Mingqiao Mo

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.

Dependency-Guided Code Generation: Structured Matrix Decomposition and Consistency-Guided Refinement

The increasing complexity of modern software systems has made automated code generation a fundamental task in software engineering. However, existing approaches often fail to adequately capture the intricate, multi-level dependencies among code entities, leading to generated code that is logically incomplete or difficult to integrate into real-world systems. To address this limitation, we propose a dependency-aware code generation framework that explicitly models interactions among code entities through a graph-based representation. We decompose dependencies into two complementary components: a quantized matrix that captures strong, explicit relations, and a sparse low-rank factorization that models weaker, implicit interactions. The decomposition is efficiently learned via an alternating optimization procedure. During code generation, the learned dependency structure is incorporated as a constraint, ensuring both semantic coherence and structural consistency of the generated code. Furthermore, we introduce a sparse triplet representation for strong dependencies, significantly improving storage efficiency and computational scalability. Extensive experiments demonstrate that our approach consistently produces code with superior semantic alignment and structural fidelity compared to existing methods.

PathSymphony: Harmonizing symbolic planning and Large Language Models for curriculum-guided mathematical reasoning