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

arXiv: https://arxiv.org/abs/2605.05873 · HTML: https://mlsanity.com/paper/2605.05873/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 13 of its 43 references that are in the map.
- First posted on arXiv 7 May 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 13 of 13)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [FrontierScience: Evaluating AI's Ability to Perform Expert-Level Scientific Tasks](https://mlsanity.com/paper/2601.21165/) (2026)
- [ER-Reason: A Benchmark Dataset for LLM Clinical Reasoning in the Emergency Room](https://mlsanity.com/paper/2505.22919/) (2025)
- [Certified Self-Consistency: Statistical Guarantees and Test-Time Training for Reliable Reasoning in LLMs](https://mlsanity.com/paper/2510.17472/) (2025)
- [DynScaling: Efficient Verifier-free Inference Scaling via Dynamic and Integrated Sampling](https://mlsanity.com/paper/2506.16043/) (2025)
- [CGES: Confidence-Guided Early Stopping for Efficient and Accurate Self-Consistency](https://mlsanity.com/paper/2511.02603/) (2025)
- [Locally minimax optimal confidence sets for the best model](https://mlsanity.com/paper/2503.21639/) (2025)

## Built on by (most cited first, 2 of 2)

- [MARS: Margin-Adversarial Risk-controlled Stopping for Parallel LLM Test-time Scaling](https://mlsanity.com/paper/2606.12935/) (2026)
- [Adaptive Self-Consistency: From Black-Box Sampling to Distribution-Valued Feedback](https://mlsanity.com/paper/2609.38931/) (2026)

## Abstract (arXiv)

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.