The Cost of a Physics Prior Is Bounded by the Ablation Gap
Shape-constrained and physics-informed learning reports an accuracy cost of enforcing a prior and treats it as a property of the prior. We show it is mostly a property of the free features and the validation split. Let P be the excess risk of restricting a hypothesis class to functions with a shape constraint on features S, and D the excess risk of the ablated model that ignores S. Because a function constant in x_j is both non-decreasing and non-increasing in x_j, the ablated class is contained in the constrained class, so 0 <= P <= D for every risk functional, with no convexity, smoothness, or realizability assumption. Empirically the bound is a sign test: a constrained model must never...
| Authors | Boris Kriuk |
|---|---|
| Primary category | cs.AI |
| Published | 21 August 2026 |
| Last updated at source | 21 August 2026 |
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