Xinqing Ma

Zenan Li, Zhaoyu Li, Kaiyu Yang et al.

Mathematical reasoning demands two critical, complementary skills: constructing rigorous proofs for true statements and discovering counterexamples that disprove false ones. However, current AI efforts in mathematics focus almost exclusively on proof construction, often neglecting the equally important task of finding counterexamples. In this paper, we address this gap by fine-tuning large language models (LLMs) to reason about and generate counterexamples. We formalize this task as formal counterexample generation, which requires LLMs not only to propose candidate counterexamples but also to produce formal proofs that can be automatically verified in the Lean 4 theorem prover. To enable effective learning, we introduce a symbolic mutation strategy that synthesizes diverse training data by systematically extracting theorems and discarding selected hypotheses, thereby producing diverse counterexample instances. Together with curated datasets, this strategy enables a multi-reward expert iteration framework that substantially enhances both the effectiveness and efficiency of training LLMs for counterexample generation and theorem proving. Experiments on three newly collected benchmarks validate the advantages of our approach, showing that the mutation strategy and training framework yield significant performance gains.

Senrong Xu, Tianyu Wang, Zenan Li et al.

Conformal prediction (CP) provides a comprehensive framework to produce statistically rigorous uncertainty sets for black-box machine learning models. To further improve the efficiency of CP, conformal correction is proposed to fine-tune or wrap the base model with an extra module using a conformal-aware inefficiency loss. In this work, we empirically and theoretically identify a trade-off between the CP efficiency and the entropy of model prediction. We then propose an entropy-constrained conformal correction method, exploring a better Pareto optimum between efficiency and entropy. Extensive experimental results on both computer vision and graph datasets demonstrate the efficacy of the proposed method. For instance, it can significantly improve the efficiency of state-of-the-art CP methods by up to 34.4%, given an entropy threshold.

Xiaolin Yan, Yangxing Liu, Jiazhang Zheng et al.

Large language models (LLMs) have recently achieved significant advances in reasoning and demonstrated their advantages in solving challenging problems. Yet, their effectiveness in the semiconductor display industry remains limited due to a lack of domain-specific training and expertise. To bridge this gap, we present X-Intelligence 3.0, the first high-performance reasoning model specifically developed for the semiconductor display industry. This model is designed to deliver expert-level understanding and reasoning for the industry's complex challenges. Leveraging a carefully curated industry knowledge base, the model undergoes supervised fine-tuning and reinforcement learning to enhance its reasoning and comprehension capabilities. To further accelerate development, we implemented an automated evaluation framework that simulates expert-level assessments. We also integrated a domain-specific retrieval-augmented generation (RAG) mechanism, resulting in notable performance gains on benchmark datasets. Despite its relatively compact size of 32 billion parameters, X-Intelligence 3.0 outperforms SOTA DeepSeek-R1-671B across multiple evaluations. This demonstrates its exceptional efficiency and establishes it as a powerful solution to the longstanding reasoning challenges faced by the semiconductor display industry.