High-dimensional Optimization with Applications to Compute-Optimal Neural Scaling Laws
Courtney Paquette (McGill University)
Given the massive scale of modern ML models, we now only get a single shot to train them effectively. This restricts our ability to test multiple architectures and hyper-parameter configurations. Instead, we need to understand how these models scale, allowing us to experiment with smaller problems and then apply those insights to larger-scale models. In this talk, I will present a framework for analyzing scaling laws in stochastic learning algorithms using a power-law random features model (PLRF), leveraging high-dimensional probability and random matrix theory. I will then use this scaling law to address the compute-optimal question: How should we choose model size and hyper-parameters to achieve the best possible performance in the most compute-efficient manner? Then using this PLRF model, I will devise a new momentum-based algorithm that (provably) improves the scaling law exponent. Finally, I will present some numerical experiments on LSTMs that show how this new stochastic algorithm can be applied to real data to improve the compute-optimal exponent.
Courtney Paquette is an assistant professor at McGill University in the Mathematics and Statistics department, a CIFAR AI Chair (MILA), and an active member of the Montreal Machine Learning Optimization Group (MTL MLOpt) at MILA. Her research broadly focuses on designing and analyzing algorithms for large-scale optimization problems, motivated by applications in data science, and using techniques that draw from a variety of fields, including probability, complexity theory, and convex and nonsmooth analysis. Dr. Paquette is a lead organizer of the OPT-ML Workshop at NeurIPS since 2020, and a lead organizer (and original creator) of the High-dimensional Learning Dynamics (HiLD) Workshop at ICML.