating noise aids exploration of the manifold.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Reactivate with no input and noise during quiescence after training a noisy RNN on change-based state estimation | Noisy continuous-time RNN · Spatial position estimation | active–quiescent activity-distribution similarity | Helped |
| Train on biased behavioral trajectories (ablation) | Noisy continuous-time RNN · Spatial position estimation | active–quiescent decoded-output distribution similarity | Helped |
| Use a uniform rather than biased behavioral distribution during training (ablation) | Noisy continuous-time RNN · Spatial position estimation | active–quiescent decoded-output distribution similarity | Mixed |
| Train the network in the presence of noise (ablation) | Continuous-time RNN · Spatial position estimation | smoothness of noisy quiescent trajectories | Helped |
| Remove noise during quiescence (ablation) | RNN trained in the presence of noise · Spatial position estimation | quiescent trajectory exploration | Hurt |
| Add quiescent noise without training in the presence of noise (ablation) | RNN trained without noise · Spatial position estimation | smoothness of decoded quiescent trajectories | Hurt |
| Use continuous-time GRUs instead of vanilla RNNs (ablation) | Noisy recurrent network · Spatial position estimation | active–quiescent reactivation correspondence | Helped |
| Do not increase noise variance during quiescence (ablation) | Trained vanilla RNN · Spatial position estimation | active–quiescent distribution correspondence | No clear effect |
| Reactivate with no input and noise during quiescence after training on angular-velocity state estimation | Noisy continuous-time RNN · Head direction estimation | active–quiescent activity-distribution similarity | Helped |
| Bias training trajectories counter-clockwise (ablation) | Head direction estimation RNN · Head direction estimation | active–quiescent transition-structure correspondence | Mixed |
Surprising findings
- Networks trained without noise still produced quiescent distributions matching active-phase distributions, suggesting noise training is not strictly necessary for distributional match.
- Adding equivalent noise during quiescence to noiselessly trained networks produced erratic, non-smooth trajectories, so noise training is needed to stabilize noisy quiescent activity.
Limitations
- Theory assumes near-optimal greedy training, a stationary input distribution, and a doubled-noise quiescent phase for exact equivalence; the paper notes the doubled-noise factor is not strictly necessary.
- The theory does not explain the observed moment-to-moment transition structure of reactivation; quiescent trajectories only partially recapitulate biased transitions in head direction.
- GRUs were more sensitive to quiescent noise and results were validated only on two simulated tasks.
Experimental setup
Datasets: simulated rodent trajectories (spatial position task) simulated head direction trajectories
Benchmarks: simulated spatial position estimation simulated head direction estimation
Metrics: explained variance KL divergence between KDE estimates total variance of quiescent trajectories place cell tuning MSE decoding spatial distance error
Baselines: noiseless-trained RNN random networks uniform true distribution
Builds on: Langevin dynamics denoising score matching Gated recurrent units
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