Impact of leaky dynamics on predictive path integration accuracy in recurrent neural networks
For computational neuroscience and AI researchers studying grid cells and path integration, this work shows that leaky dynamics enhance stability and accuracy in recurrent networks.
The paper introduces adaptive time scales via a leak term in recurrent neural networks (leaky RNNs) to improve path integration. Leaky RNNs produce more accurate position estimates and more stable, regular hexagonal grid patterns compared to vanilla RNNs, especially under noise.
Experimental evidence indicates that intrinsic temporal dynamics operating across multiple time scales are closely associated with the emergence of periodic spatial activity of increasing complexity. However, how information encoded in grid-like firing patterns for path integration is processed across these intrinsic time scales remains unclear. To address this question, we introduce adaptive time scales through a leak term in recurrent neural networks (RNNs), forming leaky RNNs discretized from the continuous attractors of firing rate models. Our results demonstrate that leaky RNNs substantially enhance the emergence of well-defined and highly regular hexagonal firing patterns. Compared with vanilla RNNs lacking a leak term, the trained leaky RNNs produce more accurate position estimates while generating reliable grid-cell-like representations. Furthermore, under identical noise conditions, leaky RNNs consistently exhibit more stable dynamics and better-defined grid structures. The learned dynamics also give rise to stable torus attractors with a clear central hole, supporting robust and regular grid-like activity. Overall, the dynamic leak acts as a low-pass filtering mechanism that protects recurrent neural circuitry from noise, stabilizes network dynamics, and improves path-integration accuracy in recurrent neural networks.