In multi-output structured prediction tasks, while only one ground truth label may be provided in the training data, multiple equally valid outputs may be possible, making reliable evaluation a persistent challenge. We postulate that human evaluators implicitly use task-specific invariants, e.g., object boundaries in colorized images or named entities in translations, to judge if an output is acceptable. Under this assumption, we introduce a notion of approximate task-specific invariants and use them as diagnostic tools to evaluate a variety of existing metrics for vision and language tasks. We use these task invariants as part of a framework to systematically test metric reliability by encouraging domain-relevant invariants in model outputs via an augmented loss function. In our experiments, we observe that enforcing invariants with an augmented loss yields substantial improvements in popular distributional metrics while more traditional metrics change only marginally. Through this invariants-driven evaluation, we expose where standard metrics fail to detect meaningful differences, and we highlight the conditions under which distributional metrics succeed or still fall short.

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