Simplified derivations for high-dimensional convex learning problems
| Title: | Simplified derivations for high-dimensional convex learning problems |
|---|---|
| Authors: | Clark, David G., Sompolinsky, Haim |
| Publication Year: | 2024 |
| Collection: | Computer Science Condensed Matter Quantitative Biology |
| Subject Terms: | Condensed Matter - Disordered Systems and Neural Networks, Computer Science - Neural and Evolutionary Computing, Quantitative Biology - Neurons and Cognition |
| More Details: | Statistical-physics calculations in machine learning and theoretical neuroscience often involve lengthy derivations that obscure physical interpretation. We present concise, non-replica derivations of key results and highlight their underlying similarities. Using a cavity approach, we analyze high-dimensional learning problems: perceptron classification of points and manifolds, and kernel ridge regression. These problems share a common structure--a bipartite system of interacting feature and datum variables--enabling a unified analysis. For perceptron-capacity problems, we identify a symmetry that allows derivation of correct capacities through a na\"ive method. Comment: Submission to SciPost; 28 pages, 1 figure; fixed typos, added references |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2412.01110 |
| Accession Number: | edsarx.2412.01110 |
| Database: | arXiv |
| Description not available. |