Statistical Mechanics of Support Vector Regression
A key problem in deep learning and computational neuroscience is relating the geometrical properties of neural representations to task performance.…
arXiv:2412.05439NeuroAI and Geometric Data Analysis
Our group develops mathematical theories for understanding how neurons collectively give rise to behavior in biological and artificial neural networks. Our current focus is on addressing this question through two broad approaches at the intersection of computational neuroscience and deep learning:
(1) analyzing geometries underlying neural or feature representations, embedding and transferring information, and (2) building neural network models and learning rules guided by neuroscience. To do this, we combine computational tools from theoretical physics, applied math, and machine learning. Alongside this theoretical work, we develop close collaborations with experimentalists to be inspired by and to test ideas on neural data.
Current Papers
Estimating the Spectral Moments of the Kernel Integral Operator from Finite Sample Matrices
Analyzing the structure of sampled features from an input data distribution is challenging when constrained by limited measurements in both…
arXiv:2410.17998Task-Relevant Covariance from Manifold Capacity Theory Improves Robustness in Deep Networks
Analysis of high-dimensional representations in neuroscience and deep learning traditionally places equal importance on all points in a representation, potentially…
UniReps: 2nd Edition of the Workshop on Unifying Representations in Neural Models
