Topic: toroidal manifold

Neural oscillations are ubiquitously observed in many brain areas. One proposed functional role of these oscillations is that they serve as an internal clock, or ‘frame of reference’ relative to which information can be encoded. In line with this hypothesis, there have been many empirical observations of this phase code in the brain. What are the latent dynamics and circuits that support phase coding with neural oscillations? Here, we propose a new computational hypothesis which is derived from analyzing trained recurrent neural networks (RNNs). We train RNNs on a working memory task, while al

Entorhinal grid cells, so-called because of their hexagonally tiled spatial receptive fields, are organized in modules which, collectively, are believed to form a population code for the animal’s position. Here, we apply topological data analysis to simultaneous recordings of hundreds of grid cells and show that joint activity of grid cells within a module lies on a toroidal manifold. Each position of the animal in its physical environment corresponds to a single location on the torus, and each grid cell is preferentially active within a single “field” on the torus. Toroidal firing positions p