A new framework called bulk-boundary decomposition has been introduced to enhance our understanding of how deep neural networks train. This approach reorganizes the Lagrangian into two parts: a data-independent bulk term that reflects the network's architecture and a data-dependent boundary term that captures stochastic interactions.

This article explores the complexities of online stochastic gradient descent (SGD) in training a two-layer neural network using isotropic Gaussian data. It delves into the mathematical framework and implications of the learning process, particularly focusing on the activation functions and their properties.

This article explores the scaling laws in kernel regression, focusing on loss dynamics and how learning rate schedules influence them. It highlights the gaps in current research, which mainly looks at final-step loss, and provides a theoretical analysis using stochastic gradient descent.

A recent study explores a continuous-time approach to stochastic gradient descent, revealing important conditions for convergence that enhance our understanding of training deep neural networks. This research builds on previous work by Chatterjee and is significant because it addresses challenges in minimizing expected loss in learning problems, particularly in the context of overparametrized models. Such advancements could lead to more efficient training methods in machine learning, making it a noteworthy development in the field.