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With the advent of DeepSeek-R1, a new wave of reinforcement learning (RL) methods has emerged that seem to unlock stronger mathematical reasoning. However, a closer look at the open-source ecosystem reveals a critical limitation: with…

Large language models (LLMs) have demonstrated remarkable capabilities in natural language understanding, reasoning, and problem-solving across various domains. However, their ability to perform complex, multi-step reasoning task-essential…

Reasoning abilities, especially those for solving complex math problems, are crucial components of general intelligence. Recent advances by proprietary companies, such as o-series models of OpenAI, have made remarkable progress on reasoning…

Recent language models achieve impressive results in tasks involving complex multistep reasoning, but scaling these capabilities further traditionally requires expensive collection of more annotated data. In this work, we explore the…

Chain-of-thought (CoT) reasoning has enabled large language models (LLMs) to utilize additional computation through intermediate tokens to solve complex tasks. However, we posit that typical reasoning traces contain many redundant tokens,…

Mathematical reasoning poses a significant challenge for language models due to its complex and structured nature. In this paper, we introduce DeepSeekMath 7B, which continues pre-training DeepSeek-Coder-Base-v1.5 7B with 120B math-related…

Small language models (SLMs) are more efficient, cost-effective, and customizable than large language models (LLMs), though they often underperform in specific areas like reasoning. Past methods for enhancing SLMs' reasoning, such as…

Large language models (LLMs) have seen considerable advancements in natural language understanding tasks, yet there remains a gap to bridge before attaining true artificial general intelligence, especially concerning shortcomings in…

Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems. As Large Language Models (LLMs) improve their reasoning…

Reinforcement learning (RL) with large language models shows promise in complex reasoning. However, its progress is hindered by the lack of large-scale training data that is sufficiently challenging, contamination-free and verifiable. To…

Large Language Models (LLMs) have been touted as AI models possessing advanced reasoning abilities. In theory, autoregressive LLMs with Chain-of-Thought (CoT) can perform more serial computations to solve complex reasoning tasks. However,…

While the ``deep reasoning'' paradigm has spurred significant advances in verifiable domains like mathematics, its application to open-ended, creative generation remains a critical challenge. The two dominant methods for instilling…

Large reasoning models (LRMs) have recently shown promise in solving complex math problems when optimized with Reinforcement Learning (RL). But conventional approaches rely on outcome-only rewards that provide sparse feedback, resulting in…

Large language model (LLM)-based reasoning systems have recently achieved gold medal-level performance in the IMO 2025 competition, writing mathematical proofs where, to receive full credit, each step must be not only correct but also…

Reasoning models excel at complex tasks such as coding and mathematics, yet their inference is often slow and token-inefficient. To improve the inference efficiency, post-training quantization (PTQ) usually comes with the cost of large…

Recent studies have shown that making a model spend more time thinking through longer Chain of Thoughts (CoTs) enables it to gain significant improvements in complex reasoning tasks. While current researches continue to explore the benefits…

Reasoning-capable language models achieve state-of-the-art performance in diverse complex tasks by generating long, explicit Chain-of-Thought (CoT) traces. While recent works show that base models can acquire such reasoning traces via…

Large reasoning models, such as OpenAI o1 and DeepSeek-R1, tend to become increasingly verbose as their reasoning capabilities improve. These inflated Chain-of-Thought (CoT) trajectories often exceed what the underlying problems require,…

Increasing interest in reasoning models has led math to become a prominent testing ground for algorithmic and methodological improvements. However, existing open math datasets either contain a small collection of high-quality, human-written…

Recent advancements in the field of large language models, particularly through the Chain of Thought (CoT) approach, have demonstrated significant improvements in solving complex problems. However, existing models either tend to sacrifice…