NL-PAC: Specification Ambiguity and Certified Minimax Risk Floors in LLM-Mediated Supervision

What the math gives to ML

The paper provides a constructive way to detect when natural-language supervision from a frozen LLM is fundamentally non-identifying rather than merely noisy. Its key transferable asset is the pointwise admissible target set induced by the model's decoded label distribution: the measure of inputs with multiple admissible labels gives an explicit, sample-size-independent minimax risk floor. In neural-network training, this can become an ambiguity certificate and a gating mechanism: downweight or abstain on examples whose prompt-conditioned label distribution supports competing readings, while retaining ordinary supervision on unambiguous examples. The method is most directly useful for LLM-generated labels, preference data, evaluation sets, and weak supervision, rather than as a general optimizer or architecture.