While large language models (LLMs) augmented with agentic search capabilities show promise for legal reasoning, they overlook a fundamental constraint that applicable law must match the temporal context of each case, as retroactive application of statutes violates core legal principles and leads to erroneous conclusions. Our observations reveal that current legal LLMs suffer from temporal bias anchored to their training cutoff, while search agents rarely incorporate temporal constraints into queries, and that web search alone cannot provide the precise statute and precedent citations that legal reasoning demands. To address these challenges, we propose LegalSearch-R1, an end-to-end reinforcement learning framework that pairs local statute RAG for precise article matching with online web search for broader legal knowledge, trained on temporally-indexed data spanning multiple amendment periods to enforce temporal consistency. Extensive experiments on our benchmark covering 13 legal tasks demonstrate that our 7B-parameter agent outperforms state-of-the-art deep research frameworks and specialized legal LLMs by 12.9% to 29.8%, surpasses baselines by 57.7% to 80.3% on temporal consistency, and exhibits robust out-of-domain generalization. The code and data are available at https://anonymous.4open.science/r/LegalSearch-R1.

Accurately assessing model confidence is essential for deploying large language models (LLMs) in mission-critical factual domains. While retrieval-augmented generation (RAG) is widely adopted to improve grounding, confidence calibration in RAG settings remains poorly understood. We conduct a systematic study across four benchmarks, revealing that LLMs exhibit poor calibration performance especially when noisy contexts are retrieved. Specifically, contradictory or irrelevant evidence tends to exacerbate the model’s overconfidence issue. To address this, we propose *NOVA Rules* (**NO**ise-aware **V**erbal Confidence C**A**Libration Rules) to provide a principled foundation for resolving overconfidence under noise. We further design **NOVA**, a noise-aware calibration framework that synthesizes supervision from ~2K HotpotQA examples guided by these rules. By performing supervised fine-tuning (SFT) with this data, NOVA equips models with intrinsic noise awareness without relying on stronger teacher models. Empirical results show that NOVA yields substantial gains, improving ECE scores by 10.9% in-domain and 8.0% out-of-domain. By bridging the gap between retrieval noise and verbal calibration, NOVA paves the way for both accurate and epistemically reliable LLMs.

Legal rules encompass not only codified statutes but also implicit adjudicatory principles derived from precedents that contain discretionary norms, social morality, and policy. While computational legal research has advanced in applying established rules to cases, inducing legal rules from judicial decisions remains understudied across jurisdictions. The advent of Large Language Models (LLMs) offers unprecedented potential to automate the extraction of such latent principles, yet progress is stymied by the absence of formal task definitions and benchmarks. To address this gap, we formalize Legal Rule Induction (LRI) as the task of deriving concise, generalizable doctrinal rules from analogous precedents, distilling their shared preconditions, normative behaviors, and legal consequences. We further propose a reproducible pipeline for LRI dataset construction and, instantiating it on Chinese law as a representative jurisdiction, introduce the first LRI benchmark comprising 5,121 case sets (38,088 court cases) for model tuning and 216 expert-annotated gold test sets. Experimental results reveal that: 1) State-of-the-art LLMs struggle with over-generalization and hallucination; 2) Training on our dataset markedly enhances LLMs’ capabilities in capturing nuanced rule patterns across similar cases.

We present AutoSchemaKG, a framework for fully autonomous knowledge graph construction that eliminates the need for predefined schemas. Our system leverages large language models to simultaneously extract knowledge triples and induce comprehensive schemas directly from text, modeling both entities and events while employing conceptualization to organize instances into semantic categories. Processing over 50 million documents, we construct ATLAS (Automated Triple Linking And Schema induction), a family of knowledge graphs with 900+ million nodes and 5.9 billion edges. This approach outperforms state-of-the-art baselines on multi-hop QA tasks and enhances LLM factuality. Notably, our schema induction achieves 92% semantic alignment with human-crafted schemas with zero manual intervention, demonstrating that billion-scale knowledge graphs with dynamically induced schemas can effectively complement parametric knowledge in large language models.

Large Language Model (LLM) routing is a pivotal technique for navigating a diverse landscape of LLMs, enabling the selection of the best-performing LLMs for specific user queries while balancing performance and cost. However, current routing approaches often face limitations in scalability when dealing with a large pool of specialized LLMs, or in their adaptability to extending model scope and evolving capability domains. To overcome those challenges, we propose InferenceDynamics, a flexible and scalable multi-dimensional routing framework by modeling the capability and knowledge of models. We operate it on our comprehensive dataset RouteMix, and demonstrate its effectiveness and generalizability in group-level routing using modern benchmarks including MMLU-Pro, GPQA, BigGenBench, and LiveBench, showcasing its ability to identify and leverage top-performing models for given tasks, leading to superior outcomes with cost efficiency. The broader adoption of InferenceDynamics can empower users to harness the full specialized potential of the LLM ecosystem, and our code will be made publicly available to encourage further research.

Inductive reasoning, a cornerstone of human cognition, enables generalization from limited data but hasn’t yet been fully achieved by large language models (LLMs). While modern LLMs excel at reasoning tasks, their ability to maintain stable and consistent rule abstraction under imperfect observations remains underexplored. To fill this gap, in this work, we introduce Robust Rule Induction, a task that evaluates LLMs’ capability in inferring rules from data that are fused with noisy examples. To address this task, we further propose Sample-steered Rule Refinement (SRR), a method enhancing reasoning stability via observation diversification and execution-guided feedback. Experiments across arithmetic, cryptography, and list functions reveal: (1) SRR outperforms other methods with minimal performance degradation under noise; (2) Despite slight accuracy variation, LLMs exhibit instability under noise (e.g., 0 accuracy change with only 70 consistent score);(3) Counterfactual task gaps highlight LLMs’ reliance on memorized patterns over genuine abstraction. Our findings challenge LLMs’ reasoning robustness, revealing susceptibility to hypothesis drift and pattern overfitting, while providing empirical evidence critical for developing human-like inductive systems.

Modern large language models (LLMs) employ diverse logical inference mechanisms for reasoning, making the strategic optimization of these approaches critical for advancing their capabilities. This paper systematically investigate the comparative dynamics of inductive (System 1) versus abductive/deductive (System 2) inference in LLMs. We utilize a controlled analogical reasoning environment, varying modality (textual, visual, symbolic), difficulty, and task format (MCQ / free-text). Our analysis reveals System 2 pipelines generally excel, particularly in visual/symbolic modalities and harder tasks, while System 1 is competitive for textual and easier problems. Crucially, task format significantly influences their relative advantage, with System 1 sometimes outperforming System 2 in free-text rule-execution. These core findings generalize to broader in-context learning. Furthermore, we demonstrate that advanced System 2 strategies like hypothesis selection and iterative refinement can substantially scale LLM reasoning. This study offers foundational insights and actionable guidelines for strategically deploying logical inference to enhance LLM reasoning.

Event Factuality Detection (EFD) task determines the factuality of textual events, i.e., classifying whether an event is a fact, possibility, or impossibility, which is essential for faithfully understanding and utilizing event knowledge. However, due to the lack of high-quality large-scale data, event factuality detection is under-explored in event understanding research, which limits the development of EFD community. To address these issues and provide faithful event understanding, we introduce MAVEN-FACT, a large-scale and high-quality EFD dataset based on the MAVEN dataset. MAVEN-FACT includes factuality annotations of 112,276 events, making it the largest EFD dataset. Extensive experiments demonstrate that MAVEN-FACT is challenging for both conventional fine-tuned models and large language models (LLMs). Thanks to the comprehensive annotations of event arguments and relations in MAVEN, MAVEN-FACT also supports some further analyses and we find that adopting event arguments and relations helps in event factuality detection for fine-tuned models but does not benefit LLMs. Furthermore, we preliminarily study an application case of event factuality detection and find it helps in mitigating event-related hallucination in LLMs. We will release our dataset and codes to facilitate further research on event factuality detection.

The sequential process of conceptualization and instantiation is essential to generalizable commonsense reasoning as it allows the application of existing knowledge to unfamiliar scenarios. However, existing works tend to undervalue the step of instantiation and heavilyrely on pre-built concept taxonomies and human annotations to collect both types of knowledge, resulting in a lack of instantiated knowledge to complete reasoning, high cost, and limited scalability. To tackle these challenges, we introduce CANDLE (ConceptuAlizationand INstantiation Distillation from Large Language ModEls), a distillation framework that iteratively performs contextualized conceptualization and instantiation over commonsense knowledge bases by instructing large language models to generate both types of knowledge with critic filtering. By applying CANDLE to ATOMIC (Sap et al., 2019a), we construct a comprehensive knowledge base comprising six million conceptualizations and instantiated commonsense knowledge triples. Both types of knowledge are firmly rooted in the original ATOMIC dataset, and intrinsic evaluations demonstrate their exceptional quality and diversity. Empirical results indicate that distilling CANDLE on student models provides benefits across three downstream tasks. Our data and models are publicly available at https://github.com/HKUST-KnowComp/CANDLE.