Robust Fine-Tuning of Deep Neural Networks with Hessian-based Generalization Guarantees

TL;DR

This paper introduces a Hessian-based distance measure for analyzing and improving the generalization of fine-tuned deep neural networks, especially under small datasets and noisy labels, supported by theoretical bounds and empirical results.

Contribution

It proposes a Hessian-based generalization measure for fine-tuning, provides theoretical bounds, and develops an algorithm to mitigate overfitting with noisy labels.

Findings

Hessian-based distance correlates with generalization gaps

Theoretical bounds for Hessian-based generalization

Algorithm improves performance on noisy label datasets

Abstract

We consider fine-tuning a pretrained deep neural network on a target task. We study the generalization properties of fine-tuning to understand the problem of overfitting, which has often been observed (e.g., when the target dataset is small or when the training labels are noisy). Existing generalization measures for deep networks depend on notions such as distance from the initialization (i.e., the pretrained network) of the fine-tuned model and noise stability properties of deep networks. This paper identifies a Hessian-based distance measure through PAC-Bayesian analysis, which is shown to correlate well with observed generalization gaps of fine-tuned models. Theoretically, we prove Hessian distance-based generalization bounds for fine-tuned models. We also describe an extended study of fine-tuning against label noise, where overfitting remains a critical problem. We present an algorithm and a generalization error guarantee for this algorithm under a class conditional independent noise model. Empirically, we observe that the Hessian-based distance measure can match the scale of the observed generalization gap of fine-tuned models in practice. We also test our algorithm on several image classification tasks with noisy training labels, showing gains over prior methods and decreases in the Hessian distance measure of the fine-tuned model.