The Structure Gap: When More Data Cannot Replace Structured Reasoning
AspireAI community · arXiv (cs.LG / cs.AI)
*There is a class of problem where training on more examples never quite closes the gap, and a new paper proves it.* The authors call it the structure gap: the finite-resource gap between a method that gets the governing structure and a learner that only gets examples. For a Gaussian inverse problem they prove the known-operator Wiener solver attains Bayes risk, while a dense learner in the correct linear class keeps a persistent excess risk that data alone does not remove.
They also prove a cell-coverage lower bound and an unobserved-orbit non-identifiability result. The honest limit: the claim is asymptotic, not absolute, and it holds for structure-encoded tasks.
https://arxiv.org/abs/2610.37523
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