A predictive theory of experimental design for inferring neural population geometry in large-scale recordings

Ongoing technological advances will lead to recordings with progressively increasing numbers of neurons, while trial counts may only increase modestly. The analysis of such large-scale data increasingly relies on extracting collective neural population geometry. These combined recording and analysis trends raise the fundamental need for a predictive theory of experimental design that can tell us how accurately we will be able to infer such geometry in future larger scale recordings with more neurons and trials, by extrapolating from past smaller recordings. We derive such a theory for the simplest and most widely used method for extracting population geometry: principal component analysis. Our theory can predict how the dimensionality of neural data will grow with more neurons and trials and how accurate and reliable neuronal correlations and individual neural modes of the population geometry will be. Importantly, we find a blessing of dimensionality in which recording more neurons allows population geometry to be inferred accurately with fewer trials. The need for fewer trials in larger recordings will allow for the design of new experiments with more diverse trial types. Moreover, we derive scaling laws for the performance of neural prediction, setting the stage for the derivation of scaling laws for foundation models in neuroscience. We successfully test our theory across diverse species and recording modalities.