Three Mechanisms of Feature Learning in a Linear Network
Keywords: solvable model, feature learning, neural tangent kernel
Abstract: Understanding the dynamics of neural networks in different width regimes is crucial for improving their training and performance. We present an exact solution for the learning dynamics of a one-hidden-layer linear network, with one-dimensional data, across any finite width, uniquely exhibiting both kernel and feature learning phases. This study marks a technical advancement by enabling the analysis of the training trajectory from any initialization and a detailed phase diagram under varying common hyperparameters such as width, layer-wise learning rates, and scales of output and initialization. We identify three novel prototype mechanisms specific to the feature learning regime: (1) learning by alignment, (2) learning by disalignment, and (3) learning by rescaling, which contrast starkly with the dynamics observed in the kernel regime. Our theoretical findings are substantiated with empirical evidence showing that these mechanisms also manifest in deep nonlinear networks handling real-world tasks, enhancing our understanding of neural network training dynamics and guiding the design of more effective learning strategies.
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 5039
Loading