Recent large language models (LLMs) have demonstrated strong reasoning capabilities that benefits from online reinforcement learning (RL). These capabilities have primarily been demonstrated within the left-to-right autoregressive (AR) generation paradigm. In contrast, non-autoregressive paradigms based on diffusion generate text in a coarse-to-fine manner. Although recent diffusion-based large language models (dLLMs) have achieved competitive language modeling performance compared to their AR counterparts, it remains unclear if dLLMs can also leverage recent advances in LLM reasoning. To this end, we propose d1, a framework to adapt pre-trained masked dLLMs into reasoning models via a combination of supervised finetuning (SFT) and RL. Specifically, we develop and extend techniques to improve reasoning in pretrained dLLMs: (a) we utilize a masked SFT technique to distill knowledge and instill self-improvement behavior directly from existing datasets, and (b) we introduce a novel critic-free, policy-gradient based RL algorithm called diffu-GRPO. Through empirical studies, we investigate the performance of different post-training recipes on multiple mathematical and logical reasoning benchmarks. We find that d1 yields the best performance and significantly improves performance of a state-of-the-art dLLM.
We present a novel framework that bridges the gap between the interpretability of decision trees and the advanced reasoning capabilities of large language models (LLMs) to predict startup success. Our approach leverages chain-of-thought prompting to generate detailed reasoning logs, which are subsequently distilled into structured, human-understandable logical rules. The pipeline integrates multiple enhancements - efficient data ingestion, a two-step refinement process, ensemble candidate sampling, simulated reinforcement learning scoring, and persistent memory - to ensure both stable decision-making and transparent output. Experimental evaluations on curated startup datasets demonstrate that our combined pipeline improves precision by 54% from 0.225 to 0.346 and accuracy by 50% from 0.46 to 0.70 compared to a standalone OpenAI o3 model. Notably, our model achieves over 2x the precision of a random classifier (16%). By combining state-of-the-art AI reasoning with explicit rule-based explanations, our method not only augments traditional decision-making processes but also facilitates expert intervention and continuous policy refinement. This work lays the foundation for the implementation of interpretable LLM-powered decision frameworks in high-stakes investment environments and other domains that require transparent and data-driven insights.
While reasoning models (e.g., DeepSeek R1) trained with reinforcement learning (RL), excel in textual reasoning, they struggle in scenarios requiring structured problem-solving, such as geometric reasoning, concise computation, or complex equation solving-areas where computational tools like code interpreters (CI) demonstrate distinct advantages. To bridge this gap, we propose ReTool, which enhances long-form reasoning with tool-integrated learning, including two key features: (1) dynamic interleaving of real-time code execution within natural language reasoning processes, and (2) an automated RL paradigm that allows policy rollouts with multi-turn real-time code execution and teaches the model in learning when and how to invoke tools based on outcome feedback. ReTool employs a systematic training framework, beginning with synthetic cold-start data generation to produce code-augmented long-form reasoning traces for fine-tuning base models. Subsequent RL training leverages task outcomes as rewards to iteratively refine the model's tool use strategy, enabling autonomous discovery of optimal tool invocation patterns without human priors. Experiments on the challenging MATH Olympiad benchmark AIME demonstrate ReTool's superiority: Our 32B model achieves 67% accuracy with 400 training steps, outperforming text-based RL baseline (40% accuracy, 1080 steps) in efficiency and performance. Remarkably, ReTool-32B attains 72.5% accuracy in extended settings, surpassing OpenAI's o1-preview by 27.9%. Further analysis reveals emergent behaviors such as code self-correction, signaling an ''aha moment'' in which the model autonomously masters adaptive tool use. These findings highlight the promise of outcome-driven tool integration for advancing complex mathematical reasoning and offer new insights into hybrid neuro-symbolic systems.
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.
Reinforcement learning (RL) has become a prevailing approach for fine-tuning large language models (LLMs) on complex reasoning tasks. Among recent methods, GRPO stands out for its empirical success in training models such as DeepSeek-R1, yet the sources of its effectiveness remain poorly understood. In this work, we revisit GRPO from a reinforce-like algorithm perspective and analyze its core components. Surprisingly, we find that a simple rejection sampling baseline, RAFT, which trains only on positively rewarded samples, yields competitive performance than GRPO and PPO. Our ablation studies reveal that GRPO's main advantage arises from discarding prompts with entirely incorrect responses, rather than from its reward normalization. Motivated by this insight, we propose Reinforce-Rej, a minimal extension of policy gradient that filters both entirely incorrect and entirely correct samples. Reinforce-Rej improves KL efficiency and stability, serving as a lightweight yet effective alternative to more complex RL algorithms. We advocate RAFT as a robust and interpretable baseline, and suggest that future advances should focus on more principled designs for incorporating negative samples, rather than relying on them indiscriminately. Our findings provide guidance for future work in reward-based LLM post-training.
The rise of reinforcement learning (RL) in critical real-world applications demands a fundamental rethinking of privacy in AI systems. Traditional privacy frameworks, designed to protect isolated data points, fall short for sequential decision-making systems where sensitive information emerges from temporal patterns, behavioral strategies, and collaborative dynamics. Modern RL paradigms, such as federated RL (FedRL) and RL with human feedback (RLHF) in large language models (LLMs), exacerbate these challenges by introducing complex, interactive, and context-dependent learning environments that traditional methods do not address. In this position paper, we argue for a new privacy paradigm built on four core principles: multi-scale protection, behavioral pattern protection, collaborative privacy preservation, and context-aware adaptation. These principles expose inherent tensions between privacy, utility, and interpretability that must be navigated as RL systems become more pervasive in high-stakes domains like healthcare, autonomous vehicles, and decision support systems powered by LLMs. To tackle these challenges, we call for the development of new theoretical frameworks, practical mechanisms, and rigorous evaluation methodologies that collectively enable effective privacy protection in sequential decision-making systems.
Retrieval-Augmented Generation (RAG) improves Large Language Model (LLM) performance on knowledge-intensive tasks but depends heavily on initial search query quality. Current methods, often using Reinforcement Learning (RL), typically focus on query formulation or reasoning over results, without explicitly encouraging persistence after a failed search. We introduce ReZero (Retry-Zero), a novel RL framework that directly rewards the act of retrying a search query following an initial unsuccessful attempt. This incentivizes the LLM to explore alternative queries rather than prematurely halting. ReZero demonstrates significant improvement, achieving 46.88% accuracy compared to a 25% baseline. By rewarding persistence, ReZero enhances LLM robustness in complex information-seeking scenarios where initial queries may prove insufficient.
An AI system can create and maintain knowledge only to the extent that it can verify that knowledge itself. Recent work on long Chain-of-Thought reasoning has demonstrated great potential of LLMs on solving competitive problems, but their verification ability remains to be weak and not sufficiently investigated. In this paper, we propose Heimdall, the long CoT verification LLM that can accurately judge the correctness of solutions. With pure reinforcement learning, we boost the verification accuracy from 62.5% to 94.5% on competitive math problems. By scaling with repeated sampling, the accuracy further increases to 97.5%. Through human evaluation, Heimdall demonstrates impressive generalization capabilities, successfully detecting most issues in challenging math proofs, the type of which is not included during training. Furthermore, we propose Pessimistic Verification to extend the functionality of Heimdall to scaling up the problem solving. It calls Heimdall to judge the solutions from a solver model and based on the pessimistic principle, selects the most likely correct solution with the least uncertainty. Taking DeepSeek-R1-Distill-Qwen-32B as the solver model, Pessimistic Verification improves the solution accuracy on AIME2025 from 54.2% to 70.0% with 16x compute budget and to 83.3% with more compute budget. With the stronger solver Gemini 2.5 Pro, the score reaches 93.0%. Finally, we prototype an automatic knowledge discovery system, a ternary system where one poses questions, another provides solutions, and the third verifies the solutions. Using the data synthesis work NuminaMath for the first two components, Heimdall effectively identifies problematic records within the dataset and reveals that nearly half of the data is flawed, which interestingly aligns with the recent ablation studies from NuminaMath.
Recently, deep reasoning LLMs (e.g., OpenAI o1/o3 and DeepSeek-R1) have shown promising performance in various complex tasks. Free translation is an important and interesting task in the multilingual world, which requires going beyond word-for-word translation and taking cultural differences into account. This task is still under-explored in deep reasoning LLMs. In this paper, we introduce DeepTrans, a deep reasoning translation model that learns free translation via reinforcement learning. Specifically, we carefully build a reward model with pre-defined scoring criteria on both the translation results and the thought process. Given the source sentences, the reward model teaches the deep translation model how to think and free-translate them during reinforcement learning. In this way, training DeepTrans does not need any labeled translations, avoiding the human-intensive annotation or resource-intensive data synthesis. Experimental results show the effectiveness of DeepTrans. Using Qwen2.5-7B as the backbone, DeepTrans improves performance by 16.3% in literature translation, and outperforms strong deep reasoning baselines as well as baselines that are fine-tuned with synthesized data. Moreover, we summarize the failures and interesting findings during our RL exploration. We hope this work could inspire other researchers in free translation.
Large-scale reinforcement learning (RL) methods have proven highly effective in enhancing the reasoning abilities of large language models (LLMs), particularly for tasks with verifiable solutions such as mathematics and coding. However, applying this idea to machine translation (MT), where outputs are flexibly formatted and difficult to automatically evaluate with explicit rules, remains underexplored. In this work, we introduce MT-R1-Zero, the first open-source adaptation of the R1-Zero RL framework for MT without supervised fine-tuning or cold-start. We propose a rule-metric mixed reward mechanism to guide LLMs towards improved translation quality via emergent reasoning. On the WMT 24 English-Chinese benchmark, our MT-R1-Zero-3B-Mix achieves competitive performance, surpassing TowerInstruct-7B-v0.2 by an average of 1.26 points. Meanwhile, our MT-R1-Zero-7B-Mix attains a high average score of 62.25 across all metrics, placing it on par with advanced proprietary models such as GPT-4o and Claude-3.5-Sonnet, while the MT-R1-Zero-7B-Sem variant achieves state-of-the-art scores on semantic metrics. Moreover, our work exhibits strong generalization capabilities on out-of-distribution MT tasks, robustly supporting multilingual and low-resource settings. Extensive analysis of model behavior across different initializations and reward metrics offers pioneering insight into the critical role of reward design, LLM adaptability, training dynamics, and emergent reasoning patterns within the R1-Zero paradigm for MT. Our code is available at https://github.com/fzp0424/MT-R1-Zero.
Recent advances in reinforcement learning (RL)-based post-training have led to notable improvements in large language models (LLMs), particularly in enhancing their reasoning capabilities to handle complex tasks. However, most existing methods treat the training data as a unified whole, overlooking the fact that modern LLM training often involves a mixture of data from diverse distributions-varying in both source and difficulty. This heterogeneity introduces a key challenge: how to adaptively schedule training across distributions to optimize learning efficiency. In this paper, we present a principled curriculum learning framework grounded in the notion of distribution-level learnability. Our core insight is that the magnitude of policy advantages reflects how much a model can still benefit from further training on a given distribution. Based on this, we propose a distribution-level curriculum learning framework for RL-based LLM post-training, which leverages the Upper Confidence Bound (UCB) principle to dynamically adjust sampling probabilities for different distrubutions. This approach prioritizes distributions with either high average advantage (exploitation) or low sample count (exploration), yielding an adaptive and theoretically grounded training schedule. We instantiate our curriculum learning framework with GRPO as the underlying RL algorithm and demonstrate its effectiveness on logic reasoning datasets with multiple difficulties and sources. Our experiments show that our framework significantly improves convergence speed and final performance, highlighting the value of distribution-aware curriculum strategies in LLM post-training. Code: https://github.com/ZhentingWang/DUMP.
The capabilities of the latest large language models (LLMs) have been extended from pure natural language understanding to complex reasoning tasks. However, current reasoning models often exhibit factual inaccuracies in longer reasoning chains, which poses challenges for historical reasoning and limits the potential of LLMs in complex, knowledge-intensive tasks. Historical studies require not only the accurate presentation of factual information but also the ability to establish cross-temporal correlations and derive coherent conclusions from fragmentary and often ambiguous sources. To address these challenges, we propose Kongzi, a large language model specifically designed for historical analysis. Through the integration of curated, high-quality historical data and a novel fact-reinforcement learning strategy, Kongzi demonstrates strong factual alignment and sophisticated reasoning depth. Extensive experiments on tasks such as historical question answering and narrative generation demonstrate that Kongzi outperforms existing models in both factual accuracy and reasoning depth. By effectively addressing the unique challenges inherent in historical texts, Kongzi sets a new standard for the development of accurate and reliable LLMs in professional domains.
The primary goal of my Ph.D. study is to develop provably efficient and practical algorithms for data-driven online sequential decision-making under uncertainty. My work focuses on reinforcement learning (RL), multi-armed bandits, and their applications, including recommendation systems, computer networks, video analytics, and large language models (LLMs). Online learning methods, such as bandits and RL, have demonstrated remarkable success - ranging from outperforming human players in complex games like Atari and Go to advancing robotics, recommendation systems, and fine-tuning LLMs. Despite these successes, many established algorithms rely on idealized models that can fail under model misspecifications or adversarial perturbations, particularly in settings where accurate prior knowledge of the underlying model class is unavailable or where malicious users operate within dynamic systems. These challenges are pervasive in real-world applications, where robust and adaptive solutions are critical. Furthermore, while worst-case guarantees provide theoretical reliability, they often fail to capture instance-dependent performance, which can lead to more efficient and practical solutions. Another key challenge lies in generalizing to new, unseen environments, a crucial requirement for deploying these methods in dynamic and unpredictable settings. To address these limitations, my research aims to develop more efficient, robust, instance-adaptive, and generalizable online learning algorithms for both reinforcement learning and bandits. Towards this end, I focus on developing more efficient, robust, instance-adaptive, and generalizable for both general reinforcement learning (RL) and bandits.
The rapid advancement of large language models (LLMs) has brought significant benefits to various domains while introducing substantial risks. Despite being fine-tuned through reinforcement learning, LLMs lack the capability to discern malicious content, limiting their defense against jailbreak. To address these safety concerns, we propose a feature-aware method for harmful response rejection (FMM), which detects the presence of malicious features within the model's feature space and adaptively adjusts the model's rejection mechanism. By employing a simple discriminator, we detect potential malicious traits during the decoding phase. Upon detecting features indicative of toxic tokens, FMM regenerates the current token. By employing activation patching, an additional rejection vector is incorporated during the subsequent token generation, steering the model towards a refusal response. Experimental results demonstrate the effectiveness of our approach across multiple language models and diverse attack techniques, while crucially maintaining the models' standard generation capabilities.
Large Language Models (LLMs) are changing the way we operate our society and will undoubtedly impact power systems as well - but how exactly? By integrating various data streams - including real-time grid data, market dynamics, and consumer behaviors - LLMs have the potential to make power system operations more adaptive, enhance proactive security measures, and deliver personalized energy services. This paper provides a comprehensive analysis of 30 real-world applications across eight key categories: Grid Operations and Management, Energy Markets and Trading, Personalized Energy Management and Customer Engagement, Grid Planning and Education, Grid Security and Compliance, Advanced Data Analysis and Knowledge Discovery, Emerging Applications and Societal Impact, and LLM-Enhanced Reinforcement Learning. Critical technical hurdles, such as data privacy and model reliability, are examined, along with possible solutions. Ultimately, this review illustrates how LLMs can significantly contribute to building more resilient, efficient, and sustainable energy infrastructures, underscoring the necessity of their responsible and equitable deployment.
Reasoning is a fundamental cognitive process that enables logical inference, problem-solving, and decision-making. With the rapid advancement of large language models (LLMs), reasoning has emerged as a key capability that distinguishes advanced AI systems from conventional models that empower chatbots. In this survey, we categorize existing methods along two orthogonal dimensions: (1) Regimes, which define the stage at which reasoning is achieved (either at inference time or through dedicated training); and (2) Architectures, which determine the components involved in the reasoning process, distinguishing between standalone LLMs and agentic compound systems that incorporate external tools, and multi-agent collaborations. Within each dimension, we analyze two key perspectives: (1) Input level, which focuses on techniques that construct high-quality prompts that the LLM condition on; and (2) Output level, which methods that refine multiple sampled candidates to enhance reasoning quality. This categorization provides a systematic understanding of the evolving landscape of LLM reasoning, highlighting emerging trends such as the shift from inference-scaling to learning-to-reason (e.g., DeepSeek-R1), and the transition to agentic workflows (e.g., OpenAI Deep Research, Manus Agent). Additionally, we cover a broad spectrum of learning algorithms, from supervised fine-tuning to reinforcement learning such as PPO and GRPO, and the training of reasoners and verifiers. We also examine key designs of agentic workflows, from established patterns like generator-evaluator and LLM debate to recent innovations. ...
Recently DeepSeek R1 has shown that reinforcement learning (RL) can substantially improve the reasoning capabilities of Large Language Models (LLMs) through a simple yet effective design. The core of R1 lies in its rule-based reward formulation, which leverages tasks with deterministic ground-truth answers to enable precise and stable reward computation. In the visual domain, we similarly observe that a wide range of visual understanding tasks are inherently equipped with well-defined ground-truth annotations. This property makes them naturally compatible with rule-based reward mechanisms. Motivated by this observation, we investigate the extension of R1-style reinforcement learning to Vision-Language Models (VLMs), aiming to enhance their visual reasoning capabilities. To this end, we develop VLM-R1, a dedicated framework designed to harness RL for improving VLMs' performance on general vision-language tasks. Using this framework, we further explore the feasibility of applying RL to visual domain. Experimental results indicate that the RL-based model not only delivers competitive performance on visual understanding tasks but also surpasses Supervised Fine-Tuning (SFT) in generalization ability. Furthermore, we conduct comprehensive ablation studies that uncover a series of noteworthy insights, including the presence of reward hacking in object detection, the emergence of the "OD aha moment", the impact of training data quality, and the scaling behavior of RL across different model sizes. Through these analyses, we aim to deepen the understanding of how reinforcement learning enhances the capabilities of vision-language models, and we hope our findings and open-source contributions will support continued progress in the vision-language RL community. Our code and model are available at https://github.com/om-ai-lab/VLM-R1
Large Language Models (LLMs) are emerging as promising tools for automated reinforcement learning (RL) reward design, owing to their robust capabilities in commonsense reasoning and code generation. By engaging in dialogues with RL agents, LLMs construct a Reward Observation Space (ROS) by selecting relevant environment states and defining their internal operations. However, existing frameworks have not effectively leveraged historical exploration data or manual task descriptions to iteratively evolve this space. In this paper, we propose a novel heuristic framework that enhances LLM-driven reward design by evolving the ROS through a table-based exploration caching mechanism and a text-code reconciliation strategy. Our framework introduces a state execution table, which tracks the historical usage and success rates of environment states, overcoming the Markovian constraint typically found in LLM dialogues and facilitating more effective exploration. Furthermore, we reconcile user-provided task descriptions with expert-defined success criteria using structured prompts, ensuring alignment in reward design objectives. Comprehensive evaluations on benchmark RL tasks demonstrate the effectiveness and stability of the proposed framework. Code and video demos are available at jingjjjjjie.github.io/LLM2Reward.
In this work, we establish a novel theoretical connection between supervised fine-tuning and offline reinforcement learning under the token-level Markov decision process, revealing that large language models indeed learn an implicit $Q$-function for inference. Through this theoretical lens, we demonstrate that the widely used beam search method suffers from unacceptable over-optimism, where inference errors are inevitably amplified due to inflated $Q$-value estimations of suboptimal steps. To address this limitation, we propose Supervised Optimism Correction(SOC), which introduces a simple yet effective auxiliary loss for token-level $Q$-value estimations during supervised fine-tuning. Specifically, the auxiliary loss employs implicit value regularization to boost model confidence in expert-demonstrated responses, thereby suppressing over-optimism toward insufficiently supervised responses. Extensive experiments on mathematical reasoning benchmarks, including GSM8K, MATH, and GAOKAO, showcase the superiority of the proposed SOC with beam search across a series of open-source models.
We present Kimi-VL, an efficient open-source Mixture-of-Experts (MoE) vision-language model (VLM) that offers advanced multimodal reasoning, long-context understanding, and strong agent capabilities - all while activating only 2.8B parameters in its language decoder (Kimi-VL-A3B). Kimi-VL demonstrates strong performance across challenging domains: as a general-purpose VLM, Kimi-VL excels in multi-turn agent tasks (e.g., OSWorld), matching flagship models. Furthermore, it exhibits remarkable capabilities across diverse challenging vision language tasks, including college-level image and video comprehension, OCR, mathematical reasoning, and multi-image understanding. In comparative evaluations, it effectively competes with cutting-edge efficient VLMs such as GPT-4o-mini, Qwen2.5-VL-7B, and Gemma-3-12B-IT, while surpassing GPT-4o in several key domains. Kimi-VL also advances in processing long contexts and perceiving clearly. With a 128K extended context window, Kimi-VL can process diverse long inputs, achieving impressive scores of 64.5 on LongVideoBench and 35.1 on MMLongBench-Doc. Its native-resolution vision encoder, MoonViT, further allows it to see and understand ultra-high-resolution visual inputs, achieving 83.2 on InfoVQA and 34.5 on ScreenSpot-Pro, while maintaining lower computational cost for common tasks. Building upon Kimi-VL, we introduce an advanced long-thinking variant: Kimi-VL-Thinking. Developed through long chain-of-thought (CoT) supervised fine-tuning (SFT) and reinforcement learning (RL), this model exhibits strong long-horizon reasoning capabilities. It achieves scores of 61.7 on MMMU, 36.8 on MathVision, and 71.3 on MathVista while maintaining the compact 2.8B activated LLM parameters, setting a new standard for efficient multimodal thinking models. Code and models are publicly accessible at https://github.com/MoonshotAI/Kimi-VL.
Deep reinforcement learning (DRL) has effectively enhanced gameplay experiences and game design across various game genres. However, few studies on fighting game agents have focused explicitly on enhancing player enjoyment, a critical factor for both developers and players. To address this gap and establish a practical baseline for designing enjoyability-focused agents, we propose a two-tier agent (TTA) system and conducted experiments in the classic fighting game Street Fighter II. The first tier of TTA employs a task-oriented network architecture, modularized reward functions, and hybrid training to produce diverse and skilled DRL agents. In the second tier of TTA, a Large Language Model Hyper-Agent, leveraging players' playing data and feedback, dynamically selects suitable DRL opponents. In addition, we investigate and model several key factors that affect the enjoyability of the opponent. The experiments demonstrate improvements from 64. 36% to 156. 36% in the execution of advanced skills over baseline methods. The trained agents also exhibit distinct game-playing styles. Additionally, we conducted a small-scale user study, and the overall enjoyment in the player's feedback validates the effectiveness of our TTA system.
Reinforcement learning (RL) agents have shown remarkable performances in various environments, where they can discover effective policies directly from sensory inputs. However, these agents often exploit spurious correlations in the training data, resulting in brittle behaviours that fail to generalize to new or slightly modified environments. To address this, we introduce the Causal Object-centric Model Extraction Tool (COMET), a novel algorithm designed to learn the exact interpretable causal world models (CWMs). COMET first extracts object-centric state descriptions from observations and identifies the environment's internal states related to the depicted objects' properties. Using symbolic regression, it models object-centric transitions and derives causal relationships governing object dynamics. COMET further incorporates large language models (LLMs) for semantic inference, annotating causal variables to enhance interpretability. By leveraging these capabilities, COMET constructs CWMs that align with the true causal structure of the environment, enabling agents to focus on task-relevant features. The extracted CWMs mitigate the danger of shortcuts, permitting the development of RL systems capable of better planning and decision-making across dynamic scenarios. Our results, validated in Atari environments such as Pong and Freeway, demonstrate the accuracy and robustness of COMET, highlighting its potential to bridge the gap between object-centric reasoning and causal inference in reinforcement learning.
Recent advancements in large language models have significantly improved their reasoning abilities, particularly through techniques involving search and backtracking. Backtracking naturally scales test-time compute by enabling sequential, linearized exploration via long chain-of-thought (CoT) generation. However, this is not the only strategy for scaling test-time compute: parallel sampling with best-of-n selection provides an alternative that generates diverse solutions simultaneously. Despite the growing adoption of sequential search, its advantages over parallel sampling--especially under a fixed compute budget remain poorly understood. In this paper, we systematically compare these two approaches on two challenging reasoning tasks: CountDown and Sudoku. Surprisingly, we find that sequential search underperforms parallel sampling on CountDown but outperforms it on Sudoku, suggesting that backtracking is not universally beneficial. We identify two factors that can cause backtracking to degrade performance: (1) training on fixed search traces can lock models into suboptimal strategies, and (2) explicit CoT supervision can discourage "implicit" (non-verbalized) reasoning. Extending our analysis to reinforcement learning (RL), we show that models with backtracking capabilities benefit significantly from RL fine-tuning, while models without backtracking see limited, mixed gains. Together, these findings challenge the assumption that backtracking universally enhances LLM reasoning, instead revealing a complex interaction between task structure, training data, model scale, and learning paradigm.
Despite advances in Preference Alignment (PA) for Large Language Models (LLMs), mainstream methods like Reinforcement Learning with Human Feedback (RLHF) face notable challenges. These approaches require high-quality datasets of positive preference examples, which are costly to obtain and computationally intensive due to training instability, limiting their use in low-resource scenarios. LLM unlearning technique presents a promising alternative, by directly removing the influence of negative examples. However, current research has primarily focused on empirical validation, lacking systematic quantitative analysis. To bridge this gap, we propose a framework to explore the relationship between PA and LLM unlearning. Specifically, we introduce a bi-level optimization-based method to quantify the impact of unlearning specific negative examples on PA performance. Our analysis reveals that not all negative examples contribute equally to alignment improvement when unlearned, and the effect varies significantly across examples. Building on this insight, we pose a crucial question: how can we optimally select and weight negative examples for unlearning to maximize PA performance? To answer this, we propose a framework called Unlearning to Align (U2A), which leverages bi-level optimization to efficiently select and unlearn examples for optimal PA performance. We validate the proposed method through extensive experiments, with results confirming its effectiveness.
Large reasoning models (LRMs) have recently shown impressive capabilities in complex reasoning by leveraging increased test-time computation and exhibiting behaviors akin to human-like deliberation. Despite these advances, it remains an open question whether LRMs are better calibrated - particularly in their verbalized confidence - compared to instruction-tuned counterparts. In this paper, we investigate the calibration properties of LRMs trained via supervised fine-tuning distillation on long reasoning traces (henceforth SFT reasoning models) and outcome-based reinforcement learning for reasoning (henceforth RL reasoning models) across diverse domains. Our findings reveal that LRMs significantly outperform instruction-tuned models on complex reasoning tasks in both accuracy and confidence calibration. In contrast, we find surprising trends in the domain of factuality in particular. On factuality tasks, while Deepseek-R1 shows strong calibration behavior, smaller QwQ-32B shows no improvement over instruct models; moreover, SFT reasoning models display worse calibration (greater overconfidence) compared to instruct models. Our results provide evidence for a potentially critical role of reasoning-oriented RL training in improving LLMs' capacity for generating trustworthy, self-aware outputs.
We find that the response length of reasoning LLMs, whether trained by reinforcement learning or supervised learning, drastically increases for ill-posed questions with missing premises (MiP), ending up with redundant and ineffective thinking. This newly introduced scenario exacerbates the general overthinking issue to a large extent, which we name as the MiP-Overthinking. Such failures are against the ``test-time scaling law'' but have been widely observed on multiple datasets we curated with MiP, indicating the harm of cheap overthinking and a lack of critical thinking. Surprisingly, LLMs not specifically trained for reasoning exhibit much better performance on the MiP scenario, producing much shorter responses that quickly identify ill-posed queries. This implies a critical flaw of the current training recipe for reasoning LLMs, which does not encourage efficient thinking adequately, leading to the abuse of thinking patterns. To further investigate the reasons behind such failures, we conduct fine-grained analyses of the reasoning length, overthinking patterns, and location of critical thinking on different types of LLMs. Moreover, our extended ablation study reveals that the overthinking is contagious through the distillation of reasoning models' responses. These results improve the understanding of overthinking and shed novel insights into mitigating the problem.
Recent advances in automated theorem proving (ATP) through LLMs have highlighted the potential of formal reasoning with Lean 4 codes. However, ATP has not yet be revolutionized by the recent posttraining scaling as demonstrated by Open AI O1/O3 and Deepseek R1. In this work, we investigate the entire posttraining of ATP, aiming to align it with breakthroughs in reasoning models in natural languages. To begin, we continual train current ATP models with a hybrid dataset, which consists of numerous statement-proof pairs, and additional data aimed at incorporating cognitive behaviors that emulate human reasoning and hypothesis refinement. Next, we explore reinforcement learning with the use of outcome reward returned by Lean 4 compiler. Through our designed continual training and reinforcement learning processes, we have successfully improved existing formal provers, including both DeepSeek-Prover-v1.5 and Goedel-Prover, achieving state-of-the-art performance in the field of whole-proof generation. For example, we achieve a 59.8% pass rate (pass@32) on MiniF2F. This is an on-going project and we will progressively update our findings, release our data and training details.
Geometric Machine Learning (GML) has shown that respecting non-Euclidean geometry in data spaces can significantly improve performance over naive Euclidean assumptions. In parallel, Quantum Machine Learning (QML) has emerged as a promising paradigm that leverages superposition, entanglement, and interference within quantum state manifolds for learning tasks. This paper offers a unifying perspective by casting QML as a specialized yet more expressive branch of GML. We argue that quantum states, whether pure or mixed, reside on curved manifolds (e.g., projective Hilbert spaces or density-operator manifolds), mirroring how covariance matrices inhabit the manifold of symmetric positive definite (SPD) matrices or how image sets occupy Grassmann manifolds. However, QML also benefits from purely quantum properties, such as entanglement-induced curvature, that can yield richer kernel structures and more nuanced data embeddings. We illustrate these ideas with published and newly discussed results, including hybrid classical -quantum pipelines for diabetic foot ulcer classification and structural health monitoring. Despite near-term hardware limitations that constrain purely quantum solutions, hybrid architectures already demonstrate tangible benefits by combining classical manifold-based feature extraction with quantum embeddings. We present a detailed mathematical treatment of the geometrical underpinnings of quantum states, emphasizing parallels to classical Riemannian geometry and manifold-based optimization. Finally, we outline open research challenges and future directions, including Quantum Large Language Models (LLMs), quantum reinforcement learning, and emerging hardware approaches, demonstrating how synergizing GML and QML principles can unlock the next generation of machine intelligence.
While large language models (LLMs) have demonstrated exceptional capabilities in challenging tasks such as mathematical reasoning, existing methods to enhance reasoning ability predominantly rely on supervised fine-tuning (SFT) followed by reinforcement learning (RL) on reasoning-specific data after pre-training. However, these approaches critically depend on external supervisions--such as human labelled reasoning traces, verified golden answers, or pre-trained reward models--which limits scalability and practical applicability. In this work, we propose Entropy Minimized Policy Optimization (EMPO), which makes an early attempt at fully unsupervised LLM reasoning incentivization. EMPO does not require any supervised information for incentivizing reasoning capabilities (i.e., neither verifiable reasoning traces, problems with golden answers, nor additional pre-trained reward models). By continuously minimizing the predictive entropy of LLMs on unlabeled user queries in a latent semantic space, EMPO enables purely self-supervised evolution of reasoning capabilities with strong flexibility and practicality. Our experiments demonstrate competitive performance of EMPO on both mathematical reasoning and free-form commonsense reasoning tasks. Specifically, without any supervised signals, EMPO boosts the accuracy of Qwen2.5-Math-7B Base from 30.7\% to 48.1\% on mathematical benchmarks and improves truthfulness accuracy of Qwen2.5-7B Instruct from 87.16\% to 97.25\% on TruthfulQA.
Chain-of-Thought (CoT) enhances an LLM's ability to perform complex reasoning tasks, but it also introduces new security issues. In this work, we present ShadowCoT, a novel backdoor attack framework that targets the internal reasoning mechanism of LLMs. Unlike prior token-level or prompt-based attacks, ShadowCoT directly manipulates the model's cognitive reasoning path, enabling it to hijack multi-step reasoning chains and produce logically coherent but adversarial outcomes. By conditioning on internal reasoning states, ShadowCoT learns to recognize and selectively disrupt key reasoning steps, effectively mounting a self-reflective cognitive attack within the target model. Our approach introduces a lightweight yet effective multi-stage injection pipeline, which selectively rewires attention pathways and perturbs intermediate representations with minimal parameter overhead (only 0.15% updated). ShadowCoT further leverages reinforcement learning and reasoning chain pollution (RCP) to autonomously synthesize stealthy adversarial CoTs that remain undetectable to advanced defenses. Extensive experiments across diverse reasoning benchmarks and LLMs show that ShadowCoT consistently achieves high Attack Success Rate (94.4%) and Hijacking Success Rate (88.4%) while preserving benign performance. These results reveal an emergent class of cognition-level threats and highlight the urgent need for defenses beyond shallow surface-level consistency.