If Grid Cells are the Answer, What is the Question? A Review of Normative Grid Cell Theory

For 20 years the beautiful structure in the grid cell code has presented an attractive puzzle: what computation do these representations subserve, and why does it manifest so curiously in neurons. The first question quickly attracted an answer: grid cells subserve path-integration, the ability to keep track of one's position as you move about the world. Subsequent work has only solidified this link: bottom-up mechanistic models that perform path-integration match the measured neural responses, while experimental perturbations that selectively disrupt grid cell activity impair performance on path-integration dependent tasks. A more controversial area of work has been top-down normative modelling: why has the brain chosen to compute like this? Floods of ink have been spilt attempting to build a precise link between the population's objective and the measured implementation. The holy grail is a normative link with broad predictive power which generalises to other neural systems. We review this literature and argue that, despite some controversies, the literature largely agrees that grid cells can be explained as a (1) biologically plausible (2) high fidelity, non-linearly decodable code for position that (3) subserves path-integration. As a rare area of neuroscience with mature theoretical and experimental work, this story holds lessons for normative theories of neural computations, and on the risks and rewards of integrating task-optimised neural networks into such theorising.