Long chain-of-thought (CoT) reasoning improves the performance of large language models, yet hallucinations in such settings often emerge subtly and propagate across reasoning steps. We suggest that hallucination in long CoT reasoning is better understood as an evolving latent state rather than a one-off erroneous event. Accordingly, we treat step-level hallucination judgments as local observations and introduce a cumulative prefix-level hallucination signal that tracks the global evolution of the reasoning state over the entire trajectory. Overall, our approach enables streaming hallucination detection in long CoT reasoning, providing real-time, interpretable evidence.

Personalized large language models (LLMs) adapt model behavior to individual users to enhance user satisfaction, yet personalization can inadvertently distort factual reasoning. We show that when personalized LLMs face factual queries, there exists a phenomenon where the model generates answers aligned with a user’s prior history rather than the objective truth, resulting in **personalization-induced hallucinations** that degrade factual reliability and may propagate incorrect beliefs, due to representational entanglement between personalization and factual representations. To address this issue, we propose **Factuality-Preserving Personalized Steering (FPPS)**, a lightweight inference-time approach that mitigates personalization-induced factual distortions while preserving personalized behavior. We further introduce **PFQABench**, the first benchmark designed to jointly evaluate factual and personalized question answering under personalization. Experiments across multiple LLM backbones and personalization methods show that FPPS substantially improves factual accuracy while maintaining personalized performance.

Reinforcement Learning with Verifiable Rewards (RLVR) has become a central approach for improving the reasoning ability of large language models. Recent work studies RLVR through token entropy, arguing that high-entropy tokens drive exploration and should receive stronger updates. However, they overlook the fact that most of a reasoning trajectory consists of low-entropy segments that encode stable and reusable structural patterns. Through qualitative and quantitative analyses, we find that the overlap of low-entropy segments across correct responses strongly correlates with model accuracy, while overlaps involving incorrect responses exhibit stable but unproductive patterns. Motivated by these findings, we propose LESS, a correctness-aware reinforcement framework that performs fine-grained advantage modulation over low-entropy segments. LESS amplifies segments unique to correct responses, suppresses those unique to incorrect ones, and neutralizes segments shared by both, while preserving high-entropy exploration in the underlying RL algorithm. Instantiated on top of GRPO and GSPO, LESS not only improves accuracy over strong RL baselines across three backbones and six math benchmarks, but also achieves stronger robustness of the performance floor.

In-context learning has been extensively validated in large language models. However, the mechanism and selection strategy for in-context example selection, which is a crucial ingredient in this approach, lacks systematic and in-depth research. In this paper, we propose a data compression approach to the selection of in-context examples. We introduce a two-stage method that can effectively choose relevant examples and retain sufficient information about the training dataset within the in-context examples. Our method shows a significant improvement of an average of 5.90% across five different real-world datasets using four language models.

In this paper, we address the issue of using logic rules to explain the results from legal case retrieval. The task is critical to legal case retrieval because the users (e.g., lawyers or judges) are highly specialized and require the system to provide logic, faithful, and interpretable explanations before making legal decisions. Recently, research efforts have been made to learn explainable legal case retrieval models. However, these methods usually select rationales (key sentences) from the legal cases as explanations, failing to provide faithful and logicly correct explanations. In this paper, we propose Neural-Symbolic enhanced Legal Case Retrieval (NS-LCR), a framework that explicitly conducts reasoning on the matching of legal cases through learning case-level and law-level logic rules. The learned rules are then integrated into the retrieval process in a neuro-symbolic manner. Benefiting from the logic and interpretable nature of the logic rules, NS-LCR is equipped with built-in faithful explainability. We also show that NS-LCR is a model-agnostic framework that can be plug-in for multiple legal retrieval models. To demonstrate the superiority of NS-LCR, we extend the benchmarks of LeCaRD and ELAM with manually annotated logic rules and propose a new explainability measure based on Large Language Models (LLMs). Extensive experiments show that NS-LCR can achieve state-of-the-art ranking performances, and the empirical analysis also showed that NS-LCR is capable of providing faithful explanations for legal case retrieval.