  Enhancing generalization and uncertainty quantification in pre-trained
language models (PLMs) is crucial for their effectiveness and reliability.
Building on machine learning research that established the importance of
robustness for improving generalization, we investigate the role of
representation smoothness, achieved via Jacobian and Hessian regularization, in
enhancing PLM performance. Although such regularization methods have proven
effective in computer vision, their application in natural language processing
(NLP), where PLM inputs are derived from a discrete domain, poses unique
challenges. We introduce a novel two-phase regularization approach, JacHess,
which minimizes the norms of the Jacobian and Hessian matrices within PLM
intermediate representations relative to their inputs. Our evaluation using the
GLUE benchmark demonstrates that JacHess significantly improves in-domain
generalization and calibration in PLMs, outperforming unregularized fine-tuning
and other similar regularization methods.
