# Though Language Models Err While They Strive: Conformal Prediction for Self-Correcting Scientific Generation

arXiv: https://arxiv.org/abs/2607.16704 · HTML: https://mlsanity.com/paper/2607.16704/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 42 of its 66 references that are in the map.
- First posted on arXiv 18 Jul 2026.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 30 of 42)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [SciBERT: A Pretrained Language Model for Scientific Text](https://mlsanity.com/paper/1903.10676/) (2019)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [Galactica: A Large Language Model for Science](https://mlsanity.com/paper/2211.09085/) (2022)
- [ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate](https://mlsanity.com/paper/2308.07201/) (2023)
- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [Conformal Language Modeling](https://mlsanity.com/paper/2306.10193/) (2023)
- [Language Models with Conformal Factuality Guarantees](https://mlsanity.com/paper/2402.10978/) (2024)
- [Large language model validity via enhanced conformal prediction methods](https://mlsanity.com/paper/2406.09714/) (2024)
- [Batch Multivalid Conformal Prediction](https://mlsanity.com/paper/2209.15145/) (2022)
- [Practical Adversarial Multivalid Conformal Prediction](https://mlsanity.com/paper/2206.01067/) (2022)
- [A Theoretical Understanding of Self-Correction through In-context Alignment](https://mlsanity.com/paper/2405.18634/) (2024)
- [PhyX: Does Your Model Have the "Wits" for Physical Reasoning?](https://mlsanity.com/paper/2505.15929/) (2025)
- [On Structured Prediction Theory with Calibrated Convex Surrogate Losses](https://mlsanity.com/paper/1703.02403/) (2017)
- [Efficient Toxic Content Detection by Bootstrapping and Distilling Large Language Models](https://mlsanity.com/paper/2312.08303/) (2023)
- [Computing Full Conformal Prediction Set with Approximate Homotopy](https://mlsanity.com/paper/1909.09365/) (2019)
- [Enhancing Advanced Visual Reasoning Ability of Large Language Models](https://mlsanity.com/paper/2409.13980/) (2024)
- [Enhancing Intent Understanding for Ambiguous prompt: A Human-Machine Co-Adaption Strategy](https://mlsanity.com/paper/2501.15167/) (2025)
- [MedConv: Convolutions Beat Transformers on Long-Tailed Bone Density Prediction](https://mlsanity.com/paper/2502.00631/) (2025)
- [Conformal inference is (almost) free for neural networks trained with early stopping](https://mlsanity.com/paper/2301.11556/) (2023)
- [Conformal Language Model Reasoning with Coherent Factuality](https://mlsanity.com/paper/2505.17126/) (2025)
- [PDTrim: Targeted Pruning for Prefill-Decode Disaggregation in Inference](https://mlsanity.com/paper/2509.04467/) (2025)
- [Multimodal Multi-Agent Empowered Legal Judgment Prediction](https://mlsanity.com/paper/2601.12815/) (2026)
- [Neural Structured Prediction for Inductive Node Classification](https://mlsanity.com/paper/2204.07524/) (2022)

## Abstract (arXiv)

Large language models frequently violate fundamental scientific principles when generating technical content, undermining their reliability in scientific applications. We introduce Scientific Feasibility Control SFC, a graph-structured conformal prediction framework that provides statistical guarantees for scientific reasoning validity through progressive absolute-coherent-factuality validation. Our approach decomposes scientific reasoning into atomic absolute-coherent-factuality units requiring both individual correctness against physical laws and logical substantiation from preceding context, addressing the cascade effect where early scientific errors contaminate subsequent reasoning steps. Unlike independence-based methods that treat claims in isolation, SFC models logical dependencies as approximate deducibility graphs and operates through real-time validation with dynamic branching when scientific violations are detected, the system branches to alternative generation paths using verified context as foundation. We demonstrate SFC across established scientific reasoning benchmarks including PhyX multimodal physics, MATH, ScienceQA, and ARC Challenge, achieving 50.1 percent accuracy on PhyX physics reasoning, substantially outperforming recent reasoning models including DeepSeek-R1 49.8 percent and GPT-4 45.8 percent while providing 91.7 percent scientific validity with formal conformal coverage guarantees at alpha equals 0.10 confidence level and reducing scientific law violations by 73 percent across multiple model architectures.