Optimal Transport Theory to Extract Spiking Motifs

Spatiotemporal spike motifs, i.e. repeating temporal sequences, of neural activity are thought to carry information beyond average firing rates, yet extracting such motifs from noisy spike trains remains challenging. In particular, most approaches rely on bin-by-bin comparisons that are sensitive to bin size and temporal jitter. Here, we investigate the use of the Earth Mover’s Distance (EMD), a metric from optimal transport theory, as a reconstruction loss for learning spiking motifs. We compare EMD to the conventional mean squared error (MSE) by training single-layer autoencoders with tied positive weights to reconstruct neural raster plots. Using synthetic spike trains with known ground-truth motifs, we systematically evaluate how each loss recovers spatiotemporal structure under varying numbers of training samples and different noise regimes, including temporal jitter, sequence warping, neuron dropout, and additive Poisson noise. We show that EMD-based training is more robust to temporal jitter and sequence warping, and more reliably estimates aligned spike timings when the number of training samples is limited. In contrast, MSE better captures the full spike distribution, i.e. the relative timing of the spikes as well as their temporal precision, when large datasets are available and is more resilient to additive noise. Applying the same framework to Neuropixels recordings from the Allen Institute visual coding dataset reveals that motifs learned with EMD are more discriminative of visual stimuli than those learned with MSE. Together, these results highlight the advantages of optimal transport–based losses for learning spatiotemporal motifs in neural population activity.