Daily Papers

Large Language Models (LLM) with reasoning capabilities offer a promising path for improving candidate evaluation in planning frameworks, but their relative performance against traditional non-reasoning models remains largely underexplored. In this study, we benchmark a distilled 1.5B parameter reasoning model (DeepSeek-R1) against several state-of-the-art non-reasoning LLMs within a generator-discriminator LLM planning framework for the text-to-SQL task. For this, we introduce a novel method for extracting soft scores from the chain-of-thought (CoT) outputs from reasoning that enables fine-grained ranking of candidates. Our central hypothesis is that reasoning models are more effective discriminators than non-reasoning LLMs. Our results show that distilled DeepSeek-R1-1.5B achieves up to 87% higher F1 and 3.7% better discrimination accuracy than CodeLlama-7B, as well as 3.7% higher execution accuracy than CodeLlama-13B, despite having significantly fewer parameters. Furthermore, we find that there is a limit to the logical capabilities of reasoning models, and only providing more context or allowing more compute budget for reasoning is not enough to improve their discrimination performance. Finally, we demonstrate that, unlike non-reasoning LLMs, reasoning models find generation more challenging than discrimination and may underperform as generators compared to smaller non-reasoning LLMs. Our work highlights the potential of reasoning models as discriminators in agentic frameworks, far outweighing their capabilities as generators, offering insights into their optimal role within LLM planning infrastructures.

Large Language Models (LLMs) achieve impressive reasoning capabilities at the cost of substantial inference overhead, posing substantial deployment challenges. Although distilled Small Language Models (SLMs) significantly enhance efficiency, their performance suffers as they fail to follow LLMs' reasoning paths. Luckily, we reveal that only a small fraction of tokens genuinely diverge reasoning paths between LLMs and SLMs. Most generated tokens are either identical or exhibit neutral differences, such as minor variations in abbreviations or expressions. Leveraging this insight, we introduce **Roads to Rome (R2R)**, a neural token routing method that selectively utilizes LLMs only for these critical, path-divergent tokens, while leaving the majority of token generation to the SLM. We also develop an automatic data generation pipeline that identifies divergent tokens and generates token-level routing labels to train the lightweight router. We apply R2R to combine R1-1.5B and R1-32B models from the DeepSeek family, and evaluate on challenging math, coding, and QA benchmarks. With an average activated parameter size of 5.6B, R2R surpasses the average accuracy of R1-7B by 1.6x, outperforming even the R1-14B model. Compared to R1-32B, it delivers a 2.8x wall-clock speedup with comparable performance, advancing the Pareto frontier of test-time scaling efficiency. Our code is available at https://github.com/thu-nics/R2R.

Reinforcement learning (RL) has recently become a strong recipe for training reasoning LLMs that produce long chains of thought (LongCoT). Yet the standard RL "thinking environment", where the state is the prompt plus all prior reasoning tokens, makes the state unbounded and forces attention-based policies to pay quadratic compute as thoughts lengthen. We revisit the environment itself. We propose Markovian Thinking, a paradigm in which the policy advances reasoning while conditioning on a constant-size state, decoupling thinking length from context size. As an immediate consequence this yields linear compute with constant memory. We instantiate this idea with Delethink, an RL environment that structures reasoning into fixed-size chunks. Within each chunk, the model thinks as usual; at the boundary, the environment resets the context and reinitializes the prompt with a short carryover. Through RL, the policy learns to write a textual state near the end of each chunk sufficient for seamless continuation of reasoning after reset. Trained in this environment, an R1-Distill 1.5B model reasons in 8K-token chunks yet thinks up to 24K tokens, matching or surpassing LongCoT-RL trained with a 24K budget. With test-time scaling, Delethink continues to improve where LongCoT plateaus. The effect of linear compute is substantial: we empirically estimate at 96K average thinking length LongCoT-RL costs 27 H100-months vs. 7 for Delethink. Analysis at RL initialization shows off-the-shelf reasoning models (1.5B-120B) often sample Markovian traces zero-shot across diverse benchmarks, providing positive samples that make RL effective at scale. Our results show that redesigning the thinking environment is a powerful lever: it enables very long reasoning without quadratic overhead and opens a path toward efficient, scalable reasoning LLMs.

Recent studies show that the reasoning capabilities of Large Language Models (LLMs) can be improved by applying Reinforcement Learning (RL) to question-answering (QA) tasks in areas such as math and coding. With a long context length, LLMs may learn to perform search, as indicated by the self-correction behavior observed in DeepSeek R1. However, this search behavior is often imprecise and lacks confidence, resulting in long, redundant responses and highlighting deficiencies in intuition and verification. Inspired by the Dual Process Theory in psychology, we introduce a simple modification to the QA task that includes four stages: Fast Thinking, where the LLM must answer within a strict token budget; Verification, where the model evaluates its initial response; Slow Thinking, where it refines the initial response with more deliberation; and Summarization, where it distills the refinement from the previous stage into precise steps. Our proposed task improves average accuracy from 24.9% to 27.9% for Qwen2.5-1.5B, and from 45.9% to 49.8% for DeepSeek-R1-Qwen-1.5B. Notably, for Qwen2.5-1.5B, the Fast Thinking mode alone achieves 26.8% accuracy using fewer than 1000 tokens, demonstrating substantial inference efficiency gains. These findings suggest that intuition and deliberative reasoning are distinct, complementary systems benefiting from targeted training.

In this paper, we address the challenge of enforcing strict schema adherence in large language model (LLM) generation by leveraging LLM reasoning capabilities. Building on the DeepSeek R1 reinforcement learning framework, our approach trains structured reasoning skills of a 1.5B parameter model through a novel pipeline that combines synthetic reasoning dataset construction with custom reward functions under Group Relative Policy Optimization (GRPO). Specifically, we first perform R1 reinforcement learning on a 20K sample unstructured-to-structured dataset, mirroring the original DeepSeek R1 methods, to establish core reasoning abilities. Subsequently, we performed supervised fine-tuning on a separate 10K reasoning sample dataset, focusing on refining schema adherence for downstream tasks. Despite the relatively modest training scope, requiring approximately 20 hours on an 8xH100 GPU cluster for GRPO training and 3 hours on 1xA100 for SFT, our model demonstrates robust performance in enforcing schema consistency. We compare our ThinkJSON approach against the original DeepSeek R1 (671B), distilled versions of DeepSeek R1 (Qwen-1.5B and Qwen-7B), and Gemini 2.0 Flash (70B), showcasing its effectiveness in real-world applications. Our results underscore the practical utility of a resource-efficient framework for schema-constrained text generation.

In this paper, we propose a simple and efficient method for value model training on long-context reasoning traces. Compared to existing process reward models (PRMs), our method does not require a fine-grained notion of "step," which is difficult to define for long-context reasoning models. By collecting a dataset of 2.5 million reasoning traces, we train a 1.5B token-level value model and apply it to DeepSeek models for improved performance with test-time compute scaling. We find that block-wise value-guided search (VGS) with a final weighted majority vote achieves better test-time scaling than standard methods such as majority voting or best-of-n. With an inference budget of 64 generations, VGS with DeepSeek-R1-Distill-1.5B achieves an average accuracy of 45.7% across four competition math benchmarks (AIME 2024 & 2025, HMMT Feb 2024 & 2025), reaching parity with o3-mini-medium. Moreover, VGS significantly reduces the inference FLOPs required to achieve the same performance of majority voting. Our dataset, model and codebase are open-sourced.

In this report, we present the third technical report on the development of slow-thinking models as part of the STILL project. As the technical pathway becomes clearer, scaling RL training has become a central technique for implementing such reasoning models. We systematically experiment with and document the effects of various factors influencing RL training, conducting experiments on both base models and fine-tuned models. Specifically, we demonstrate that our RL training approach consistently improves the Qwen2.5-32B base models, enhancing both response length and test accuracy. Furthermore, we show that even when a model like DeepSeek-R1-Distill-Qwen-1.5B has already achieved a high performance level, it can be further refined through RL training, reaching an accuracy of 39.33% on AIME 2024. Beyond RL training, we also explore the use of tool manipulation, finding that it significantly boosts the reasoning performance of large reasoning models. This approach achieves a remarkable accuracy of 86.67% with greedy search on AIME 2024, underscoring its effectiveness in enhancing model capabilities. We release our resources at the STILL project website: https://github.com/RUCAIBox/Slow_Thinking_with_LLMs.

Large reasoning models (LRMs) are proficient at generating explicit, step-by-step reasoning sequences before producing final answers. However, such detailed reasoning can introduce substantial computational overhead and latency, particularly for simple problems. To address this over-thinking problem, we explore how to equip LRMs with adaptive thinking capabilities: enabling them to dynamically decide whether or not to engage in explicit reasoning based on problem complexity. Building on R1-style distilled models, we observe that inserting a simple ellipsis ("...") into the prompt can stochastically trigger either a thinking or no-thinking mode, revealing a latent controllability in the reasoning behavior. Leveraging this property, we propose AutoThink, a multi-stage reinforcement learning (RL) framework that progressively optimizes reasoning policies via stage-wise reward shaping. AutoThink learns to invoke explicit reasoning only when necessary, while defaulting to succinct responses for simpler tasks. Experiments on five mainstream mathematical benchmarks demonstrate that AutoThink achieves favorable accuracy-efficiency trade-offs compared to recent prompting and RL-based pruning methods. It can be seamlessly integrated into any R1-style model, including both distilled and further fine-tuned variants. Notably, AutoThink improves relative accuracy by 6.4 percent while reducing token usage by 52 percent on DeepSeek-R1-Distill-Qwen-1.5B, establishing a scalable and adaptive reasoning paradigm for LRMs. Project Page: https://github.com/ScienceOne-AI/AutoThink.

Large Reasoning Models (LRMs) have shown remarkable capabilities in solving complex problems through reinforcement learning (RL), particularly by generating long reasoning traces. However, these extended outputs often exhibit substantial redundancy, which limits the efficiency of LRMs. In this paper, we investigate RL-based approaches to promote reasoning efficiency. Specifically, we first present a unified framework that formulates various efficient reasoning methods through the lens of length-based reward shaping. Building on this perspective, we propose a novel Length-bAsed StEp Reward shaping method (LASER), which employs a step function as the reward, controlled by a target length. LASER surpasses previous methods, achieving a superior Pareto-optimal balance between performance and efficiency. Next, we further extend LASER based on two key intuitions: (1) The reasoning behavior of the model evolves during training, necessitating reward specifications that are also adaptive and dynamic; (2) Rather than uniformly encouraging shorter or longer chains of thought (CoT), we posit that length-based reward shaping should be difficulty-aware i.e., it should penalize lengthy CoTs more for easy queries. This approach is expected to facilitate a combination of fast and slow thinking, leading to a better overall tradeoff. The resulting method is termed LASER-D (Dynamic and Difficulty-aware). Experiments on DeepSeek-R1-Distill-Qwen-1.5B, DeepSeek-R1-Distill-Qwen-7B, and DeepSeek-R1-Distill-Qwen-32B show that our approach significantly enhances both reasoning performance and response length efficiency. For instance, LASER-D and its variant achieve a +6.1 improvement on AIME2024 while reducing token usage by 63%. Further analysis reveals our RL-based compression produces more concise reasoning patterns with less redundant "self-reflections". Resources are at https://github.com/hkust-nlp/Laser.

We introduce SIRI, Scaling Iterative Reinforcement Learning with Interleaved Compression, a simple yet effective RL approach for Large Reasoning Models (LRMs) that enables more efficient and accurate reasoning. Existing studies have observed repetitive thinking patterns in LRMs, and attempts to reduce them often come at the cost of performance. In this paper, we show that this trade-off can be overcome through a training regime that iteratively alternates between compressing and expanding the reasoning budget, by dynamically adjusting the maximum rollout length during training. The compression phase cuts the rollout length, forcing the model to make precise and valuable decisions within a limited context, which effectively reduces redundant tokens and increases reasoning density. The expansion phase then relaxes the length limit, providing space for the model to explore and plan in long-horizon settings. Remarkably, we find that after each compression-expansion cycle, the model's performance improves even as its output length decreases, steadily pushing it closer to the Pareto frontier in the performance-efficiency trade-off. Training on DeepSeek-R1-Distill-Qwen-1.5B, SIRI-low improves performance on AIME24 by 43.2% while reducing token usage by 46.9% after three iterations, and SIRI-high achieves the highest accuracy compared to all other methods (Figure 1). Our findings shed light on the potential of periodically oscillating the LRM's output truncation length during training to dynamically balance exploration and efficiency in reasoning, converging towards an optimal "sweet spot" between the two. Our models are publicly available.

While scaling the length of responses at test-time has been shown to markedly improve the reasoning abilities and performance of large language models (LLMs), it often results in verbose outputs and increases inference cost. Prior approaches for efficient test-time scaling, typically using universal budget constraints or query-level length optimization, do not leverage historical information from previous encounters with the same problem during training. We hypothesize that this limits their ability to progressively make solutions more concise over time. To address this, we present History-Aware Policy Optimization (HAPO), which keeps track of a history state (e.g., the minimum length over previously generated correct responses) for each problem. HAPO employs a novel length reward function based on this history state to incentivize the discovery of correct solutions that are more concise than those previously found. Crucially, this reward structure avoids overly penalizing shorter incorrect responses with the goal of facilitating exploration towards more efficient solutions. By combining this length reward with a correctness reward, HAPO jointly optimizes for correctness and efficiency. We use HAPO to train DeepSeek-R1-Distill-Qwen-1.5B, DeepScaleR-1.5B-Preview, and Qwen-2.5-1.5B-Instruct, and evaluate HAPO on several math benchmarks that span various difficulty levels. Experiment results demonstrate that HAPO effectively induces LLMs' concise reasoning abilities, producing length reductions of 33-59% with accuracy drops of only 2-5%.

Recent advances in model distillation demonstrate that data from advanced reasoning models (e.g., DeepSeek-R1, OpenAI's o1) can effectively transfer complex reasoning abilities to smaller, efficient student models. However, standard practices employ rejection sampling, discarding incorrect reasoning examples -- valuable, yet often underutilized data. This paper addresses the critical question: How can both positive and negative distilled reasoning traces be effectively leveraged to maximize LLM reasoning performance in an offline setting? To this end, We propose Reinforcement Distillation (REDI), a two-stage framework. Stage 1 learns from positive traces via Supervised Fine-Tuning (SFT). Stage 2 further refines the model using both positive and negative traces through our proposed REDI objective. This novel objective is a simple, reference-free loss function that outperforms established methods like DPO and SimPO in this distillation context. Our empirical evaluations demonstrate REDI's superiority over baseline Rejection Sampling SFT or SFT combined with DPO/SimPO on mathematical reasoning tasks. Notably, the Qwen-REDI-1.5B model, post-trained on just 131k positive and negative examples from the open Open-R1 dataset, achieves an 83.1% score on MATH-500 (pass@1). Its performance matches or surpasses that of DeepSeek-R1-Distill-Qwen-1.5B (a model post-trained on 800k proprietary data) across various mathematical reasoning benchmarks, establishing a new state-of-the-art for 1.5B models post-trained offline with openly available data.

Test-time scaling has been shown to substantially improve large language models' (LLMs) mathematical reasoning. However, for a large portion of mathematical corpora, especially theorem proving, RLVR's scalability is limited: intermediate reasoning is crucial, while final answers are difficult to directly and reliably verify. Meanwhile, token-level SFT often degenerates into rote memorization rather than inducing longer chains of thought. Inspired by BERT's self-supervised tasks, we propose MR-RLVR (Masked-and-Reordered RLVR), which constructs process-level self-supervised rewards via "masked-then-fill" and "step reordering" to extract learnable signals from intermediate reasoning. Our training pipeline comprises two stages: we first perform self-supervised training on sampled mathematical calculation and proof data; we then conduct RLVR fine-tuning on mathematical calculation datasets where only outcomes are verifiable. We implement MR-RLVR on Qwen2.5-3B and DeepSeek-R1-Distill-Qwen-1.5B, and evaluate on AIME24, AIME25, AMC23, and MATH500. Under a fixed sampling and decoding budget, MR-RLVR achieves average relative gains over the original RLVR of +9.86% Pass@1, +5.27% Pass@5, and +4.00% Pass@8. These results indicate that incorporating process-aware self-supervised signals can effectively enhance RLVR's scalability and performance in only outcome-verifiable settings.

Large Language Models (LLMs) have demonstrated remarkable progress in complex reasoning tasks through both post-training and test-time scaling laws. While prevalent test-time scaling approaches are often realized by using external reward models to guide the model generation process, we find only marginal gains can be acquired when scaling a model post-trained on specific reasoning tasks. We identify that the limited improvement stems from distribution discrepancies between the specific post-trained generator and the general reward model. To address this, we propose a framework that incentivizes LLMs to self-verify their own answers. By unifying answer generation and verification within a single reinforcement learning (RL) process, we train models that can effectively assess the correctness of their own solutions. The trained model can further scale its performance during inference time by verifying its generations, without the need for external verifiers. We train our self-verification models based on Qwen2.5-Math-7B and DeepSeek-R1-Distill-Qwen-1.5B, demonstrating its capabilities across varying reasoning context lengths. Experiments on multiple mathematical reasoning benchmarks show that our models can not only improve post-training performance but also enable effective test-time scaling. Our code is available at https://github.com/mansicer/self-verification.

Recently, large reasoning models have achieved impressive performance on various tasks by employing human-like deep thinking. However, the lengthy thinking process substantially increases inference overhead, making efficiency a critical bottleneck. In this work, we first demonstrate that NoThinking, which prompts the reasoning model to skip thinking and directly generate the final solution, is a better choice for relatively simple tasks in terms of both performance and efficiency. Motivated by this, we propose AdaptThink, a novel RL algorithm to teach reasoning models to choose the optimal thinking mode adaptively based on problem difficulty. Specifically, AdaptThink features two core components: (1) a constrained optimization objective that encourages the model to choose NoThinking while maintaining the overall performance; (2) an importance sampling strategy that balances Thinking and NoThinking samples during on-policy training, thereby enabling cold start and allowing the model to explore and exploit both thinking modes throughout the training process. Our experiments indicate that AdaptThink significantly reduces the inference costs while further enhancing performance. Notably, on three math datasets, AdaptThink reduces the average response length of DeepSeek-R1-Distill-Qwen-1.5B by 53% and improves its accuracy by 2.4%, highlighting the promise of adaptive thinking-mode selection for optimizing the balance between reasoning quality and efficiency. Our codes and models are available at https://github.com/THU-KEG/AdaptThink.

Realignment becomes necessary when a language model (LM) fails to meet expected performance. We propose a flexible realignment framework that supports quantitative control of alignment degree during training and inference. This framework incorporates Training-time Realignment (TrRa), which efficiently realigns the reference model by leveraging the controllable fusion of logits from both the reference and already aligned models. For example, TrRa reduces token usage by 54.63% on DeepSeek-R1-Distill-Qwen-1.5B without any performance degradation, outperforming DeepScaleR-1.5B's 33.86%. To complement TrRa during inference, we introduce a layer adapter that enables smooth Inference-time Realignment (InRa). This adapter is initialized to perform an identity transformation at the bottom layer and is inserted preceding the original layers. During inference, input embeddings are simultaneously processed by the adapter and the original layer, followed by the remaining layers, and then controllably interpolated at the logit level. We upgraded DeepSeek-R1-Distill-Qwen-7B from a slow-thinking model to one that supports both fast and slow thinking, allowing flexible alignment control even during inference. By encouraging deeper reasoning, it even surpassed its original performance.

Recent advances have demonstrated that integrating reinforcement learning with rule-based rewards can significantly enhance the reasoning capabilities of large language models, even without supervised fine-tuning. However, prevalent reinforcement learning algorithms such as GRPO and its variants like DAPO, suffer from a coarse granularity issue when computing the advantage. Specifically, they compute rollout-level advantages that assign identical values to every token within a sequence, failing to capture token-specific contributions and hindering effective learning. To address this limitation, we propose Key-token Advantage Estimation (KTAE) - a novel algorithm that estimates fine-grained, token-level advantages without introducing additional models. KTAE leverages the correctness of sampled rollouts and applies statistical analysis to quantify the importance of individual tokens within a sequence to the final outcome. This quantified token-level importance is then combined with the rollout-level advantage to obtain a more fine-grained token-level advantage estimation. Empirical results show that models trained with GRPO+KTAE and DAPO+KTAE outperform baseline methods across five mathematical reasoning benchmarks. Notably, they achieve higher accuracy with shorter responses and even surpass R1-Distill-Qwen-1.5B using the same base model.

We show that reinforcement learning with verifiable reward using one training example (1-shot RLVR) is effective in incentivizing the math reasoning capabilities of large language models (LLMs). Applying RLVR to the base model Qwen2.5-Math-1.5B, we identify a single example that elevates model performance on MATH500 from 36.0% to 73.6%, and improves the average performance across six common mathematical reasoning benchmarks from 17.6% to 35.7%. This result matches the performance obtained using the 1.2k DeepScaleR subset (MATH500: 73.6%, average: 35.9%), which includes the aforementioned example. Similar substantial improvements are observed across various models (Qwen2.5-Math-7B, Llama3.2-3B-Instruct, DeepSeek-R1-Distill-Qwen-1.5B), RL algorithms (GRPO and PPO), and different math examples (many of which yield approximately 30% or greater improvement on MATH500 when employed as a single training example). In addition, we identify some interesting phenomena during 1-shot RLVR, including cross-domain generalization, increased frequency of self-reflection, and sustained test performance improvement even after the training accuracy has saturated, a phenomenon we term post-saturation generalization. Moreover, we verify that the effectiveness of 1-shot RLVR primarily arises from the policy gradient loss, distinguishing it from the "grokking" phenomenon. We also show the critical role of promoting exploration (e.g., by adding entropy loss with an appropriate coefficient) in 1-shot RLVR training. As a bonus, we observe that applying entropy loss alone, without any outcome reward, significantly enhances Qwen2.5-Math-1.5B's performance on MATH500 by 27.4%. These findings can inspire future work on RLVR data efficiency and encourage a re-examination of both recent progress and the underlying mechanisms in RLVR. Our code, model, and data are open source at https://github.com/ypwang61/One-Shot-RLVR

Large Reasoning Models (LRMs) like o1 and DeepSeek-R1 have shown remarkable progress in natural language reasoning with long chain-of-thought (CoT), yet they remain inefficient or inaccurate when handling complex mathematical operations. Addressing these limitations through computational tools (e.g., computation libraries and symbolic solvers) is promising, but it introduces a technical challenge: Code Interpreter (CI) brings external knowledge beyond the model's internal text representations, thus the direct combination is not efficient. This paper introduces CoRT, a post-training framework for teaching LRMs to leverage CI effectively and efficiently. As a first step, we address the data scarcity issue by synthesizing code-integrated reasoning data through Hint-Engineering, which strategically inserts different hints at appropriate positions to optimize LRM-CI interaction. We manually create 30 high-quality samples, upon which we post-train models ranging from 1.5B to 32B parameters, with supervised fine-tuning, rejection fine-tuning and reinforcement learning. Our experimental results demonstrate that Hint-Engineering models achieve 4\% and 8\% absolute improvements on DeepSeek-R1-Distill-Qwen-32B and DeepSeek-R1-Distill-Qwen-1.5B respectively, across five challenging mathematical reasoning datasets. Furthermore, Hint-Engineering models use about 30\% fewer tokens for the 32B model and 50\% fewer tokens for the 1.5B model compared with the natural language models. The models and code are available at https://github.com/ChengpengLi1003/CoRT.

Large reasoning models (LRMs) like OpenAI-o1 have shown impressive capabilities in natural language reasoning. However, these models frequently demonstrate inefficiencies or inaccuracies when tackling complex mathematical operations. While integrating computational tools such as Code Interpreters (CIs) offers a promising solution, it introduces a critical challenge: a conflict between the model's internal, probabilistic reasoning and the external, deterministic knowledge provided by the CI, which often leads models to unproductive deliberation. To overcome this, we introduce CoRT (Code-Optimized Reasoning Training), a post-training framework designed to teach LRMs to effectively utilize CIs. We propose Hint-Engineering, a new data synthesis strategy that strategically injects diverse hints at optimal points within reasoning paths. This approach generates high-quality, code-integrated reasoning data specifically tailored to optimize LRM-CI interaction. Using this method, we have synthesized 30 high-quality samples to post-train models ranging from 1.5B to 32B parameters through supervised fine-tuning. CoRT further refines the multi-round interleaving of external CI usage and internal thinking by employing rejection sampling and reinforcement learning. Our experimental evaluations demonstrate CoRT's effectiveness, yielding absolute improvements of 4\% and 8\% on DeepSeek-R1-Distill-Qwen-32B and DeepSeek-R1-Distill-Qwen-1.5B, respectively, across five challenging mathematical reasoning datasets. Moreover, CoRT significantly enhances efficiency, reducing token usage by approximately 30\% for the 32B model and 50\% for the 1.5B model compared to pure natural language reasoning baselines. The models and code are available at: https://github.com/ChengpengLi1003/CoRT.

Enhancing the reasoning capabilities of large language models (LLMs) typically relies on massive computational resources and extensive datasets, limiting accessibility for resource-constrained settings. Our study investigates the potential of reinforcement learning (RL) to improve reasoning in small LLMs, focusing on a 1.5-billion-parameter model, DeepSeek-R1-Distill-Qwen-1.5B, under strict constraints: training on 4 NVIDIA A40 GPUs (48 GB VRAM each) within 24 hours. Adapting the Group Relative Policy Optimization (GRPO) algorithm and curating a compact, high-quality mathematical reasoning dataset, we conducted three experiments to explore model behavior and performance. Our results demonstrate rapid reasoning gains - e.g., AMC23 accuracy rising from 63% to 80% and AIME24 reaching 46.7%, surpassing o1-preview - using only 7,000 samples and a $42 training cost, compared to thousands of dollars for baseline models. However, challenges such as optimization instability and length constraints emerged with prolonged training. These findings highlight the efficacy of RL-based fine-tuning for small LLMs, offering a cost-effective alternative to large-scale approaches. We release our code and datasets as open-source resources, providing insights into trade-offs and laying a foundation for scalable, reasoning-capable LLMs in resource-limited environments. All are available at https://github.com/knoveleng/open-rs.

Large reasoning models (LRMs) can do complex reasoning via long chain-of-thought (CoT) involving cognitive strategies such as backtracking and self-correction. Recent studies suggest that some models inherently possess these long reasoning abilities, which may be unlocked via extra training. Our work first investigates whether we can elicit such behavior without any training. To this end, we propose a decoding-time approach, ThinkLogit, which utilizes logits arithmetic (Liu et al., 2024) to tune a target large LM for long reasoning using a substantially smaller model as guider. We then show that we can further boost performance by training the guider model with preference optimization over correct/incorrect reasoning pairs sampled from both the target and guider model -- a setup we refer to as ThinkLogit-DPO. Our experiments demonstrate that ThinkLogit and ThinkLogit-DPO achieve a relative improvement in pass@1 by 26% and 29%, respectively, over four mathematical datasets using the Qwen2.5-32B when guided by R1-Distill-Qwen-1.5B -- a model 21x smaller. Lastly, we show that ThinkLogit can transfer long reasoning skills acquired through reinforcement learning, improving pass@1 by 13% relative compared to the Qwen2.5-32B base model. Our work presents a computationally-efficient method to elicit long reasoning in large models with minimal or no additional training.

Reinforcement learning, such as PPO and GRPO, has powered recent breakthroughs in LLM reasoning. Scaling rollout to sample more prompts enables models to selectively use higher-quality data for training, which can stabilize RL training and improve model performance. However, this comes at the cost of significant computational overhead. In this paper, we show that a substantial portion of this overhead can be avoided by skipping uninformative prompts before rollout. Our analysis of reward dynamics reveals a strong temporal consistency in prompt value: prompts that are uninformative in one epoch of training are likely to remain uninformative in future epochs. Based on these insights, we propose GRESO (GRPO with Efficient Selective Rollout), an online, lightweight pre-rollout filtering algorithm that predicts and skips uninformative prompts using reward training dynamics. By evaluating GRESO on a broad range of math reasoning benchmarks and models, such as Qwen2.5-Math-1.5B, DeepSeek-R1-Distill-Qwen-1.5B, and Qwen2.5-Math-7B, we show that GRESO achieves up to 2.4x wall-clock time speedup in rollout and up to 2.0x speedup in total training time without accuracy degradation.

Reward models are central to both reinforcement learning (RL) with language models and inference-time verification. However, existing reward models often lack temporal consistency, leading to ineffective policy updates and unstable RL training. We introduce TDRM, a method for learning smoother and more reliable reward models by minimizing temporal differences (TD) for training-time reinforcement learning and inference-time verification. Experiments show that TD-trained process reward models (PRMs) improve performance across Best-of-N (up to 6.6%) and tree-search (up to 23.7%) settings. When combined with Reinforcement Learning with Verifiable Rewards (RLVR), TD-trained PRMs lead to more data-efficient RL -- achieving comparable performance with just 2.5k data to what baseline methods require 50.1k data to attain -- and yield higher-quality language model policies in 8 model variants (5 series), e.g., Qwen2.5-(0.5B, 1,5B), GLM4-9B-0414, GLM-Z1-9B-0414, Qwen2.5-Math-(1.5B, 7B), and DeepSeek-R1-Distill-Qwen-(1.5B, 7B). We release all code at https://github.com/THUDM/TDRM.

In this paper, we propose \textsc{FastCuRL}, a simple yet efficient Curriculum Reinforcement Learning approach with context window extending strategy to accelerate the reinforcement learning training efficiency for R1-like reasoning models while enhancing their performance in tackling complex reasoning tasks with long chain-of-thought rationales, particularly with a 1.5B parameter language model. \textsc{FastCuRL} consists of two main procedures: length-aware training data segmentation and context window extension training. Specifically, the former first splits the original training data into three different levels by the input prompt length, and then the latter leverages segmented training datasets with a progressively increasing context window length to train the reasoning model. Experimental results demonstrate that \textsc{FastCuRL}-1.5B-Preview surpasses DeepScaleR-1.5B-Preview across all five datasets (including MATH 500, AIME 2024, AMC 2023, Minerva Math, and OlympiadBench) while only utilizing 50\% of training steps. Furthermore, all training stages for FastCuRL-1.5B-Preview are completed using just a single node with 8 GPUs.

We introduce our first-generation reasoning models, DeepSeek-R1-Zero and DeepSeek-R1. DeepSeek-R1-Zero, a model trained via large-scale reinforcement learning (RL) without supervised fine-tuning (SFT) as a preliminary step, demonstrates remarkable reasoning capabilities. Through RL, DeepSeek-R1-Zero naturally emerges with numerous powerful and intriguing reasoning behaviors. However, it encounters challenges such as poor readability, and language mixing. To address these issues and further enhance reasoning performance, we introduce DeepSeek-R1, which incorporates multi-stage training and cold-start data before RL. DeepSeek-R1 achieves performance comparable to OpenAI-o1-1217 on reasoning tasks. To support the research community, we open-source DeepSeek-R1-Zero, DeepSeek-R1, and six dense models (1.5B, 7B, 8B, 14B, 32B, 70B) distilled from DeepSeek-R1 based on Qwen and Llama.

R1-style Reinforcement Learning (RL) significantly enhances Large Language Models' reasoning capabilities, yet the mechanism behind rule-based RL remains unclear. We found that small-scale SFT has significant influence on RL but shows poor efficiency. To explain our observations, we propose an analytical framework and compare the efficiency of SFT and RL by measuring sample effect. Hypothetical analysis show that SFT efficiency is limited by training data. Guided by our analysis, we propose Re-distillation, a technique that fine-tunes pretrain model through small-scale distillation from the RL-trained policy. Experiments on Knight & Knave and MATH datasets demonstrate re-distillation's surprising efficiency: re-distilled models match RL performance with far fewer samples and less computation. Empirical verification shows that sample effect is a good indicator of performance improvements. As a result, on K&K dataset, our re-distilled Qwen2.5-1.5B model surpasses DeepSeek-V3-0324 with only 1K SFT samples. On MATH, Qwen2.5-1.5B fine-tuned with re-distilled 500 samples matches its instruct-tuned variant without RL. Our work explains several interesting phenomena in R1-style RL, shedding light on the mechanisms behind its empirical success. Code is available at: https://github.com/on1262/deep-reasoning

Challenging the prevailing consensus that small models inherently lack robust reasoning, this report introduces VibeThinker-1.5B, a 1.5B-parameter dense model developed via our Spectrum-to-Signal Principle (SSP). This challenges the prevailing approach of scaling model parameters to enhance capabilities, as seen in models like DeepSeek R1 (671B) and Kimi k2 (>1T). The SSP framework first employs a Two-Stage Diversity-Exploring Distillation (SFT) to generate a broad spectrum of solutions, followed by MaxEnt-Guided Policy Optimization (RL) to amplify the correct signal. With a total training cost of only $7,800, VibeThinker-1.5B demonstrates superior reasoning capabilities compared to closed-source models like Magistral Medium and Claude Opus 4, and performs on par with open-source models like GPT OSS-20B Medium. Remarkably, it surpasses the 400x larger DeepSeek R1 on three math benchmarks: AIME24 (80.3 vs. 79.8), AIME25 (74.4 vs. 70.0), and HMMT25 (50.4 vs. 41.7). This is a substantial improvement over its base model (6.7, 4.3, and 0.6, respectively). On LiveCodeBench V6, it scores 51.1, outperforming Magistral Medium's 50.3 and its base model's 0.0. These findings demonstrate that small models can achieve reasoning capabilities comparable to large models, drastically reducing training and inference costs and thereby democratizing advanced AI research.

How to design reinforcement learning (RL) tasks that effectively unleash the reasoning capability of large language models (LLMs) remains an open question. Existing RL tasks (e.g., math, programming, and constructing reasoning tasks) suffer from three key limitations: (1) Scalability. They rely heavily on human annotation or expensive LLM synthesis to generate sufficient training data. (2) Verifiability. LLMs' outputs are hard to verify automatically and reliably. (3) Controllable Difficulty. Most tasks lack fine-grained difficulty control, making it hard to train LLMs to develop reasoning ability from easy to hard. To address these limitations, we propose Saturn, a SAT-based RL framework that uses Boolean Satisfiability (SAT) problems to train and evaluate LLM reasoning. Saturn enables scalable task construction, rule-based verification, and precise difficulty control. Saturn designs a curriculum learning pipeline that continuously improves LLMs' reasoning capability by constructing SAT tasks of increasing difficulty and training LLMs from easy to hard. To ensure stable training, we design a principled mechanism to control difficulty transitions. We introduce Saturn-2.6k, a dataset of 2,660 SAT problems with varying difficulty. It supports the evaluation of how LLM reasoning changes with problem difficulty. We apply Saturn to DeepSeek-R1-Distill-Qwen and obtain Saturn-1.5B and Saturn-7B. We achieve several notable results: (1) On SAT problems, Saturn-1.5B and Saturn-7B achieve average pass@3 improvements of +14.0 and +28.1, respectively. (2) On math and programming tasks, Saturn-1.5B and Saturn-7B improve average scores by +4.9 and +1.8 on benchmarks (e.g., AIME, LiveCodeBench). (3) Compared to the state-of-the-art (SOTA) approach in constructing RL tasks, Saturn achieves further improvements of +8.8%. We release the source code, data, and models to support future research.

We propose GeoUni, the first unified geometry expert model capable of generating problem solutions and diagrams within a single framework in a way that enables the creation of unique and individualized geometry problems. Traditionally, solving geometry problems and generating diagrams have been treated as separate tasks in machine learning, with no models successfully integrating both to support problem creation. However, we believe that mastery in geometry requires frictionless integration of all of these skills, from solving problems to visualizing geometric relationships, and finally, crafting tailored problems. Our extensive experiments demonstrate that GeoUni, with only 1.5B parameters, achieves performance comparable to larger models such as DeepSeek-R1 with 671B parameters in geometric reasoning tasks. GeoUni also excels in generating precise geometric diagrams, surpassing both text-to-image models and unified models, including the GPT-4o image generation. Most importantly, GeoUni is the only model capable of successfully generating textual problems with matching diagrams based on specific knowledge points, thus offering a wider range of capabilities that extend beyond current models.

Recent advancements in reasoning language models have demonstrated remarkable performance in complex tasks, but their extended chain-of-thought reasoning process increases inference overhead. While quantization has been widely adopted to reduce the inference cost of large language models, its impact on reasoning models remains understudied. In this study, we conduct the first systematic study on quantized reasoning models, evaluating the open-sourced DeepSeek-R1-Distilled Qwen and LLaMA families ranging from 1.5B to 70B parameters, and QwQ-32B. Our investigation covers weight, KV cache, and activation quantization using state-of-the-art algorithms at varying bit-widths, with extensive evaluation across mathematical (AIME, MATH-500), scientific (GPQA), and programming (LiveCodeBench) reasoning benchmarks. Our findings reveal that while lossless quantization can be achieved with W8A8 or W4A16 quantization, lower bit-widths introduce significant accuracy risks. We further identify model size, model origin, and task difficulty as critical determinants of performance. Contrary to expectations, quantized models do not exhibit increased output lengths. In addition, strategically scaling the model sizes or reasoning steps can effectively enhance the performance. All quantized models and codes will be open-sourced in https://github.com/ruikangliu/Quantized-Reasoning-Models.

Sophisticated instrumentation for AI systems might have indicators that signal misalignment from human values, not unlike a "check engine" light in cars. One such indicator of misalignment is deceptiveness in generated responses. Future AI instrumentation may have the ability to detect when an LLM generates deceptive responses while reasoning about seemingly plausible but incorrect answers to factual questions. In this work, we demonstrate that linear probes on LLMs internal activations can detect deception in their responses with extremely high accuracy. Our probes reach a maximum of greater than 90% accuracy in distinguishing between deceptive and non-deceptive arguments generated by llama and qwen models ranging from 1.5B to 14B parameters, including their DeepSeek-r1 finetuned variants. We observe that probes on smaller models (1.5B) achieve chance accuracy at detecting deception, while larger models (greater than 7B) reach 70-80%, with their reasoning counterparts exceeding 90%. The layer-wise probe accuracy follows a three-stage pattern across layers: near-random (50%) in early layers, peaking in middle layers, and slightly declining in later layers. Furthermore, using an iterative null space projection approach, we find multitudes of linear directions that encode deception, ranging from 20 in Qwen 3B to nearly 100 in DeepSeek 7B and Qwen 14B models.

We report a peculiar observation that LLMs can assign hidden meanings to sequences that seem visually incomprehensible to humans: for example, a nonsensical phrase consisting of Byzantine musical symbols is recognized by gpt-4o as "say abracadabra". Moreover, some models can communicate using these sequences. Some of these meanings are hypothesized to partly originate in the massive spurious correlations due to BPE tokenization. We systematically evaluate the presence of such abilities in a wide range of models: Claude-3.5 Haiku, Claude-3.5 Sonnet (New and Old), Claude-3.7 Sonnet, gpt-4o mini, gpt-4o, o1-mini, Llama-3.3 70B, DeepSeek-R1-Distill-Lllama 70B, Qwen2.5 1.5B, Qwen2.5 32B, Phi-3.5 mini, GigaChat-Max, Vikhr-Llama-3.2 1B. We argue that this observation might have far-reaching consequences for both safety and security of the modern and future LLMs and systems that employ them. As an illustration, we show that applying this method in combination with simple templates is sufficient to jailbreak previous generation models, with ASR = 0.4 on gpt-4o mini. Our code and data artifacts are available at https://github.com/L3G5/llm-hidden-meanings