An Adaptive Tangent Feature Perspective of Neural Networks
This work offers theoretical insights into neural network feature learning, which is incremental for researchers in machine learning theory.
The paper tackles the problem of understanding feature learning in neural networks by proposing a framework that analyzes linear models in a tangent feature space with adaptive transformations, showing that this leads to an optimization with structured regularization encouraging low-rank solutions and providing insights into kernel alignment when target functions are poorly represented.
In order to better understand feature learning in neural networks, we propose a framework for understanding linear models in tangent feature space where the features are allowed to be transformed during training. We consider linear transformations of features, resulting in a joint optimization over parameters and transformations with a bilinear interpolation constraint. We show that this optimization problem has an equivalent linearly constrained optimization with structured regularization that encourages approximately low rank solutions. Specializing to neural network structure, we gain insights into how the features and thus the kernel function change, providing additional nuance to the phenomenon of kernel alignment when the target function is poorly represented using tangent features. We verify our theoretical observations in the kernel alignment of real neural networks.