Zigzag Persistence of Neural Responses to Time-Varying Stimuli

We use topological data analysis to study neural population activity in the Sensorium 2023 dataset, which records responses from thousands of mouse visual cortex neurons to diverse video stimuli. For each video, we build frame-by-frame cubical complexes from neuronal activity and apply zigzag persistent homology to capture how topological structure evolves over time. These dynamics are summarized with persistence landscapes, providing a compact vectorized representation of temporal features. We focus on one-dimensional topological features-loops in the data-that reflect coordinated, cyclical patterns of neural co-activation. To test their informativeness, we compare repeated trials of different videos by clustering their resulting topological neural representations. Our results show that these topological descriptors reliably distinguish neural responses to distinct stimuli. This work highlights a connection between evolving neuronal activity and interpretable topological signatures, advancing the use of topological data analysis for uncovering neural coding in complex dynamical systems.