Shortcut Features as Top Eigenfunctions of NTK: A Linear Neural Network Case and More

TL;DR

This paper analyzes shortcut learning in neural networks through the lens of NTK eigenfunctions, revealing that shortcut features with larger eigenvalues dominate the learned representations, a phenomenon observed in both linear and more complex networks.

Contribution

It introduces a novel eigenfunction perspective of NTK to explain shortcut learning, extending findings from linear to nonlinear neural networks.

Findings

Shortcut features correspond to larger NTK eigenvalues.

Large eigenvalue features influence network output even after training.

Shortcut learning persists beyond max-margin bias explanations.

Abstract

One of the chronic problems of deep-learning models is shortcut learning. In a case where the majority of training data are dominated by a certain feature, neural networks prefer to learn such a feature even if the feature is not generalizable outside the training set. Based on the framework of Neural Tangent Kernel (NTK), we analyzed the case of linear neural networks to derive some important properties of shortcut learning. We defined a feature of a neural network as an eigenfunction of NTK. Then, we found that shortcut features correspond to features with larger eigenvalues when the shortcuts stem from the imbalanced number of samples in the clustered distribution. We also showed that the features with larger eigenvalues still have a large influence on the neural network output even after training, due to data variances in the clusters. Such a preference for certain features remains even when a margin of a neural network output is controlled, which shows that the max-margin bias is not the only major reason for shortcut learning. These properties of linear neural networks are empirically extended for more complex neural networks as a two-layer fully-connected ReLU network and a ResNet-18.