The advancement of reasoning capabilities in Large Language Models (LLMs) requires substantial amounts of high-quality reasoning data, particularly in mathematics. Existing data synthesis methods, such as data augmentation from annotated training sets or direct question generation based on relevant knowledge points and documents, have expanded datasets but face challenges in mastering the internal logic of the problem during generation and ensuring the verifiability of the solutions. To address these issues, we propose RV-Syn, a novel Rational and Verifiable mathematical Synthesis approach. RV-Syn first constructs a structured library of mathematical operations and then composes them into executable computational graphs, which serve as verifiable solution blueprints. These graphs are subsequently back-translated into complex problems, enabling solution-guided, logic-aware problem generation while inherently ensuring the verifiability of the solving process. Experimental results show RV-Syn surpasses existing synthesis methods, including those involving human-crafted problems. Our method achieves a 6.3% performance gain over the previous state-of-the-art synthetic data on LLaMA-3-8B and demonstrates superior data efficiency, outperforming others with only half the training data (50k vs. 100k), enabling a more scalable and robust reasoning dataset generation framework.

Large reasoning models (LRMs) are typically trained using reinforcement learning with verifiable reward (RLVR) to enhance their reasoning abilities. In this paradigm, policies are updated using both positive and negative self-generated rollouts, which correspond to distinct ***sample polarities***. In this paper, we provide a systematic investigation into how these sample polarities affect RLVR training dynamics and behaviors. We find that positive samples sharpen existing correct reasoning patterns, while negative samples encourage exploration of new reasoning paths. We further explore how adjusting the advantage values of positive and negative samples at both the polarity level and the token level affects RLVR training. Based on these insights, we propose an **A**daptive and **A**symmetric token-level **A**dvantage shaping method for **P**olicy **O**ptimization, namely **A3PO**, that more precisely allocates advantage signals to key tokens across different polarities. Experiments across five reasoning benchmarks demonstrate the effectiveness of our approach.

This paper presents a novel extension of neural scaling laws to Mixture-of-Experts (MoE) models, focusing on the optimal allocation of compute between expert and attention sub-layers. As MoE architectures have emerged as an efficient method for scaling model capacity without proportionally increasing computation, determining the optimal expert-attention compute ratio becomes critical. We define the ratio r as the fraction of total FLOPs per token dedicated to the expert layers versus the attention layers, and explore how this ratio interacts with the overall compute budget and model sparsity. Through extensive experiments with GPT-style MoE Transformers, we empirically find that the optimal ratio r\* follows a power-law relationship with total compute and varies with sparsity. Our analysis leads to an explicit formula for r\*, enabling precise control over the expert-attention compute allocation. We generalize the Chinchilla scaling law by incorporating this architectural parameter, providing a new framework for tuning MoE models beyond size and data. Our findings offer practical guidelines for designing efficient MoE models, optimizing performance while respecting fixed compute budgets.

This paper poses two critical issues in evaluating base models (without post-training): (1) Unstable evaluation during training: in the early stages of pre-training, the models lack the capability to answer questions as required, leading to unstable evaluation results. This instability makes it difficult to provide solid conclusions to guide the training, especially for key experiments such as data ablation and scaling law. (2) Inconsistency between base and instruct models: base models generally exhibit poorer evaluation performance compared to corresponding instruct models. This gap poses a challenge for assessing whether a base model with better evaluation can truly lead to a better instruct model. To address these issues, we propose **B**ase model **O**riented **S**ystematic **E**valuation (**BOSE**), a method specifically designed to optimize the evaluation of base models. Specifically, BOSE introduces two key innovations: In-Context Light-instruction Prompt (**ICLiP**) for open-ended tasks and **Blank-ppl** for multi-choice tasks with candidate options, which transforms the standard perplexity (ppl) metric into a fill-in-the-blank format to mitigate early-stage evaluation fluctuations. Furthermore, we are the first to propose Kendall’s rank correlation to quantitatively measure the evaluation stability and consistency. Experimental results demonstrate that BOSE significantly enhances both the stability of evaluations during pre-training and the consistency between base and instruct models, thereby providing more reliable guidance for the LLMs’ training.

Recent advancements in long chain-of-thoughts (long CoTs) have significantly improved the reasoning capabilities of large language models (LLMs). Existing work finds that the capability of long CoT reasoning can be efficiently elicited by tuning on only a few examples and can easily transfer to other tasks. This motivates us to investigate whether long CoT reasoning is a general capability for LLMs. In this work, we conduct an empirical analysis for this question from the perspective of representation. We find that LLMs do encode long CoT reasoning as a general capability, with a clear distinction from vanilla CoTs. Furthermore, domain-specific representations are also required for the effective transfer of long CoT reasoning. Inspired by these findings, we propose GLORE, a novel representation engineering method to unleash the general long CoT reasoning capabilities of LLMs. Extensive experiments demonstrate the effectiveness and efficiency of GLORE in both in-domain and cross-domain scenarios. The code is available at https://github.com/txy77/GLoRE.

Large language models (LLMs) have demonstrated exceptional performance in text generation within current NLP research. However, the lack of factual accuracy is still a dark cloud hanging over the LLM skyscraper. Structural knowledge prompting (SKP) is a prominent paradigm to integrate external knowledge into LLMs by incorporating structural representations, achieving state-of-the-art results in many knowledge-intensive tasks. However, existing methods often focus on specific problems, lacking a comprehensive exploration of the generalization and capability boundaries of SKP. This paper aims to evaluate and rethink the generalization capability of the SKP paradigm from four perspectives including Granularity, Transferability, Scalability, and Universality. To provide a thorough evaluation, we introduce a novel multi-granular, multi-level benchmark called SUBARU, consisting of 9 different tasks with varying levels of granularity and difficulty. Through extensive experiments, we draw key conclusions regarding the generalization of SKP, offering insights to guide the future development and extension of the SKP paradigm.