Reasoning without Gold Standards: A Proxy-Judge Theory of Autoformalization
Autoformalization, the task of converting informal reasoning into machine-checkable formal proofs, has hit a scaling wall: expert-validated reference solutions don't exist at meaningful scale, and multiple valid formalizations exist for single arguments. This paper proposes a reference-free evaluation framework using structured property checks across multiple dimensions instead of exact-match scoring. The shift matters because it reframes how AI systems can be trained and evaluated on open-ended reasoning tasks where ground truth is ambiguous or expensive. This pattern extends beyond mathematics to any domain where correctness admits multiple valid solutions, reshaping how researchers approach training data scarcity in formal reasoning.
Modelwire context
ExplainerThe deeper provocation here is not about autoformalization specifically but about evaluation philosophy: the paper argues that proxy judges built from structured property checks can substitute for gold-standard reference solutions across any open-ended reasoning domain, which is a claim about measurement theory as much as it is about formal proof.
This connects directly to the graph isomorphism paper covered the same day ('Detecting Differences Is Not Understanding Structure'), which exposed how benchmark scores can be systematically misleading when evaluation design fails to probe the right properties. Both papers are circling the same underlying problem: current evaluation methods reward surface-level pattern matching rather than genuine structural correctness. The proxy-judge framework proposed here is essentially an attempt to build evaluation instruments that are harder to game by construction. The DecSelfMask paper from the same day also touches adjacent territory, using model-driven signal extraction as a substitute for expensive human annotation, which is the same resource-scarcity pressure driving reference-free evaluation in formal reasoning.
If a major formal verification benchmark adopts property-based proxy scoring within the next twelve months and published results show lower variance across model families than exact-match scoring, that would validate the core claim. If adoption stays confined to the original authors, the framework likely lacks the tooling to generalize.
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MentionsAutoformalization
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