A Topological Deep Learning Framework for Neural Spike Decoding

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.