PNNL

Abstract

Neural manifolds summarize the intrinsic structure of the information encoded by a population of neurons. Advances in experimental techniques have made recording from multiple brain regions simultaneously increasingly commonplace, raising the possibility of studying how these manifolds relate across populations. However, when the involved manifolds are nonlinear and may code for multiple unknown variables simultaneously, it is challenging to extract robust and falsifiable information about their relationships. We introduce a framework, called the method of analogous cycles, for matching topological features of neural manifolds using only observed dissimilarity matrices within and between neural populations. We demonstrate via analysis of simulations and in vivo experimental data that this method can be used to correctly identify multiple shared circular coordinate systems across both stimuli and inferred neural manifolds, and conversely that it rejects matching features that are not intrinsic to one of the systems. Further, as this method is deterministic and does not rely on dimensionality reduction or optimization methods, it is amenable to direct mathematical investigation and interpretation in terms of the underlying neural activity. We thus propose this as a suitable foundation for a theory of cross-population analysis via neural manifolds.