Establish the incremental benefit of derivative and curvature regularization

Determine whether derivative or curvature regularization provides an incremental predictive benefit over plain HermNet when evaluated under fixed-predictor experimental settings.

Background

The paper studies Gaussian derivative and curvature penalties as optional function-space regularizers that can be transformed consistently across polynomial bases. In the main jointly learned five-update experiment, curvature regularization improves HermNet, but separate fixed-predictor studies do not establish the same incremental effect. The unresolved issue is therefore whether these penalties improve plain HermNet itself, rather than merely preserving or enhancing a comparison-level advantage under particular jointly learned settings.