Simultaneous, cortex-wide and cellular-resolution neuronal population dynamics reveal an unbounded scaling of dimensionality with neuron number

The brain's remarkable properties arise from 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, what would be the biological utility of such a redundant and metabolically costly encoding scheme and what is the appropriate resolution and scale of neural recording to understand brain function? Imaging the activity of one million neurons at cellular resolution and near-simultaneously across mouse cortex, we demonstrate an unbounded scaling of dimensionality with neuron number. While half of the neural variance lies within sixteen behavior-related dimensions, we find this unbounded scaling of dimensionality to correspond to an ever-increasing number of internal variables without immediate behavioral correlates. The activity patterns underlying these higher dimensions are fine-grained and cortex-wide, highlighting that large-scale recording is required to uncover the full neural substrates of internal and potentially cognitive processes.