Compressibility Measures Complexity: Minimum Description Length Meets Singular Learning Theory
Machine Learning
2025-10-15 v1 Machine Learning
Abstract
We study neural network compressibility by using singular learning theory to extend the minimum description length (MDL) principle to singular models like neural networks. Through extensive experiments on the Pythia suite with quantization, factorization, and other compression techniques, we find that complexity estimates based on the local learning coefficient (LLC) are closely, and in some cases, linearly correlated with compressibility. Our results provide a path toward rigorously evaluating the limits of model compression.
Cite
@article{arxiv.2510.12077,
title = {Compressibility Measures Complexity: Minimum Description Length Meets Singular Learning Theory},
author = {Einar Urdshals and Edmund Lau and Jesse Hoogland and Stan van Wingerden and Daniel Murfet},
journal= {arXiv preprint arXiv:2510.12077},
year = {2025}
}
Comments
33 pages, 21 figures