Large-scale neural recordings contain high-dimensional structure that cannot be easily captured by existing data visualization methods. We therefore developed an embedding algorithm called Rastermap, which captures highly nonlinear relationships between neurons, and provides useful visualizations by assigning each neuron to a location in the embedding space. Compared to standard algorithms such as t-SNE and UMAP, Rastermap finds finer and higher dimensional patterns of neural variability, as measured by quantitative benchmarks. We applied Rastermap to a variety of datasets, including spontaneous neural activity, neural activity during a virtual reality task, widefield neural imaging data during a 2AFC task, artificial neural activity from an agent playing atari games, and neural responses to visual textures. We found within these datasets unique subpopulations of neurons encoding abstract properties of the environment.

Interpreting high-dimensional datasets requires new computational and analytical methods. We developed such methods to extract and analyze neural activity from 20,000 neurons recorded simultaneously in awake, behaving mice. The neural activity was not low-dimensional as commonly thought, but instead was high-dimensional and obeyed a power-law scaling across its eigenvalues. We developed a theory that proposes that neural responses to external stimuli maximize information capacity while maintaining a smooth neural code. We then observed power-law eigenvalue scaling in many real-world datasets, and therefore developed a nonlinear manifold embedding algorithm called Rastermap that can capture such high-dimensional structure.