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The brain's spatial orientation system uses different neuron ensembles to aidin environment-based navigation. Two of the ways brains encode spatialinformation is through head direction cells and grid cells. Brains use headdirection cells to determine orientation whereas grid cells consist of layersof decked neurons that overlay to provide environment-based navigation. Theseneurons fire in ensembles where several neurons fire at once to activate asingle head direction or grid. We want to capture this firing structure and useit to decode head direction grid cell data. Understanding, representing, anddecoding these neural structures requires models that encompass higher orderconnectivity, more than the 1-dimensional connectivity that traditionalgraph-based models provide. To that end, in this work, we develop a topologicaldeep learning framework for neural spike train decoding. Our framework combinesunsupervised simplicial complex discovery with the power of deep learning via anew architecture we develop herein called a simplicial convolutional recurrentneural network. Simplicial complexes, topological spaces that use not onlyvertices and edges but also higher-dimensional objects, naturally generalizegraphs and capture more than just pairwise relationships. Additionally, thisapproach does not require prior knowledge of the neural activity beyond spikecounts, which removes the need for similarity measurements. The effectivenessand versatility of the simplicial convolutional neural network is demonstratedon head direction and trajectory prediction via head direction and grid celldatasets.

A Topological Deep Learning Framework for Neural Spike Decoding