Rethinking Influence Functions of Neural Networks in the Over-parameterized Regime

Abstract

Understanding the black-box prediction for neural networks is challenging. To achieve this, early studies have designed influence function (IF) to measure the effect of removing a single training point on neural networks. However, the classic implicit Hessian-vector product (IHVP) method for calculating IF is fragile, and theoretical analysis of IF in the context of neural networks is still lacking. To this end, we utilize the neural tangent kernel (NTK) theory to calculate IF for the neural network trained with regularized mean-square loss, and prove that the approximation error can be arbitrarily small when the width is sufficiently large for two-layer ReLU networks. We analyze the error bound for the classic IHVP method in the over-parameterized regime to understand when and why it fails or not. In detail, our theoretical analysis reveals that (1) the accuracy of IHVP depends on the regularization term, and is pretty low under weak regularization; (2) the accuracy of IHVP has a significant correlation with the probability density of corresponding training points. We further borrow the theory from NTK to understand the IFs better, including quantifying the complexity for influential samples and depicting the variation of IFs during the training dynamics. Numerical experiments on real-world data confirm our theoretical results and demonstrate our findings.

To appear in AAAI 2022

References in corpus (9)

• Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks
• Gradient Descent with Early Stopping is Provably Robust to Label Noise for Overparameterized Neural Networks
• Enhanced Convolutional Neural Tangent Kernels
• Diverse Neural Network Learns True Target Functions
• Neural Tangents: Fast and Easy Infinite Neural Networks in Python
• Distillation $\approx$ Early Stopping? Harvesting Dark Knowledge Utilizing Anisotropic Information Retrieval For Overparameterized Neural Network
• Repairing without Retraining: Avoiding Disparate Impact with Counterfactual Distributions
• HYDRA: Hypergradient Data Relevance Analysis for Interpreting Deep Neural Networks
• Understanding Instance-based Interpretability of Variational Auto-Encoders

Cited by in corpus (2)

• Training Data Influence Analysis and Estimation: A Survey
• Identifying a Training-Set Attack's Target Using Renormalized Influence Estimation