# Simplified derivations for high-dimensional convex learning problems

arXiv: https://arxiv.org/abs/2412.01110 · HTML: https://mlsanity.com/paper/2412.01110/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2024.

## Built on by (most cited first, 1 of 1)

- [An Asymptotic Theory of Chain-of-Thought in In-Context Learning](https://mlsanity.com/paper/2606.03217/) (2026)

## Abstract (arXiv)

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 naive method.