Estimating the Local Learning Coefficient at Scale
This work addresses the challenge of quantifying model complexity at scale for researchers in machine learning, but it is incremental as it builds on existing methods and focuses on a specific model type.
The paper tackled the problem of estimating the local learning coefficient (LLC) for large-scale deep learning models, which had not been done before, and successfully measured it accurately for deep linear networks with up to 100 million parameters, demonstrating rescaling invariance.
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.