Quantifying and Optimizing Simplicity via Polynomial Representations

arXiv:2605.29823v1 Announce Type: new Abstract: Deep networks often exhibit a preference for "simple" solutions, and such a simplicity bias is widely believed to play a key role in generalization. Yet a broadly applicable, quantitative measure of simplicity remains elusive. We introduce polynomial representations as a distribution-aware, low-dimensional surrogate for neural functions: we approximate a network's predictive behavior along data-dependent interpolation paths using orthogonal polynom