Huiyan Wang | Searcharxiv

arXiv2026

When is LLM-Based Program Reasoning Correct? A Completion Semantics for LLM-Based Code Inference

Due to token and cognitive limits, Large Language Models (LLMs) typically perform program reasoning over incomplete code fragments/prompts rather than complete programs. Such reasoning therefore must rely on {assumptions about omitted code and context. As a result, the meaning of an inference over a program fragment is not absolute, but depends on an implicit completion model describing how the fragment may be refined into a complete program. In this paper, we introduce completion semantics for LLM-based program reasoning. We formalize incomplete programs as denoting a space of possible refinements and define the correctness of existential inferences relative to a completion model. Under this view, a reported bug is correct whenever there exists a completion within the model that witnesses the bug. This perspective explains why many LLM-generated reports are neither simply correct nor incorrect, but instead depend on assumptions about omitted context. We have instantiated our approach in the form of a witness-generation workflow that concretizes completions underlying an inference by constructing executable refinements of the original program fragment. Witnesses serve both as evidence for existential claims and as a mechanism for exposing the assumptions required to support them. We evaluate our approach on real-world LLM-generated bug reports and program-analysis tasks. Our results show that witness generation effectively distinguishes inferences supported by plausible completions from those requiring unrealistic assumptions, providing a practical mechanism for validating reasoning over incomplete programs.

cs.PL↗

arXiv2025

LTA-thinker: Latent Thought-Augmented Training Framework for Large Language Models on Complex Reasoning

Complex Reasoning in Large Language Models can be dynamically optimized using Test-Time Scaling (TTS) to mitigate Overthinking. Methods such as Coconut, SoftCoT and its variant are effective in continuous latent space inference, the core bottleneck still lies in the efficient generation and utilization of high-quality Latent Thought. Drawing from the theory of SoftCoT++ that a larger variance in the generated Latent Thought distribution more closely approximates the golden truth distribution, we propose a Latent Thought-Augmented Training Framework--LTA-Thinker, which improves distributional variance and enhances reasoning performance from two perspectives. First, LTA-Thinker constructs a Latent Thought generation architecture based on a learnable prior. This architecture aims to increase the variance distribution of generated Latent Thought Vectors in order to simplify the overall structure and raise the performance ceiling. Second, LTA-Thinker introduces a distribution-based directional optimization paradigm that jointly constrains both distribution locality and distribution scale. This mechanism improves information efficiency and computational cost through a multi-objective co-training strategy, which combines standard Supervised Fine-Tuning (SFT) loss with two novel losses: Semantic Alignment Loss, which utilizes KL divergence to ensure that the Latent Thought is highly relevant to the semantics of the question; Reasoning Focus Loss, which utilizes a contrastive learning mechanism to guide the model to focus on the most critical reasoning steps. Experiments show that LTA-thinker achieves state-of-the-art (SOTA) performance among various baselines and demonstrates a higher performance ceiling and better scaling effects.

cs.AI↗