The brain's spatial orientation system uses different neuron ensembles to aid
in environment-based navigation. One of the ways brains encode spatial
information is through grid cells, layers of decked neurons that overlay to
provide environment-based navigation. These neurons fire in ensembles where
several neurons fire at once to activate a single grid. We want to capture this
firing structure and use it to decode grid cell data. Understanding,
representing, and decoding these neural structures require models that
encompass higher order connectivity than traditional graph-based models may
provide. To that end, in this work, we develop a topological deep learning
framework for neural spike train decoding. Our framework combines unsupervised
simplicial complex discovery with the power of deep learning via a new
architecture we develop herein called a simplicial convolutional recurrent
neural network (SCRNN). Simplicial complexes, topological spaces that use not
only vertices and edges but also higher-dimensional objects, naturally
generalize graphs and capture more than just pairwise relationships.
Additionally, this approach does not require prior knowledge of the neural
activity beyond spike counts, which removes the need for similarity
measurements. The effectiveness and versatility of the SCRNN is demonstrated on
head direction data to test its performance and then applied to grid cell
datasets with the task to automatically predict trajectories