arXiv:2605.25920v1 Announce Type: cross Abstract: 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://github.com/AlexFanw/LegalSearch-R1.

arXiv:2510.07972v2 Announce Type: replace Abstract: Query-product relevance prediction is a foundational technology in e-commerce search engines and has become increasingly important in AI-driven e-commerce. The recent emergence of LLMs, particularly their CoT reasoning capabilities, offers promising opportunities for developing relevance systems that are both more interpretable and more robust. However, existing training paradigms have notable limitations: SFT and DPO suffer from poor generalization on long-tail queries and from a lack of fine-grained, stepwise supervision to enforce rule-aligned reasoning. In contrast, reinforcement learning with verification rewards (RLVR) suffers from sparse feedback, which provides insufficient signal to correct erroneous intermediate steps, thereby undermining logical consistency and limiting performance in complex inference scenarios. To address these challenges, we introduce the Stepwise Hybrid Examination Reinforcement Learning framework for search relevance (SHE). At its core is Stepwise Reward Policy Optimization (SRPO), a reinforcement learning algorithm that leverages step-level rewards generated by a hybrid of a high-quality generative stepwise reward model and a human-annotated offline verifier, prioritizing learning from critical correct and incorrect reasoning steps. To bolster robustness and generalization, SHE further integrates a dual-strategy optimization: diversified data filtering, which broadens the exploration of reasoning trajectories to preempt policy entropy collapse, and a multi-stage curriculum learning protocol that systematically orchestrates progressive capability acquisition. Extensive experiments on real-world search benchmarks show that SHE improves both reasoning quality and relevance-prediction accuracy in large-scale e-commerce settings, outperforming SFT, DPO, GRPO, and other baselines, while also enhancing interpretability and robustness.