Simultaneously recorded neuronal time series offer a powerful window into how neural populations collectively encode information. We present an analysis framework that applies topological data analysis (TDA) to ensembles of spiking activity recorded from dozens of neurons at once. Using spike train distance metrics, we construct geometric representations of the data that allow Vietoris–Rips filtrations and persistence barcodes to capture the structure of neural population dynamics across recording sessions and stimulus conditions.

We evaluate the discriminability of neural responses through leave-one-out classification on persistence summaries and further characterize network-level encoding using persistence landscapes. Our results demonstrate that population-level topology provides richer and more robust information than analyses restricted to single neurons. By integrating TDA with established spike train metrics and optimal transport methods, this work illustrates how topology can uncover structure in high-dimensional neural recordings and advance our understanding of population coding.