Coherently Remapping Toroidal Cells But Not Grid Cells are Responsible for Path Integration in Virtual Agents

Abstract

Animals employ a neural system to map physical environmental position to neural activity and encode allocentric location. Grid cells, proposedly a vital component of this system, form a population code of space by firing in characteristic tessellated triangles of locations. This population code remaps across environments and behavioural states, independently of specific sensory inputs, pointing to a substrate of standard computation across environments, which many speculate to be path integration. However, testing whether these cells are crucial for path integration is outside the scope of current experiments and calls for complementary methods, possibly given by computational models. Recently, normative artificial neural network models have shown that path integration and grid-cell-like activity can be found in recurrent neural networks (RNNs) trained to navigate in a simulated two-dimensional environment. Remarkably, the emergent spatial profile of these grid-like cells is similar to biological cell responses in that they set up a toroidal structure. Here, we extend the RNN normative model to multiple environments and show that cells that form the toroidal structure are crucial for path integration. However, cells selected through the grid cell score, a common defining property of grid cells, are much less important and comparable to randomly selected cells. Moreover, we show that the model can navigate multiple environments and that toroidal cells remap across environments in a biologically plausible way. Results demonstrate a causal relation between toroidal cells and path integration in virtual agents and propose a mechanism of remapping in grid cells based on remapping in place cells. The work is anticipated to impact both experimental and computational neuroscience and machine learning due to the methods employed and the evaluation of results. For example, we propose explicit experiments that can evaluate both the models validity and the role of grid cells in navigation. Moreover, the model may elucidate how high-dimensional data is mapped to low-dimensional structures, possibly providing a substrate for interpolation.