LLM judges are increasingly being used to evaluate open-ended model responses, often in no-reference settings where a ground-truth answer is unavailable. However, can they reliably assess in such evaluation setups? We explore this question in this paper through a two stage pipeline with a) calibration experiments that assess the judge model's knowledge of the task it is evaluating, and b) sensitivity experiments that assess how the judge model's performance is impacted by the presence and positioning of the reference answer in the prompt. Across experiments covering three languages, we show that the judge models we evaluated tend to over-credit incorrect answers in the absence of a reference answer, and adding reference answer information to the prompt flips the judge model's correct/incorrect decisions by as much as 85% in some experimental settings. Comparison with a subset of human annotations shows that these reference-driven changes generally align with human judgments. Our results emphasize the need for calibrating the LLM judges with a sample with reference-aware evaluation before using them in reference-free setups reliably, and our methodology provides a blueprint for researchers and practitioners in doing such calibration of LLM judges for other tasks.
Complex reasoning tasks increasingly require systems to produce outputs whose correctness cannot be judged by exact match against a single reference. Autoformalization (AF) is a representative example; it asks a model to translate informal mathematical or logical reasoning into a formally checkable object, yet expert-validated formalizations do not scale beyond toy cases and a single informal argument can admit many valid formal renderings. Progress therefore depends on whether partial, structured proxies can substitute for exact references. We introduce a reference-free proxy-judge framework for AF that replaces gold-standard matching with a vector of per-axis property checks. The framework organizes the proxy along three structural scopes that cover global properties of the elicited object, per-module properties internal to its sub-components, and cross-domain properties that re-align it to the informal source, and aggregates each axis into a verdict vector. The vector drives a reflective refinement loop in which a violated coordinate routes the controller to a matching repair target, so each iteration changes only what is judged wrong. Under bounded judge noise, the expected intrinsic gap contracts geometrically to a noise-dependent plateau. Across seven formalization backbones on miniF2F, ProofNet, e-SNLI, and ProntoQA, refinement consistently lifts Pass Rate over the single-shot ICL baseline, and the per-axis proxy outperforms a matched scalar proxy on benchmarks where the baseline has room to improve. Structured proxy judgments therefore provide both a practical refinement signal and a theoretical handle on convergence when exact references are unavailable.