Continuous attractor dynamics in spatial navigation: from population geometry to flexible computation

A central computational problem in spatial navigation is how spatial representations remain stable under noise and uncertainty, and update reliable estimations of continuous variables such as head-direction and position, which respectively rely on the head-direction system and the grid-cells system in the entorhinal cortex. The two systems demonstrate strong population-level dynamics, suggesting a potential framework to explain the critical problem of spatial representations. Currently, the framework involves continuous attractor networks and the neural field theories as an unified perspective, from which the population activity can be described as evolving of continuous variables on a low-dimensional attractor manifold, together with the selective instantiation of these dynamics across symmetry-related or context-dependent subspaces. From this viewpoint, a key question is how different sources of information, such as self-motion, sensory cues and environmental structure, interact with attractor dynamics to regulate the evolution and stability of population states. Specifically, external inputs can stabilize attractor states by anchoring them to landmarks; intrinsic network connectivity, symmetry, and multi-timescale dynamics determine whether an attractor is stable and whether it supports continuous motion; environmental boundaries and geometric constraints can systematically shape the local geometry of spatial activity patterns; direction- or context-dependent signals may selectively recruit neuronal subpopulations with specific tuning preferences; and cross-level organization of attractor dynamics, enabling a unified representational and control framework from individual decision-making to collective behavioral organization. Through the joint action of these mechanistic dimensions, continuous attractor representations are able to support the core computations required for navigation. More broadly, this perspective provides a theoretical foundation for understanding how continuous spatial representations are computed, read out, and flexibly manipulated to support planning and behavioral control.