Learning with Hidden Factorial Structure

TL;DR

This paper investigates whether neural networks can exploit hidden factorial structures in high-dimensional data, demonstrating that such structures enable more efficient learning of discrete distributions and influence generalization.

Contribution

It introduces a controlled experimental framework to test neural networks' ability to leverage hidden factorial structures in data, providing empirical evidence of their role in learning efficiency.

Findings

Neural networks exploit hidden factorial structures to learn discrete distributions more efficiently.

Structural assumptions affect the models' capacity for generalization.

Experimental results support the hypothesis that complex tasks can be decomposed into simpler subtasks.

Abstract

Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the curse of dimensionality. Inspired by results from nonparametric statistics, we hypothesize that this phenomenon can be partially explained in terms of decomposition of complex tasks into simpler subtasks. In this paper, we present a controlled experimental framework to test whether neural networks can indeed exploit such "hidden factorial structures". We find that they do leverage these latent patterns to learn discrete distributions more efficiently. We also study the interplay between our structural assumptions and the models' capacity for generalization.