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

Researchers propose CITE, an algorithm that enables reliable certification of Large Language Model outputs through multiple sampling while controlling error rates under data-dependent stopping conditions. The method addresses a critical challenge in LLM reliability by providing statistical guarantees without requiring advance knowledge of possible answer categories.

The paper tackles a fundamental problem in deploying Large Language Models: determining when to stop sampling outputs and how to confidently certify that a particular answer represents the true mode of the model's response distribution. Current self-consistency approaches in LLMs lack rigorous statistical guarantees about false certification rates, making them unsuitable for high-stakes applications requiring error control.

The CITE algorithm introduces anytime-valid statistical inference through intersection-union testing with e-processes, a sophisticated mathematical framework. This approach is particularly valuable because stopping decisions can be made adaptively based on observed data without sacrificing statistical rigor. The researchers prove the algorithm controls false certification at prescribed error levels regardless of when sampling halts, and establish minimax optimal rates that demonstrate efficiency. The category-set-size-free property is significant because LLMs can generate diverse outputs, and practitioners often cannot enumerate all possible answers beforehand.

For the AI development community, this work bridges a critical gap between practical LLM deployment and statistical soundness. While self-consistency has become standard for improving reasoning in language models, having formal error control enables applications in medicine, law, and finance where certification accuracy directly impacts outcomes. The extension to confidence-weighted voting shows the method's flexibility.

The research signals growing maturity in AI reliability frameworks. As LLMs become increasingly integrated into decision-critical systems, techniques for provable error control become commercially valuable. Future implications include regulatory compliance advantages and competitive positioning for AI systems that can demonstrate statistical guarantees. The matching lower bounds suggest limited room for algorithmic improvement, establishing these results as reference standards.

• →CITE algorithm provides provably controlled false certification rates for LLM outputs without requiring prior knowledge of answer categories
• →The method enables adaptive data-driven stopping rules while maintaining statistical guarantees, addressing a critical deployment challenge
• →Minimax optimal rates are established with matching lower bounds, indicating theoretical efficiency of the approach
• →Anytime-valid certification framework makes LLM outputs more suitable for high-stakes applications requiring formal error control
• →Empirical results demonstrate improved performance in diffuse-tail settings relevant to real-world LLM behavior