Our new paper brilliantly lead by @itamarlandau "A predictive theory of experimental design for inferring neural population geometry in large-scale recordings." biorxiv.org/content/10.64898… Our theory can say a lot about the geometry of new data *before* it is collected, by extrapolating from past data. We quantitatively predict: 1) How neural dimensionality, and the reliability of neural correlations and individual neural PCA modes grows with neurons and trials. This allows one to design experiments before the data is collected. 2) We find a "blessing of dimensionality" whereby recording more neurons actually allows us to record *fewer* trials while still reliably inferring neural population geometry. This opens the door to new types of experiments with many more complex trial types. 3) We develop scaling laws for neural prediction using masked autoencoders - a key technology for building foundation models in neuroscience. In the simple setting of linear autoencoders on a single session, we find power law behavior of prediction performance and autoencoder size with neurons and trials, and we trace these power law exponents for neural prediction to power law signals in collective neural modes of the brain. 4) We test our theory across multiple species (mouse, monkey, human) and recoding modalities (electrophysiology, calcium imaging, and fMRI). See @itamarlandau's excellent thread for more information: xitter.cf/itamarlandau/status/20… Also, yet another fun collaboration with Mark Schnitzer!