  We address the problem of enhancing model robustness through regularization.
Specifically, we focus on methods that regularize the model posterior
difference between clean and noisy inputs. Theoretically, we provide a
connection of two recent methods, Jacobian Regularization and Virtual
Adversarial Training, under this framework. Additionally, we generalize the
posterior differential regularization to the family of $f$-divergences and
characterize the overall regularization framework in terms of Jacobian matrix.
Empirically, we systematically compare those regularizations and standard BERT
training on a diverse set of tasks to provide a comprehensive profile of their
effect on model in-domain and out-of-domain generalization. For both fully
supervised and semi-supervised settings, our experiments show that regularizing
the posterior differential with $f$-divergence can result in well-improved
model robustness. In particular, with a proper $f$-divergence, a BERT-base
model can achieve comparable generalization as its BERT-large counterpart for
in-domain, adversarial and domain shift scenarios, indicating the great
potential of the proposed framework for boosting model generalization for NLP
models.
