A new dynamic shift mechanism based on cyclic group theory for continuous attractor neural networks

Spatial cognition plays a crucial role in enabling animals to navigate effectively, whether hunting prey or exploring for food. Continuous attractor neural networks (CANNs) have been developed to model spatial cells, such as head direction cells, place cells and grid cells. However, how to maintain long-term spatial memory and accurately transfer network activity in CANNs is still unclear. We design a modified version of CANNs that can maintain long-term spatial memory without external cues. Based on this redesigned CANN, we propose a novel dynamic shift mechanism. It leverages cyclic group theory to dynamically adjust connections between neurons. These synaptic changes effectively shift the network activity according to speed information. Interestingly, our method exhibits anticipatory and delayed transfers, analogous to the predictive coding observed in the brain’s entorhinal speed cells and grid cells. Compared to the existing biological shift mechanism, our method demonstrates significant advantages in both computation speed and path-integration accuracy. Notably, our approach facilitates vector-based navigation with high accuracy. We rigorously verified its effectiveness through mathematical analysis and further validated it with simulated and real-world data. Experimental results demonstrate that our method accurately determines the navigation vector, enabling precise navigation between the current location and the target position. This work has established a comprehensive theoretical framework encompassing the entire process from inputs to cognition coding, and further extending to vector-based navigation, laying the foundation for practical implementation in bio-inspired robot navigation systems.