  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.
