Learning with Hidden Factorial Structure
This addresses the challenge of high-dimensional learning for researchers, but it is incremental as it builds on existing ideas about data structures.
The paper tackled the problem of statistical learning in high-dimensional spaces by testing if neural networks can exploit hidden factorial structures in data, finding that they leverage these latent patterns to learn discrete distributions more efficiently.
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.