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Inference-Time Conformal Reasoning with Valid Factuality Control for Large Language Models

ICML 2026 · Large language models › Reasoning and chain of thought · approach: Efficient and adaptive thinking · 0 citations (OpenAlex)

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Proposes Inference-Time Conformal Reasoning (ITCR), which integrates conformal prediction into reasoning-graph generation with a nested, size-penalized non-conformity score so generation stops when a calibrated threshold is crossed, yielding no-false and no-miss coverage guarantees.

Problem

Post-hoc conformal factuality control over LLM reasoning graphs cannot intervene during generation, and node-wise uncertainty ignores ancestor dependencies in multi-step reasoning.

Approach

Learn a graph-level factuality uncertainty function over ancestor-closed subgraphs and add a size penalty lambda*|V_U| so the non-conformity score is monotone under expansion; calibrate a threshold and stop expansion when it is crossed, giving nested subgraphs and valid coverage at inference time.

Key results

• ITCR achieves valid coverage (within 0.01 tolerance) on MATH, GSM8K and QA for no-miss and no-false targets at alpha 0.05 and 0.1, with best efficiency among valid methods (e.g., MATH no-false alpha=0.1 efficiency 34.77% vs ITCR-MAX 35.72% which is also valid but ITCR-MAX has 35.72 bolded).
• Downstream correction: ITCR yields PCR-NCR of 26.87 vs -58.08 for PostCal on GSM8K with LLaMA-3.1-8B; reported average improvement of 18.77%.
• ITCR uses fewer tokens and lower runtime than PostCal across three backbones on GSM8K (e.g., LLaMA 1919.50 vs 2092.80 tokens).

Surprising findings

• Heuristic aggregations such as ITCR-SUM and ITCR-AVG frequently fail coverage in the no-miss setting, and CPL fails coverage in most no-miss settings.
• In the no-false MATH setting, ITCR-MAX and ITCR-SUM reach higher efficiency numbers only when valid; ITCR-SUM retains 0% nodes at alpha=0.05 on MATH no-false.

Limitations

• Guarantees assume exchangeability between calibration and test graphs; distribution shift can break coverage.
• Guarantee is defined with respect to the constructed reasoning graph and its factuality labels; imperfect claim decomposition or dependency extraction may affect semantic factuality.
• Dependency graphs are produced by LLM prompting; on the sample study 90% of examples were linear chains, limiting evaluation of genuine DAG structure.

Experimental setup

Datasets: MATH GSM8K QA world-knowledge benchmark (from prior CPL work)

Benchmarks: MATH GSM8K QA

Metrics: empirical coverage (no-miss, no-false) retained/removed node efficiency PCR NCR PCR-NCR token usage runtime

Baselines: CPL ITCR-MAX ITCR-SUM ITCR-AVG PostCal

Builds on: conformal language modeling coherent factuality (CPL) conformal prediction

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