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

arXiv: https://arxiv.org/abs/2606.08831 · HTML: https://mlsanity.com/paper/2606.08831/

## Key facts

- Cited by 3 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 11 of its 70 references that are in the map.
- First posted on arXiv 7 Jun 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, 11 of 11)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformal Prediction with Large Language Models for Multi-Choice Question Answering](https://mlsanity.com/paper/2305.18404/) (2023)
- [Faithful Reasoning Using Large Language Models](https://mlsanity.com/paper/2208.14271/) (2022)
- [Conformal Prediction Sets for Deep Generative Models via Reduction to Conformal Regression](https://mlsanity.com/paper/2503.10512/) (2025)
- [CONFLARE: CONFormal LArge language model REtrieval](https://mlsanity.com/paper/2404.04287/) (2024)
- [RF-GNN: Random Forest Boosted Graph Neural Network for Social Bot Detection](https://mlsanity.com/paper/2304.08239/) (2023)
- [Thinking with Nothinking Calibration: A New In-Context Learning Paradigm in Reasoning Large Language Models](https://mlsanity.com/paper/2508.03363/) (2025)
- [GraphMind: Theorem Selection and Conclusion Generation Framework with Dynamic GNN for LLM Reasoning](https://mlsanity.com/paper/2511.19078/) (2025)

## Built on by (most cited first, 3 of 3)

- [Certify or Refuse: A Cross-Model Map for Selective Risk Control with Coverage Floors under Covariate Shift](https://mlsanity.com/paper/2608.10893/) (2026)
- [Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Study](https://mlsanity.com/paper/2609.07395/) (2026)
- [G-CARB: Graph-Localized Conformal Agent Risk Budget for Compositional Harm](https://mlsanity.com/paper/2610.05563/) (2026)

## Abstract (arXiv)

Large language models (LLMs) increasingly perform multi-step reasoning, where intermediate claims form implicit directed acyclic graphs whose node correctness is structurally conditioned on their ancestors. This makes factuality uncertainty structural, rather than a trivial accumulation of node-wise errors, and necessitates inference-time uncertainty quantification over the reasoning structure. While conformal prediction (CP) offers flexible user-specified factuality control, existing work remains post-hoc and cannot intervene during generation. To fill the gap between CP's flexibility and its post-hoc limitation, we propose an Inference-Time Conformal Reasoning (ITCR) framework that integrates CP directly into reasoning graph generation. ITCR learns a structure-level factuality uncertainty function that aggregates claim-level factuality signals over reasoning graphs without complex modeling assumptions. We then design the non-conformity score based on graph-level factuality uncertainty and calibrate the conformal threshold to decide when to stop generation. We theoretically show such generation is nested, yielding valid coverage guarantees for factuality control. Experiments over multiple datasets and coverage objectives demonstrate empirically valid coverage. In downstream reasoning tasks, inference-time calibrated graphs yield more accurate generation than post-hoc pruned graphs.