Self-Supervised Grid Cells Without Path Integration

Grid cells, found in the medial Entorhinal Cortex, are known for their regular spatial firing patterns. These cells have been proposed as the neural solution to a range of computational tasks, from performing path integration, to serving as a metric for space. Their exact function, however, remains fiercely debated. In this work, we explore the consequences of demanding distance preservation over small spatial scales in networks subject to a capacity constraint. We consider two distinct self-supervised models, a feedforward network that learns to solve a purely spatial encoding task, and a recurrent network that solves the same problem during path integration. Surprisingly, we find that this task leads to the emergence of highly grid cell-like representations in both networks. However, the recurrent network also features units with band-like representations. We subsequently prune velocity inputs to subsets of recurrent units, and find that their grid score is negatively correlated with path integration contribution. Thus, grid cells emerge without path integration in the feedforward network, and they appear substantially less important than band cells for path integration in the recurrent network. Our work provides a minimal model for learning grid-like spatial representations, and questions the role of grid cells as neural path integrators. Instead, it seems that distance preservation and high population capacity is a more likely candidate task for learning grid cells in artificial neural networks.