Statistical Mechanics of Deep Residual Networks in the Feature Learning Regime

Objective

"Since their introduction a decade ago, neural networks with residual connections have come to dominate the field of artificial neural architectures thanks to their outstanding performance, and are nowadays the building blocks of most state-of-the-art, scalable AI systems. Nevertheless, despite their widespread use, relatively little is known about the quantitative mechanisms underlying feature learning in these architectures and how to improve their inference capabilities. To this aim, ""Statistical Mechanics of Deep Residual Networks in the Feature Learning Regime"" (SM-DeepResNet) lays the groundwork to close this gap and achieve a broad theoretical understanding of residual learning. Leveraging recent successful applications of statistical mechanics to the study of deep fully connected architectures, SM-DeepResNet will contributes to: (i) building a novel statistical-mechanics-inspired framework to study deep residual nets in the feature learning regime, providing low-dimensional predictive models that theoretically describe their behavior through scaling limits; (ii) addressing two major open problems in deep learning theory: the computation of the Neural Scaling Law exponents and the implementation of hyperparameter transferability, by analytically exploiting the predictive capabilities of the aforementioned foundational theories. SM-DeepResNet synergizes the applicant’s core competency in computational physics with the supervisors' expertise in statistical mechanics (host institution) and in deep learning mathematics (associated partner). The main purpose of this broad program is to unveil the entangled roles of structured data, width and depth in overparameterized deep residual neural networks, ultimately contributing to the development of effective strategies for the next generation of AI architectures."