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Poster A71 in Poster Session A - Tuesday, August 6, 2024, 4:15 – 6:15 pm, Johnson Ice Rink
Estimating shape distances on neural representations with limited samples
Brett W. Larsen1, Dean A. Pospisil2, Sarah E. Harvey2, Alex H. Williams2,3; 1Flatiron Institue, 2Princeton University, 3New York University
Quantitative comparisons of neural population dynamics across biological systems—e.g. different subjects, animal species, or brain areas—and to artificial network dynamics are of longstanding interest to systems neuroscience. Many metrics of functional, population-level similarity have been proposed including Representational Similarity Analysis (RSA), Centered Kernel Alignment (CKA), and shape distances. However, we still have a poor grasp on fundamental questions: How many neurons, trials, and behavioral conditions do we need to experimentally measure in order to accurately assess the similarity of two neural populations? Here, we mathematically derive concrete answers to these questions for the Procrustes shape distance—a measure of representational distance with desirable theoretical properties (symmetry and triangle inequality). We find that the problem is challenging for high-dimensional manifolds—for example, to compensate for a twofold increase in dimensionality, there must be a fourfold increase in the number of sampled conditions. To mitigate these challenges, we introduce a new method-of-moments estimator with a tunable bias-variance tradeoff. We show that this estimator achieves superior performance to standard estimators, particularly in high-dimensional settings. Furthermore, since our approach bounds the bias and variance of the estimate, it naturally produces a confidence interval, which we show to be an accurate reflection of uncertainty in simulation and on semi-synthetic experimental datasets with established ground truth. Finally, we leverage this new estimator to analyze mouse visual cortical responses to 2800 natural images. Thus, we lay the foundation for a rigorous statistical theory for high-dimensional shape analysis, and we contribute a new estimation method well-suited to practical scientific settings.
Keywords: representational geometry shape metrics dissimilarity metrics