Estimating the Local Learning Coefficient at Scale
Abstract
The \textit{local learning coefficient} (LLC) is a principled way of quantifying model complexity, originally derived in the context of Bayesian statistics using singular learning theory (SLT). Several methods are known for numerically estimating the local learning coefficient, but so far these methods have not been extended to the scale of modern deep learning architectures or data sets. Using a method developed in {\tt arXiv:2308.12108 [stat.ML]} we empirically show how the LLC may be measured accurately and self-consistently for deep linear networks (DLNs) up to 100M parameters. We also show that the estimated LLC has the rescaling invariance that holds for the theoretical quantity.
Cite
@article{arxiv.2402.03698,
title = {Estimating the Local Learning Coefficient at Scale},
author = {Zach Furman and Edmund Lau},
journal= {arXiv preprint arXiv:2402.03698},
year = {2024}
}
Comments
This paper has been expanded and merged with arXiv:2308.12108 to form a more comprehensive study. Please refer to the latest version of that preprint for the most up-to-date manuscript