Topic: grid cell torus

In neuroscience, we record neural activity over time. We can try to make sense of this data by studying the (low-dimensional) space the activity is constrained to. To identify these spaces, one typically either treats the rows (neurons / spike trains) or the columns (timepoints / population vectors) of the activity matrix as points. In general, these two perspectives will not give the same space, obscuring the underlying structure of the data. Here, we provide a unified framework for thinking about this challenge in neural data. We show that if rows and columns are convex on the space(s),