Contemporary progress in Large Language Models (LLMs) has revealed notable inferential capacities via reinforcement learning (RL) employing verifiable rewards. However, “zero-RL” approaches relying on fixed prompt templates introduce substantial sampling inefficiencies for weak LLMs, as most problems generate invalid outputs during accuracy-driven filtration. To solve this, we propose Cog-Rethinker, a novel hierarchical metacognitive RL framework. Cog-Rethinker enhances the rollout procedure by improving sample utilization through a two-stage framework leveraging human cognition. First, it prompts the policy to decompose zero-accuracy problems into subproblems. Second, it prompts the policy to refine answers by referencing previous wrong solutions. Moreover, to enable cold-starts and maintain train-test consistency, Cog-Rethinker applies supervised fine-tuning using correct samples from these stages. Experimental results demonstrate Cog-Rethinker’s superior performance on mathematical reasoning benchmarks and its improved sample efficiency that accelerates convergence compared to baselines.

Formal verification can provide strong mathematical guarantees about software correctness, but it typically requires developers to write detailed formal specifications (e.g., contracts and loop invariants), which is costly and error-prone. We introduce AutoSpec+, an LLM-driven neuro-symbolic demonstration system that reframes specification writing as constrained structured synthesis: large language models generate candidate specifications at the granularity of proof-relevant program components, while a symbolic verifier acts as a deterministic critic that checks legality, satisfiability, and proof adequacy, rejecting or repairing candidates in an iterative loop. This design turns unconstrained text generation into constrained structured synthesis, substantially reducing hallucinations and producing proof-ready annotations. We evaluate AutoSpec+ on seven benchmark suites, showing strong effectiveness. We release an open-source, Dockerized system with ensemble LLM backends and inter-modular verification support for reproducible demonstration and deployment

Large language models (LLM) not only have revolutionized the field of natural language processing (NLP) but also have the potential to reshape many other fields, e.g., recommender systems (RS). However, most of the related work treats an LLM as a component of the conventional recommendation pipeline (e.g., as a feature extractor), which may not be able to fully leverage the generative power of LLM. Instead of separating the recommendation process into multiple stages, such as score computation and re-ranking, this process can be simplified to one stage with LLM: directly generating recommendations from the complete pool of items. This survey reviews the progress, methods, and future directions of LLM-based generative recommendation by examining three questions: 1) What generative recommendation is, 2) Why RS should advance to generative recommendation, and 3) How to implement LLM-based generative recommendation for various RS tasks. We hope that this survey can provide the context and guidance needed to explore this interesting and emerging topic.

Existing legal judgment prediction methods usually only consider one single case fact description as input, which may not fully utilize the information in the data such as case relations and frequency. In this paper, we propose a new perspective that introduces some contrastive case relations to construct case triples as input, and a corresponding judgment prediction framework with case triples modeling (CTM). Our CTM can more effectively utilize beneficial information to refine the encoding and decoding processes through three customized modules, including the case triple module, the relational attention module, and the category decoder module. Finally, we conduct extensive experiments on two public datasets to verify the effectiveness of our CTM, including overall evaluation, compatibility analysis, ablation studies, analysis of gain source and visualization of case representations.