Emergent attractor-like dynamics support stable and generalizable path integration in recurrent neural networks

Path integration, essential to mammalian navigation, involves interactions between grid cells and place cells in the brain. Continuous attractor network models can reproduce key features of grid-cell activity, but many rely on predefined synaptic connectivity, leaving open how similar recurrent dynamics could emerge through task-driven learning. Here, we developed a task-optimized three-layer recurrent neural network with a place-field-like readout (RNN_PF) for path integration and compared it with a variant using a Cartesian-coordinate readout. The network received velocity input and was trained to predict position. Following training, the recurrent layer developed grid-like spatial representations and exhibited attractor-like population dynamics without explicitly imposed recurrent connectivity. Persistent cohomology analysis further revealed a toroidal population manifold consistent with continuous attractor organization, while systematic matrix-freezing analysis identified the functional roles of individual weight matrices. The trained RNN_PF exhibited accurate path integration and robust generalization to novel trajectories and to a translated environment. This work provides a task-driven computational framework for investigating how structured readout constraints and learning objectives can shape spatial representations and attractor-like dynamics.