# Generalization in Machine Learning via Analytical Learning Theory

## TL;DR

This paper presents a measure-theoretic learning framework that analyzes individual problem instances without statistical assumptions, leading to a new regularization method that improves deep learning performance.

## Contribution

It introduces a novel measure-theoretic theory for machine learning, providing a new perspective and regularization approach that outperforms existing methods on standard datasets.

## Key findings

- New regularization method outperforms previous methods on CIFAR-10, CIFAR-100, and SVHN.
- The theory offers insights into one-shot learning, representation learning, and curriculum learning.
- Provides a measure-theoretic analysis of individual problem instances, differing from traditional statistical approaches.

## Abstract

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.