TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysLectNotes.105
TI  - Simplified derivations for high-dimensional convex learning problems
PY  - 2025/10/23
UR  - https://www.scipost.org/SciPostPhysLectNotes.105
JF  - SciPost Physics Lecture Notes
JA  - SciPost Phys. Lect. Notes
SP  - 105
A1  - Clark, David
AU  - Sompolinsky, Haim
AB  - Statistical-physics calculations in machine learning and theoretical neuroscience often involve lengthy derivations that obscure physical interpretation. Here, we give concise, non-replica derivations of several key results and highlight their underlying similarities. In particular, using a cavity approach, we analyze three high-dimensional learning problems: perceptron classification of points, perceptron classification of manifolds, and kernel ridge regression. These problems share a common structure—a bipartite system of interacting feature and datum variables—enabling a unified analysis. Furthermore, for perceptron-capacity problems, we identify a symmetry that allows derivation of correct capacities through a naïve method.
ER  -

@Article{10.21468/SciPostPhysLectNotes.105,
	title={{Simplified derivations for high-dimensional convex learning problems}},
	author={David G. Clark and Haim Sompolinsky},
	journal={SciPost Phys. Lect. Notes},
	pages={105},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhysLectNotes.105},
	url={https://scipost.org/10.21468/SciPostPhysLectNotes.105},
}