DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning

The capacity for complex mathematical reasoning is a key benchmark for artificial intelligence. While reinforcement learning (RL) applied to LLMs shows promise, progress is significantly hindered by the lack of large-scale training data that is sufficiently challenging, possesses verifiable answer formats suitable for RL, and is free from contamination with evaluation benchmarks. To address these limitations, we introduce DeepMath-103K, a new, large-scale dataset comprising approximately 103K mathematical problems, specifically designed to train advanced reasoning models via RL. DeepMath-103K is curated through a rigorous pipeline involving source analysis, stringent decontamination against numerous benchmarks, and filtering for high difficulty (primarily Levels 5-9), significantly exceeding existing open resources in challenge. Each problem includes a verifiable final answer, enabling rule-based RL, and three distinct R1-generated solutions suitable for diverse training paradigms like supervised fine-tuning or distillation. Spanning a wide range of mathematical topics, DeepMath-103K promotes the development of generalizable reasoning. We demonstrate that models trained on DeepMath-103K achieve significant improvements on challenging mathematical benchmarks, validating its effectiveness. We release DeepMath-103K publicly to facilitate community progress in building more capable AI reasoning systems: https://github.com/zwhe99/DeepMath.

Dancing with Critiques: Enhancing LLM Reasoning with Stepwise Natural Language Self-Critique

Enhancing the reasoning capabilities of large language models (LLMs), particularly for complex tasks requiring multi-step logical deductions, remains a significant challenge. Traditional inference time scaling methods utilize scalar reward signals from process reward models to evaluate candidate reasoning steps, but these scalar rewards lack the nuanced qualitative information essential for understanding and justifying each step. In this paper, we propose a novel inference-time scaling approach -- stepwise natural language self-critique (PANEL), which employs self-generated natural language critiques as feedback to guide the step-level search process. By generating rich, human-readable critiques for each candidate reasoning step, PANEL retains essential qualitative information, facilitating better-informed decision-making during inference. This approach bypasses the need for task-specific verifiers and the associated training overhead, making it broadly applicable across diverse tasks. Experimental results on challenging reasoning benchmarks, including AIME and GPQA, demonstrate that PANEL significantly enhances reasoning performance, outperforming traditional scalar reward-based methods. Our code is available at https://github.com/puddingyeah/PANEL to support and encourage future research in this promising field.

RaSA: Rank-Sharing Low-Rank Adaptation

Low-rank adaptation (LoRA) has been prominently employed for parameter-efficient fine-tuning of large language models (LLMs). However, the limited expressive capacity of LoRA, stemming from the low-rank constraint, has been recognized as a bottleneck, particularly in rigorous tasks like code generation and mathematical reasoning. To address this limitation, we introduce Rank-Sharing Low-Rank Adaptation (RaSA), an innovative extension that enhances the expressive capacity of LoRA by leveraging partial rank sharing across layers. By forming a shared rank pool and applying layer-specific weighting, RaSA effectively increases the number of ranks without augmenting parameter overhead. Our theoretically grounded and empirically validated approach demonstrates that RaSA not only maintains the core advantages of LoRA but also significantly boosts performance in challenging code and math tasks. Code, data and scripts are available at: https://github.com/zwhe99/RaSA.

The First Few Tokens Are All You Need: An Efficient and Effective Unsupervised Prefix Fine-Tuning Method for Reasoning Models

Improving the reasoning capabilities of large language models (LLMs) typically requires supervised fine-tuning with labeled data or computationally expensive sampling. We introduce Unsupervised Prefix Fine-Tuning (UPFT), which leverages the observation of Prefix Self-Consistency -- the shared initial reasoning steps across diverse solution trajectories -- to enhance LLM reasoning efficiency. By training exclusively on the initial prefix substrings (as few as 8 tokens), UPFT removes the need for labeled data or exhaustive sampling. Experiments on reasoning benchmarks show that UPFT matches the performance of supervised methods such as Rejection Sampling Fine-Tuning, while reducing training time by 75% and sampling cost by 99%. Further analysis reveals that errors tend to appear in later stages of the reasoning process and that prefix-based training preserves the model's structural knowledge. This work demonstrates how minimal unsupervised fine-tuning can unlock substantial reasoning gains in LLMs, offering a scalable and resource-efficient alternative to conventional approaches.

Thoughts Are All Over the Place: On the Underthinking of o1-Like LLMs

Large language models (LLMs) such as OpenAI's o1 have demonstrated remarkable abilities in complex reasoning tasks by scaling test-time compute and exhibiting human-like deep thinking. However, we identify a phenomenon we term underthinking, where o1-like LLMs frequently switch between different reasoning thoughts without sufficiently exploring promising paths to reach a correct solution. This behavior leads to inadequate depth of reasoning and decreased performance, particularly on challenging mathematical problems. To systematically analyze this issue, we conduct experiments on three challenging test sets and two representative open-source o1-like models, revealing that frequent thought switching correlates with incorrect responses. We introduce a novel metric to quantify underthinking by measuring token efficiency in incorrect answers. To address underthinking, we propose a decoding strategy with thought switching penalty TIP that discourages premature transitions between thoughts, encouraging deeper exploration of each reasoning path. Experimental results demonstrate that our approach improves accuracy across challenging datasets without requiring model fine-tuning. Our findings contribute to understanding reasoning inefficiencies in o1-like LLMs and offer a practical solution to enhance their problem-solving capabilities.

Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs

The remarkable performance of models like the OpenAI o1 can be attributed to their ability to emulate human-like long-time thinking during inference. These models employ extended chain-of-thought (CoT) processes, exploring multiple strategies to enhance problem-solving capabilities. However, a critical question remains: How to intelligently and efficiently scale computational resources during testing. This paper presents the first comprehensive study on the prevalent issue of overthinking in these models, where excessive computational resources are allocated for simple problems with minimal benefit. We introduce novel efficiency metrics from both outcome and process perspectives to evaluate the rational use of computational resources by o1-like models. Using a self-training paradigm, we propose strategies to mitigate overthinking, streamlining reasoning processes without compromising accuracy. Experimental results show that our approach successfully reduces computational overhead while preserving model performance across a range of testsets with varying difficulty levels, such as GSM8K, MATH500, GPQA, and AIME.

Draft Model Knows When to Stop: A Self-Verification Length Policy for Speculative Decoding

Speculative Decoding (SD) has become an important technique in accelerating the inference speed of large language models. Conventional SD methods employ a fixed draft length, which ignores the token generation difficulty across tasks. Consequently, in this paper, we address such an issue and introduce SVIP - a difficulty-aware dynamic draft length policy for speculative decoding systems. Based on a theoretical lower bound of draft token acceptance rate and its inference-time approximation, SVIP adaptively determines the lengths of draft sequences based on the entropy of each draft token distribution. Experimental results on mainstream SD benchmarks and frameworks demonstrate the superior performance of SVIP, achieving up to 20\% walltime speedup on SpecBench over baseline SD methods and 60\% speedup on MT-Bench for long-form generation of up to 8K tokens. Moreover, SVIP is totally training-free and compatible with any existing SD methods that generate draft tokens autoregressively. Experimental results also show that SVIP yields consistent walltime improvement on top of GliDe & CaPE and EAGLE-2.

Weak-to-Strong Preference Optimization: Stealing Reward from Weak Aligned Model

Aligning language models (LMs) with human preferences has become a key area of research, enabling these models to meet diverse user needs better. Inspired by weak-to-strong generalization, where a strong LM fine-tuned on labels generated by a weaker model can consistently outperform its weak supervisor, we extend this idea to model alignment. In this work, we observe that the alignment behavior in weaker models can be effectively transferred to stronger models and even exhibit an amplification effect. Based on this insight, we propose a method called Weak-to-Strong Preference Optimization (WSPO), which achieves strong model alignment by learning the distribution differences before and after the alignment of the weak model. Experiments demonstrate that WSPO delivers outstanding performance, improving the win rate of Qwen2-7B-Instruct on Arena-Hard from 39.70 to 49.60, achieving a remarkable 47.04 length-controlled win rate on AlpacaEval 2, and scoring 7.33 on MT-bench. Our results suggest that using the weak model to elicit a strong model with a high alignment ability is feasible.

VoxelTrack: Exploring Voxel Representation for 3D Point Cloud Object Tracking

Current LiDAR point cloud-based 3D single object tracking (SOT) methods typically rely on point-based representation network. Despite demonstrated success, such networks suffer from some fundamental problems: 1) It contains pooling operation to cope with inherently disordered point clouds, hindering the capture of 3D spatial information that is useful for tracking, a regression task. 2) The adopted set abstraction operation hardly handles density-inconsistent point clouds, also preventing 3D spatial information from being modeled. To solve these problems, we introduce a novel tracking framework, termed VoxelTrack. By voxelizing inherently disordered point clouds into 3D voxels and extracting their features via sparse convolution blocks, VoxelTrack effectively models precise and robust 3D spatial information, thereby guiding accurate position prediction for tracked objects. Moreover, VoxelTrack incorporates a dual-stream encoder with cross-iterative feature fusion module to further explore fine-grained 3D spatial information for tracking. Benefiting from accurate 3D spatial information being modeled, our VoxelTrack simplifies tracking pipeline with a single regression loss. Extensive experiments are conducted on three widely-adopted datasets including KITTI, NuScenes and Waymo Open Dataset. The experimental results confirm that VoxelTrack achieves state-of-the-art performance (88.3%, 71.4% and 63.6% mean precision on the three datasets, respectively), and outperforms the existing trackers with a real-time speed of 36 Fps on a single TITAN RTX GPU. The source code and model will be released.

P2P: Part-to-Part Motion Cues Guide a Strong Tracking Framework for LiDAR Point Clouds

3D single object tracking (SOT) methods based on appearance matching has long suffered from insufficient appearance information incurred by incomplete, textureless and semantically deficient LiDAR point clouds. While motion paradigm exploits motion cues instead of appearance matching for tracking, it incurs complex multi-stage processing and segmentation module. In this paper, we first provide in-depth explorations on motion paradigm, which proves that (\textbf{i}) it is feasible to directly infer target relative motion from point clouds across consecutive frames; (\textbf{ii}) fine-grained information comparison between consecutive point clouds facilitates target motion modeling. We thereby propose to perform part-to-part motion modeling for consecutive point clouds and introduce a novel tracking framework, termed \textbf{P2P}. The novel framework fuses each corresponding part information between consecutive point clouds, effectively exploring detailed information changes and thus modeling accurate target-related motion cues. Following this framework, we present P2P-point and P2P-voxel models, incorporating implicit and explicit part-to-part motion modeling by point- and voxel-based representation, respectively. Without bells and whistles, P2P-voxel sets a new state-of-the-art performance ($\sim$\textbf{89\%}, \textbf{72\%} and \textbf{63\%} precision on KITTI, NuScenes and Waymo Open Dataset, respectively). Moreover, under the same point-based representation, P2P-point outperforms the previous motion tracker M$^2$Track by \textbf{3.3\%} and \textbf{6.7\%} on the KITTI and NuScenes, while running at a considerably high speed of \textbf{107 Fps} on a single RTX3090 GPU. The source code and pre-trained models are available at \url{https://github.com/haooozi/P2P}.