Emergence and scaling laws in SGD learning of shallow neural networks

The article titled "Emergence and scaling laws in SGD learning of shallow neural networks," published on November 5, 2025, investigates the dynamics of online stochastic gradient descent (SGD) when training a two-layer neural network. The study specifically employs isotropic Gaussian data as input, providing a controlled data distribution for analysis. Central to the research is the mathematical framework that characterizes the learning process, with particular attention to the properties of activation functions used within the network. This focus on activation functions sheds light on how they influence the behavior and efficiency of SGD in shallow architectures. The work aligns with recent contextual studies emphasizing online learning methods and shallow model types, reinforcing the relevance of SGD in contemporary machine learning research. By exploring these scaling laws and emergent phenomena, the article contributes to a deeper understanding of training dynamics in neural networks with limited depth. Overall, it offers valuable insights into the interplay between training methods, model structure, and data characteristics in the context of shallow neural network learning.