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

2026-04-17

AI Summary

This study investigates the impact of intrinsic multiscale temporal dynamics on grid cell coding within path integration. To this end, leaky dynamics are introduced for the first time as a low-pass filtering mechanism into recurrent neural networks (RNNs), yielding a continuous attractor–based leaky RNN capable of adaptive timescale modeling. This approach stabilizes network dynamics and facilitates the emergence of regular hexagonal grid activity patterns alongside toroidal attractors with a central hole. Compared to conventional RNNs, the proposed model achieves substantially higher positional estimation accuracy and demonstrates enhanced dynamic robustness and more stable grid representations, even under noisy conditions.

Technology Category

Cognitive Modeling & Cognitive Systems: Neural Spike CodingMachine Learning: Large Multimodal Models (LMMs)Intelligent Robots: State Estimation

Application Category

Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsWeb Mining and Content Analysis: Models for Web evolutionSearch and Retrieval-Augmented AI: Large language models for search

Abstract

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.

Problem

• path integration
• grid cells
• leaky dynamics
• recurrent neural networks
• temporal dynamics

Innovation

• leaky RNN
• path integration
• grid cells
• attractor dynamics
• adaptive time scales