Simultaneous, cortex-wide dynamics of up to 1 million neurons reveal unbounded scaling of dimensionality with neuron number

The brain's remarkable properties arise from the collective activity of millions of neurons. Widespread application of dimensionality reduction to multi-neuron recordings implies that neural dynamics can be approximated by low-dimensional "latent" signals reflecting neural computations. However, can such low-dimensional representations truly explain the vast range of brain activity, and if not, what is the appropriate resolution and scale of recording to capture them? Imaging neural activity at cellular resolution and near-simultaneously across the mouse cortex, we demonstrate an unbounded scaling of dimensionality with neuron number in populations up to 1 million neurons. Although half of the neural variance is contained within sixteen dimensions correlated with behavior, our discovered scaling of dimensionality corresponds to an ever-increasing number of neuronal ensembles without immediate behavioral or sensory correlates. The activity patterns underlying these higher dimensions are fine grained and cortex wide, highlighting that large-scale, cellular-resolution recording is required to uncover the full substrates of neuronal computations.