Scaling Insights from Infinite-Width Theory for Next Generation Architectures and Learning Paradigms

Explore a comprehensive lecture on scaling insights derived from infinite-width theory for advanced architectures and learning paradigms. Delve into the critical role of scaling in modern machine learning and its associated challenges, such as increased training instability. Discover how infinite-width theory can be applied to establish optimal scaling rules across various architectures and learning paradigms. Examine the scaling behavior of Multilayer Perceptrons (MLPs) under Sharpness-Aware Minimization, a min-max learning formulation designed to enhance generalization. Investigate how this analysis extends to other architectures like transformers, ResNets, and CNNs. Learn about the unique scaling behavior of structured state space models (SSMs), which have emerged as efficient alternatives to transformers. Understand the need for specialized approaches in analyzing SSMs due to their unique transition matrix structure. Gain insights into the scaling of SSMs within the standard minimization framework and explore the implications of specialized scaling strategies.