# Generalization in Machine Learning via Analytical Learning Theory

arXiv: https://arxiv.org/abs/1802.07426 · HTML: https://mlsanity.com/paper/1802.07426/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2018.

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

- [A Theoretical Analysis of Generalization Dynamics in Neural Networks under Gradient Descent with Weight Decay](https://mlsanity.com/paper/2609.07755/) (2026)

## Abstract (arXiv)

This paper introduces a novel measure-theoretic theory for machine learning that does not require statistical assumptions. Based on this theory, a new regularization method in deep learning is derived and shown to outperform previous methods in CIFAR-10, CIFAR-100, and SVHN. Moreover, the proposed theory provides a theoretical basis for a family of practically successful regularization methods in deep learning. We discuss several consequences of our results on one-shot learning, representation learning, deep learning, and curriculum learning. Unlike statistical learning theory, the proposed learning theory analyzes each problem instance individually via measure theory, rather than a set of problem instances via statistics. As a result, it provides different types of results and insights when compared to statistical learning theory.