# Leakage and Second-Order Dynamics Improve Hippocampal RNN Replay

arXiv: https://arxiv.org/abs/2602.18401 · HTML: https://mlsanity.com/paper/2602.18401/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 101 references that are in the map.
- First posted on arXiv 20 Feb 2026.

## Builds on (most cited first, 18 of 18)

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- [The Hamiltonian brain: efficient probabilistic inference with excitatory-inhibitory neural circuit dynamics](https://mlsanity.com/paper/1407.0973/) (2014)
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## Abstract (arXiv)

Biological neural networks (like the hippocampus) can internally generate "replay" resembling stimulus-driven activity. Recent computational models of replay use noisy recurrent neural networks (RNNs) trained to path-integrate. Replay in these networks has been described as Langevin sampling, but new modifiers of noisy RNN replay have surpassed this description. We re-examine noisy RNN replay as sampling to understand or improve it in three ways: (1) Under simple assumptions, we prove that the gradients replay activity should follow are time-varying and difficult to estimate, but readily motivate the use of hidden state leakage in RNNs for replay. (2) We confirm that hidden state adaptation (negative feedback) encourages exploration in replay, but show that it incurs non-Markov sampling that also slows replay. (3) We propose the first model of temporally compressed replay in noisy path-integrating RNNs through hidden state momentum, connect it to underdamped Langevin sampling, and show that, together with adaptation, it counters slowness while maintaining exploration. We verify our findings via path-integration of 2D triangular and T-maze paths and of high-dimensional paths of synthetic rat place cell activity.