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<p>Intrinsic temporal dynamics across multiple timescales are closely linked to the emergence of complex periodic spatial activity. However, how information encoded in grid-like firing patterns for path integration is processed across these intrinsic time scales remains unclear. To investigate this, we introduce a leak term in recurrent neural networks (leaky RNNs), derived from the continuous attractor dynamics of firing rate models. Leaky RNNs enhance the formation of regular hexagonal firing patterns, produce more accurate position estimates, and maintain stable dynamics under both noise-free and noisy conditions compared with vanilla RNNs. The learned dynamics give rise to stable torus attractors, supporting robust grid-like activity. Overall, the leak term acts as a low-pass filter, stabilizing network dynamics and improving path-integration accuracy.</p>

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Impact of leaky dynamics on predictive path integration accuracy in recurrent neural networks

  • 期刊论文

  • 发表日期：

    2026年6月26日

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  • Yanlin Zhang,
  • Yan Zhang,
  • Muhua Zheng,
  • Kesheng Xu

摘要

Intrinsic temporal dynamics across multiple timescales are closely linked to the emergence of complex periodic spatial activity. However, how information encoded in grid-like firing patterns for path integration is processed across these intrinsic time scales remains unclear. To investigate this, we introduce a leak term in recurrent neural networks (leaky RNNs), derived from the continuous attractor dynamics of firing rate models. Leaky RNNs enhance the formation of regular hexagonal firing patterns, produce more accurate position estimates, and maintain stable dynamics under both noise-free and noisy conditions compared with vanilla RNNs. The learned dynamics give rise to stable torus attractors, supporting robust grid-like activity. Overall, the leak term acts as a low-pass filter, stabilizing network dynamics and improving path-integration accuracy.