Position: Solve Layerwise Linear Models First to Understand Neural Dynamical Phenomena (Neural Collapse, Emergence, Lazy/Rich Regime, and Grokking)
Abstract
In physics, complex systems are often simplified into minimal, solvable models that retain only the core principles. In machine learning, layerwise linear models (e.g., linear neural networks) act as simplified representations of neural network dynamics. These models follow the dynamical feedback principle, which describes how layers mutually govern and amplify each other’s evolution. This principle extends beyond the simplified models, successfully explaining a wide range of dynamical phenomena in deep neural networks, including neural collapse, emergence, lazy and rich regimes, and grokking. In this position paper, we call for the use of layerwise linear models retaining the core principles of neural dynamical phenomena to accelerate the science of deep learning.
Cite
Text
Nam et al. "Position: Solve Layerwise Linear Models First to Understand Neural Dynamical Phenomena (Neural Collapse, Emergence, Lazy/Rich Regime, and Grokking)." Proceedings of the 42nd International Conference on Machine Learning, 2025.Markdown
[Nam et al. "Position: Solve Layerwise Linear Models First to Understand Neural Dynamical Phenomena (Neural Collapse, Emergence, Lazy/Rich Regime, and Grokking)." Proceedings of the 42nd International Conference on Machine Learning, 2025.](https://mlanthology.org/icml/2025/nam2025icml-position/)BibTeX
@inproceedings{nam2025icml-position,
title = {{Position: Solve Layerwise Linear Models First to Understand Neural Dynamical Phenomena (Neural Collapse, Emergence, Lazy/Rich Regime, and Grokking)}},
author = {Nam, Yoonsoo and Lee, Seok Hyeong and Dominé, Clémentine Carla Juliette and Park, Yeachan and London, Charles and Choi, Wonyl and Göring, Niclas Alexander and Lee, Seungjai},
booktitle = {Proceedings of the 42nd International Conference on Machine Learning},
year = {2025},
pages = {81897-81929},
volume = {267},
url = {https://mlanthology.org/icml/2025/nam2025icml-position/}
}