Daily Papers

Existing research on instruction following largely focuses on tasks with simple instructions and short responses. In this work, we explore multi-constraint instruction following for generating long-form text. We create Suri, a dataset with 20K human-written long-form texts paired with LLM-generated backtranslated instructions that contain multiple complex constraints. Because of prohibitive challenges associated with collecting human preference judgments on long-form texts, preference-tuning algorithms such as DPO are infeasible in our setting; thus, we propose Instructional ORPO (I-ORPO), an alignment method based on the ORPO algorithm. Instead of receiving negative feedback from dispreferred responses, I-ORPO obtains negative feedback from synthetically corrupted instructions generated by an LLM. Using Suri, we perform supervised and I-ORPO fine-tuning on Mistral-7b-Instruct-v0.2. The resulting models, Suri-SFT and Suri-I-ORPO, generate significantly longer texts (~5K tokens) than base models without significant quality deterioration. Our human evaluation shows that while both SFT and I-ORPO models satisfy most constraints, Suri-I-ORPO generations are generally preferred for their coherent and informative incorporation of the constraints. We release our code at https://github.com/chtmp223/suri.

While recent preference alignment algorithms for language models have demonstrated promising results, supervised fine-tuning (SFT) remains imperative for achieving successful convergence. In this paper, we study the crucial role of SFT within the context of preference alignment, emphasizing that a minor penalty for the disfavored generation style is sufficient for preference-aligned SFT. Building on this foundation, we introduce a straightforward and innovative reference model-free monolithic odds ratio preference optimization algorithm, ORPO, eliminating the necessity for an additional preference alignment phase. We demonstrate, both empirically and theoretically, that the odds ratio is a sensible choice for contrasting favored and disfavored styles during SFT across the diverse sizes from 125M to 7B. Specifically, fine-tuning Phi-2 (2.7B), Llama-2 (7B), and Mistral (7B) with ORPO on the UltraFeedback alone surpasses the performance of state-of-the-art language models with more than 7B and 13B parameters: achieving up to 12.20% on AlpacaEval_{2.0} (Figure 1), 66.19% on IFEval (instruction-level loose, Table 6), and 7.32 in MT-Bench (Figure 12). We release code and model checkpoints for Mistral-ORPO-alpha (7B) and Mistral-ORPO-beta (7B).

Direct Alignment Algorithms (DAAs) simplify language model alignment by replacing reinforcement learning (RL) and reward modeling (RM) in Reinforcement Learning from Human Feedback (RLHF) with direct policy optimization. DAAs can be classified by their ranking losses (pairwise vs. pointwise), by the rewards used in those losses (e.g., likelihood ratios of policy and reference policy, or odds ratios), or by whether a Supervised Fine-Tuning (SFT) phase is required (two-stage vs. one-stage). We first show that one-stage methods underperform two-stage methods. To address this, we incorporate an explicit SFT phase and introduce the beta parameter, controlling the strength of preference optimization, into single-stage ORPO and ASFT. These modifications improve their performance in Alpaca Eval 2 by +3.46 (ORPO) and +8.27 (ASFT), matching two-stage methods like DPO. Further analysis reveals that the key factor is whether the approach uses pairwise or pointwise objectives, rather than the specific implicit reward or loss function. These results highlight the importance of careful evaluation to avoid premature claims of performance gains or overall superiority in alignment algorithms.

Post-training alignment algorithms are predominantly evaluated as black boxes, obscuring how they reshape language models' internal computations. We present a systematic mechanistic analysis of six preference-optimization methods: PPO, DPO, SimPO, ORPO, GRPO, and KTO across three open-weight model families. By integrating layer-wise linear probing, Sparse Autoencoders, and crosscoders, we localize preference representations and quantify alignment-induced geometric transformations in latent space. We find that preference signals consistently concentrate in early--mid or mid--late layers, but different objectives induce qualitatively distinct representational shifts. KTO and GRPO enhance linear separability through constructive feature sharing and sparse, high-salience recruitment. In contrast, DPO and ORPO degrade separability via non-constructive geometric rotation and feature attenuation, while PPO and SimPO largely preserve baseline geometry. These transformations exhibit architecture-dependent variability, demonstrating that behavioral alignment does not imply uniform internal restructuring. Our findings establish alignment as a heterogeneous intervention, motivate standardized feature-level auditing for safety and interpretability, and highlight the need for mechanism-aware optimization objectives.

Gradient-based preference optimization methods for large language model (LLM) alignment suffer from preference collapse, converging to narrow behavioral modes while neglecting preference diversity. We introduce EvoPref, a multi-objective evolutionary algorithm that maintains populations of Low-Rank Adaptation (LoRA) adapters optimized across helpfulness, harmlessness, and honesty objectives using Non-dominated Sorting Genetic Algorithm II (NSGA-II) selection with archive-based diversity preservation. Our primary contribution is demonstrating that population-based methods discover substantially more diverse alignments than gradient descent. On standard benchmarks, EvoPref improves preference coverage by 18% (median 82.5% vs. 70.0% for ORPO, p<0.001, Wilcoxon, n=30) and reduces collapse rates by 47% (11.0% vs. 20.6%, p<0.001), while achieving competitive alignment quality (median 75.5% RewardBench vs. 75.0% for ORPO, p<0.05). We provide theoretical motivation extending recent multi-objective evolutionary algorithm (MOEA) runtime analysis (Dang et al., 2025) suggesting why archive-based methods escape collapse more effectively than single-trajectory optimization. Comprehensive comparisons against MOEA/D, SMS-EMOA, CMA-ES, and gradient baselines (DPO, IPO, KTO, ORPO) with rigorous statistical testing (Friedman with Holm correction, Vargha-Delaney effect sizes, median with IQR) confirm that multi-objective selection with diversity preservation is essential. This work establishes evolutionary optimization as a principled paradigm for diverse LLM alignment.

We introduce ORPO-Distill, a general-purpose method for cross-architecture LLM distillation that formulates the problem as a preference optimization task. Unlike standard CoT distillation, the approach transfers knowledge through diverse reasoning traces. It employs an Odds-Ratio Preference Optimization objective that contrasts teacher and student traces for more effective learning, and adopts a mixed-policy strategy for utilizing student-generated outputs, outperforming both off- and on-policy alternatives. Experiments on five datasets and multiple student models show consistent improvements over conventional black-box KD baselines.

Large Language Models (LLMs) have emerged as powerful tools for complex Operations Research (OR) in automating optimization modeling. However, current methodologies heavily rely on prompt engineering (e.g., multi-agent cooperation) with proprietary LLMs, raising data privacy concerns that could be prohibitive in industry applications. To tackle this issue, we propose training open-source LLMs for optimization modeling. We identify four critical requirements for the training dataset of OR LLMs, design and implement OR-Instruct, a semi-automated process for creating synthetic data tailored to specific requirements. We also introduce the IndustryOR benchmark, the first industrial benchmark for testing LLMs on solving real-world OR problems. We apply the data from OR-Instruct to various open-source LLMs of 7b size (termed as ORLMs), resulting in a significantly improved capability for optimization modeling. Our best-performing ORLM achieves state-of-the-art performance on the NL4OPT, MAMO, and IndustryOR benchmarks. Our code and data will be available at https://github.com/Cardinal-Operations/ORLM.

Large language models (LLMs) demonstrate strong mathematical reasoning, but reliance on closed-source APIs for OR tasks raises privacy concerns, and training open-source models from scratch incurs high compute costs. We introduce OR-Toolformer, which fine-tunes Llama-3.1-8B-Instruct with a semi-automatic data synthesis pipeline that generates diverse OR problem-answer pairs and augments the model with external solvers to produce API calls. On three of four standard benchmarks, OR-Toolformer achieves up to 80.1% execution accuracy, exceeding size-matched baselines by over 4.3%. In zero-shot evaluation on two unseen OR problem types, it attains 54% average accuracy, a 21 percentage-point improvement over the strongest baseline. These findings validate the efficacy of tool-augmented fine-tuning LLMs for accurate and generalizable OR problem modeling and solving.

Standard reinforcement learning from human feedback (RLHF) trains a reward model on pairwise preference data and then uses it for policy optimization. However, while reward models are optimized to capture relative preferences, existing policy optimization techniques rely on absolute reward magnitudes during training. In settings where the rewards are non-verifiable such as summarization, instruction following, and chat completion, this misalignment often leads to suboptimal performance. We introduce Group Ordinal Policy Optimization (GOPO), a policy optimization method that uses only the ranking of the rewards and discards their magnitudes. Our rank-based transformation of rewards provides several gains, compared to Group Relative Policy Optimization (GRPO), in settings with non-verifiable rewards: (1) consistently higher training/validation reward trajectories, (2) improved LLM-as-judge evaluations across most intermediate training steps, and (3) reaching a policy of comparable quality in substantially less training steps than GRPO. We demonstrate consistent improvements across a range of tasks and model sizes.

Reinforcement Learning from Human Feedback (RLHF) has been highly successful in aligning large language models with human preferences. While prevalent methods like DPO have demonstrated strong performance, they frame interactions with the language model as a bandit problem, which limits their applicability in real-world scenarios where multi-turn conversations are common. Additionally, DPO relies on the Bradley-Terry model assumption, which does not adequately capture the non-transitive nature of human preferences. In this paper, we address these challenges by modeling the alignment problem as a two-player constant-sum Markov game, where each player seeks to maximize their winning rate against the other across all steps of the conversation. Our approach Optimistic Multi-step Preference Optimization (OMPO) is built upon the optimistic online mirror descent algorithm~rakhlin2013online,joulani17a. Theoretically, we provide a rigorous analysis for the convergence of OMPO and show that OMPO requires O(ε^{-1}) policy updates to converge to an ε-approximate Nash equilibrium. We also validate the effectiveness of our method on multi-turn conversations dataset and math reasoning dataset.

Language model alignment methods such as reinforcement learning from human feedback (RLHF) have led to impressive advances in language model capabilities, but are limited by a widely observed phenomenon known as overoptimization, where the quality of the language model degrades over the course of the alignment process. As the model optimizes performance with respect to an offline reward model, it overfits to inaccuracies and drifts away from preferred responses covered by the data. To discourage such distribution shift, KL-regularization is widely employed in existing offline alignment methods, but overoptimization continues to harm performance. Lending theoretical insight into the source of these empirical observations, we first show that the KL-regularization is too weak to prevent overfitting, then raise the following question: is it possible to design an efficient algorithm that is provably robust to overoptimization? We address this question with a new algorithm for offline alignment, χ^2-Preference Optimization (χPO). χPO is a one-line change to Direct Preference Optimization (DPO; Rafailov et al., 2023), which only involves modifying the logarithmic link function in the DPO objective. Despite this minimal change, χPO implicitly implements the principle of pessimism in the face of uncertainty via regularization with the χ^2-divergence -- which quantifies uncertainty more effectively than KL-regularization -- and provably alleviates overoptimization, achieving sample-complexity guarantees based on single-policy concentrability -- the gold standard in offline reinforcement learning. χPO's simplicity and strong guarantees make it the first practical and general-purpose offline alignment algorithm that is provably robust to overoptimization.

Mathematical word problem-solving has long been recognized as a complex task for small language models (SLMs). A recent study hypothesized that the smallest model size, needed to achieve over 80% accuracy on the GSM8K benchmark, is 34 billion parameters. To reach this level of performance with smaller models, researcher often train SLMs to generate Python code or use tools to help avoid calculation errors. Additionally, they employ ensembling, where outputs of up to 100 model runs are combined to arrive at a more accurate result. Result selection is done using consensus, majority vote or a separate a verifier model used in conjunction with the SLM. Ensembling provides a substantial boost in accuracy but at a significant cost increase with multiple calls to the model (e.g., Phi-GSM uses top-48 to boost the performance from 68.2 to 81.5). In this work, we present Orca-Math, a 7-billion-parameter SLM based on the Mistral-7B, which achieves 86.81% on GSM8k without the need for multiple model calls or the use of verifiers, code execution or any other external tools. Our approach has the following key elements: (1) A high quality synthetic dataset of 200K math problems created using a multi-agent setup where agents collaborate to create the data, (2) An iterative learning techniques that enables the SLM to practice solving problems, receive feedback on its solutions and learn from preference pairs incorporating the SLM solutions and the feedback. When trained with Supervised Fine-Tuning alone, Orca-Math achieves 81.50% on GSM8k pass@1 metric. With iterative preference learning, Orca-Math achieves 86.81% pass@1. Orca-Math surpasses the performance of significantly larger models such as LLAMA-2-70B, WizardMath-70B, Gemini-Pro, ChatGPT-3.5. It also significantly outperforms other smaller models while using much smaller data (hundreds of thousands vs. millions of problems).

Instruction following (IF) is a critical capability for large language models (LLMs). However, handling complex instructions with multiple constraints remains challenging. Previous methods typically select preference pairs based on the number of constraints they satisfy, introducing noise where chosen examples may fail to follow some constraints and rejected examples may excel in certain respects over the chosen ones. To address the challenge of aligning with multiple preferences, we propose a simple yet effective method called Reverse Preference Optimization (RPO). It mitigates noise in preference pairs by dynamically reversing the constraints within the instruction to ensure the chosen response is perfect, alleviating the burden of extensive sampling and filtering to collect perfect responses. Besides, reversal also enlarges the gap between chosen and rejected responses, thereby clarifying the optimization direction and making it more robust to noise. We evaluate RPO on two multi-turn IF benchmarks, Sysbench and Multi-IF, demonstrating average improvements over the DPO baseline of 4.6 and 2.5 points (on Llama-3.1 8B), respectively. Moreover, RPO scales effectively across model sizes (8B to 70B parameters), with the 70B RPO model surpassing GPT-4o.

We study the problem of global maximization of a function f given a finite number of evaluations perturbed by noise. We consider a very weak assumption on the function, namely that it is locally smooth (in some precise sense) with respect to some semi-metric, around one of its global maxima. Compared to previous works on bandits in general spaces (Kleinberg et al., 2008; Bubeck et al., 2011a) our algorithm does not require the knowledge of this semi-metric. Our algorithm, StoSOO, follows an optimistic strategy to iteratively construct upper confidence bounds over the hierarchical partitions of the function domain to decide which point to sample next. A finite-time analysis of StoSOO shows that it performs almost as well as the best specifically-tuned algorithms even though the local smoothness of the function is not known.

In this paper, we introduce and apply Operations Research Question Answering (ORQA), a new benchmark designed to assess the generalization capabilities of Large Language Models (LLMs) in the specialized technical domain of Operations Research (OR). This benchmark evaluates whether LLMs can emulate the knowledge and reasoning skills of OR experts when confronted with diverse and complex optimization problems. The dataset, developed by OR experts, features real-world optimization problems that demand multistep reasoning to construct their mathematical models. Our evaluations of various open source LLMs, such as LLaMA 3.1, DeepSeek, and Mixtral, reveal their modest performance, highlighting a gap in their ability to generalize to specialized technical domains. This work contributes to the ongoing discourse on LLMs generalization capabilities, offering valuable insights for future research in this area. The dataset and evaluation code are publicly available.

Recent advancements in aligning large language models via reinforcement learning have achieved remarkable gains in solving complex reasoning problems, but at the cost of expensive on-policy rollouts and limited exploration of diverse reasoning paths. In this work, we introduce TreePO, involving a self-guided rollout algorithm that views sequence generation as a tree-structured searching process. Composed of dynamic tree sampling policy and fixed-length segment decoding, TreePO leverages local uncertainty to warrant additional branches. By amortizing computation across common prefixes and pruning low-value paths early, TreePO essentially reduces the per-update compute burden while preserving or enhancing exploration diversity. Key contributions include: (1) a segment-wise sampling algorithm that alleviates the KV cache burden through contiguous segments and spawns new branches along with an early-stop mechanism; (2) a tree-based segment-level advantage estimation that considers both global and local proximal policy optimization. and (3) analysis on the effectiveness of probability and quality-driven dynamic divergence and fallback strategy. We empirically validate the performance gain of TreePO on a set reasoning benchmarks and the efficiency saving of GPU hours from 22\% up to 43\% of the sampling design for the trained models, meanwhile showing up to 40\% reduction at trajectory-level and 35\% at token-level sampling compute for the existing models. While offering a free lunch of inference efficiency, TreePO reveals a practical path toward scaling RL-based post-training with fewer samples and less compute. Home page locates at https://m-a-p.ai/TreePO.

Aligning large language models (LLMs) with human preferences is critical for real-world deployment, yet existing methods like RLHF face computational and stability challenges. While DPO establishes an offline paradigm with single hyperparameter beta, subsequent methods like SimPO reintroduce complexity through dual parameters (beta, gamma). We propose {ReLU-based Preference Optimization (RePO)}, a streamlined algorithm that eliminates beta via two advances: (1) retaining SimPO's reference-free margins but removing beta through gradient analysis, and (2) adopting a ReLU-based max-margin loss that naturally filters trivial pairs. Theoretically, RePO is characterized as SimPO's limiting case (beta to infty), where the logistic weighting collapses to binary thresholding, forming a convex envelope of the 0-1 loss. Empirical results on AlpacaEval 2 and Arena-Hard show that RePO outperforms DPO and SimPO across multiple base models, requiring only one hyperparameter to tune.

As the era of large language models (LLMs) on behalf of users unfolds, Preference Optimization (PO) methods have become a central approach to aligning LLMs with human preferences and improving performance. We propose Maximum a Posteriori Preference Optimization (MaPPO), a framework for learning from preferences that explicitly incorporates prior reward knowledge into the optimization objective. While existing methods such as Direct Preference Optimization (DPO) and its variants treat preference learning as a Maximum Likelihood Estimation (MLE) problem, MaPPO extends this paradigm by integrating prior reward estimates into a principled Maximum a Posteriori (MaP) objective. This not only generalizes DPO and its variants, but also enhances alignment by mitigating the oversimplified binary classification of responses. More importantly, MaPPO introduces no additional hyperparameter, and supports preference optimization in both offline and online settings. In addition, MaPPO can be used as a plugin with consistent improvement on DPO variants, including widely used SimPO, IPO, and CPO. Extensive empirical evaluations of different model sizes and model series on three standard benchmarks, including MT-Bench, AlpacaEval 2.0, and Arena-Hard, demonstrate consistent improvements in alignment performance without sacrificing computational efficiency.

Large Language Models have achieved remarkable success in natural language processing tasks, with Reinforcement Learning playing a key role in adapting them to specific applications. However, obtaining ground truth answers for training LLMs in mathematical problem-solving is often challenging, costly, and sometimes unfeasible. This research delves into the utilization of format and length as surrogate signals to train LLMs for mathematical problem-solving, bypassing the need for traditional ground truth answers.Our study shows that a reward function centered on format correctness alone can yield performance improvements comparable to the standard GRPO algorithm in early phases. Recognizing the limitations of format-only rewards in the later phases, we incorporate length-based rewards. The resulting GRPO approach, leveraging format-length surrogate signals, not only matches but surpasses the performance of the standard GRPO algorithm relying on ground truth answers in certain scenarios, achieving 40.0\% accuracy on AIME2024 with a 7B base model. Through systematic exploration and experimentation, this research not only offers a practical solution for training LLMs to solve mathematical problems and reducing the dependence on extensive ground truth data collection, but also reveals the essence of why our label-free approach succeeds: base model is like an excellent student who has already mastered mathematical and logical reasoning skills, but performs poorly on the test paper, it simply needs to develop good answering habits to achieve outstanding results in exams , in other words, to unlock the capabilities it already possesses.

We study the problem of black-box optimization of a function f of any dimension, given function evaluations perturbed by noise. The function is assumed to be locally smooth around one of its global optima, but this smoothness is unknown. Our contribution is an adaptive optimization algorithm, POO or parallel optimistic optimization, that is able to deal with this setting. POO performs almost as well as the best known algorithms requiring the knowledge of the smoothness. Furthermore, POO works for a larger class of functions than what was previously considered, especially for functions that are difficult to optimize, in a very precise sense. We provide a finite-time analysis of POO's performance, which shows that its error after n evaluations is at most a factor of sqrt(ln n) away from the error of the best known optimization algorithms using the knowledge of the smoothness.

Optimizer selection for large-scale model training has become a system-level design decision constrained jointly by compute, memory, tuning budget, and task diversity, yet the landscape of over one hundred methods remains fragmented. We therefore present OmniOpt, a unified survey and benchmark cookbook of optimizers for the research community. OmniOpt rests on four coupled components. First, we treat every optimizer update as a structured transformation through a five-stage meta-pipeline, and show that most methods engage only one or two of these stages. Second, we use norm-constrained linear minimization oracles (LMOs) to unify different optimizers. Third, these two views ground a dual-dimension taxonomy, one dimension assigning each method to a mechanism family and the other recording the measurable training objectives it aims to improve. Fourth, and at the core of this paper, we instantiate the full taxonomy in a unified cross-domain benchmark spanning representative optimizers, model scales, and training regimes from language model pretraining to image classification, systematically analyzing each method family across multiple effect objectives and laying out their trade-offs. OmniOpt thus supplies the research community with an operational coordinate system for selecting optimizers under explicit mechanism and objective assumptions, and charts a direction for the future development of the optimizer community.

With the growing utilization of large language models (LLMs) across domains, alignment towards human preferences has become one of the most critical aspects of training models. At the forefront of state-of-the-art human alignment methods are preference optimization methods (*PO). However, prior research has often concentrated on identifying the best-performing method, typically involving a grid search over hyperparameters, which can be impractical for general practitioners. In this paper, we aim to identify the algorithm that, while being performant, is simultaneously more robust to varying hyperparameters, thereby increasing the likelihood of achieving better results. We focus on a realistic out-of-distribution (OOD) scenario that mirrors real-world applications of human alignment, offering practical insights into the strengths and weaknesses of these methods. Furthermore, to better understand the shortcomings of generations from the different methods, we analyze the model generations through the lens of KL divergence of the SFT model and the response length statistics. Our analysis reveals that the widely adopted DPO method consistently produces lengthy responses of inferior quality that are very close to the SFT responses. Motivated by these findings, we propose an embarrassingly simple extension to the DPO algorithm, LN-DPO, resulting in more concise responses without sacrificing quality compared to the policy obtained by vanilla DPO.

Both online and offline RLHF methods such as PPO and DPO have been extremely successful in aligning AI with human preferences. Despite their success, the existing methods suffer from a fundamental problem that their optimal solution is highly task-dependent (i.e., not robust to out-of-distribution (OOD) tasks). Here we address this challenge by proposing Self-Improving Robust Preference Optimization SRPO, a practical and mathematically principled offline RLHF framework that is completely robust to the changes in the task. The key idea of SRPO is to cast the problem of learning from human preferences as a self-improvement process, which can be mathematically expressed in terms of a min-max objective that aims at joint optimization of self-improvement policy and the generative policy in an adversarial fashion. The solution for this optimization problem is independent of the training task and thus it is robust to its changes. We then show that this objective can be re-expressed in the form of a non-adversarial offline loss which can be optimized using standard supervised optimization techniques at scale without any need for reward model and online inference. We show the effectiveness of SRPO in terms of AI Win-Rate (WR) against human (GOLD) completions. In particular, when SRPO is evaluated on the OOD XSUM dataset, it outperforms the celebrated DPO by a clear margin of 15% after 5 self-revisions, achieving WR of 90%.

Operations research (OR) is widely deployed to solve critical decision-making problems with complex objectives and constraints, impacting manufacturing, logistics, finance, and healthcare outcomes. While Large Language Models (LLMs) have shown promising results in various domains, their practical application in industry-relevant operations research (OR) problems presents significant challenges and opportunities. Preliminary industrial applications of LLMs for operations research face two critical deployment challenges: 1) Self-correction focuses on code syntax rather than mathematical accuracy, causing costly errors; 2) Complex expert selection creates unpredictable workflows that reduce transparency and increase maintenance costs, making them impractical for time-sensitive business applications. To address these business limitations, we introduce ORMind, a cognitive-inspired framework that enhances optimization through counterfactual reasoning. Our approach emulates human cognition, implementing an end-to-end workflow that systematically transforms requirements into mathematical models and executable solver code. It is currently being tested internally in Lenovo's AI Assistant, with plans to enhance optimization capabilities for both business and consumer customers. Experiments demonstrate that ORMind outperforms existing methods, achieving a 9.5\% improvement on the NL4Opt dataset and a 14.6\% improvement on the ComplexOR dataset.

Residual context is key to unlocking the speed-quality Pareto frontier of diffusion language models (DLMs) by carrying forward predictive distributions across denoising steps. Yet turning this seemingly simple mechanism into an effective learning paradigm is far from simple: there is no clear recipe for how residual context should be learned. We introduce ORL, a framework for on-policy residual learning in DLMs. Algorithmically, we identify that residual learning is inherently on-policy. ORL learns from model-induced residual trajectories on the fly and introduces an entropy-contraction objective that sharpens predictions as the model revisits its own predictions. System-wise, exact residual supervision requires capturing, retaining, and reprocessing many trajectory-dependent states. ORL co-designs the algorithm with asynchronous residual capture and transport, specialized block-diffusion attention, and packed compute-balanced training, making it practical at scale. On a 4B DLM converted from Qwen3-4B, ORL improves tokens per forward (TPF) by up to 6.2x and, with our dlmrt engine, end-to-end throughput by approximately 6.9x at comparable or better quality. In single-request serving on one H100, this mode achieves a stronger speed-quality Pareto frontier than autoregressive models with EAGLE3 and DFlash speculative decoding under both strict and relaxed verification, running 1.74x faster than DFlash at matched accuracy. ORL also transfers to existing DLMs: on LLaDA-2.1-mini, 36 H100-hours and 4.2M self-generated tokens, about 10x less data than prior LLaDA recipes, yield up to 1.5x higher TPF and up to 3x higher throughput at comparable quality, and on DiffusionGemma, ORL raises TPF by 1.1-1.2x. With dlmrt and NVFP4 quantization, ORL models decode a single request at up to 5,046 tokens/s on one B200, 7,708 on eight B200s, and 2,788 on a consumer RTX 5090, with comparable quality.

There often is a dilemma between ease of optimization and robust out-of-distribution (OoD) generalization. For instance, many OoD methods rely on penalty terms whose optimization is challenging. They are either too strong to optimize reliably or too weak to achieve their goals. We propose to initialize the networks with a rich representation containing a palette of potentially useful features, ready to be used by even simple models. On the one hand, a rich representation provides a good initialization for the optimizer. On the other hand, it also provides an inductive bias that helps OoD generalization. Such a representation is constructed with the Rich Feature Construction (RFC) algorithm, also called the Bonsai algorithm, which consists of a succession of training episodes. During discovery episodes, we craft a multi-objective optimization criterion and its associated datasets in a manner that prevents the network from using the features constructed in the previous iterations. During synthesis episodes, we use knowledge distillation to force the network to simultaneously represent all the previously discovered features. Initializing the networks with Bonsai representations consistently helps six OoD methods achieve top performance on ColoredMNIST benchmark. The same technique substantially outperforms comparable results on the Wilds Camelyon17 task, eliminates the high result variance that plagues other methods, and makes hyperparameter tuning and model selection more reliable.

The class of direct preference optimization (DPO) algorithms has emerged as a promising approach for solving the alignment problem in foundation models. These algorithms work with very limited feedback in the form of pairwise preferences and fine-tune models to align with these preferences without explicitly learning a reward model. While the form of feedback used by these algorithms makes the data collection process easy and relatively more accurate, its ambiguity in terms of the quality of responses could have negative implications. For example, it is not clear if a decrease (increase) in the likelihood of preferred (dispreferred) responses during the execution of these algorithms could be interpreted as a positive or negative phenomenon. In this paper, we study how to design algorithms that can leverage additional information in the form of rating gap, which informs the learner how much the chosen response is better than the rejected one. We present new algorithms that can achieve faster statistical rates than DPO in presence of accurate rating gap information. Moreover, we theoretically prove and empirically show that the performance of our algorithms is robust to inaccuracy in rating gaps. Finally, we demonstrate the solid performance of our methods in comparison to a number of DPO-style algorithms across a wide range of LLMs and evaluation benchmarks.

Diffusion Large Language Models (dLLMs) break the rigid left-to-right constraint of traditional LLMs, enabling token generation in arbitrary orders. Intuitively, this flexibility implies a solution space that strictly supersets the fixed autoregressive trajectory, theoretically unlocking superior reasoning potential for general tasks like mathematics and coding. Consequently, numerous works have leveraged reinforcement learning (RL) to elicit the reasoning capability of dLLMs. In this paper, we reveal a counter-intuitive reality: arbitrary order generation, in its current form, narrows rather than expands the reasoning boundary of dLLMs. We find that dLLMs tend to exploit this order flexibility to bypass high-uncertainty tokens that are crucial for exploration, leading to a premature collapse of the solution space. This observation challenges the premise of existing RL approaches for dLLMs, where considerable complexities, such as handling combinatorial trajectories and intractable likelihoods, are often devoted to preserving this flexibility. We demonstrate that effective reasoning is better elicited by intentionally forgoing arbitrary order and applying standard Group Relative Policy Optimization (GRPO) instead. Our approach, JustGRPO, is minimalist yet surprisingly effective (e.g., 89.1% accuracy on GSM8K) while fully retaining the parallel decoding ability of dLLMs. Project page: https://nzl-thu.github.io/the-flexibility-trap

In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we study the landscape of BO through the lens of penalty methods, in which the upper- and lower-level objectives are combined in a weighted sum with penalty parameter sigma > 0. In particular, we establish a strong connection between the penalty function and the hyper-objective by explicitly characterizing the conditions under which the values and derivatives of the two must be O(sigma)-close. A by-product of our analysis is the explicit formula for the gradient of hyper-objective when the lower-level problem has multiple solutions under minimal conditions, which could be of independent interest. Next, viewing the penalty formulation as O(sigma)-approximation of the original BO, we propose first-order algorithms that find an epsilon-stationary solution by optimizing the penalty formulation with sigma = O(epsilon). When the perturbed lower-level problem uniformly satisfies the small-error proximal error-bound (EB) condition, we propose a first-order algorithm that converges to an epsilon-stationary point of the penalty function, using in total O(epsilon^{-3}) and O(epsilon^{-7}) accesses to first-order (stochastic) gradient oracles when the oracle is deterministic and oracles are noisy, respectively. Under an additional assumption on stochastic oracles, we show that the algorithm can be implemented in a fully {\it single-loop} manner, i.e., with O(1) samples per iteration, and achieves the improved oracle-complexity of O(epsilon^{-3}) and O(epsilon^{-5}), respectively.

As creative writing tasks do not have singular correct answers, large language models (LLMs) trained to perform these tasks should be able to generate diverse valid outputs. However, LLM post-training often focuses on improving generation quality but neglects to facilitate output diversity. Hence, in creative writing generation, we investigate post-training approaches to promote both output diversity and quality. Our core idea is to include deviation -- the degree of difference between a training sample and all other samples with the same prompt -- in the training objective to facilitate learning from rare high-quality instances. By adopting our approach to direct preference optimization (DPO) and odds ratio preference optimization (ORPO), we demonstrate that we can promote the output diversity of trained models while minimally decreasing quality. Our best model with 8B parameters could achieve on-par diversity as a human-created dataset while having output quality similar to the best instruction-tuned models we examined, GPT-4o and DeepSeek-R1. We further validate our approaches with a human evaluation, an ablation, and a comparison to an existing diversification approach, DivPO.

Out-of-distribution (OOD) detection is vital to safety-critical machine learning applications and has thus been extensively studied, with a plethora of methods developed in the literature. However, the field currently lacks a unified, strictly formulated, and comprehensive benchmark, which often results in unfair comparisons and inconclusive results. From the problem setting perspective, OOD detection is closely related to neighboring fields including anomaly detection (AD), open set recognition (OSR), and model uncertainty, since methods developed for one domain are often applicable to each other. To help the community to improve the evaluation and advance, we build a unified, well-structured codebase called OpenOOD, which implements over 30 methods developed in relevant fields and provides a comprehensive benchmark under the recently proposed generalized OOD detection framework. With a comprehensive comparison of these methods, we are gratified that the field has progressed significantly over the past few years, where both preprocessing methods and the orthogonal post-hoc methods show strong potential.

Reinforcement Learning with Verifiable Rewards (RLVR) has markedly enhanced the reasoning abilities of large language models (LLMs). Its success, however, largely depends on strong base models with rich world knowledge, yielding only modest improvements for small-size language models (SLMs). To address this limitation, we investigate Guided GRPO, which injects ground-truth reasoning steps into roll-out trajectories to compensate for SLMs' inherent weaknesses. Through a comprehensive study of various guidance configurations, we find that naively adding guidance delivers limited gains. These insights motivate G^2RPO-A, an adaptive algorithm that automatically adjusts guidance strength in response to the model's evolving training dynamics. Experiments on mathematical reasoning and code-generation benchmarks confirm that G^2RPO-A substantially outperforms vanilla GRPO. Our code and models are available at https://github.com/T-Lab-CUHKSZ/G2RPO-A.

A single language model (LM), despite aligning well with an average labeler through reinforcement learning from human feedback (RLHF), may not universally suit diverse human preferences. Recent approaches therefore opt for customization by collecting multi-dimensional feedback and creating distinct reward models (RMs) for each dimension (e.g., helpfulness, harmlessness, or honesty). Different LMs can then be optimized for different preferences using multi-objective RLHF (MORLHF) with different reward weightings. Yet, RL fine-tuning is unstable and resource-heavy, especially for MORLHF with diverse and usually conflicting objectives. In this paper, we present Multi-Objective Direct Preference Optimization (MODPO), an RL-free algorithm that extends Direct Preference Optimization (DPO) for multiple alignment objectives with minimal overheads. Essentially, MODPO folds language modeling directly into reward modeling, training LMs as implicit collective reward models (cRMs) that combine all objectives with specific weightings. While theoretically guaranteed to produce the same optimal solutions as MORLHF, MODPO is practically more stable and computationally efficient. Empirical results from safety alignment and long-form question answering confirm that MODPO matches or outperforms existing methods, consistently producing a Pareto front of LMs that cater to diverse preferences with 3 times less computational resources compared to MORLHF.

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 supervised fine-tuning and distillation, often depend on costly external signals, resulting in SLMs being overly confident with limited supervision signals, thus limiting their abilities. Therefore, this study enables SLMs to learn to reason from self-iterative feedback. By combining odds ratio preference optimization (ORPO), we fine-tune and align SLMs using positive and negative signals generated by themselves. Additionally, we introduce process supervision for rewards in preference alignment by sampling-based inference simulation and process reward models. Compared to Supervised Fine-Tuning (SFT), our method improves the performance of Gemma-2B by 12.43 (Acc) on GSM8K and 3.95 (Pass@1) on MBPP. Furthermore, the proposed method also demonstrated superior out-of-domain generalization capabilities on MMLU_Math and HumanEval.

Agentic tool use has gained traction with the rise of agentic tool calling, yet most existing work overlooks the complexity of multi-turn tool interactions. We introduce OrchDAG, a synthetic data generation pipeline that models tool execution as directed acyclic graphs (DAGs) with controllable complexity. Using this dataset, we benchmark model performance and propose a graph-based reward to enhance RLVR training. Experiments show that the dataset presents a challenging but solvable benchmark, and the proposed reward is effective when combined with GRPO-style algorithms, highlighting the importance of leveraging topological structure and data complexity in multi-turn tool use.

Direct Preference Optimization (DPO) is a widely used offline preference optimization algorithm that reparameterizes reward functions in reinforcement learning from human feedback (RLHF) to enhance simplicity and training stability. In this work, we propose SimPO, a simpler yet more effective approach. The effectiveness of SimPO is attributed to a key design: using the average log probability of a sequence as the implicit reward. This reward formulation better aligns with model generation and eliminates the need for a reference model, making it more compute and memory efficient. Additionally, we introduce a target reward margin to the Bradley-Terry objective to encourage a larger margin between the winning and losing responses, further enhancing the algorithm's performance. We compare SimPO to DPO and its latest variants across various state-of-the-art training setups, including both base and instruction-tuned models like Mistral and Llama3. We evaluated on extensive instruction-following benchmarks, including AlpacaEval 2, MT-Bench, and the recent challenging Arena-Hard benchmark. Our results demonstrate that SimPO consistently and significantly outperforms existing approaches without substantially increasing response length. Specifically, SimPO outperforms DPO by up to 6.4 points on AlpacaEval 2 and by up to 7.5 points on Arena-Hard. Our top-performing model, built on Llama3-8B-Instruct, achieves a remarkable 44.7 length-controlled win rate on AlpacaEval 2 -- surpassing Claude 3 Opus on the leaderboard, and a 33.8 win rate on Arena-Hard -- making it the strongest 8B open-source model.

We propose Process-Aware Policy Optimization (PAPO), a method that integrates process-level evaluation into Group Relative Policy Optimization (GRPO) through decoupled advantage normalization, to address two limitations of existing reward designs. Outcome reward models (ORM) evaluate only final-answer correctness, treating all correct responses identically regardless of reasoning quality, and gradually lose the advantage signal as groups become uniformly correct. Process reward models (PRM) offer richer supervision, but directly using PRM scores causes reward hacking, where models exploit verbosity to inflate scores while accuracy collapses. PAPO resolves both by composing the advantage from an outcome component Aout, derived from ORM and normalized over all responses, and a process component Aproc, derived from a rubric-based PRM and normalized exclusively among correct responses. This decoupled design ensures that Aout anchors training on correctness while Aproc differentiates reasoning quality without distorting the outcome signal. Experiments across multiple model scales and six benchmarks demonstrate that PAPO consistently outperforms ORM, reaching 51.3% vs.\ 46.3% on OlympiadBench while continuing to improve as ORM plateaus and declines.

Optimization Modeling (OM) is essential for solving complex decision-making problems. However, the process remains time-consuming and error-prone, heavily relying on domain experts. While Large Language Models (LLMs) show promise in addressing these challenges through their natural language understanding and reasoning capabilities, current approaches face three critical limitations: high benchmark labeling error rates reaching up to 42%, narrow evaluation scope that only considers optimal values, and computational inefficiency due to heavy reliance on multi-agent systems or model fine-tuning. In this work, we first enhance existing datasets through systematic error correction and more comprehensive annotation. Additionally, we introduce LogiOR, a new optimization modeling benchmark from the logistics domain, containing more complex problems with standardized annotations. Furthermore, we present ORThought, a novel framework that leverages expert-level optimization modeling principles through chain-of-thought reasoning to automate the OM process. Through extensive empirical evaluation, we demonstrate that ORThought outperforms existing approaches, including multi-agent frameworks, with particularly significant advantages on complex optimization problems. Finally, we provide a systematic analysis of our method, identifying critical success factors and failure modes, providing valuable insights for future research on LLM-based optimization modeling.

Given the damping factor α and precision tolerance ε, andersen2006local introduced Approximate Personalized PageRank (APPR), the de facto local method for approximating the PPR vector, with runtime bounded by Θ(1/(αε)) independent of the graph size. Recently, fountoulakis2022open asked whether faster local algorithms could be developed using O(1/(sqrtαε)) operations. By noticing that APPR is a local variant of Gauss-Seidel, this paper explores the question of whether standard iterative solvers can be effectively localized. We propose to use the locally evolving set process, a novel framework to characterize the algorithm locality, and demonstrate that many standard solvers can be effectively localized. Let operatorname{vol}{ (S_t)} and overlineγ_{t} be the running average of volume and the residual ratio of active nodes textstyle S_{t} during the process. We show operatorname{vol}{ (S_t)}/overlineγ_{t} leq 1/ε and prove APPR admits a new runtime bound O(operatorname{vol}(S_t)/(αoverlineγ_{t})) mirroring the actual performance. Furthermore, when the geometric mean of residual reduction is Θ(sqrtα), then there exists c in (0,2) such that the local Chebyshev method has runtime O(operatorname{vol}(S_{t})/(sqrtα(2-c))) without the monotonicity assumption. Numerical results confirm the efficiency of this novel framework and show up to a hundredfold speedup over corresponding standard solvers on real-world graphs.

We present any4, a learned 4-bit weight quantization solution for large language models (LLMs) providing arbitrary numeric representations without requiring pre-processing of weights or activations. any4 yields higher accuracy compared to other related 4-bit numeric representation types: int4, fp4 and nf4, as evaluated on a range of model sizes, generations and families (Llama 2, Llama 3, Mistral and Mixtral). While any4 does not require preprocessing of weights or activations, it is also competitive with orthogonal techniques that require such preprocessing (e.g., AWQ and GPTQ). We also experiment with any3 and any2 and show competitiveness at lower bits. Additionally, we show that we can calibrate using a single curated diverse sample rather than hundreds of samples from a dataset as done in most quantization approaches. We also open source tinygemm, a latency optimized GPU matrix multiplication library for LLMs, that implements any4 using a GPU-efficient lookup table strategy along with other common quantization methods. We open source our code at https://github.com/facebookresearch/any4 .

Large language model (LLM) agents are increasingly used to assist with operations research (OR) modeling, yet existing OR-oriented benchmarks often reduce evaluation to one-shot translation from a self-contained problem statement into a mathematical formulation or solver program. Such settings abstract away two characteristics of real industrial OR workflows: persistent multi-artifact workspaces and multi-stage task lifecycles. We introduce OR-Space, a full-lifecycle workspace benchmark for evaluating industrial optimization agents across model construction, model revision, and grounded explanation. Each instance is an executable workspace containing business documents, structured data, optional code artifacts, solver outputs, and task-specific evaluators distributed across interdependent files. OR-Space defines three task modes: Build, where agents construct solver-ready optimization models from heterogeneous artifacts; Revise, where agents modify existing models under changing requirements or solver feedback while preserving valid prior logic; and Explain, where agents answer grounded questions about solutions, constraints, and business implications using evidence spread across workspace artifacts. By combining persistent workspaces with lifecycle-oriented tasks, OR-Space evaluates whether agents can perform reliable optimization work beyond end-to-end text generation. We describe the benchmark design, evaluation protocol, and quality-control pipeline, and position OR-Space as a benchmark for studying the reliability, failure modes, and practical readiness of LLM agents in industrial OR workflows.

We present DuPO, a dual learning-based preference optimization framework that generates annotation-free feedback via a generalized duality. DuPO addresses two key limitations: Reinforcement Learning with Verifiable Rewards (RLVR)'s reliance on costly labels and applicability restricted to verifiable tasks, and traditional dual learning's restriction to strictly dual task pairs (e.g., translation and back-translation). Specifically, DuPO decomposes a primal task's input into known and unknown components, then constructs its dual task to reconstruct the unknown part using the primal output and known information (e.g., reversing math solutions to recover hidden variables), broadening applicability to non-invertible tasks. The quality of this reconstruction serves as a self-supervised reward to optimize the primal task, synergizing with LLMs' ability to instantiate both tasks via a single model. Empirically, DuPO achieves substantial gains across diverse tasks: it enhances the average translation quality by 2.13 COMET over 756 directions, boosts the mathematical reasoning accuracy by an average of 6.4 points on three challenge benchmarks, and enhances performance by 9.3 points as an inference-time reranker (trading computation for accuracy). These results position DuPO as a scalable, general, and annotation-free paradigm for LLM optimization.

In this paper, we aim to align large language models with the ever-changing, complex, and diverse human values (e.g., social norms) across time and locations. This presents a challenge to existing alignment techniques, such as supervised fine-tuning, which internalize values within model parameters. To overcome this, we propose an On-the-fly Preference Optimization (OPO) method, which is a real-time alignment that works in a streaming way. It employs an external memory to store established rules for alignment, which can constrain LLMs' behaviors without further training, allowing for convenient updates and customization of human values. We also introduce a scalable evaluation to assess the proposed method more effectively. Experimental results on both human-annotated and auto-generated questions from legal and moral domains indicate the effectiveness of the proposed OPO method. Our code and data are released at https://github.com/GAIR-NLP/OPO.

Large language models trained with reinforcement learning with verifiable rewards tend to trade accuracy for length--inflating response lengths to achieve gains in accuracy. While longer answers may be warranted for harder problems, many tokens are merely "filler": repetitive, verbose text that makes no real progress. We introduce GFPO (Group Filtered Policy Optimization), which curbs this length explosion by sampling larger groups per problem during training and filtering responses to train on based on two key metrics: (1) response length and (2) token efficiency: reward per token ratio. By sampling more at training time, we teach models to think less at inference time. On the Phi-4-reasoning model, GFPO cuts GRPO's length inflation by 46-71% across challenging STEM and coding benchmarks (AIME 24/25, GPQA, Omni-MATH, LiveCodeBench) while maintaining accuracy. Optimizing for reward per token further increases reductions in length inflation to 71-85%. We also propose Adaptive Difficulty GFPO, which dynamically allocates more training resources to harder problems based on real-time difficulty estimates, improving the balance between computational efficiency and accuracy especially on difficult questions. GFPO demonstrates that increased training-time compute directly translates to reduced test-time compute--a simple yet effective trade-off for efficient reasoning.

Recent advances in Multimodal Large Language Models (MLLMs) have enabled models to perform both understanding and generation of multimodal data in a unified manner. However, achieving a fine-grained alignment between input prompts and generated images remains a major challenge especially in text-to-image generation. Therefore, recent works have introduced self-improving mechanisms based on self-generated data and self-feedback to efficiently mitigate this challenge without relying on external large-scale data or models. However, existing self-improving approaches have not focused on fine-grained visual details especially at the object level in generating training data or providing a feedback, and thus they still struggle to resolve the object hallucination problem in text-to-image generation. To tackle this problem, we propose an Object-centric Self-improving Preference Optimization (OSPO), a self-improving framework for enhancing object-level text-image alignment. OSPO is designed to explicitly address the need for constructing and leveraging object-level hard negative data and an object-centric optimization in improving object-specific fidelity. In specific, OSPO consists of: (1) Initial Prompt Generation (2) Hard Preference Pair Generation (3) Filtering and Selection (4) Object-centric Preference Optimization with Conditional Preference Loss. Extensive experiments on compositional image generation benchmarks demonstrate that OSPO significantly improves fine-grained alignment in text-to-image generation, surpassing not only prior self-improving methods but also diffusion-based specialized image generation models.

In online algorithm selection (OAS), instances of an algorithmic problem class are presented to an agent one after another, and the agent has to quickly select a presumably best algorithm from a fixed set of candidate algorithms. For decision problems such as satisfiability (SAT), quality typically refers to the algorithm's runtime. As the latter is known to exhibit a heavy-tail distribution, an algorithm is normally stopped when exceeding a predefined upper time limit. As a consequence, machine learning methods used to optimize an algorithm selection strategy in a data-driven manner need to deal with right-censored samples, a problem that has received little attention in the literature so far. In this work, we revisit multi-armed bandit algorithms for OAS and discuss their capability of dealing with the problem. Moreover, we adapt them towards runtime-oriented losses, allowing for partially censored data while keeping a space- and time-complexity independent of the time horizon. In an extensive experimental evaluation on an adapted version of the ASlib benchmark, we demonstrate that theoretically well-founded methods based on Thompson sampling perform specifically strong and improve in comparison to existing methods.

The Quantum Approximate Optimization Algorithm (QAOA) is a prominent variational algorithm used for solving combinatorial optimization problems such as the Max-Cut problem. A key challenge in QAOA lies in efficiently identifying suitable parameters (gamma, beta) that lead to high-quality solutions. In this paper, we propose a framework that combines Fully Informed Particle Swarm Optimization (FIPSO) with adaptive gradient correction using the Adam Optimizer to navigate the QAOA parameter space. This approach aims to avoid issues such as barren plateaus and convergence to local minima. The proposed algorithm is evaluated against two classes of graph instances, Erdos Renyi and Watts-Strogatz. Experimental results across multiple QAOA depths consistently demonstrate superior performance compared to random initialization, underscoring the effectiveness and robustness of the proposed optimization framework.

We prove theoretically that the GRPO RL algorithm induces a non-trivial process reward model (PRM), under certain assumptions regarding within-group overlap of token sequences across completions. We then show empirically that these assumptions are met under real-world conditions: GRPO does in fact induce a non-trivial PRM. Leveraging the framework of GRPO-as-a-PRM, we identify a flaw in the GRPO objective: non-uniformly distributed process steps hinder both exploration and exploitation (under different conditions). We propose a simple modification to the algorithm to mitigate this defect (lambda-GRPO), and show that LLMs trained with lambda-GRPO achieve higher validation accuracy and performance on downstream reasoning tasks-and reach peak performance more rapidly-than LLMs trained with standard GRPO. Our results call into question the advantage of costly, explicitly-defined PRMs for GRPO: we show that it is possible to instead leverage the hidden, built-in PRM structure within the vanilla GRPO algorithm to boost model performance with a negligible impact on training time and cost.

Recent progress in aligning image and video generative models with Group Relative Policy Optimization (GRPO) has improved human preference alignment, but existing variants remain inefficient due to sequential rollouts and large numbers of sampling steps, unreliable credit assignment: sparse terminal rewards are uniformly propagated across timesteps, failing to capture the varying criticality of decisions during denoising. In this paper, we present BranchGRPO, a method that restructures the rollout process into a branching tree, where shared prefixes amortize computation and pruning removes low-value paths and redundant depths. BranchGRPO introduces three contributions: (1) a branching scheme that amortizes rollout cost through shared prefixes while preserving exploration diversity; (2) a reward fusion and depth-wise advantage estimator that transforms sparse terminal rewards into dense step-level signals; and (3) pruning strategies that cut gradient computation but leave forward rollouts and exploration unaffected. On HPDv2.1 image alignment, BranchGRPO improves alignment scores by up to 16\% over DanceGRPO, while reducing per-iteration training time by nearly 55\%. A hybrid variant, BranchGRPO-Mix, further accelerates training to 4.7x faster than DanceGRPO without degrading alignment. On WanX video generation, it further achieves higher Video-Align scores with sharper and temporally consistent frames compared to DanceGRPO. Codes are available at https://fredreic1849.github.io/BranchGRPO-Webpage/{BranchGRPO}.

We investigate a narrow but common failure mode of GRPO-style reinforcement learning in the context of sparse verifiable rewards: early updates contain more responses with negative advantages than those with positive advantages, while response-level length normalization ties the magnitude of the update to the length of the output. We propose Hysteretic Policy Optimization (HPO), a minimal modification of GRPO that reduces the weight of negative-advantage updates and replaces per-response length normalization with mean-length normalization. We further introduce Adaptive HPO (A-HPO), which sets the hysteretic weight based on batch-level advantage-sign statistics, thereby removing the need for tuning a fixed hysteretic weight. In our TeleLogs and Countdown experiments, A-HPO improves the reward per update compared to GRPO, with the largest gains in early sparse reward regimes. On TeleLogs, A-HPO achieves a final reward of 0.84, outperforming SAPO by 5%, GSPO by 11%, and GRPO by 15%, while maintaining a comparable response-length. On Countdown, A-HPO achieves the largest gains in initial and most difficult configurations across 1.5B-7B models. Ablation studies on the hysteretic weight show that the gains of A-HPO come from better balancing the contributions of positive and negative advantages compared to positive-only or fully symmetric updates.

We present Future-KL Influenced Policy Optimization (FIPO), a reinforcement learning algorithm designed to overcome reasoning bottlenecks in large language models. While GRPO style training scales effectively, it typically relies on outcome-based rewards (ORM) that distribute a global advantage uniformly across every token in a trajectory. We argue that this coarse-grained credit assignment imposes a performance ceiling by failing to distinguish critical logical pivots from trivial tokens. FIPO addresses this by incorporating discounted future-KL divergence into the policy update, creating a dense advantage formulation that re-weights tokens based on their influence on subsequent trajectory behavior. Empirically, FIPO enables models to break through the length stagnation seen in standard baselines. Evaluated on Qwen2.5-32B, FIPO extends the average chain-of-thought length from roughly 4,000 to over 10,000 tokens and increases AIME 2024 Pass@1 accuracy from 50.0% to a peak of 58.0% (converging at approximately 56.0\%). This outperforms both DeepSeek-R1-Zero-Math-32B (around 47.0%) and o1-mini (approximately 56.0%). Our results suggest that establishing dense advantage formulations is a vital path for evolving ORM-based algorithms to unlock the full reasoning potential of base models. We open-source our training system, built on the verl framework.

Preference optimization is a standard alignment method for generative models, yet extending it to continuous-time dynamics remains non-trivial. In flow matching, reward-driven updates modify transport trajectories without an inherent constraint to the pretrained data manifold and can move terminal samples off the pretrained support. We formalize this failure mode as manifold drift. Theoretically, we show that optimal flow matching recovers the terminal data distribution, whereas a preference update leaves the pretrained manifold whenever its induced terminal displacement has a nonzero normal component. As a remedy, we propose ThermoDPO, a temperature-controlled objective that anchors pairwise preference optimization on preferred samples. Across temperature regimes, this objective connects rejection sampling fine-tuning and FlowDPO and controls a pointwise reconstruction-based surrogate for manifold distance. To counteract diminished signals at low temperatures, we further introduce a weighted variant, ThermoDPO-weighted. On the main toy benchmark, ThermoDPO-weighted attains a StrictScore of 0.899, compared with 0.629 for FlowDPO and 0.857 for FlowDPO+RFT. On SD3.5-M at CFG = 4.5, it improves OCR by 47.5% and the average of four metrics by 16.0%.

Reinforcement learning algorithms are fundamental to align large language models with human preferences and to enhance their reasoning capabilities. However, current reinforcement learning algorithms often suffer from training instability due to loose on-policy constraints and computational inefficiency due to auxiliary models. In this work, we propose On-Policy RL with Optimal reward baseline (OPO), a novel and simplified reinforcement learning algorithm designed to address these challenges. OPO emphasizes the importance of exact on-policy training, which empirically stabilizes the training process and enhances exploration. Moreover, OPO introduces the optimal reward baseline that theoretically minimizes gradient variance. We evaluate OPO on mathematical reasoning benchmarks. The results demonstrate its superior performance and training stability without additional models or regularization terms. Furthermore, OPO achieves lower policy shifts and higher output entropy, encouraging more diverse and less repetitive responses. These results highlight OPO as a promising direction for stable and effective reinforcement learning in large language model alignment and reasoning tasks. The implementation is provided at https://github.com/microsoft/LMOps/tree/main/opo.

Reinforcement learning (RL) is widely used for post-training large language models (LLMs) in code editing, where group-relative methods, such as GRPO, are popular due to their critic-free and normalized advantage estimation. However, in real-world code-editing scenarios, reward distributions are often skewed with unpredictable noise, leading to distorted advantage computation and increased rollout outliers. To address this issue, we propose Group Adaptive Policy Optimization (GAPO), which adaptively finds an interval with the highest SNR (Signal to Noise Ratio) per prompt and uses the median of that interval as an adaptive Q to replace the group mean in advantage calculation to reduce noise further. This adaptive Q robustly handles rollout noise while remaining plug-and-play and efficient. We evaluate GAPO on nine instruction-tuned LLMs (3B-14B) using a collected large dataset of 51,844 real-world, history-aware code-editing tasks spanning 10 programming languages. GAPO yields up to 4.35 in-domain (ID) and 5.30 out-of-domain (OOD) exact-match improvements over GRPO and its variant DAPO, while achieving lower clipping ratios and higher GPU throughput. Code: https://github.com/TsingZ0/verl-GAPO.

Solving a linear system Ax=b is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are often impossible or too expensive to identify; thus in practice sub-optimal heuristics are used. We consider the common setting in which many related linear systems need to be solved, e.g. during a single numerical simulation. In this scenario, can we sequentially choose parameters that attain a near-optimal overall number of iterations, without extra matrix computations? We answer in the affirmative for Successive Over-Relaxation (SOR), a standard solver whose parameter omega has a strong impact on its runtime. For this method, we prove that a bandit online learning algorithm--using only the number of iterations as feedback--can select parameters for a sequence of instances such that the overall cost approaches that of the best fixed omega as the sequence length increases. Furthermore, when given additional structural information, we show that a contextual bandit method asymptotically achieves the performance of the instance-optimal policy, which selects the best omega for each instance. Our work provides the first learning-theoretic treatment of high-precision linear system solvers and the first end-to-end guarantees for data-driven scientific computing, demonstrating theoretically the potential to speed up numerical methods using well-understood learning algorithms.

Automating scientific discovery in complex, experiment-driven domains requires more than iterative mutation of programs; it demands structured hypothesis management, environment interaction, and principled reflection. We present OR-Agent, a configurable multi-agent research framework designed for automated exploration in rich experimental environments. OR-Agent organizes research as a structured tree-based workflow that explicitly models branching hypothesis generation and systematic backtracking, enabling controlled management of research trajectories beyond simple mutation-crossover loops. At its core, we introduce an evolutionary-systematic ideation mechanism that unifies evolutionary selection of research starting points, comprehensive research plan generation, and coordinated exploration within a research tree. We introduce a hierarchical optimization-inspired reflection system in which short-term reflections act as verbal gradients, long-term reflections as verbal momentum, and memory compression as semantic weight decay, collectively forming a principled mechanism for governing research dynamics. We conduct extensive experiments across classical combinatorial optimization benchmarks as well as simulation-based cooperative driving scenarios. Results demonstrate that OR-Agent outperforms strong evolutionary baselines while providing a general, extensible, and inspectable framework for AI-assisted scientific discovery. All code and experimental data are publicly available at https://github.com/qiliuchn/OR-Agent.

We introduce Orthrus, a simple and efficient dual-architecture framework that unifies the exact generation fidelity of autoregressive Large Language Models (LLMs) with the high-speed parallel token generation of diffusion models. The sequential nature of standard autoregressive decoding represents a fundamental bottleneck for high-throughput inference. While diffusion language models attempt to break this barrier via parallel generation, they suffer from significant performance degradation, high training costs, and a lack of rigorous convergence guarantees. Orthrus resolves this dichotomy natively. Designed to seamlessly integrate into existing Transformers, the framework augments a frozen LLM with a lightweight, trainable module to create a parallel diffusion view alongside the standard autoregressive view. In this unified system, both views attend to the exact same high-fidelity Key-Value (KV) cache; the autoregressive head executes context pre-filling to construct accurate KV representations, while the diffusion head executes parallel generation. By employing an exact consensus mechanism between the two views, Orthrus guarantees lossless inference, delivering up to a 7.8x speedup with only an O(1) memory cache overhead and minimal parameter additions.

The last year has witnessed the rapid progress of large language models (LLMs) across diverse domains. Among them, CodeLLMs have garnered particular attention because they can not only assist in completing various programming tasks but also represent the decision-making and logical reasoning capabilities of LLMs. However, current CodeLLMs mainly focus on pre-training and supervised fine-tuning scenarios, leaving the alignment stage, which is important for post-training LLMs, under-explored. This work first identifies that the commonly used PPO algorithm may be suboptimal for the alignment of CodeLLM because the involved reward rules are routinely coarse-grained and potentially flawed. We then advocate addressing this using the DPO algorithm. Based on only preference data pairs, DPO can render the model rank data automatically, giving rise to a fine-grained rewarding pattern more robust than human intervention. We also contribute a pipeline for collecting preference pairs for DPO on CodeLLMs. Studies show that our method significantly improves the performance of existing CodeLLMs on benchmarks such as MBPP and HumanEval.

While test-time scaling has enabled large language models to solve highly difficult tasks, state-of-the-art results come at exorbitant compute costs. These inefficiencies can be attributed to the miscalibration of post-trained language models, and the lack of calibration in popular sampling techniques. Here, we present Online Reasoning Calibration (ORCA), a framework for calibrating the sampling process that draws upon conformal prediction and test-time training. Specifically, we introduce a meta-learning procedure that updates the calibration module for each input. This allows us to provide valid confidence estimates under distributional shift, e.g. in thought patterns that occur across different stages of reasoning, or in prompt distributions between model development and deployment. ORCA not only provides theoretical guarantees on conformal risks, but also empirically shows higher efficiency and generalization across different reasoning tasks. At risk level δ=0.1, ORCA improves Qwen2.5-32B efficiency on in-distribution tasks with savings up to 47.5% with supervised labels and 40.7% with self-consistency labels. Under zero-shot out-of-domain settings, it improves MATH-500 savings from 24.8% of the static calibration baseline to 67.0% while maintaining a low empirical error rate, and the same trend holds across model families and downstream benchmarks. Our code is publicly available at https://github.com/wzekai99/ORCA.

Multimodal large language models (MLLMs) have become a prevailing paradigm for unified video perception. However, post-training on large multi-task datasets remains challenging, as existing reinforcement learning methods sample on-policy groups with few high-quality rollouts even with costly chain-of-thought (CoT) generation. In this paper, we study the sample efficiency and scalability of RL post-training for video MLLMs and introduce OraRL. We identify an overlooked role for annotations: Beyond scoring rollouts, each can enter its on-policy group as an oracle rollout, a direct positive optimization target. Direct oracle integration, however, is nontrivial: a high-reward oracle raises the group baseline and inverts otherwise positive policy advantages, a failure we term advantage inversion. At the core of OraRL is a decoupled advantage estimator: policy rollouts determine an oracle-free baseline, while the oracle-policy gap modulates both a directional gain and a separate detached oracle advantage. Sign-balanced pruning improves efficiency: by retaining only the oracle and the strongest rollouts of each sign, OraRL requires just 2.2x the step time of SFT, less than half the 4.9x required by GRPO with CoT. OraRL scales with model size and data, surpassing its backbone from 0.8B to 9B and GRPO up to 100k prompts. Without chain-of-thought, Video-ORA-9B decodes in 130 ms instead of 4,780 ms. Compared with the respective prior best models, it raises temporal mIoU from 62.5 to 66.0, tracking AO from 73.0 to 78.2, segmentation from 64.3 to 70.4, and the three-benchmark spatial-intelligence macro average from 51.0 to 56.1; on VSI-Bench, it scores 73.1 against 55.0 for GPT-5 and 55.1 for Gemini-3-Pro.

Structured pruning is a commonly used technique in deploying deep neural networks (DNNs) onto resource-constrained devices. However, the existing pruning methods are usually heuristic, task-specified, and require an extra fine-tuning procedure. To overcome these limitations, we propose a framework that compresses DNNs into slimmer architectures with competitive performances and significant FLOPs reductions by Only-Train-Once (OTO). OTO contains two keys: (i) we partition the parameters of DNNs into zero-invariant groups, enabling us to prune zero groups without affecting the output; and (ii) to promote zero groups, we then formulate a structured-sparsity optimization problem and propose a novel optimization algorithm, Half-Space Stochastic Projected Gradient (HSPG), to solve it, which outperforms the standard proximal methods on group sparsity exploration and maintains comparable convergence. To demonstrate the effectiveness of OTO, we train and compress full models simultaneously from scratch without fine-tuning for inference speedup and parameter reduction, and achieve state-of-the-art results on VGG16 for CIFAR10, ResNet50 for CIFAR10 and Bert for SQuAD and competitive result on ResNet50 for ImageNet. The source code is available at https://github.com/tianyic/only_train_once.

Reinforcement Learning with Human Feedback (RLHF) and its variants have made huge strides toward the effective alignment of large language models (LLMs) to follow instructions and reflect human values. More recently, Direct Alignment Algorithms (DAAs) have emerged in which the reward modeling stage of RLHF is skipped by characterizing the reward directly as a function of the policy being learned. Examples include Direct Preference Optimization (DPO) and Simple Preference Optimization (SimPO). These methods often suffer from likelihood displacement, a phenomenon by which the probabilities of preferred responses are often reduced undesirably. In this paper, we argue that, for DAAs the reward (function) shape matters. We introduce AlphaPO, a new DAA method that leverages an alpha-parameter to help change the shape of the reward function beyond the standard log reward. AlphaPO helps maintain fine-grained control over likelihood displacement and over-optimization. Compared to SimPO, one of the best performing DAAs, AlphaPO leads to about 7\% to 10\% relative improvement in alignment performance for the instruct versions of Mistral-7B and Llama3-8B. The analysis and results presented highlight the importance of the reward shape, and how one can systematically change it to affect training dynamics, as well as improve alignment performance.

Large reasoning models that use long chain-of-thought excel at problem-solving yet waste compute on redundant checks. Curbing this overthinking is hard: training-time length penalties can cripple ability, while inference-time early-exit adds system overhead. To bridge this gap, we propose Step-GRPO, a novel post-training framework that internalizes dynamic early-exit capabilities directly into the model. Step-GRPO shifts the optimization objective from raw tokens to semantic steps by utilizing linguistic markers to structure reasoning. We introduce a Dynamic Truncated Rollout mechanism that exposes the model to concise high-confidence trajectories during exploration, synergized with a Step-Aware Relative Reward that dynamically penalizes redundancy based on group-level baselines. Extensive experiments across three model sizes on diverse benchmarks demonstrate that Step-GRPO achieves a superior accuracy-efficiency trade-off. On Qwen3-8B, our method reduces token consumption by 32.0\% compared to the vanilla model while avoiding the accuracy degradation observed in traditional length-penalty methods.

Prompt optimization offers a practical and broadly applicable alternative to fine-tuning for improving large language model (LLM) performance. However, existing methods often rely on costly output generation, self-critiquing abilities, or human-annotated preferences, which limit their scalability, especially for smaller or non-instruction-tuned models. We introduce PMPO (Probabilistic Metric Prompt Optimization), a unified framework that refines prompts using token-level cross-entropy loss as a direct, lightweight evaluation signal. PMPO identifies low-quality prompt segments by masking and measuring their impact on loss, then rewrites and selects improved variants by minimizing loss over positive and negative examples. Unlike prior methods, it requires no output sampling or human evaluation during optimization, relying only on forward passes and log-likelihoods. PMPO supports both supervised and preference-based tasks through a closely aligned loss-based evaluation strategy. Experiments show that PMPO consistently outperforms prior methods across model sizes and tasks: it achieves the highest average accuracy on BBH, performs strongly on GSM8K and AQUA-RAT, and improves AlpacaEval 2.0 win rates by over 19 points. These results highlight PMPO's effectiveness, efficiency, and broad applicability.

We investigate safe multi-agent reinforcement learning, where agents seek to collectively maximize an aggregate sum of local objectives while satisfying their own safety constraints. The objective and constraints are described by {\it general utilities}, i.e., nonlinear functions of the long-term state-action occupancy measure, which encompass broader decision-making goals such as risk, exploration, or imitations. The exponential growth of the state-action space size with the number of agents presents challenges for global observability, further exacerbated by the global coupling arising from agents' safety constraints. To tackle this issue, we propose a primal-dual method utilizing shadow reward and κ-hop neighbor truncation under a form of correlation decay property, where κ is the communication radius. In the exact setting, our algorithm converges to a first-order stationary point (FOSP) at the rate of Oleft(T^{-2/3}right). In the sample-based setting, we demonstrate that, with high probability, our algorithm requires mathcal{O}left(ε^{-3.5}right) samples to achieve an ε-FOSP with an approximation error of O(φ_0^{2κ}), where φ_0in (0,1). Finally, we demonstrate the effectiveness of our model through extensive numerical experiments.

Direct Preference Optimization (DPO) is a method for enhancing model performance by directly optimizing for the preferences or rankings of outcomes, instead of traditional loss functions. This approach has proven effective in aligning Large Language Models (LLMs) with human preferences. Despite its widespread use across various tasks, DPO has been criticized for its sensitivity to the effectiveness of Supervised Fine-Tuning (SFT) and its limitations in enabling models to learn human-preferred responses, leading to less satisfactory performance. To address these limitations, we propose Aligned Supervised Fine-Tuning (ASFT), an effective approach that better aligns LLMs with pair-wise datasets by optimizing absolute likelihood for each response, rather than using the Bradley-Terry model, and eliminates the need for a reference model. Through theoretical gradient analysis, we demonstrate that ASFT mitigates the issue where the DPO loss function decreases the probability of generating human-dispreferred data at a faster rate than it increases the probability of producing preferred data. Additionally, we compare ASFT to DPO and its latest variants, such as the single-step approach ORPO, using the latest instruction-tuned model Llama3, which has been fine-tuned on UltraFeedback and HH-RLHF. We evaluated performance on instruction-following benchmarks like MT-Bench and traditional text generation metrics such as BLEU-4 and ROUGE-L. Extensive experiments demonstrate that ASFT is an effective alignment approach, consistently outperforming existing methods.

The deployment of large language models (LLMs) raises significant ethical and safety concerns. While LLM alignment techniques are adopted to improve model safety and trustworthiness, adversaries can exploit these techniques to undermine safety for malicious purposes, resulting in misalignment. Misaligned LLMs may be published on open platforms to magnify harm. To address this, additional safety alignment, referred to as realignment, is necessary before deploying untrusted third-party LLMs. This study explores the efficacy of fine-tuning methods in terms of misalignment, realignment, and the effects of their interplay. By evaluating four Supervised Fine-Tuning (SFT) and two Preference Fine-Tuning (PFT) methods across four popular safety-aligned LLMs, we reveal a mechanism asymmetry between attack and defense. While Odds Ratio Preference Optimization (ORPO) is most effective for misalignment, Direct Preference Optimization (DPO) excels in realignment, albeit at the expense of model utility. Additionally, we identify model-specific resistance, residual effects of multi-round adversarial dynamics, and other noteworthy findings. These findings highlight the need for robust safeguards and customized safety alignment strategies to mitigate potential risks in the deployment of LLMs. Our code is available at https://github.com/zhangrui4041/The-Art-of-Mis-alignment.

We study the process through which reasoning models trained with reinforcement learning on verifiable rewards (RLVR) can learn to solve new problems. We find that RLVR drives performance in two main ways: (1) by compressing pass@k into pass@1 and (2) via "capability gain" in which models learn to solve new problems that they previously could not solve even at high k. We find that while capability gain exists across model scales, learning to solve new problems is primarily driven through self-distillation. We demonstrate these findings across model scales ranging from 0.5B to 72B parameters on >500,000 reasoning problems with prompts and verifiable final answers across math, science, and code domains. We further show that we can significantly improve pass@k rates by leveraging natural language guidance for the model to consider within context while still requiring the model to derive a solution chain from scratch. Based of these insights, we derive Guide -- a new class of online training algorithms. Guide adaptively incorporates hints into the model's context on problems for which all rollouts were initially incorrect and adjusts the importance sampling ratio for the "off-policy" trajectories in order to optimize the policy for contexts in which the hints are no longer present. We describe variants of Guide for GRPO and PPO and empirically show that Guide-GRPO on 7B and 32B parameter models improves generalization over its vanilla counterpart with up to 4% macro-average improvement across math benchmarks. We include careful ablations to analyze Guide's components and theoretically analyze Guide's learning efficiency.

Zeroth-order (ZO) fine-tuning is attractive for large language models because it replaces backpropagation with forward objective evaluations. Existing implementations nevertheless execute ZO algorithms inside conventional training loops, even though their dominant work is repeated scoring under nearby parameter states. This creates a workload-runtime mismatch: the algorithm asks for structured inference-style scoring, while the system exposes a sequence of fragmented training-loop steps. We show that LLM ZO fine-tuning is an inference-dominated workload and execute its repeated scoring phase through a serving runtime. On OPT-13B SST-2, the resulting vLLM execution path completes the 20k-step LoZO run in 0.51 estimated training hours versus 4.15 hours for the official LoZO baseline under the matched LoRA-only setting, an 8.13x speedup, while reaching 0.922 final evaluation accuracy and 0.931 final full-validation accuracy. In core-step scaling experiments across OPT-1.3B to OPT-13B, the same runtime reorganization gives 2.34x--7.72x speedups. A MeZO-style high-rank factorized experiment shows that the same runtime paradigm can track a MeZO-like loss trajectory while running up to 2.55x faster. More broadly, representing ZO updates as dynamic adapter states suggests a practical path toward inference-time training, where lightweight adaptation can be scheduled as an inference-like workload rather than as a separate training job.

Trust Region Policy Optimization (TRPO) is a popular and empirically successful policy search algorithm in reinforcement learning (RL). It iteratively solved the surrogate problem which restricts consecutive policies to be close to each other. TRPO is an on-policy algorithm. On-policy methods bring many benefits, like the ability to gauge each resulting policy. However, they typically discard all the knowledge about the policies which existed before. In this work, we use a replay buffer to borrow from the off-policy learning setting to TRPO. Entropy regularization is usually used to improve policy optimization in reinforcement learning. It is thought to aid exploration and generalization by encouraging more random policy choices. We add an Entropy regularization term to advantage over π, accumulated over time steps, in TRPO. We call this update EnTRPO. Our experiments demonstrate EnTRPO achieves better performance for controlling a Cart-Pole system compared with the original TRPO

Outlier detection (OD) has a vast literature as it finds numerous real-world applications. Being an unsupervised task, model selection is a key bottleneck for OD without label supervision. Despite a long list of available OD algorithms with tunable hyperparameters, the lack of systematic approaches for unsupervised algorithm and hyperparameter selection limits their effective use in practice. In this paper, we present FoMo-0D, a pre-trained Foundation Model for zero/0-shot OD on tabular data, which bypasses the hurdle of model selection altogether. Having been pre-trained on synthetic data, FoMo-0D can directly predict the (outlier/inlier) label of test samples without parameter fine-tuning -- requiring no labeled data, and no additional training or hyperparameter tuning when given a new task. Extensive experiments on 57 real-world datasets against 26 baselines show that FoMo-0D is highly competitive; outperforming the majority of the baselines with no statistically significant difference from the 2nd best method. Further, FoMo-0D is efficient in inference time requiring only 7.7 ms per sample on average, with at least 7x speed-up compared to previous methods. To facilitate future research, our implementations for data synthesis and pre-training as well as model checkpoints are openly available at https://github.com/A-Chicharito-S/FoMo-0D.

Orthrus is a hybrid autoregressive-diffusion architecture that accelerates autoregressive language-model inference by generating multiple tokens in parallel while using a frozen autoregressive backbone. Its central claim is that an intra-model consensus mechanism enables lossless speculative decoding, producing the same output sequence as the autoregressive model. We independently reproduce Orthrus and examine this claim under different numerical precisions. Under BF16 inference, exact trajectory matching occurs in only 45% of cases for the authors' checkpoint and 43% for our independently trained model across 1,190 prompts from 12 domains. The probability of exact matching is also strongly associated with the response-conditional perplexity of the reference model. Despite this trajectory divergence, Orthrus does not show systematic degradation on downstream lm-eval-harness benchmarks. In contrast, repeating the trajectory evaluation with FP32 yields exact trajectory matching on all evaluated prompts. These results show that the practical losslessness of Orthrus depends on numerical precision and that exact trajectory equivalence should be evaluated separately from downstream task performance.

Reinforcement learning (RL) has emerged as a powerful tool for fine-tuning large language models (LLMs) to improve complex reasoning abilities. However, state-of-the-art policy optimization methods often suffer from high computational overhead and memory consumption, primarily due to the need for multiple generations per prompt and the reliance on critic networks or advantage estimates of the current policy. In this paper, we propose A*-PO, a novel two-stage policy optimization framework that directly approximates the optimal advantage function and enables efficient training of LLMs for reasoning tasks. In the first stage, we leverage offline sampling from a reference policy to estimate the optimal value function V*, eliminating the need for costly online value estimation. In the second stage, we perform on-policy updates using a simple least-squares regression loss with only a single generation per prompt. Theoretically, we establish performance guarantees and prove that the KL-regularized RL objective can be optimized without requiring complex exploration strategies. Empirically, A*-PO achieves competitive performance across a wide range of mathematical reasoning benchmarks, while reducing training time by up to 2times and peak memory usage by over 30% compared to PPO, GRPO, and REBEL. Implementation of A*-PO can be found at https://github.com/ZhaolinGao/A-PO.

Direct preference optimization (DPO) is a successful fine-tuning strategy for aligning large language models with human preferences without the need to train a reward model or employ reinforcement learning. DPO, as originally formulated, relies on binary preference data and fine-tunes a language model to increase the likelihood of a preferred response over a dispreferred response. However, not all preference pairs are equal: while in some cases the preferred response is only slightly better than the dispreferred response, there can be a stronger preference for one response when, for example, the other response includes harmful or toxic content. In this paper, we propose a generalization of DPO, termed DPO with an offset (ODPO), that does not treat every preference pair equally during fine-tuning. Intuitively, ODPO requires the difference between the likelihood of the preferred and dispreferred response to be greater than an offset value. The offset is determined based on the extent to which one response is preferred over another. Our experiments on various tasks suggest that ODPO significantly outperforms DPO in aligning language models, especially when the number of preference pairs is limited.

Recent advancements in flow-matching have enabled high-quality text-to-image generation. However, the deterministic nature of flow-matching models makes them poorly suited for reinforcement learning, a key tool for improving image quality and human alignment. Prior work has introduced stochasticity by perturbing latents with random noise, but such perturbations are inefficient and unstable. We propose Smart-GRPO, the first method to optimize noise perturbations for reinforcement learning in flow-matching models. Smart-GRPO employs an iterative search strategy that decodes candidate perturbations, evaluates them with a reward function, and refines the noise distribution toward higher-reward regions. Experiments demonstrate that Smart-GRPO improves both reward optimization and visual quality compared to baseline methods. Our results suggest a practical path toward reinforcement learning in flow-matching frameworks, bridging the gap between efficient training and human-aligned generation.

Large language models have demonstrated strong reasoning capabilities in complex tasks through tool integration, which is typically framed as a Markov Decision Process and optimized with trajectory-level RL algorithms such as GRPO. However, a common class of reasoning tasks, iterative optimization, presents distinct challenges: the agent interacts with the same underlying environment state across turns, and the value of a trajectory is determined by the best turn-level reward rather than cumulative returns. Existing GRPO-based methods cannot perform fine-grained, turn-level optimization in such settings, while black-box optimization methods discard prior knowledge and reasoning capabilities. To address this gap, we propose Turn-Level GRPO (TL-GRPO), a lightweight RL algorithm that performs turn-level group sampling for fine-grained optimization. We evaluate TL-GRPO on analog circuit sizing (ACS), a challenging scientific optimization task requiring multiple simulations and domain expertise. Results show that TL-GRPO outperforms standard GRPO and Bayesian optimization methods across various specifications. Furthermore, our 30B model trained with TL-GRPO achieves state-of-the-art performance on ACS tasks under same simulation budget, demonstrating both strong generalization and practical utility.

Domain adaptation aims to turn a general-purpose large language model (LLM) into an expert for a target domain. While the dominant SFT+RL pipeline offers a convenient cold start, it may reduce exploration diversity and introduces additional complexity through multi-stage optimization. These limitations motivate RL-only adaptation. However, pure on-policy RL suffers from a cold-start problem, while mixed-policy RL still falls short: informative tokens in teacher outputs are learned too slowly in early training, and stale teacher outputs can hinder later improvement. We identify these two failure modes as Gradient Starvation and Teacher-Distribution Anchoring. To address them, we propose One-stage Policy Optimization (OnePO), which treats teacher outputs as transient guidance for policy improvement. OnePO combines Adaptive Objective Evolution to strengthen learning on informative low-probability teacher tokens and Teacher Retirement to discard teacher outputs once the current policy can surpass them. On medical adaptation, OnePO achieves 67.2 on HealthBench (Total) with only 20K training samples, outperforming SFT+RL and pure RL by 2.7 and 7.4 points, respectively. We further scale OnePO to produce HuatuoGPT-3, an open-source medical LLM series whose 27B variant reaches 70.1 on HealthBench (Total) and 71.4 on HealthBench Professional, surpassing frontier models such as GPT-6 Astra. Models and code are available at https://github.com/FreedomIntelligence/HuatuoGPT-3.

Text-to-motion generation is essential for advancing the creative industry but often presents challenges in producing consistent, realistic motions. To address this, we focus on fine-tuning text-to-motion models to consistently favor high-quality, human-preferred motions, a critical yet largely unexplored problem. In this work, we theoretically investigate the DPO under both online and offline settings, and reveal their respective limitation: overfitting in offline DPO, and biased sampling in online DPO. Building on our theoretical insights, we introduce Semi-online Preference Optimization (SoPo), a DPO-based method for training text-to-motion models using "semi-online" data pair, consisting of unpreferred motion from online distribution and preferred motion in offline datasets. This method leverages both online and offline DPO, allowing each to compensate for the other's limitations. Extensive experiments demonstrate that SoPo outperforms other preference alignment methods, with an MM-Dist of 3.25% (vs e.g. 0.76% of MoDiPO) on the MLD model, 2.91% (vs e.g. 0.66% of MoDiPO) on MDM model, respectively. Additionally, the MLD model fine-tuned by our SoPo surpasses the SoTA model in terms of R-precision and MM Dist. Visualization results also show the efficacy of our SoPo in preference alignment. Our project page is https://sopo-motion.github.io.

Large language models are increasingly deployed as autonomous agents for multi-step tasks in executable environments, yet their ability to perform realistic operations research (OR) work remains unclear. Existing OR evaluations often decouple modeling from solving, rely on pre-formalized or text-only instances, and rarely test the full workflow from operational artifacts to validated decisions. In this work, we introduce ORAgentBench, an execution-grounded benchmark for evaluating autonomous agents on challenging end-to-end operations research tasks. It contains 107 human-reviewed tasks across diverse operational scenarios, each packaged in an isolated environment with a natural-language brief, multi-file data, configuration artifacts, and a required submission schema. Agents must write and run solution code, and their submissions are evaluated by hidden validators for schema validity, hard-constraint feasibility, and normalized objective quality. Experiments with fourteen frontier agent-model configurations show that current agents remain far from reliable OR practice. The best agent passes only 35.51% of all tasks and 20.59% of hard tasks, and many feasible submissions still fall below the required quality threshold. Failure analysis further shows that errors are dominated by strategic weaknesses, including missed operational rules, brittle formulations, weak feasible-solution construction, and insufficient solution improvement. OR-specific procedural skills increase hard-task feasibility, but do not reliably improve solution quality or pass rate. These results suggest that progress in OR agents requires moving beyond plausible optimization code toward dependable, high-quality operational decision-making.

Large Language Models (LLMs) perform well across diverse tasks, but aligning them with human demonstrations is challenging. Recently, Reinforcement Learning (RL)-free methods like Direct Preference Optimization (DPO) have emerged, offering improved stability and scalability while retaining competitive performance relative to RL-based methods. However, while RL-free methods deliver satisfactory performance, they require significant data to develop a robust Supervised Fine-Tuned (SFT) model and an additional step to fine-tune this model on a preference dataset, which constrains their utility and scalability. In this paper, we introduce Triple Preference Optimization (TPO), a new preference learning method designed to align an LLM with three preferences without requiring a separate SFT step and using considerably less data. Through a combination of practical experiments and theoretical analysis, we show the efficacy of TPO as a single-step alignment strategy. Specifically, we fine-tuned the Phi-2 (2.7B) and Mistral (7B) models using TPO directly on the UltraFeedback dataset, achieving superior results compared to models aligned through other methods such as SFT, DPO, KTO, IPO, CPO, and ORPO. Moreover, the performance of TPO without the SFT component led to notable improvements in the MT-Bench score, with increases of +1.27 and +0.63 over SFT and DPO, respectively. Additionally, TPO showed higher average accuracy, surpassing DPO and SFT by 4.2% and 4.97% on the Open LLM Leaderboard benchmarks. Our code is publicly available at https://github.com/sahsaeedi/triple-preference-optimization .

Finding high-quality solutions quickly is an important objective in motion planning. This is especially true for high-degree-of-freedom robots. Satisficing planners have traditionally found feasible solutions quickly but provide no guarantees on their optimality, while almost-surely asymptotically optimal (a.s.a.o.) planners have probabilistic guarantees on their convergence towards an optimal solution but are more computationally expensive. This paper uses the AO-x meta-algorithm to extend the satisficing RRT-Connect planner to optimal planning. The resulting Asymptotically Optimal RRT-Connect (AORRTC) finds initial solutions in similar times as RRT-Connect and uses any additional planning time to converge towards the optimal solution in an anytime manner. It is proven to be probabilistically complete and a.s.a.o. AORRTC was tested with the Panda (7 DoF) and Fetch (8 DoF) robotic arms on the MotionBenchMaker dataset. These experiments show that AORRTC finds initial solutions as fast as RRT-Connect and faster than the tested state-of-the-art a.s.a.o. algorithms while converging to better solutions faster. AORRTC finds solutions to difficult high-DoF planning problems in milliseconds where the other a.s.a.o. planners could not consistently find solutions in seconds. This performance was demonstrated both with and without single instruction/multiple data (SIMD) acceleration.

Prompt engineering is effective but labor-intensive, motivating automated optimization methods. Existing methods typically require labeled datasets, which are often unavailable, and produce verbose, repetitive prompts. We introduce PrefPO, a minimal prompt optimization approach inspired by reinforcement learning from human feedback (RLHF). Its preference-based approach reduces the need for labeled data and hyperparameter tuning-only a starting prompt and natural language criteria are needed. PrefPO uses an LLM discriminator to express pairwise preferences over model outputs and provide feedback to an LLM optimizer, iteratively improving performance. We evaluate PrefPO on 9 BIG-Bench Hard (BBH) tasks and IFEval-Hard, a newly-curated, challenging subset of IFEval. PrefPO matches or exceeds SOTA methods, including GEPA, MIPRO, and TextGrad, on 6/9 tasks and performs comparably to TextGrad on IFEval-Hard (82.4% vs 84.5%). Unlike other methods, PrefPO can optimize in both labeled and unlabeled settings. Without labels, PrefPO closely matches its labeled performance on 6/9 tasks, proving effective without ground truth. PrefPO also improves prompt hygiene: we find existing methods produce prompts 14.7x their original length or with 34% repetitive content; PrefPO reduces these issues by 3-5x. Furthermore, both LLM and human judges rate PrefPO's prompts higher than TextGrad's. Finally, we identify prompt hacking in prompt optimizers, where methods game evaluation criteria, and find PrefPO is susceptible at half the rate of TextGrad (37% vs 86%), generating fewer brittle, misaligned prompts.

Recent developments in Large Language Model (LLM) agents are revolutionizing Autonomous Software Engineering (ASE), enabling automated coding, problem fixes, and feature improvements. However, localization -- precisely identifying software problems by navigating to relevant code sections -- remains a significant challenge. Current approaches often yield suboptimal results due to a lack of effective integration between LLM agents and precise code search mechanisms. This paper introduces OrcaLoca, an LLM agent framework that improves accuracy for software issue localization by integrating priority-based scheduling for LLM-guided action, action decomposition with relevance scoring, and distance-aware context pruning. Experimental results demonstrate that OrcaLoca becomes the new open-source state-of-the-art (SOTA) in function match rate (65.33%) on SWE-bench Lite. It also improves the final resolved rate of an open-source framework by 6.33 percentage points through its patch generation integration.

In modern logistics management systems, route planning requires high efficiency. The Open Capacitated Vehicle Routing Problem (OCVRP) deals with finding optimal delivery routes for a fleet of vehicles serving geographically distributed customers, without requiring the vehicles to return to the depot after deliveries. The present study is comparative in nature and speaks of two algorithms for OCVRP solution: Ant Colony Optimization (ACO), a nature-inspired metaheuristic; and Google OR-Tools, an industry-standard toolkit for optimization. Both implementations were developed in Python and using a custom dataset. Performance appraisal was based on routing efficiency, computation time, and scalability. The results show that ACO allows flexibility in routing parameters while OR-Tools runs much faster with more consistency and requires less input. This could help choose among routing strategies for scalable real-time logistics systems.

Large language models (LLMs) are increasingly used to formulate optimization models from natural-language problem descriptions, yet realistic operations research (OR) requests are often incomplete: missing objectives, constraints, or business rules can change the resulting mathematical program. Existing evaluations largely assume a complete specification and therefore overlook whether an agent knows when clarification is needed before modeling. We introduce OR-Clarify, a benchmark for pre-formulation clarification. Each task presents a partial public problem description, withholds structured hidden slots, and evaluates agents through bounded interaction with a simulated user. The benchmark supports both openended and choice-based clarification, and measures slot recovery, stopping behavior, silent assumptions, and interaction cost. We further propose Interactive Optimization (InterOPT), a two-stage framework that identifies unresolved formulation-critical gaps and uses them to guide whether to ask the next question or to stop. In our choice-based experiments, InterOPT substantially outperforms all baselines in exact slot recovery; in the open-ended setting, it remains competitive with strong prior methods. Together, OR-Clarify and InterOPT reframe OR assistance as a selective completeness decision: clarify when needed, stop when ready, and quantify what remains missing.

Assigning one of K options to each of N groups under a total cost budget is a recurring problem in efficient AI, including mixed-precision quantization, non-uniform pruning, and expert selection. The objective, typically model loss, depends jointly on all assignments and does not decompose across groups, preventing combinatorial solvers from directly optimizing the true objective and forcing reliance on proxy formulations. Methods such as evolutionary search evaluate the actual loss but lack gradient information, while penalty-based approaches enforce the budget only approximately and often require extensive hyperparameter tuning. We present a new approach by showing that, under softmax relaxation, the budget constraint defines a smooth Riemannian manifold in logit space with unusually simple geometry. The normal vector admits a closed-form expression, shifting logits along the cost vector changes expected cost monotonically, and vector transport reduces to a single inner product. Building on these properties, we propose Riemannian Constrained Optimization (RCO), which augments a standard Adam step with tangent projection, binary-search retraction, and momentum transport. Combined with Gumbel straight-through estimation and budget-constrained dynamic programming for discrete feasibility, RCO enables first-order optimization of the actual loss under exact budget enforcement without introducing constraint-specific hyperparameters. Across both synthetic benchmarks and realistic LLM compression settings, RCO matches or exceeds state-of-the-art methods while often requiring substantially less wall-clock time. Source code is available at https://github.com/IST-DASLab/RCO.

Despite the remarkable progress of multimodal large language models (MLLMs), they continue to face challenges in achieving competitive performance on ordinal regression (OR; a.k.a. ordinal classification). To address this issue, this paper presents OrderChain, a novel and general prompting paradigm that improves the ordinal understanding ability of MLLMs by specificity and commonality modeling. Specifically, our OrderChain consists of a set of task-aware prompts to facilitate the specificity modeling of diverse OR tasks and a new range optimization Chain-of-Thought (RO-CoT), which learns a commonality way of thinking about OR tasks by uniformly decomposing them into multiple small-range optimization subtasks. Further, we propose a category recursive division (CRD) method to generate instruction candidate category prompts to support RO-CoT automatic optimization. Comprehensive experiments show that LLaVA model with our OrderChain improves baseline LLaVA significantly on diverse OR datasets, e.g., from 47.5\% to 93.2\% accuracy on the Adience dataset for age estimation, and from 30.0\% to 85.7\% accuracy on the Diabetic Retinopathy dataset. Notably, LLaVA with our OrderChain also remarkably outperforms state-of-the-art methods by 27% on accuracy and 0.24 on MAE on the Adience dataset. To our best knowledge, our OrderChain is the first work that augments MLLMs for OR tasks, and the effectiveness is witnessed across a spectrum of OR datasets. Project Page: https://order-chain.github.io/.

Evolutionary program synthesis systems such as AlphaEvolve, OpenEvolve, and ShinkaEvolve offer a new approach to AI-assisted mathematical discovery. These systems utilize teams of large language models (LLMs) to generate candidate solutions to a problem as human readable code. These candidate solutions are then 'evolved' with the goal of improving them beyond what an LLM can produce in a single shot. While existing mathematical applications have mostly focused on problems of establishing bounds (e.g., sphere packing), the program synthesis approach is well suited to any problem where the solution takes the form of an explicit construction. With this in mind, in this paper we explore the use of OpenEvolve for combinatorial bijection discovery. We describe the results of applying OpenEvolve to three bijection construction problems involving Dyck paths, two of which are known and one of which is open. We find that while systems like OpenEvolve show promise as a valuable tool for combinatorialists, the problem of finding novel, research-level bijections remains a challenging task for current frontier systems, reinforcing the need for human mathematicians in the loop. We describe some lessons learned for others in the field interested in exploring the use of these systems.

With the rise of artificial intelligence (AI), applying large language models (LLMs) to Operations Research (OR) problem-solving has attracted increasing attention. Most existing approaches attempt to improve OR problem-solving through prompt engineering or fine-tuning strategies for LLMs. However, these methods are fundamentally constrained by the limited capabilities of non-reasoning LLMs. To overcome these limitations, we propose OR-LLM-Agent, an AI agent built on reasoning LLMs for automated OR problem solving. The agent decomposes the task into three sequential stages: mathematical modeling, code generation, and debugging. Each task is handled by a dedicated sub-agent, which enables more targeted reasoning. We also construct BWOR, a high-quality dataset for evaluating LLM performance on OR tasks. Our analysis shows that existing benchmarks such as NL4OPT, MAMO, and IndustryOR suffer from certain issues, making them less suitable for reliably evaluating LLM performance. In contrast, BWOR provides a more consistent and discriminative assessment of model capabilities. Experimental results demonstrate that OR-LLM-Agent outperforms advanced methods, including GPT-o3, Gemini 2.5 Pro, and ORLM, by at least 7% in accuracy. These results demonstrate the effectiveness of task decomposition for OR problem solving.

Direct Preference Optimization (DPO) has emerged as a prominent algorithm for the direct and robust alignment of Large Language Models (LLMs) with human preferences, offering a more straightforward alternative to the complex Reinforcement Learning from Human Feedback (RLHF). Despite its promising efficacy, DPO faces a notable drawback: "verbosity", a common over-optimization phenomenon also observed in RLHF. While previous studies mainly attributed verbosity to biased labels within the data, we propose that the issue also stems from an inherent algorithmic length reliance in DPO. Specifically, we suggest that the discrepancy between sequence-level Kullback-Leibler (KL) divergences between chosen and rejected sequences, used in DPO, results in overestimated or underestimated rewards due to varying token lengths. Empirically, we utilize datasets with different label lengths to demonstrate the presence of biased rewards. We then introduce an effective downsampling approach, named SamPO, to eliminate potential length reliance. Our experimental evaluations, conducted across three LLMs of varying scales and a diverse array of conditional and open-ended benchmarks, highlight the efficacy of SamPO in mitigating verbosity, achieving improvements of 5% to 12% over DPO through debaised rewards. Our codes can be accessed at: https://github.com/LuJunru/SamPO/.

Recent large reasoning models (LRMs) driven by reinforcement learning algorithms (e.g., GRPO) have achieved remarkable performance on challenging reasoning tasks. However, these models suffer from overthinking, generating unnecessarily long and redundant reasoning even for simple questions, which substantially increases computational cost and response latency. While existing methods incorporate length rewards to GRPO to promote concise reasoning, they incur significant performance degradation. We identify the root cause: when rewards for correct but long rollouts are penalized, GRPO's group-relative advantage function can assign them negative advantages, actively discouraging valid reasoning. To overcome this, we propose Decoupled Reward Policy Optimization (DRPO), a novel framework that decouples the length-based learning signal of correct rollouts from incorrect ones. DRPO ensures that reward signals for correct rollouts are normalized solely within the positive group, shielding them from interference by negative samples. The DRPO's objective is grounded in integrating an optimized positive data distribution, which maximizes length-based rewards under a KL regularization, into a discriminative objective. We derive a closed-form solution for this distribution, enabling efficient computation of the objective and its gradients using only on-policy data and importance weighting. Of independent interest, this formulation is general and can incorporate other preference rewards of positive data beyond length. Experiments on mathematical reasoning tasks demonstrate DRPO's significant superiority over six efficient reasoning baselines. Notably, with a 1.5B model, our method achieves 77\% length reduction with only 1.1\% performance loss on simple questions like GSM8k dataset, while the follow-up baseline sacrifices 4.3\% for 68\% length reduction.

We revisit the noisy binary search model of Karp and Kleinberg, in which we have n coins with unknown probabilities p_i that we can flip. The coins are sorted by increasing p_i, and we would like to find where the probability crosses (to within varepsilon) of a target value tau. This generalized the fixed-noise model of Burnashev and Zigangirov , in which p_i = 1{2} pm varepsilon, to a setting where coins near the target may be indistinguishable from it. Karp and Kleinberg showed that Theta(1{varepsilon^2} log n) samples are necessary and sufficient for this task. We produce a practical algorithm by solving two theoretical challenges: high-probability behavior and sharp constants. We give an algorithm that succeeds with probability 1-delta from \[ 1{C_{\tau, \varepsilon}} \cdot \left(\lg n + O(\log^{2/3} n \log^{1/3} 1{\delta} + \log 1{\delta})\right) \] samples, where C_{tau, varepsilon} is the optimal such constant achievable. For delta > n^{-o(1)} this is within 1 + o(1) of optimal, and for delta ll 1 it is the first bound within constant factors of optimal.

Direct Preference Optimization (DPO) has emerged as a popular alternative to Reinforcement Learning from Human Feedback (RLHF), offering theoretical equivalence with simpler implementation. We prove this equivalence is conditional rather than universal, depending on an implicit assumption frequently violated in practice: the RLHF-optimal policy must prefer human-preferred responses. When this assumption fails, DPO optimizes relative advantage over the reference policy rather than absolute alignment with human preferences, leading to pathological convergence where policies decrease DPO loss while preferring dispreferred responses. We characterize when this assumption is violated, show the existence of an undesirable solution space, and prove that DPO and RLHF optimize fundamentally different objectives in such cases. To address this, we introduce Constrained Preference Optimization (CPO), augmenting RLHF with constraints for provable alignment. We further provide a geometric interpretation through soft margin ranking, revealing that DPO implements margin ranking with potentially negative targets. Our theoretical analysis establishes when DPOs' guarantees hold and provides solutions preserving simplicity with provable alignment. Comprehensive experiments on standard benchmarks demonstrate that CPO achieves state-of-the-art performance. Code is available at: https://github.com/visitworld123/CPO.

Reinforcement learning from verifiable rewards (e.g. GRPO) is the engine behind today's reasoning models, yet it grades only the final answer. On hard problems this trains models to write more rather than to think better, since the trace itself is never graded and no label for good thinking exists. We introduce Agon, which makes two competing models each other's graders. Both attempt the same problem; in alternating roles, one drafts a solution and the other reads it while solving, and each is rewarded for out-solving the other. To win, a model must out-reason a rival that has seen its work, so reasoning is judged implicitly during training, with no process labels and no reward model. Because both models are optimized, each faces a progressively stronger rival, which single-model RL cannot provide. The two need only be comparably strong and behaviorally different. At inference the pair deploys as it trains, a two-stage cascade in which one model drafts and the other answers after reading the draft. On the hard split of DeepMath with Qwen3, this doubles GRPO's pass@1, roughly eight times the gain of an untrained Mixture-of-Agents pass over the same base. The ordering replicates on competitive-programming code and across model families (Qwen3.5, Gemma 4). For now the models talk in text; the next step is to let them reason together in latent space.

Direct Preference Optimization (DPO) has proven effective at improving the performance of large language models (LLMs) on downstream tasks such as reasoning and alignment. In this work, we propose Step-Controlled DPO (SCDPO), a method for automatically providing stepwise error supervision by creating negative samples of mathematical reasoning rationales that start making errors at a specified step. By applying these samples in DPO training, SCDPO can better align the model to understand reasoning errors and output accurate reasoning steps. We apply SCDPO to both code-integrated and chain-of-thought solutions, empirically showing that it consistently improves the performance compared to naive DPO on three different SFT models, including one existing SFT model and two models we finetuned. Qualitative analysis of the credit assignment of SCDPO and DPO demonstrates the effectiveness of SCDPO at identifying errors in mathematical solutions. We then apply SCDPO to an InternLM2-20B model, resulting in a 20B model that achieves high scores of 88.5% on GSM8K and 58.1% on MATH, rivaling all other open-source LLMs, showing the great potential of our method.

Reinforcement learning with verifiable rewards (RLVR) improves reasoning in large language models. Yet, typical RLVR approaches fail on difficult problems: when a model cannot generate any correct solutions, it receives zero learning signal. Providing privileged guidance during training, such as solution prefixes, can help overcome this learning cliff by steering the model towards {correct solutions with non-zero reward}. {We call these rollouts off-context: they are generated from a training prompt that contains privileged guidance, while the target objective is defined by the original prompt without that guidance.} {We introduce} Off-Context GRPO (OC-GRPO), a minimally modified variant of GRPO that uses guided rollouts but applies an importance-corrected objective to steer the update back toward the original unguided objective, avoiding the mismatch that destabilizes uncorrected guided training. Empirically, our algorithm achieves a 3.9\% absolute improvement (13.8\% relative gain) over vanilla GRPO on average across standard mathematical reasoning benchmarks with negligible additional cost.

The alignment of large language models (LLMs) often assumes that using more clean data yields better outcomes, overlooking the match between model capacity and example difficulty. Challenging this, we propose a new principle: Preference data vary in difficulty, and overly difficult examples hinder alignment, by exceeding the model's capacity. Through systematic experimentation, we validate this principle with three key findings: (1) preference examples vary in difficulty, as evidenced by consistent learning orders across alignment runs; (2) overly difficult examples significantly degrade performance across four LLMs and two datasets; and (3) the capacity of a model dictates its threshold for handling difficult examples, underscoring a critical relationship between data selection and model capacity. Building on this principle, we introduce Selective DPO, which filters out overly difficult examples. This simple adjustment improves alignment performance by 9-16% in win rates on the AlpacaEval 2 benchmark compared to the DPO baseline, suppressing a series of DPO variants with different algorithmic adjustments. Together, these results illuminate the importance of aligning data difficulty with model capacity, offering a transformative perspective for improving alignment strategies in LLMs. Code is available at https://github.com/glorgao/SelectiveDPO.

Tool calling allows large language models (LLMs) to invoke external computation during problem solving, a useful capability in various fields including AI for mathematics. We study this setting through weighted sum-of-squares (SOS) decomposition, a machine-checkable route to proving polynomial nonnegativity and hence polynomial inequalities. A candidate decomposition can be checked exactly, but finding one requires choosing among non-unique regroupings and coordinating multiple symbolic transformations. We develop an agent that combines algebraic task training, symbolic tools, and verifier-grounded optimization for this task. Rather than training only on the composite SOS task, we construct 1.35 million synthetic examples covering eight supporting polynomial tasks together with weighted-SOS decomposition. We first apply supervised fine-tuning (SFT) to direct algebra problems and simulated symbolic traces, and then use Group Relative Policy Optimization (GRPO) with task-specific symbolic rewards. The SFT corpus contains no native tool-calling messages; at evaluation, the agent uses native SymPy calls for expansion, collection, reordering, and factorization. Every final SOS answer is checked by exact expansion and coefficient comparison. On held-out, same-generator synthetic problems, the full SFT+GRPO+tools system is the strongest of four evaluated configurations, reaching 78.96% verified success on weighted SOS, compared with 44.73% for the base model with the same tools, and 91.75% macro accuracy across nine polynomial tasks. Within this controlled setting, our work provides a case study of combining domain-specific skill training, executable tools, and verifier feedback, and may inform the design of tool-calling agents in other domains with exactly checkable outputs.

The success of Deepseek-R1 has drawn the LLM community's attention to reinforcement learning (RL) methods like GRPO. However, such rule-based 0/1 outcome reward methods lack the capability to regulate the intermediate reasoning processes during chain-of-thought (CoT) generation, leading to severe overthinking phenomena. In response, recent studies have designed reward functions to reinforce models' behaviors in producing shorter yet correct completions. Nevertheless, we observe that these length-penalty reward functions exacerbate RL training instability: as the completion length decreases, model accuracy abruptly collapses, often occurring early in training. To address this issue, we propose a simple yet effective solution GRPO-lambda, an efficient and stabilized variant of GRPO, which dynamically adjusts the reward strategy by monitoring the correctness ratio among completions within each query-sampled group. A low correctness ratio indicates the need to avoid length penalty that compromises CoT quality, triggering a switch to length-agnostic 0/1 rewards that prioritize reasoning capability. A high ratio maintains length penalties to boost efficiency. Experimental results show that our approach avoids training instability caused by length penalty while maintaining the optimal accuracy-efficiency trade-off. On the GSM8K, GPQA, MATH-500, AMC 2023, and AIME 2024 benchmarks, it improves average accuracy by 1.48% while reducing CoT sequence length by 47.3%.

Reinforcement Learning (RL) has emerged as a central paradigm for advancing Large Language Models (LLMs), where pre-training and RL post-training share the same log-likelihood formulation. In contrast, recent RL approaches for diffusion models, most notably Denoising Diffusion Policy Optimization (DDPO), optimize an objective different from the pretraining objectives--score/flow matching loss. In this work, we establish a novel theoretical analysis: DDPO is an implicit form of score/flow matching with noisy targets, which increases variance and slows convergence. Building on this analysis, we introduce Advantage Weighted Matching (AWM), a policy-gradient method for diffusion. It uses the same score/flow-matching loss as pretraining to obtain a lower-variance objective and reweights each sample by its advantage. In effect, AWM raises the influence of high-reward samples and suppresses low-reward ones while keeping the modeling objective identical to pretraining. This unifies pretraining and RL conceptually and practically, is consistent with policy-gradient theory, reduces variance, and yields faster convergence. This simple yet effective design yields substantial benefits: on GenEval, OCR, and PickScore benchmarks, AWM delivers up to a 24times speedup over Flow-GRPO (which builds on DDPO), when applied to Stable Diffusion 3.5 Medium and FLUX, without compromising generation quality. Code is available at https://github.com/scxue/advantage_weighted_matching.

Mathematical reasoning presents a significant challenge for Large Language Models (LLMs) due to the extensive and precise chain of reasoning required for accuracy. Ensuring the correctness of each reasoning step is critical. To address this, we aim to enhance the robustness and factuality of LLMs by learning from human feedback. However, Direct Preference Optimization (DPO) has shown limited benefits for long-chain mathematical reasoning, as models employing DPO struggle to identify detailed errors in incorrect answers. This limitation stems from a lack of fine-grained process supervision. We propose a simple, effective, and data-efficient method called Step-DPO, which treats individual reasoning steps as units for preference optimization rather than evaluating answers holistically. Additionally, we have developed a data construction pipeline for Step-DPO, enabling the creation of a high-quality dataset containing 10K step-wise preference pairs. We also observe that in DPO, self-generated data is more effective than data generated by humans or GPT-4, due to the latter's out-of-distribution nature. Our findings demonstrate that as few as 10K preference data pairs and fewer than 500 Step-DPO training steps can yield a nearly 3% gain in accuracy on MATH for models with over 70B parameters. Notably, Step-DPO, when applied to Qwen2-72B-Instruct, achieves scores of 70.8% and 94.0% on the test sets of MATH and GSM8K, respectively, surpassing a series of closed-source models, including GPT-4-1106, Claude-3-Opus, and Gemini-1.5-Pro. Our code, data, and models are available at https://github.com/dvlab-research/Step-DPO.

On-policy distillation (OPD) has emerged as a widely used paradigm for post-training large language models, reducing the train--test mismatch of conventional distillation by supervising the student on its own generated trajectories. However, existing OPD objectives remain largely token-local and outcome-agnostic, optimizing teacher--student agreement at each prefix despite reasoning quality being determined at the trajectory level. Reinforcement learning with verifiable rewards (RLVR), particularly Group Relative Policy Optimization (GRPO), provides complementary outcome-level supervision but suffers from sparse rewards and coarse credit assignment. We show that OPD and RLVR exhibit complementary blind spots: teacher signals provide dense local guidance but are weakly aligned with rollout correctness, whereas group-relative rewards capture task success but provide coarse token-level credit and vanish on all-failure groups. We introduce DiffGate, an outcome-gated objective that combines GRPO with selective, bounded teacher guidance. Teacher supervision is applied only to failed trajectories, scaled by group difficulty, and smoothly bounded to prevent extreme teacher--student discrepancies from dominating optimization. The verifier therefore determines which trajectories receive teacher guidance, while the teacher provides dense token-level update directions within those trajectories. Across Qwen3-0.6B and Qwen3-1.7B students, DiffGate improves code avg@8 over matched GRPO by +1.7 and +1.8 points and pass@8 by +1.6 and +5.7 points, respectively. On mathematics, avg@8 remains within 0.5 points of GRPO while pass@8 improves by +1.1 and +3.9 points. Overall, DiffGate improves pass@8 across all four model--domain settings, demonstrating improved solution coverage under our evaluation protocol.

Inference scaling empowers LLMs with unprecedented reasoning ability, with reinforcement learning as the core technique to elicit complex reasoning. However, key technical details of state-of-the-art reasoning LLMs are concealed (such as in OpenAI o1 blog and DeepSeek R1 technical report), thus the community still struggles to reproduce their RL training results. We propose the Decoupled Clip and Dynamic sAmpling Policy Optimization (DAPO) algorithm, and fully open-source a state-of-the-art large-scale RL system that achieves 50 points on AIME 2024 using Qwen2.5-32B base model. Unlike previous works that withhold training details, we introduce four key techniques of our algorithm that make large-scale LLM RL a success. In addition, we open-source our training code, which is built on the verl framework, along with a carefully curated and processed dataset. These components of our open-source system enhance reproducibility and support future research in large-scale LLM RL.

The study of hardest and easiest fitness landscapes is an active area of research. Recently, Kaufmann, Larcher, Lengler and Zou conjectured that for the self-adjusting (1,lambda)-EA, Adversarial Dynamic BinVal (ADBV) is the hardest dynamic monotone function to optimize. We introduce the function Switching Dynamic BinVal (SDBV) which coincides with ADBV whenever the number of remaining zeros in the search point is strictly less than n/2, where n denotes the dimension of the search space. We show, using a combinatorial argument, that for the (1+1)-EA with any mutation rate p in [0,1], SDBV is drift-minimizing among the class of dynamic monotone functions. Our construction provides the first explicit example of an instance of the partially-ordered evolutionary algorithm (PO-EA) model with parameterized pessimism introduced by Colin, Doerr and F\'erey, building on work of Jansen. We further show that the (1+1)-EA optimizes SDBV in Theta(n^{3/2}) generations. Our simulations demonstrate matching runtimes for both static and self-adjusting (1,lambda) and (1+lambda)-EA. We further show, using an example of fixed dimension, that drift-minimization does not equal maximal runtime.

Direct Preference Optimization (DPO) aligns text-to-image (T2I) generation models with human preferences using pairwise preference data. Although substantial resources are expended in collecting and labeling datasets, a critical aspect is often neglected: preferences vary across individuals and should be represented with more granularity. To address this, we propose SmPO-Diffusion, a novel method for modeling preference distributions to improve the DPO objective, along with a numerical upper bound estimation for the diffusion optimization objective. First, we introduce a smoothed preference distribution to replace the original binary distribution. We employ a reward model to simulate human preferences and apply preference likelihood averaging to improve the DPO loss, such that the loss function approaches zero when preferences are similar. Furthermore, we utilize an inversion technique to simulate the trajectory preference distribution of the diffusion model, enabling more accurate alignment with the optimization objective. Our approach effectively mitigates issues of excessive optimization and objective misalignment present in existing methods through straightforward modifications. Our SmPO-Diffusion achieves state-of-the-art performance in preference evaluation, outperforming baselines across metrics with lower training costs. The project page is https://jaydenlyh.github.io/SmPO-project-page/.

Code generation models have shown significant potential for programming tasks. However, existing training methods like supervised fine-tuning face key limitations: they do not effectively teach models to prioritize correct over incorrect solutions in ambiguous situations, nor do they effectively optimize the runtime efficiency of the generated code. To address these challenges, we propose CodeDPO, a framework that integrates preference learning into code generation to improve two key code preference factors: code correctness and efficiency. CodeDPO employs a novel dataset construction method, utilizing a self-generation-and-validation mechanism that simultaneously generates and evaluates code and test cases. The underlying assumption is that test cases executable by multiple code snippets provide more reliable validation, and code that passes more tests is more likely to be correct. Through this self-validation process, our PageRank-inspired algorithm iteratively updates the ranking score of each code snippet, ultimately creating a code preference optimization dataset based on correctness and efficiency. CodeDPO is flexible and scalable, generating diverse preference optimization data without depending on external resources. Through comprehensive evaluations of five widely used benchmarks, CodeDPO demonstrates significant improvements in correctness and efficiency compared to existing methods. Our experiments prove that CodeDPO enhances the capabilities of LLMs in code generation and provides a robust foundation for conducting code preference optimization in more complex and challenging real-world scenarios.

Because it is difficult to precisely specify complex objectives, reinforcement learning policies are often optimized using proxy reward functions that only approximate the true goal. However, optimizing proxy rewards frequently leads to reward hacking: the optimized reward function ceases to be a good proxy and the resulting policy performs poorly with respect to the unspecified true reward. Principled solutions to reward hacking have been impeded by the lack of a good definition for the problem. To address this gap, we introduce a definition of reward hacking based on the correlation between proxy and true rewards for states and actions seen by a "base policy" that breaks down under optimization. We show that this definition captures reward hacking behavior across several realistic settings, including in reinforcement learning from human feedback (RLHF). Using our formulation, we show theoretically that regularization to the base policy can effectively prevent reward hacking. While the current practice in RLHF applies a KL penalty between action distributions for this purpose, our theory suggests regularizing the chi^2 divergence between the policies' occupancy measures can be more effective. We intuitively show the benefits of this type of regularization and demonstrate that it better mitigates reward hacking in practice across four realistic settings, including RLHF. Our code is available at https://github.com/cassidylaidlaw/orpo.

Existing studies on preference optimization (PO) have centered on constructing pairwise preference data following simple heuristics, such as maximizing the margin between preferred and dispreferred completions based on human (or AI) ranked scores. However, none of these heuristics has a full theoretical justification. In this work, we develop a novel PO framework that provides theoretical guidance to effectively sample dispreferred completions. To achieve this, we formulate PO as minimizing the negative log-likelihood (NLL) of a probability model and propose to estimate its normalization constant via a sampling strategy. As we will demonstrate, these estimative samples can act as dispreferred completions in PO. We then select contrastive divergence (CD) as the sampling strategy, and propose a novel MC-PO algorithm that applies the Monte Carlo (MC) kernel from CD to sample hard negatives w.r.t. the parameterized reward model. Finally, we propose the OnMC-PO algorithm, an extension of MC-PO to the online setting. On popular alignment benchmarks, MC-PO outperforms existing SOTA baselines, and OnMC-PO leads to further improvement.

State-of-the-art language models can exhibit impressive reasoning refinement capabilities on math, science or coding tasks. However, recent work demonstrates that even the best models struggle to identify when and where to refine without access to external feedback. Outcome-based Reward Models (ORMs), trained to predict correctness of the final answer indicating when to refine, offer one convenient solution for deciding when to refine. Process Based Reward Models (PRMs), trained to predict correctness of intermediate steps, can then be used to indicate where to refine. But they are expensive to train, requiring extensive human annotations. In this paper, we propose Stepwise ORMs (SORMs) which are trained, only on synthetic data, to approximate the expected future reward of the optimal policy or V^{star}. More specifically, SORMs are trained to predict the correctness of the final answer when sampling the current policy many times (rather than only once as in the case of ORMs). Our experiments show that SORMs can more accurately detect incorrect reasoning steps compared to ORMs, thus improving downstream accuracy when doing refinements. We then train global refinement models, which take only the question and a draft solution as input and predict a corrected solution, and local refinement models which also take as input a critique indicating the location of the first reasoning error. We generate training data for both models synthetically by reusing data used to train the SORM. We find combining global and local refinements, using the ORM as a reranker, significantly outperforms either one individually, as well as a best of three sample baseline. With this strategy we can improve the accuracy of a LLaMA-2 13B model (already fine-tuned with RL) on GSM8K from 53\% to 65\% when greedily sampled.

In neural combinatorial optimization (CO), reinforcement learning (RL) can turn a deep neural net into a fast, powerful heuristic solver of NP-hard problems. This approach has a great potential in practical applications because it allows near-optimal solutions to be found without expert guides armed with substantial domain knowledge. We introduce Policy Optimization with Multiple Optima (POMO), an end-to-end approach for building such a heuristic solver. POMO is applicable to a wide range of CO problems. It is designed to exploit the symmetries in the representation of a CO solution. POMO uses a modified REINFORCE algorithm that forces diverse rollouts towards all optimal solutions. Empirically, the low-variance baseline of POMO makes RL training fast and stable, and it is more resistant to local minima compared to previous approaches. We also introduce a new augmentation-based inference method, which accompanies POMO nicely. We demonstrate the effectiveness of POMO by solving three popular NP-hard problems, namely, traveling salesman (TSP), capacitated vehicle routing (CVRP), and 0-1 knapsack (KP). For all three, our solver based on POMO shows a significant improvement in performance over all recent learned heuristics. In particular, we achieve the optimality gap of 0.14% with TSP100 while reducing inference time by more than an order of magnitude.

The LogSumExp function, dual to the Kullback-Leibler (KL) divergence, plays a central role in many important optimization problems, including entropy-regularized optimal transport (OT) and distributionally robust optimization (DRO). In practice, when the number of exponential terms inside the logarithm is large or infinite, optimization becomes challenging since computing the gradient requires differentiating every term. We propose a novel convexity- and smoothness-preserving approximation to LogSumExp that can be efficiently optimized using stochastic gradient methods. This approximation is rooted in a sound modification of the KL divergence in the dual, resulting in a new f-divergence called the Safe KL divergence. Our experiments and theoretical analysis of the LogSumExp-based stochastic optimization, arising in DRO and continuous OT, demonstrate the advantages of our approach over existing baselines.

Despite advances in pretraining with extended context lengths, large language models (LLMs) still face challenges in effectively utilizing real-world long-context information, primarily due to insufficient long-context alignment caused by data quality issues, training inefficiencies, and the lack of well-designed optimization objectives. To address these limitations, we propose a framework named Short-to-Long Preference Optimization (SoLoPO), decoupling long-context preference optimization (PO) into two components: short-context PO and short-to-long reward alignment (SoLo-RA), supported by both theoretical and empirical evidence. Specifically, short-context PO leverages preference pairs sampled from short contexts to enhance the model's contextual knowledge utilization ability. Meanwhile, SoLo-RA explicitly encourages reward score consistency utilization for the responses when conditioned on both short and long contexts that contain identical task-relevant information. This facilitates transferring the model's ability to handle short contexts into long-context scenarios. SoLoPO is compatible with mainstream preference optimization algorithms, while substantially improving the efficiency of data construction and training processes. Experimental results show that SoLoPO enhances all these algorithms with respect to stronger length and domain generalization abilities across various long-context benchmarks, while achieving notable improvements in both computational and memory efficiency.

This study focuses on the topic of offline preference-based reinforcement learning (PbRL), a variant of conventional reinforcement learning that dispenses with the need for online interaction or specification of reward functions. Instead, the agent is provided with fixed offline trajectories and human preferences between pairs of trajectories to extract the dynamics and task information, respectively. Since the dynamics and task information are orthogonal, a naive approach would involve using preference-based reward learning followed by an off-the-shelf offline RL algorithm. However, this requires the separate learning of a scalar reward function, which is assumed to be an information bottleneck of the learning process. To address this issue, we propose the offline preference-guided policy optimization (OPPO) paradigm, which models offline trajectories and preferences in a one-step process, eliminating the need for separately learning a reward function. OPPO achieves this by introducing an offline hindsight information matching objective for optimizing a contextual policy and a preference modeling objective for finding the optimal context. OPPO further integrates a well-performing decision policy by optimizing the two objectives iteratively. Our empirical results demonstrate that OPPO effectively models offline preferences and outperforms prior competing baselines, including offline RL algorithms performed over either true or pseudo reward function specifications. Our code is available on the project website: https://sites.google.com/view/oppo-icml-2023 .

Group Relative Policy Optimization (GRPO) has been shown to be an effective algorithm when an accurate reward model is available. However, such a highly reliable reward model is not available in many real-world tasks. In this paper, we particularly focus on multi-objective settings, in which we identify that GRPO is vulnerable to reward hacking, optimizing only one of the objectives at the cost of the others. To address this issue, we propose MO-GRPO, an extension of GRPO with a simple normalization method to reweight the reward functions automatically according to the variances of their values. We first show analytically that MO-GRPO ensures that all reward functions contribute evenly to the loss function while preserving the order of preferences, eliminating the need for manual tuning of the reward functions' scales. Then, we evaluate MO-GRPO experimentally in four domains: (i) the multi-armed bandits problem, (ii) simulated control task (Mo-Gymnasium), (iii) machine translation tasks on the WMT benchmark (En-Ja, En-Zh), and (iv) instruction following task. MO-GRPO achieves stable learning by evenly distributing correlations among the components of rewards, outperforming GRPO, showing MO-GRPO to be a promising algorithm for multi-objective reinforcement learning problems.

Offline reinforcement learning (ORL) holds great promise for robot learning due to its ability to learn from arbitrary pre-generated experience. However, current ORL benchmarks are almost entirely in simulation and utilize contrived datasets like replay buffers of online RL agents or sub-optimal trajectories, and thus hold limited relevance for real-world robotics. In this work (Real-ORL), we posit that data collected from safe operations of closely related tasks are more practical data sources for real-world robot learning. Under these settings, we perform an extensive (6500+ trajectories collected over 800+ robot hours and 270+ human labor hour) empirical study evaluating generalization and transfer capabilities of representative ORL methods on four real-world tabletop manipulation tasks. Our study finds that ORL and imitation learning prefer different action spaces, and that ORL algorithms can generalize from leveraging offline heterogeneous data sources and outperform imitation learning. We release our dataset and implementations at URL: https://sites.google.com/view/real-orl

Diffusion Language Models (DLMs) offer order-agnostic generation that can explore many possible decoding trajectories. However, current decoding methods commit to a single trajectory, limiting exploration in trajectory space. We introduce Order-Token Search to explore this space through jointly searching over generation order and token values. Its core is a likelihood estimator that scores denoising actions, enabling stable pruning and efficient exploration of diverse trajectories. Across mathematical reasoning and coding benchmarks, Order-Token Search consistently outperforms baselines on GSM8K, MATH500, Countdown, and HumanEval (3.1%, 3.8%, 7.9%, and 6.8% absolute over backbone), matching or surpassing diffu-GRPO post-trained d1-LLaDA. Our work establishes joint search as a key component for advancing decoding in DLMs.

Direct Preference Optimization (DPO) has emerged as a cornerstone of reinforcement learning from human feedback (RLHF) due to its simplicity and efficiency. However, existing DPO-based methods typically treat all preference pairs equally, overlooking substantial variations in data quality and learning difficulty, which leads to inefficient data utilization and suboptimal performance. To address this limitation, we propose Uni-DPO, a unified dynamic preference optimization framework that jointly considers (a) the inherent quality of preference pairs and (b) the model's evolving performance during training. By adaptively reweighting samples based on both factors, Uni-DPO enables more effective use of preference data and achieves superior performance. Extensive experiments across models and benchmarks demonstrate the effectiveness and generalization of Uni-DPO. On textual tasks, Gemma-2-9B-IT fine-tuned with Uni-DPO surpasses the leading LLM, Claude 3 Opus, by 6.7 points on Arena-Hard. On mathematical and multimodal tasks, Uni-DPO consistently outperforms baseline methods across all benchmarks, providing strong empirical evidence of its effectiveness and robustness.

Direct Preference Optimization (DPO) often struggles with long-chain mathematical reasoning. Existing approaches, such as Step-DPO, typically improve this by focusing on the first erroneous step in the reasoning chain. However, they overlook all other steps and rely heavily on humans or GPT-4 to identify erroneous steps. To address these issues, we propose Full-Step-DPO, a novel DPO framework tailored for mathematical reasoning. Instead of optimizing only the first erroneous step, it leverages step-wise rewards from the entire reasoning chain. This is achieved by training a self-supervised process reward model, which automatically scores each step, providing rewards while avoiding reliance on external signals. Furthermore, we introduce a novel step-wise DPO loss, which dynamically updates gradients based on these step-wise rewards. This endows stronger reasoning capabilities to language models. Extensive evaluations on both in-domain and out-of-domain mathematical reasoning benchmarks across various base language models, demonstrate that Full-Step-DPO achieves superior performance compared to state-of-the-art baselines.

Large-scale alignment pipelines typically pair a policy model with a separately trained reward model whose parameters remain frozen during reinforcement learning (RL). This separation creates a complex, resource-intensive pipeline and suffers from a performance ceiling due to a static reward signal. We propose a novel framework, Unified Reward & Policy Optimization (URPO), that unifies instruction-following ("player") and reward modeling ("referee") within a single model and a single training phase. Our method recasts all alignment data-including preference pairs, verifiable reasoning, and open-ended instructions-into a unified generative format optimized by a single Group-Relative Policy Optimization (GRPO) loop. This enables the model to learn from ground-truth preferences and verifiable logic while simultaneously generating its own rewards for open-ended tasks. Experiments on the Qwen2.5-7B model demonstrate URPO's superiority. Our unified model significantly outperforms a strong baseline using a separate generative reward model, boosting the instruction-following score on AlpacaEval from 42.24 to 44.84 and the composite reasoning average from 32.66 to 35.66. Furthermore, URPO cultivates a superior internal evaluator as a byproduct of training, achieving a RewardBench score of 85.15 and surpassing the dedicated reward model it replaces (83.55). By eliminating the need for a separate reward model and fostering a co-evolutionary dynamic between generation and evaluation, URPO presents a simpler, more efficient, and more effective path towards robustly aligned language models.

As large language models (LLMs) reach high scores on established mathematical benchmarks, such as GSM8K and MATH, the research community has turned to International Mathematical Olympiad (IMO) problems to push the evaluation frontier. However, existing Olympiad-level benchmarks suffer from practical constraints that introduce grading noise and potential bias, such as heterogeneous answer formats requiring model-based judges and a reliance on potentially flawed solutions. We introduce RIMO, a two-track benchmark designed to preserve peak Olympiad difficulty while eliminating this evaluation noise. The first track, RIMO-N, rewrites 335 IMO problems to admit a single, unique integer answer, allowing for deterministic correctness checking. The second track, RIMO-P, features 456 proof problems with expert-checked solutions, which are decomposed into a sequence of sub-problems to evaluate the step-by-step reasoning process via an automated grading system. Our benchmarking of ten frontier LLMs, including GPT-4o and Gemini 2.5 Flash, reveals that while these systems excel on older benchmarks, their performance drops sharply on RIMO. These results highlight a substantial gap between current LLM capabilities and actual Olympiad-level reasoning. By providing a challenging yet easy-to-evaluate suite, RIMO offers a high-resolution yardstick for future research, presenting a clear target for closing the profound reasoning gap our findings expose.