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