Recent studies have demonstrated the effectiveness of LLM test-time scaling. However, existing approaches to incentivize LLMs’ deep thinking abilities generally require large-scale data or significant training efforts. Meanwhile, it remains unclear how to improve the thinking abilities of less powerful base models. In this work, we introduce S^2R, an efficient framework that enhances LLM reasoning by teaching models to self-verify and self-correct during inference. Specifically, we first initialize LLMs with iterative self-verification and self-correction behaviors through supervised fine-tuning on carefully curated data. The self-verification and self-correction skills are then further strengthened by outcome-level and process-level reinforcement learning with minimized resource requirements. Our results demonstrate that, with only 3.1k behavior initialization samples, Qwen2.5-math-7B achieves an accuracy improvement from 51.0% to 81.6%, outperforming models trained on an equivalent amount of long-CoT distilled data. We also discuss the effect of different RL strategies on enhancing LLMs’ deep reasoning. Extensive experiments and analysis based on three base models across both in-domain and out-of-domain benchmarks validate the effectiveness of S^2R.

Evaluating the step-by-step reliability of large language model (LLM) reasoning, such as Chain-of-Thought, remains challenging due to the difficulty and cost of obtaining high-quality step-level supervision. In this paper, we introduce Self-Play Critic (SPC), a novel approach where a critic model evolves its ability to assess reasoning steps through adversarial self-play games, eliminating the need for manual step-level annotation. SPC involves fine-tuning two copies of a base model to play two roles, namely a "sneaky generator" that deliberately produces erroneous steps designed to be difficult to detect, and a "critic" that analyzes the correctness of reasoning steps. These two models engage in an adversarial game in which the generator aims to fool the critic, while the critic model seeks to identify the generator's errors. Using reinforcement learning based on the game outcomes, the models iteratively improve; the winner of each confrontation receives a positive reward and the loser receives a negative reward, driving continuous self-evolution. Experiments on three reasoning process benchmarks (ProcessBench, PRM800K, DeltaBench) demonstrate that our SPC progressively enhances its error detection capabilities (e.g., accuracy increases from 70.8% to 77.7% on ProcessBench) and surpasses strong baselines, including distilled R1 model. Furthermore, SPC can guide the test-time search of diverse LLMs and significantly improve their mathematical reasoning performance on MATH500 and AIME2024, surpassing those guided by state-of-the-art process reward models.

With the development of foundation models such as large language models, zero-shot transfer learning has become increasingly significant. This is highlighted by the generative capabilities of NLP models like GPT-4, and the retrieval-based approaches of CV models like CLIP, both of which effectively bridge the gap between seen and unseen data. In the realm of graph learning, the continuous emergence of new graphs and the challenges of human labeling also amplify the necessity for zero-shot transfer learning, driving the exploration of approaches that can generalize across diverse graph data without necessitating dataset-specific and label-specific fine-tuning. In this study, we extend such paradigms to Zero-shot transferability in Graphs by introducing ZeroG, a new framework tailored to enable cross-dataset generalization. Addressing the inherent challenges such as feature misalignment, mismatched label spaces, and negative transfer, we leverage a language model to encode both node attributes and class semantics, ensuring consistent feature dimensions across datasets. We also propose a prompt-based subgraph sampling module that enriches the semantic information and structure information of extracted subgraphs using prompting nodes and neighborhood aggregation, respectively. We further adopt a lightweight fine-tuning strategy that reduces the risk of overfitting and maintains the zero-shot learning efficacy of the language model. The results underscore the effectiveness of our model in achieving significant cross-dataset zero-shot transferability, opening pathways for the development of graph foundation models.

The emergence of large language models (LLMs) has revolutionized the way we interact with graphs, leading to a new paradigm called GraphLLM. Despite the rapid development of GraphLLM methods in recent years, the progress and understanding of this field remain unclear due to the lack of a benchmark with consistent experimental protocols. To bridge this gap, we introduce GLBench, the first comprehensive benchmark for evaluating GraphLLM methods in both supervised and zero-shot scenarios. GLBench provides a fair and thorough evaluation of different categories of GraphLLM methods, along with traditional baselines such as graph neural networks. Through extensive experiments on a collection of real-world datasets with consistent data processing and splitting strategies, we have uncovered several key findings. Firstly, GraphLLM methods outperform traditional baselines in supervised settings, with LLM-as-enhancers showing the most robust performance. However, using LLMs as predictors is less effective and often leads to uncontrollable output issues. We also notice that no clear scaling laws exist for current GraphLLM methods. In addition, both structures and semantics are crucial for effective zero-shot transfer, and our proposed simple baseline can even outperform several models tailored for zero-shot scenarios. The data and code of the benchmark can be found at https://github.com/NineAbyss/GLBench.