Zigzag Persistence of Neural Responses to Time-Varying Stimuli

TL;DR

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.

Abstract

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.

Figures (7)

• Figure 1: Middle frame for each video type considered in this work: Naturalistic (upper left), Gaussian (upper right), Waves (bottom left), Moving Dot (bottom right).
• Figure 2: Spatial sampling geometry. Neuron positions for a representative mouse–video pair, shown in three projections: X–Y (left), X–Z (center), and Y–Z (right). The laminar stack of regularly spaced z-planes is visible, and within-plane coverage appears uniform. Coordinates are normalized to the imaging volume.
• Figure 3: Left: Within-plane sampling density. Distribution of pairwise X–Y distances between neurons for each z-plane (overlaid histograms). The vertical dashed line marks the normalized inter-plane spacing ($\approx 0.111$), serving as a reference scale. The similar distributions across planes indicate uniform sampling density within each image plane. Right: Depth sampling balance. Bar plot of neuron counts per z-plane for the same mouse–video pair. Cell counts are broadly balanced across planes, with only minor variability, confirming uniform sampling in depth.
• Figure 4: Left: Fluorescence response overview. Heatmap of single-trial fluorescence traces for a random subset of 200 neurons, sorted by z-plane. Each row is a neuron, each column a video frame. This illustrates the diversity and temporal structure of neural responses across the imaging volume. Right: Per-plane average fluorescence dynamics. Mean fluorescence trace (solid line) and standard error (shaded area) for each z-plane, showing depth-dependent response dynamics and variability across neurons and planes.
• Figure 5: Schematic representation of the full zigzag pipeline.