CITE: Anytime-Valid Statistical Inference in LLM Self-Consistency

• URL: http://arxiv.org/abs/2605.05873v1
• Date: Thu, 07 May 2026 08:41:51 GMT
• Title: CITE: Anytime-Valid Statistical Inference in LLM Self-Consistency
• Abstract summary: We study anytime-valid certification of a prespecified target answer as unique mode of the model's response distribution.<n>We propose the Certification by Intersection-union Testing with E-processes (CITE) algorithm, which provably controls false certification at any prescribed level.<n>We also prove an category-set-size-free stopping-time rate, establish matching minimax lower bounds up to constants in the main regime, and extend the construction to confidence-weighted voting.
• Score: 10.34950275095264
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large language models often improve reasoning by sampling multiple outputs and aggregating their final answers, but precise and efficient control of error levels remains a challenging task. In particular, deciding when to stop sampling remains difficult when the stopping rule is data-dependent and the set of possible answers is not known in advance. We study anytime-valid certification of a prespecified target answer as the unique mode of the model's response distribution, a guarantee distinct from answer correctness. We propose the Certification by Intersection-union Testing with E-processes (CITE) algorithm, which provably controls false certification at any prescribed level under arbitrary data-driven stopping, without requiring prior knowledge of the answer category set. We also prove an category-set-size-free stopping-time rate, establish matching minimax lower bounds up to constants in the main regime, and extend the construction to confidence-weighted voting. Simulations and LLM self-consistency experiments show empirical error control and improved certification in diffuse-tail settings.

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