Daily Papers

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.

Finding meaningful and accurate dense rewards is a fundamental task in the field of reinforcement learning (RL) that enables agents to explore environments more efficiently. In traditional RL settings, agents learn optimal policies through interactions with an environment guided by reward signals. However, when these signals are sparse, delayed, or poorly aligned with the intended task objectives, agents often struggle to learn effectively. Dense reward functions, which provide informative feedback at every step or state transition, offer a potential solution by shaping agent behavior and accelerating learning. Despite their benefits, poorly crafted reward functions can lead to unintended behaviors, reward hacking, or inefficient exploration. This problem is particularly acute in complex or high-dimensional environments where handcrafted rewards are difficult to specify and validate. To address this, recent research has explored a variety of approaches, including inverse reinforcement learning, reward modeling from human preferences, and self-supervised learning of intrinsic rewards. While these methods offer promising directions, they often involve trade-offs between generality, scalability, and alignment with human intent. This proposal explores several approaches to dealing with these unsolved problems and enhancing the effectiveness and reliability of dense reward construction in different RL applications.

Dense process rewards have proven a more effective alternative to the sparse outcome-level rewards in the inference-time scaling of large language models (LLMs), particularly in tasks requiring complex multi-step reasoning. While dense rewards also offer an appealing choice for the reinforcement learning (RL) of LLMs since their fine-grained rewards have the potential to address some inherent issues of outcome rewards, such as training efficiency and credit assignment, this potential remains largely unrealized. This can be primarily attributed to the challenges of training process reward models (PRMs) online, where collecting high-quality process labels is prohibitively expensive, making them particularly vulnerable to reward hacking. To address these challenges, we propose PRIME (Process Reinforcement through IMplicit rEwards), which enables online PRM updates using only policy rollouts and outcome labels through implict process rewards. PRIME combines well with various advantage functions and forgoes the dedicated reward model training phrase that existing approaches require, substantially reducing the development overhead. We demonstrate PRIME's effectiveness on competitional math and coding. Starting from Qwen2.5-Math-7B-Base, PRIME achieves a 15.1% average improvement across several key reasoning benchmarks over the SFT model. Notably, our resulting model, Eurus-2-7B-PRIME, surpasses Qwen2.5-Math-7B-Instruct on seven reasoning benchmarks with 10% of its training data.

In settings where labeled verifiable training data is the binding constraint, each checked example should be allocated carefully. The standard practice is to use this data directly on the model that will be deployed, for example by running GRPO on the deployment student. We argue that this is often an inefficient allocation because it overlooks a reward-density principle: sparse sequence-level reward should train models where exploration is productive, while dense token-level teacher reward should be used where the aim is to compress behavior into a smaller model. In this view, GRPO-style sparse RL and OPD-style dense teacher supervision are not separate recipes; they are different reward-density regimes. The allocation rule is simple: use scarce labeled training data upstream on the strongest model that can turn it into reward-shaped behavior, then transfer that behavior downstream as dense supervision. We evaluate this rule on verifiable math with Qwen3 and Llama models. At fixed Qwen3-1.7B deployment-student size, an RL-improved 8B teacher distilled through the dense bridge outperforms direct GRPO on the same student, while transfer from the same teacher before RL underperforms. The bridge is important: a forward-KL warmup on teacher rollouts followed by OPD on student rollouts is consistently strongest on MATH before any post-bridge student-side sparse RL, and also gives the best pre-Stage~3 AIME endpoints for the canonical 8B/14B teachers. The bridge also makes later student-side sparse RL effective: GRPO that is weak on a cold student lifts MATH from 75.4% to 78.5% after the bridge and outperforms a matched replay control by 2.8 points. The operational principal is to avoid using scarce labeled data on the least prepared policy: use sparse reward for teacher-side discovery, dense transfer for student compression, and student-side sparse reward only after the bridge.

Reinforcement learning (RL) can align language models with non-differentiable reward signals, such as human preferences. However, a major challenge arises from the sparsity of these reward signals - typically, there is only one reward for the entire generation. This sparsity of rewards can lead to inefficient and unstable learning. In this paper, we introduce a novel framework leveraging the critique ability of LLMs to produce dense rewards throughout the learning process. Our approach incorporates a critic language model alongside the policy model. This critic is prompted with the task description, question, policy model's output, and environment's reward signal as input, and provides token or span-level dense rewards that reflect the quality of each segment of the output. We assess our approach on three text generation tasks: sentiment control, language model detoxification, and summarization. Experimental results show that incorporating artificial dense rewards in training yields consistent performance gains over the PPO baseline with holistic rewards. Furthermore, in a setting where the same model serves as both policy and critic, we demonstrate that "self-critique" rewards also boost learning efficiency.

Effective reward design is a central challenge in Reinforcement Learning (RL) for code generation. Mainstream pass/fail outcome rewards enforce functional correctness via executing unit tests, but the resulting sparsity limits potential performance gains. While recent work has explored external Reward Models (RM) to generate richer, continuous rewards, the learned RMs suffer from reward misalignment and prohibitive computational cost. In this paper, we introduce VeRPO (Verifiable Dense Reward Policy Optimization), a novel RL framework for code generation that synthesizes robust and dense rewards fully grounded in verifiable execution feedback. The core idea of VeRPO is constructing dense rewards from weighted partial success: by dynamically estimating the difficulty weight of each unit test based on the execution statistics during training, a dense reward is derived from the sum of weights of the passed unit tests. To solidify the consistency between partial success and end-to-end functional correctness, VeRPO further integrates the dense signal with global execution outcomes, establishing a robust and dense reward paradigm relying solely on verifiable execution feedback. Extensive experiments across diverse benchmarks and settings demonstrate that VeRPO consistently outperforms outcome-driven and RM-based baselines, achieving up to +8.83\% gain in pass@1 with negligible time cost (< 0.02\%) and zero GPU memory overhead.

Reinforcement learning has become a cornerstone technique for developing reasoning models in complex tasks, ranging from mathematical problem-solving to imaginary reasoning. The optimization of these models typically relies on policy gradient methods, whose efficacy hinges on the accurate estimation of an advantage function. However, prevailing methods typically employ static advantage estimation, a practice that leads to inefficient credit assignment by neglecting the dynamic utility of training samples over time. This limitation results in suboptimal policy updates, which in turn manifest as slower convergence rates and increased learning instability, as models fail to adapt to evolving sample utilities effectively. To address this problem, we introduce ADORA (Advantage Dynamics via Online Rollout Adaptation), a novel framework for policy optimization. ADORA dynamically adjusts the advantage function's weighting by adaptively categorizing training data into temporarily advantageous and disadvantageous samples, based on their evolving utility during online model rollouts. This tailored data differentiation strategy allows ADORA to be seamlessly integrated into existing policy optimization algorithms without significant architectural modifications, enabling the policy to prioritize learning from more informative experiences and thereby achieve more efficient policy updates. Extensive evaluations across diverse model families and varying data scales demonstrate that ADORA is a robust and efficient framework. It significantly enhances long reasoning in both geometric and mathematical tasks, consistently achieving notable performance gains without requiring sensitive hyperparameter tuning.

Enhancing the reasoning capabilities of large language models effectively using reinforcement learning (RL) remains a crucial challenge. Existing approaches primarily adopt two contrasting advantage estimation granularities: Token-level methods (e.g., PPO) aim to provide the fine-grained advantage signals but suffer from inaccurate estimation due to difficulties in training an accurate critic model. On the other extreme, trajectory-level methods (e.g., GRPO) solely rely on a coarse-grained advantage signal from the final reward, leading to imprecise credit assignment. To address these limitations, we propose Segment Policy Optimization (SPO), a novel RL framework that leverages segment-level advantage estimation at an intermediate granularity, achieving a better balance by offering more precise credit assignment than trajectory-level methods and requiring fewer estimation points than token-level methods, enabling accurate advantage estimation based on Monte Carlo (MC) without a critic model. SPO features three components with novel strategies: (1) flexible segment partition; (2) accurate segment advantage estimation; and (3) policy optimization using segment advantages, including a novel probability-mask strategy. We further instantiate SPO for two specific scenarios: (1) SPO-chain for short chain-of-thought (CoT), featuring novel cutpoint-based partition and chain-based advantage estimation, achieving 6-12 percentage point improvements in accuracy over PPO and GRPO on GSM8K. (2) SPO-tree for long CoT, featuring novel tree-based advantage estimation, which significantly reduces the cost of MC estimation, achieving 7-11 percentage point improvements over GRPO on MATH500 under 2K and 4K context evaluation. We make our code publicly available at https://github.com/AIFrameResearch/SPO.

Large reasoning models (LRMs) aim to solve diverse and complex problems through structured reasoning. Recent advances in group-based policy optimization methods have shown promise in enabling stable advantage estimation without reliance on process-level annotations. However, these methods rely on advantage gaps induced by high-quality samples within the same batch, which makes the training process fragile and inefficient when intra-group advantages collapse under challenging tasks. To address these problems, we propose a reinforcement learning mechanism named \textbf{R^3} that along three directions: (1) a cross-context \underline{\textbf{R}eplay} strategy that maintains the intra-group advantage by recalling valuable examples from historical trajectories of the same query, (2) an in-context self-\underline{\textbf{R}eflection} mechanism enabling models to refine outputs by leveraging past failures, and (3) a structural entropy \underline{\textbf{R}anking reward}, which assigns relative rewards to truncated or failed samples by ranking responses based on token-level entropy patterns, capturing both local exploration and global stability. We implement our method on Deepseek-R1-Distill-Qwen-1.5B and train it on the DeepscaleR-40k in the math domain. Experiments demonstrate our method achieves SoTA performance on several math benchmarks, representing significant improvements and fewer reasoning tokens over the base models. Code and model will be released.

Learned sparse and dense representations capture different successful approaches to text retrieval and the fusion of their results has proven to be more effective and robust. Prior work combines dense and sparse retrievers by fusing their model scores. As an alternative, this paper presents a simple approach to densifying sparse representations for text retrieval that does not involve any training. Our densified sparse representations (DSRs) are interpretable and can be easily combined with dense representations for end-to-end retrieval. We demonstrate that our approach can jointly learn sparse and dense representations within a single model and then combine them for dense retrieval. Experimental results suggest that combining our DSRs and dense representations yields a balanced tradeoff between effectiveness and efficiency.

Reinforcement Learning with Verifiable Rewards (RLVR) for large language models (LLMs) has achieved remarkable progress in enhancing LLMs' reasoning capabilities on tasks with clear correctness criteria, such as mathematical reasoning tasks. Several training metrics, such as entropy or response length, have been observed to correlate with different reasoning behaviors in reinforcement learning. Prior approaches incorporate such priors through reward or advantage shaping, which often relies on hand-crafted penalties and preferences (e.g., higher-is-better or lower-is-better). However, without careful hyperparameter tuning, these directional priors can be overly biased and may lead to failure. To this end, we introduce Conditional advANtage estimatiON (CANON), amplifying the impact of the target metric without presuming its direction. Specifically, CANON regroups the sampled responses into two groups based on the higher or lower value of a target metric, measures which metric trend contributes to better performance through inter-group comparison, and identifies the better response within the same group. In summary, CANON based on entropy consistently outperforms prior methods across three LLMs on both math reasoning and high-complexity logic tasks. When applied to response length, CANON further improves token efficiency, yielding a more favorable Pareto frontier in the performance-cost trade-off.

Mixture-of-Experts (MoE) has become a dominant architecture for scaling Large Language Models (LLMs) efficiently by decoupling total parameters from computational cost. However, this decoupling creates a critical challenge: predicting the model capacity of a given MoE configurations (e.g., expert activation ratio and granularity) remains an unresolved problem. To address this gap, we introduce Efficiency Leverage (EL), a metric quantifying the computational advantage of an MoE model over a dense equivalent. We conduct a large-scale empirical study, training over 300 models up to 28B parameters, to systematically investigate the relationship between MoE architectural configurations and EL. Our findings reveal that EL is primarily driven by the expert activation ratio and the total compute budget, both following predictable power laws, while expert granularity acts as a non-linear modulator with a clear optimal range. We integrate these discoveries into a unified scaling law that accurately predicts the EL of an MoE architecture based on its configuration. To validate our derived scaling laws, we designed and trained Ling-mini-beta, a pilot model for Ling-2.0 series with only 0.85B active parameters, alongside a 6.1B dense model for comparison. When trained on an identical 1T high-quality token dataset, Ling-mini-beta matched the performance of the 6.1B dense model while consuming over 7x fewer computational resources, thereby confirming the accuracy of our scaling laws. This work provides a principled and empirically-grounded foundation for the scaling of efficient MoE models.

Reinforcement learning (RL) has emerged as an effective approach for enhancing the reasoning capabilities of large language models (LLMs), especially in scenarios where supervised fine-tuning (SFT) falls short due to limited chain-of-thought (CoT) data. Among RL-based post-training methods, group relative advantage estimation, as exemplified by Group Relative Policy Optimization (GRPO), has attracted considerable attention for eliminating the dependency on the value model, thereby simplifying training compared to traditional approaches like Proximal Policy Optimization (PPO). However, we observe that exsiting group relative advantage estimation method still suffers from training inefficiencies, particularly when the estimated advantage approaches zero. To address this limitation, we propose Advantage-Augmented Policy Optimization (AAPO), a novel RL algorithm that optimizes the cross-entropy (CE) loss using advantages enhanced through a momentum-based estimation scheme. This approach effectively mitigates the inefficiencies associated with group relative advantage estimation. Experimental results on multiple mathematical reasoning benchmarks demonstrate the superior performance of AAPO.

Group Relative Policy Optimization (GRPO) assigns a single scalar advantage to all tokens in a completion. For structured generations with explicit segments and objectives, this couples unrelated reward signals across segments, leading to objective interference and misattributed credit. We propose Blockwise Advantage Estimation, a family of GRPO-compatible methods that assigns each objective its own advantage and applies it only to the tokens in the corresponding text block, reducing reliance on hand-designed scalar rewards and scaling naturally to additional objectives. A key challenge is estimating advantages for later blocks whose rewards are conditioned on sampled prefixes; standard unbiased approaches require expensive nested rollouts from intermediate states. Concretely, we introduce an Outcome-Conditioned Baseline that approximates intermediate state values using only within-group statistics by stratifying samples according to a prefix-derived intermediate outcome. On math tasks with uncertainty estimation, our method mitigates reward interference, is competitive with a state-of-the-art reward-designed approach, and preserves test-time gains from confidence-weighted ensembling. More broadly, it provides a modular recipe for optimizing sequential objectives in structured generations without additional rollouts.

Methods for controlling large language models (LLMs), including local weight fine-tuning, LoRA-based adaptation, and activation-based interventions, are often studied in isolation, obscuring their connections and making comparison difficult. In this work, we present a unified view that frames these interventions as dynamic weight updates induced by a control signal, placing them within a single conceptual framework. Building on this view, we propose a unified preference-utility analysis that separates control effects into preference, defined as the tendency toward a target concept, and utility, defined as coherent and task-valid generation, and measures both on a shared log-odds scale using polarity-paired contrastive examples. Across methods, we observe a consistent trade-off between preference and utility: stronger control increases preference while predictably reducing utility. We further explain this behavior through an activation manifold perspective, in which control shifts representations along target-concept directions to enhance preference, while utility declines primarily when interventions push representations off the model's valid-generation manifold. Finally, we introduce a new steering approach SPLIT guided by this analysis that improves preference while better preserving utility. Code is available at https://github.com/zjunlp/EasyEdit/blob/main/examples/SPLIT.md.

To combine the advantages of Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), recent methods have integrated ''hints'' into post-training, which are prefix segments of complete reasoning trajectories, aiming for powerful knowledge expansion and reasoning generalization. However, existing hint-based RL methods typically ignore difficulty when scheduling hint ratios and estimating relative advantages, leading to unstable learning and excessive imitation of off-policy hints. In this work, we propose ADHint, which treats difficulty as a key factor in both hint-ratio schedule and relative-advantage estimation to achieve a better trade-off between exploration and imitation. Specifically, we propose Adaptive Hint with Sample Difficulty Prior, which evaluates each sample's difficulty under the policy model and accordingly schedules an appropriate hint ratio to guide its rollouts. We also introduce Consistency-based Gradient Modulation and Selective Masking for Hint Preservation to modulate token-level gradients within hints, preventing biased and destructive updates. Additionally, we propose Advantage Estimation with Rollout Difficulty Posterior, which leverages the relative difficulty of rollouts with and without hints to estimate their respective advantages, thereby achieving more balanced updates. Extensive experiments across diverse modalities, model scales, and domains demonstrate that ADHint delivers superior reasoning ability and out-of-distribution generalization, consistently surpassing existing methods in both pass@1 and avg@8. Our code and dataset will be made publicly available upon paper acceptance.

The transformer architecture by Vaswani et al. (2017) is now ubiquitous across application domains, from natural language processing to speech processing and image understanding. We propose DenseFormer, a simple modification to the standard architecture that improves the perplexity of the model without increasing its size -- adding a few thousand parameters for large-scale models in the 100B parameters range. Our approach relies on an additional averaging step after each transformer block, which computes a weighted average of current and past representations -- we refer to this operation as Depth-Weighted-Average (DWA). The learned DWA weights exhibit coherent patterns of information flow, revealing the strong and structured reuse of activations from distant layers. Experiments demonstrate that DenseFormer is more data efficient, reaching the same perplexity of much deeper transformer models, and that for the same perplexity, these new models outperform transformer baselines in terms of memory efficiency and inference time.

Recent works have explored the use of weight sparsity to improve the training efficiency (test accuracy w.r.t training FLOPs) of deep neural networks (DNNs). These works aim to reduce training FLOPs but training with sparse weights often leads to accuracy loss or requires longer training schedules, making the resulting training efficiency less clear. In contrast, we focus on using sparsity to increase accuracy while using the same FLOPs as the dense model and show training efficiency gains through higher accuracy. In this work, we introduce Sparse-IFT, a family of Sparse Iso-FLOP Transformations which are used as drop-in replacements for dense layers to improve their representational capacity and FLOP efficiency. Each transformation is parameterized by a single hyperparameter (sparsity level) and provides a larger search space to find optimal sparse masks. Without changing any training hyperparameters, replacing dense layers with Sparse-IFT leads to significant improvements across computer vision (CV) and natural language processing (NLP) tasks, including ResNet-18 on ImageNet (+3.5%) and GPT-3 Small on WikiText-103 (-0.4 PPL), both matching larger dense model variants that use 2x or more FLOPs. To our knowledge, this is the first work to demonstrate the use of sparsity for improving the accuracy of dense models via a simple-to-use set of sparse transformations. Code is available at: https://github.com/CerebrasResearch/Sparse-IFT.

Credit assignment, the process of attributing credit or blame to individual agents for their contributions to a team's success or failure, remains a fundamental challenge in multi-agent reinforcement learning (MARL), particularly in environments with sparse rewards. Commonly-used approaches such as value decomposition often lead to suboptimal policies in these settings, and designing dense reward functions that align with human intuition can be complex and labor-intensive. In this work, we propose a novel framework where a large language model (LLM) generates dense, agent-specific rewards based on a natural language description of the task and the overall team goal. By learning a potential-based reward function over multiple queries, our method reduces the impact of ranking errors while allowing the LLM to evaluate each agent's contribution to the overall task. Through extensive experiments, we demonstrate that our approach achieves faster convergence and higher policy returns compared to state-of-the-art MARL baselines.

Recent advances in reinforcement learning for foundation models, such as Group Relative Policy Optimization (GRPO), have significantly improved the performance of foundation models on reasoning tasks. Notably, the advantage function serves as a central mechanism in GRPO for ranking the trajectory importance. However, existing explorations encounter both advantage reversion and advantage mirror problems, which hinder the reasonable advantage allocation across different query samples. In this work, we propose an easy but effective GRPO strategy, Mixed Advantage Policy Optimization (MAPO). We reveal that the trajectory appears with different certainty and propose the advantage percent deviation for samples with high-certainty trajectories. Furthermore, we dynamically reweight the advantage function for samples with varying trajectory certainty, thereby adaptively configuring the advantage function to account for sample-specific characteristics. Comparison with related state-of-the-art methods, along with ablation studies on different advantage variants, validates the effectiveness of our approach.

Reinforcement Learning has become a standard paradigm for aligning Large Language Models with human intent and task requirements. While Group Relative Policy Optimization offers an efficient, value-model-free alternative to Proximal Policy Optimization, adapting it to real-world multi-reward settings remains challenging. Standard scalarization practices, such as Reward Combination and Advantage Combination, suffer from significant drawbacks: Reward Combination frequently generates advantages with excessively large squared magnitudes that lead to training instability, while Advantage Combination relies on static hyperparameters and ignores cross-objective correlations. To address these limitations, we propose Dynamic Variance-adaptive Advantage Optimization (DVAO), which dynamically adjusts combination weights based on the empirical reward variance of each objective within a rollout group, effectively up-weighting objectives with a stronger learning signal while suppressing noisy ones. We mathematically prove that DVAO maintains bounded advantage magnitudes for stable training and introduces a self-adaptive cross-objective regularization mechanism. Extensive experiments on mathematical reasoning and tool-use benchmarks using Qwen3 and Qwen2.5 models demonstrate that DVAO significantly outperforms baseline methods, achieving a superior multi-objective Pareto frontier and robust training stability.

Reinforcement Learning with Verifiable Rewards (RLVR) strengthens LLM reasoning, but training often oscillates between {entropy collapse} and {entropy explosion}. We trace both hazards to the mean baseline used in value-free RL (e.g., GRPO and DAPO), which improperly penalizes negative-advantage samples under reward outliers. We propose {Quantile Advantage Estimation} (QAE), replacing the mean with a group-wise K-quantile baseline. QAE induces a response-level, two-regime gate: on hard queries (p <= 1 - K) it reinforces rare successes, while on easy queries (p > 1 - K) it targets remaining failures. Under first-order softmax updates, we prove {two-sided entropy safety}, giving lower and upper bounds on one-step entropy change that curb explosion and prevent collapse. Empirically, this minimal modification stabilizes entropy, sparsifies credit assignment (with tuned K, roughly 80% of responses receive zero advantage), and yields sustained pass@1 gains on Qwen3-8B/14B-Base across AIME 2024/2025 and AMC 2023. These results identify {baseline design} -- rather than token-level heuristics -- as the primary mechanism for scaling RLVR.

When fine-tuning pre-trained Large Language Models (LLMs) to align with human values and intentions, maximizing the estimated reward can lead to superior performance, but it also introduces potential risks due to deviations from the reference model's intended behavior. Most existing methods typically introduce KL divergence to constrain deviations between the trained model and the reference model; however, this may not be sufficient in certain applications that require tight risk control. In this paper, we introduce Risk-aware Direct Preference Optimization (Ra-DPO), a novel approach that incorporates risk-awareness by employing a class of nested risk measures. This approach formulates a constrained risk-aware advantage function maximization problem and then converts the Bradley-Terry model into a token-level representation. The objective function maximizes the likelihood of the policy while suppressing the deviation between a trained model and the reference model using a sequential risk ratio, thereby enhancing the model's risk-awareness. Experimental results across three open-source datasets: IMDb Dataset, Anthropic HH Dataset, and AlpacaEval, demonstrate the proposed method's superior performance in balancing alignment performance and model drift. Our code is opensourced at https://github.com/zlj123-max/Ra-DPO.

The sparse Mixture-of-Experts (MoE) architecture is increasingly favored for scaling Large Language Models (LLMs) efficiently, but it depends on heterogeneous compute and memory resources. These factors jointly affect system Cost, Accuracy, and Performance (CAP), making trade-offs inevitable. Existing benchmarks often fail to capture these trade-offs accurately, complicating practical deployment decisions. To address this, we introduce MoE-CAP, a benchmark specifically designed for MoE systems. Our analysis reveals that achieving an optimal balance across CAP is difficult with current hardware; MoE systems typically optimize two of the three dimensions at the expense of the third-a dynamic we term the MoE-CAP trade-off. To visualize this, we propose the CAP Radar Diagram. We further introduce sparsity-aware performance metrics-Sparse Memory Bandwidth Utilization (S-MBU) and Sparse Model FLOPS Utilization (S-MFU)-to enable accurate performance benchmarking of MoE systems across diverse hardware platforms and deployment scenarios.

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

Recently, dense contrastive learning has shown superior performance on dense prediction tasks compared to instance-level contrastive learning. Despite its supremacy, the properties of dense contrastive representations have not yet been carefully studied. Therefore, we analyze the theoretical ideas of dense contrastive learning using a standard CNN and straightforward feature matching scheme rather than propose a new complex method. Inspired by the analysis of the properties of instance-level contrastive representations through the lens of alignment and uniformity on the hypersphere, we employ and extend the same lens for the dense contrastive representations to analyze their underexplored properties. We discover the core principle in constructing a positive pair of dense features and empirically proved its validity. Also, we introduces a new scalar metric that summarizes the correlation between alignment-and-uniformity and downstream performance. Using this metric, we study various facets of densely learned contrastive representations such as how the correlation changes over single- and multi-object datasets or linear evaluation and dense prediction tasks. The source code is publicly available at: https://github.com/SuperSupermoon/DenseCL-analysis

Long-horizon robotic manipulation remains challenging for reinforcement learning (RL) because sparse rewards provide limited guidance for credit assignment. Practical policy improvement thus relies on richer intermediate supervision, such as dense progress rewards, which are costly to obtain and ill-suited to non-monotonic behaviors such as backtracking and recovery. To address this, we propose Advantage Reward Modeling (ARM), a framework that shifts from hard-to-quantify absolute progress to estimating relative advantage. We introduce a cost-effective tri-state labeling strategy -- Progressive, Regressive, and Stagnant -- that reduces human cognitive overhead while ensuring high cross-annotator consistency. By training on these intuitive signals, ARM enables automated progress annotation for both complete demonstrations and fragmented DAgger-style data. Integrating ARM into an offline RL pipeline allows for adaptive action-reward reweighting, effectively filtering suboptimal samples. Our approach achieves a 99.4% success rate on a challenging long-horizon towel-folding task, demonstrating improved stability and data efficiency over current VLA baselines with near-zero human intervention during policy training.

Large language models (LLMs) face a daunting challenge due to the excessive computational and memory requirements of the commonly used Transformer architecture. While state space model (SSM) is a new type of foundational network architecture offering lower computational complexity, their performance has yet to fully rival that of Transformers. This paper introduces DenseSSM, a novel approach to enhance the flow of hidden information between layers in SSMs. By selectively integrating shallowlayer hidden states into deeper layers, DenseSSM retains fine-grained information crucial for the final output. Dense connections enhanced DenseSSM still maintains the training parallelizability and inference efficiency. The proposed method can be widely applicable to various SSM types like RetNet and Mamba. With similar model size, DenseSSM achieves significant improvements, exemplified by DenseRetNet outperforming the original RetNet with up to 5% accuracy improvement on public benchmarks.

In this research. we analyze the potential of Feature Density (HD) as a way to comparatively estimate machine learning (ML) classifier performance prior to training. The goal of the study is to aid in solving the problem of resource-intensive training of ML models which is becoming a serious issue due to continuously increasing dataset sizes and the ever rising popularity of Deep Neural Networks (DNN). The issue of constantly increasing demands for more powerful computational resources is also affecting the environment, as training large-scale ML models are causing alarmingly-growing amounts of CO2, emissions. Our approach 1s to optimize the resource-intensive training of ML models for Natural Language Processing to reduce the number of required experiments iterations. We expand on previous attempts on improving classifier training efficiency with FD while also providing an insight to the effectiveness of various linguistically-backed feature preprocessing methods for dialog classification, specifically cyberbullying detection.

Dense-to-sparse gating mixture of experts (MoE) has recently become an effective alternative to a well-known sparse MoE. Rather than fixing the number of activated experts as in the latter model, which could limit the investigation of potential experts, the former model utilizes the temperature to control the softmax weight distribution and the sparsity of the MoE during training in order to stabilize the expert specialization. Nevertheless, while there are previous attempts to theoretically comprehend the sparse MoE, a comprehensive analysis of the dense-to-sparse gating MoE has remained elusive. Therefore, we aim to explore the impacts of the dense-to-sparse gate on the maximum likelihood estimation under the Gaussian MoE in this paper. We demonstrate that due to interactions between the temperature and other model parameters via some partial differential equations, the convergence rates of parameter estimations are slower than any polynomial rates, and could be as slow as O(1/log(n)), where n denotes the sample size. To address this issue, we propose using a novel activation dense-to-sparse gate, which routes the output of a linear layer to an activation function before delivering them to the softmax function. By imposing linearly independence conditions on the activation function and its derivatives, we show that the parameter estimation rates are significantly improved to polynomial rates.

Reinforcement learning has significantly enhanced the reasoning capabilities of Large Language Models (LLMs) in complex problem-solving tasks. Recently, the introduction of DeepSeek R1 has inspired a surge of interest in leveraging rule-based rewards as a low-cost alternative for computing advantage functions and guiding policy optimization. However, a common challenge observed across many replication and extension efforts is that when multiple sampled responses under a single prompt converge to identical outcomes, whether correct or incorrect, the group-based advantage degenerates to zero. This leads to vanishing gradients and renders the corresponding samples ineffective for learning, ultimately limiting training efficiency and downstream performance. To address this issue, we propose a consistency-aware policy optimization framework that introduces a structured global reward based on outcome consistency, the global loss based on it ensures that, even when model outputs show high intra-group consistency, the training process still receives meaningful learning signals, which encourages the generation of correct and self-consistent reasoning paths from a global perspective. Furthermore, we incorporate an entropy-based soft blending mechanism that adaptively balances local advantage estimation with global optimization, enabling dynamic transitions between exploration and convergence throughout training. Our method introduces several key innovations in both reward design and optimization strategy. We validate its effectiveness through substantial performance gains on multiple mathematical reasoning benchmarks, highlighting the proposed framework's robustness and general applicability. Code of this work has been released at https://github.com/hijih/copo-code.git.

The success of many RL techniques heavily relies on human-engineered dense rewards, which typically demand substantial domain expertise and extensive trial and error. In our work, we propose DrS (Dense reward learning from Stages), a novel approach for learning reusable dense rewards for multi-stage tasks in a data-driven manner. By leveraging the stage structures of the task, DrS learns a high-quality dense reward from sparse rewards and demonstrations if given. The learned rewards can be reused in unseen tasks, thus reducing the human effort for reward engineering. Extensive experiments on three physical robot manipulation task families with 1000+ task variants demonstrate that our learned rewards can be reused in unseen tasks, resulting in improved performance and sample efficiency of RL algorithms. The learned rewards even achieve comparable performance to human-engineered rewards on some tasks. See our project page (https://sites.google.com/view/iclr24drs) for more details.

Dense retrieval has become a prominent method to obtain relevant context or world knowledge in open-domain NLP tasks. When we use a learned dense retriever on a retrieval corpus at inference time, an often-overlooked design choice is the retrieval unit in which the corpus is indexed, e.g. document, passage, or sentence. We discover that the retrieval unit choice significantly impacts the performance of both retrieval and downstream tasks. Distinct from the typical approach of using passages or sentences, we introduce a novel retrieval unit, proposition, for dense retrieval. Propositions are defined as atomic expressions within text, each encapsulating a distinct factoid and presented in a concise, self-contained natural language format. We conduct an empirical comparison of different retrieval granularity. Our results reveal that proposition-based retrieval significantly outperforms traditional passage or sentence-based methods in dense retrieval. Moreover, retrieval by proposition also enhances the performance of downstream QA tasks, since the retrieved texts are more condensed with question-relevant information, reducing the need for lengthy input tokens and minimizing the inclusion of extraneous, irrelevant information.

Many contrastive representation learning methods learn a single global representation of an entire image. However, dense contrastive representation learning methods such as DenseCL (Wang et al., 2021) can learn better representations for tasks requiring stronger spatial localization of features, such as multi-label classification, detection, and segmentation. In this work, we study how to improve the quality of the representations learned by DenseCL by modifying the training scheme and objective function, and propose DenseCL++. We also conduct several ablation studies to better understand the effects of: (i) various techniques to form dense negative pairs among augmentations of different images, (ii) cross-view dense negative and positive pairs, and (iii) an auxiliary reconstruction task. Our results show 3.5% and 4% mAP improvement over SimCLR (Chen et al., 2020a) andDenseCL in COCO multi-label classification. In COCO and VOC segmentation tasks, we achieve 1.8% and 0.7% mIoU improvements over SimCLR, respectively.

In Reinforcement Learning with Verifiable Rewards (RLVR), constructing a robust advantage baseline is critical for policy gradients, effectively guiding the policy model to reinforce desired behaviors. Recent research has introduced Generalist Value Models (such as V_0), which achieve pre-trained value estimation by explicitly encoding model capabilities in-context, eliminating the need to synchronously update the value model alongside the policy model. In this paper, we propose V_{0.5}, which adaptively fuses the baseline predicted by such value model (acting as a prior) with the empirical mean derived from sparse rollouts. This constructs a robust baseline that balances computational efficiency with extremely low variance. Specifically, we introduce a real-time statistical testing and dynamic budget allocation. This balances the high variance caused by sparse sampling against the systematic bias (or hallucinations) inherent in the value model's prior. By constructing a hypothesis test to evaluate the prior's reliability in real-time, the system dynamically allocates additional rollout budget on demand. This mechanism minimizes the baseline estimator's Mean Squared Error (MSE), guaranteeing stable policy gradients, even under extreme sparsity with a group size of 4. Extensive evaluations across six mathematical reasoning benchmarks demonstrate that V_{0.5} significantly outperforms GRPO and DAPO, achieving faster convergence and over some 10% performance improvement.

Large language models have demonstrated exceptional performance across a wide range of tasks. However, dense models usually suffer from sparse activation, where many activation values tend towards zero (i.e., being inactivated). We argue that this could restrict the efficient exploration of model representation space. To mitigate this issue, we propose Finedeep, a deep-layered fine-grained expert architecture for dense models. Our framework partitions the feed-forward neural network layers of traditional dense models into small experts, arranges them across multiple sub-layers. A novel routing mechanism is proposed to determine each expert's contribution. We conduct extensive experiments across various model sizes, demonstrating that our approach significantly outperforms traditional dense architectures in terms of perplexity and benchmark performance while maintaining a comparable number of parameters and floating-point operations. Moreover, we find that Finedeep achieves optimal results when balancing depth and width, specifically by adjusting the number of expert sub-layers and the number of experts per sub-layer. Empirical results confirm that Finedeep effectively alleviates sparse activation and efficiently utilizes representation capacity in dense models.

Sparse Mixture of Experts (MoE) large language models (LLMs) are gradually becoming the mainstream approach for ultra-large-scale models. Existing optimization efforts for MoE models have focused primarily on coarse-grained MoE architectures. With the emergence of DeepSeek Models, fine-grained MoE models are gaining popularity, yet research on them remains limited. Therefore, we want to discuss the efficiency dynamic under different service loads. Additionally, fine-grained models allow deployers to reduce the number of routed experts, both activated counts and total counts, raising the question of how this reduction affects the trade-off between MoE efficiency and performance. Our findings indicate that while deploying MoE models presents greater challenges, it also offers significant optimization opportunities. Reducing the number of activated experts can lead to substantial efficiency improvements in certain scenarios, with only minor performance degradation. Reducing the total number of experts provides limited efficiency gains but results in severe performance degradation. Our method can increase throughput by at least 10\% without any performance degradation. Overall, we conclude that MoE inference optimization remains an area with substantial potential for exploration and improvement.

Reinforcement Learning with Verifiable Rewards (RLVR) is commonly based on group sampling to estimate advantages and stabilize policy updates. In practice, large group sizes are not feasible due to computational limits, which biases learning toward trajectories that are already likely. Smaller groups often miss rare-correct trajectories while still containing mixed rewards, concentrating probability on common solutions. We derive the probability that updates miss rare-correct modes as a function of group size, showing non-monotonic behavior, and characterize how updates redistribute mass within the correct set, revealing that unsampled-correct mass can shrink even as total correct mass grows. Motivated by this analysis, we propose a difficulty-aware advantage scaling coefficient, inspired by Focal loss, that down-weights updates on high-success prompts. The lightweight modification can be directly integrated into any group-relative RLVR algorithm such as GRPO, DAPO, and CISPO. On Qwen2.5-7B across in-domain and out-of-domain benchmarks, our method improves pass@256 from 64.1 rightarrow 70.3 (GRPO), 69.3 rightarrow 72.5 (DAPO), and 73.2 rightarrow 76.8 (CISPO), while preserving or improving pass@1, without increasing group size or computational cost.

Dense retrieval models are commonly used in Information Retrieval (IR) applications, such as Retrieval-Augmented Generation (RAG). Since they often serve as the first step in these systems, their robustness is critical to avoid failures. In this work, by repurposing a relation extraction dataset (e.g. Re-DocRED), we design controlled experiments to quantify the impact of heuristic biases, such as favoring shorter documents, in retrievers like Dragon+ and Contriever. Our findings reveal significant vulnerabilities: retrievers often rely on superficial patterns like over-prioritizing document beginnings, shorter documents, repeated entities, and literal matches. Additionally, they tend to overlook whether the document contains the query's answer, lacking deep semantic understanding. Notably, when multiple biases combine, models exhibit catastrophic performance degradation, selecting the answer-containing document in less than 3% of cases over a biased document without the answer. Furthermore, we show that these biases have direct consequences for downstream applications like RAG, where retrieval-preferred documents can mislead LLMs, resulting in a 34% performance drop than not providing any documents at all.

Reinforcement Learning with Verifiable Rewards (RLVR) elicits long chain-of-thought reasoning in large language models (LLMs), but outcome-based rewards lead to coarse-grained advantage estimation. While existing approaches improve RLVR via token-level entropy or sequence-level length control, they lack a semantically grounded, step-level measure of reasoning progress. As a result, LLMs fail to distinguish necessary deduction from redundant verification: they may continue checking after reaching a correct solution and, in extreme cases, overturn a correct trajectory into an incorrect final answer. To remedy the lack of process supervision, we introduce a training-free probing mechanism that extracts intermediate confidence and correctness and combines them into a Step Potential signal that explicitly estimates the reasoning state at each step. Building on this signal, we propose Step Potential Advantage Estimation (SPAE), a fine-grained credit assignment method that amplifies potential gains, penalizes potential drops, and applies penalty after potential saturates to encourage timely termination. Experiments across multiple benchmarks show SPAE consistently improves accuracy while substantially reducing response length, outperforming strong RL baselines and recent efficient reasoning and token-level advantage estimation methods. The code is available at https://github.com/cii030/SPAE-RL.

Recent advances in large language models (LLMs) highlight the importance of post training techniques for improving reasoning and mathematical ability. Group Relative Policy Optimization (GRPO) has shown promise in this domain by combining group relative advantage estimation, PPO style clipping, and KL regularization. However, its complexity raises the question of whether all components are necessary for fostering reasoning behaviors. We conduct a systematic analysis of GRPO and identify two key findings: (1) incorporating negative feedback is essential training solely on actions above a baseline limits learning; and (2) PPO style constraints, such as policy ratio clipping, are not required to improve mathematical reasoning or performance. Building on these insights, we propose REINFORCE with Group Relative Advantage (RGRA), a simplified variant that retains group relative advantage estimation but removes PPO style clipping and policy ratio terms. Experiments across standard mathematical benchmarks indicate that RGRA has the potential to achieve stronger performance than GRPO. Our results suggest that simpler REINFORCE based approaches can effectively enhance reasoning in LLMs, offering a more transparent and efficient alternative to GRPO.

AI agents are increasingly used to solve real-world tasks by reasoning over multi-turn user interactions and invoking external tools. However, applying reinforcement learning to such settings remains difficult: realistic objectives often lack verifiable rewards and instead emphasize open-ended behaviors; moreover, RL for multi-turn, multi-step agentic tool use is still underexplored; and building and maintaining executable tool environments is costly, limiting scale and coverage. We propose CM2, an RL framework that replaces verifiable outcome rewards with checklist rewards. CM2 decomposes each turn's intended behavior into fine-grained binary criteria with explicit evidence grounding and structured metadata, turning open-ended judging into more stable classification-style decisions. To balance stability and informativeness, our method adopts a strategy of sparse reward assignment but dense evaluation criteria. Training is performed in a scalable LLM-simulated tool environment, avoiding heavy engineering for large tool sets. Experiments show that CM2 consistently improves over supervised fine-tuning. Starting from an 8B Base model and training on an 8k-example RL dataset, CM2 improves over the SFT counterpart by 8 points on tau^-Bench, by 10 points on BFCL-V4, and by 12 points on ToolSandbox. The results match or even outperform similarly sized open-source baselines, including the judging model. CM2 thus provides a scalable recipe for optimizing multi-turn, multi-step tool-using agents without relying on verifiable rewards. Code provided by the open-source community: https://github.com/namezhenzhang/CM2-RLCR-Tool-Agent.

There is a strong link between the general concept of intelligence and the ability to collect and use information. The theory of Bayes-adaptive exploration offers an attractive optimality framework for training machines to perform complex information gathering tasks. However, the computational complexity of the resulting optimal control problem has limited the diffusion of the theory to mainstream deep AI research. In this paper we exploit the inherent mathematical structure of Bayes-adaptive problems in order to dramatically simplify the problem by making the reward structure denser while simultaneously decoupling the learning of exploitation and exploration policies. The key to this simplification comes from the novel concept of cross-value (i.e. the value of being in an environment while acting optimally according to another), which we use to quantify the value of currently available information. This results in a new denser reward structure that "cashes in" all future rewards that can be predicted from the current information state. In a set of experiments we show that the approach makes it possible to learn challenging information gathering tasks without the use of shaping and heuristic bonuses in situations where the standard RL algorithms fail.

Large language models (LLMs) achieve strong reasoning performance by allocating substantial computation at inference time, often generating long and verbose reasoning traces. While recent work on efficient reasoning reduces this overhead through length-based rewards or pruning, many approaches are post-trained under a much shorter context window than base-model training, a factor whose effect has not been systematically isolated. We first show that short-context post-training alone, using standard GRPO without any length-aware objective, already induces substantial reasoning compression-but at the cost of increasingly unstable training dynamics and accuracy degradation. To address this, we propose Step-level Advantage Selection (SAS), which operates at the reasoning-step level and assigns a zero advantage to low-confidence steps in correct rollouts and to high-confidence steps in verifier-failed rollouts, where failures often arise from truncation or verifier issues rather than incorrect reasoning. Across diverse mathematical and general reasoning benchmarks, SAS improves average Pass@1 accuracy by 0.86 points over the strongest length-aware baseline while reducing average reasoning length by 16.3%, yielding a better accuracy-efficiency trade-off.

Training LLMs as interactive agents for multi-turn decision-making remains challenging, particularly in long-horizon tasks with sparse and delayed rewards, where agents must execute extended sequences of actions before receiving meaningful feedback. Most existing reinforcement learning (RL) approaches model LLM agents as flat policies operating at a single time scale, selecting one action at each turn. In sparse-reward settings, such flat policies must propagate credit across the entire trajectory without explicit temporal abstraction, which often leads to unstable optimization and inefficient credit assignment. We propose HiPER, a novel Hierarchical Plan-Execute RL framework that explicitly separates high-level planning from low-level execution. HiPER factorizes the policy into a high-level planner that proposes subgoals and a low-level executor that carries them out over multiple action steps. To align optimization with this structure, we introduce a key technique called hierarchical advantage estimation (HAE), which carefully assigns credit at both the planning and execution levels. By aggregating returns over the execution of each subgoal and coordinating updates across the two levels, HAE provides an unbiased gradient estimator and provably reduces variance compared to flat generalized advantage estimation. Empirically, HiPER achieves state-of-the-art performance on challenging interactive benchmarks, reaching 97.4\% success on ALFWorld and 83.3\% on WebShop with Qwen2.5-7B-Instruct (+6.6\% and +8.3\% over the best prior method), with especially large gains on long-horizon tasks requiring multiple dependent subtasks. These results highlight the importance of explicit hierarchical decomposition for scalable RL training of multi-turn LLM agents.

Pre-trained Transformer language models (LM) have become go-to text representation encoders. Prior research fine-tunes deep LMs to encode text sequences such as sentences and passages into single dense vector representations for efficient text comparison and retrieval. However, dense encoders require a lot of data and sophisticated techniques to effectively train and suffer in low data situations. This paper finds a key reason is that standard LMs' internal attention structure is not ready-to-use for dense encoders, which needs to aggregate text information into the dense representation. We propose to pre-train towards dense encoder with a novel Transformer architecture, Condenser, where LM prediction CONditions on DENSE Representation. Our experiments show Condenser improves over standard LM by large margins on various text retrieval and similarity tasks.

Training large language models to reason with search engines via reinforcement learning is hindered by a fundamental credit assignment problem: existing methods such as Search-R1 provide only a sparse outcome reward after an entire multi-step trajectory, making it infeasible to attribute success or failure to individual reasoning and retrieval decisions. Process-reward methods like StepSearch alleviate this by introducing step-level supervision, but rely on heuristic rewards such as TF-IDF overlap with gold documents, and still sample k complete trajectories per example, retaining high gradient variance. We propose SLATE, a framework built on two complementary ideas: (1) truncated step-level sampling, which generates k trajectories that share a common prefix and differ only at the next step, and (2) dense LLM-as-judge rewards, which replace heuristic scoring with a capable LLM evaluator that assesses the quality of each reasoning step, search query, and answer, providing richer and more reliable supervision. We theoretically prove that under the same dense reward structure, truncated sampling reduces the variance of advantage estimates by up to a factor of T compared to full-trajectory sampling for T-step trajectories, yielding lower-variance, better-targeted policy gradients. Experiments on seven QA benchmarks confirm that SLATE consistently outperforms both sparse-reward and process-reward baselines, with the largest gains on harder multi-hop tasks and smaller models.

Recent advances in reinforcement learning (RL)-based post-training have led to notable improvements in large language models (LLMs), particularly in enhancing their reasoning capabilities to handle complex tasks. However, most existing methods treat the training data as a unified whole, overlooking the fact that modern LLM training often involves a mixture of data from diverse distributions-varying in both source and difficulty. This heterogeneity introduces a key challenge: how to adaptively schedule training across distributions to optimize learning efficiency. In this paper, we present a principled curriculum learning framework grounded in the notion of distribution-level learnability. Our core insight is that the magnitude of policy advantages reflects how much a model can still benefit from further training on a given distribution. Based on this, we propose a distribution-level curriculum learning framework for RL-based LLM post-training, which leverages the Upper Confidence Bound (UCB) principle to dynamically adjust sampling probabilities for different distrubutions. This approach prioritizes distributions with either high average advantage (exploitation) or low sample count (exploration), yielding an adaptive and theoretically grounded training schedule. We instantiate our curriculum learning framework with GRPO as the underlying RL algorithm and demonstrate its effectiveness on logic reasoning datasets with multiple difficulties and sources. Our experiments show that our framework significantly improves convergence speed and final performance, highlighting the value of distribution-aware curriculum strategies in LLM post-training. Code: https://github.com/ZhentingWang/DUMP.

A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, potentially improving credit assignment over outcome reward models (ORMs) that only provide feedback at the final step. However, collecting dense, per-step human labels is not scalable, and training PRMs from automatically-labeled data has thus far led to limited gains. To improve a base policy by running search against a PRM or using it as dense rewards for reinforcement learning (RL), we ask: "How should we design process rewards?". Our key insight is that, to be effective, the process reward for a step should measure progress: a change in the likelihood of producing a correct response in the future, before and after taking the step, corresponding to the notion of step-level advantages in RL. Crucially, this progress should be measured under a prover policy distinct from the base policy. We theoretically characterize the set of good provers and our results show that optimizing process rewards from such provers improves exploration during test-time search and online RL. In fact, our characterization shows that weak prover policies can substantially improve a stronger base policy, which we also observe empirically. We validate our claims by training process advantage verifiers (PAVs) to predict progress under such provers, and show that compared to ORMs, test-time search against PAVs is >8% more accurate, and 1.5-5times more compute-efficient. Online RL with dense rewards from PAVs enables one of the first results with 5-6times gain in sample efficiency, and >6% gain in accuracy, over ORMs.

Large Language Models (LLMs) have demonstrated remarkable capabilities, enabling language agents to excel at single-turn tasks. However, their application to complex, multi-step, and long-horizon tasks remains challenging. While reinforcement learning (RL) offers a promising avenue for addressing these challenges, mainstream approaches typically rely solely on sparse, outcome-based rewards, a limitation that becomes especially problematic for group-based RL algorithms lacking critic models, such as Group Relative Policy Optimization (GRPO). In such methods, uniformly rewarding or penalizing all actions within a trajectory can lead to training instability and suboptimal policies, because beneficial and detrimental actions are often entangled across multi-step interactions. To address this challenge, we propose SALT, a novel and lightweight framework that provides a finer-grained advantage assignment, derived solely from outcome rewards. We achieve this by constructing a graph from trajectories of the same prompt, which allows us to quantify the quality of each step and assign advantages accordingly. Crucially, SALT is designed as a plug-and-play module that seamlessly integrates with existing group-based RL algorithms, requiring no modifications to the rollout procedure and introducing negligible computational overhead. Extensive experiments on the WebShop, ALFWorld, and AppWorld benchmarks with various model sizes demonstrate that SALT consistently improves performance. We also conduct a thorough analysis to validate the design choices behind SALT and offer actionable insights.

This paper reinterprets the Synthetic Control (SC) framework through the lens of weighting philosophy, arguing that the contrast between traditional SC and Difference-in-Differences (DID) reflects two distinct modeling mindsets: sparse versus dense weighting schemes. Rather than viewing sparsity as inherently superior, we treat it as a modeling choice simple but potentially fragile. We propose an L-infinity-regularized SC method that combines the strengths of both approaches. Like DID, it employs a denser weighting scheme that distributes weights more evenly across control units, enhancing robustness and reducing overreliance on a few control units. Like traditional SC, it remains flexible and data-driven, increasing the likelihood of satisfying the parallel trends assumption while preserving interpretability. We develop an interior point algorithm for efficient computation, derive asymptotic theory under weak dependence, and demonstrate strong finite-sample performance through simulations and real-world applications.

The foundational pretraining phase determines a model's capability ceiling, as post-training struggles to overcome capability foundations established during pretraining, yet it remains critically under-explored. This stems from a structural paradox: organizations with computational resources operate under commercial pressures that inhibit transparent disclosure, while academic institutions possess research freedom but lack pretraining-scale computational resources. daVinci-LLM occupies this unexplored intersection, combining industrial-scale resources with full research freedom to advance the science of pretraining. We adopt a fully-open paradigm that treats openness as scientific methodology, releasing complete data processing pipelines, full training processes, and systematic exploration results. Recognizing that the field lacks systematic methodology for data processing, we employ the Data Darwinism framework, a principled L0-L9 taxonomy from filtering to synthesis. We train a 3B-parameter model from random initialization across 8T tokens using a two-stage adaptive curriculum that progressively shifts from foundational capabilities to reasoning-intensive enhancement. Through 200+ controlled ablations, we establish that: processing depth systematically enhances capabilities, establishing it as a critical dimension alongside volume scaling; different domains exhibit distinct saturation dynamics, necessitating adaptive strategies from proportion adjustments to format shifts; compositional balance enables targeted intensification while preventing performance collapse; how evaluation protocol choices shape our understanding of pretraining progress. By releasing the complete exploration process, we enable the community to build upon our findings and systematic methodologies to form accumulative scientific knowledge in pretraining.

Recent advances in reasoning with large language models (LLMs) have shown the effectiveness of Monte Carlo Tree Search (MCTS) for generating high-quality intermediate trajectories, particularly in math and symbolic domains. Inspired by this, we explore how MCTS-derived trajectories, traditionally used for training value or reward models, can be repurposed to improve policy optimization in preference-based reinforcement learning (RL). Specifically, we focus on Group Relative Policy Optimization (GRPO), a recent algorithm that enables preference-consistent policy learning without value networks. We propose a staged GRPO training paradigm where completions are derived from partially revealed MCTS rollouts, introducing a novel tree-structured setting for advantage estimation. This leads to a rich class of prefix-conditioned reward signals, which we analyze theoretically and empirically. Our initial results indicate that while structured advantage estimation can stabilize updates and better reflect compositional reasoning quality, challenges such as advantage saturation and reward signal collapse remain. We propose heuristic and statistical solutions to mitigate these issues and discuss open challenges for learning under staged or tree-like reward structures.

Large Language Models (LLMs) have made remarkable progress in enhancing step-by-step reasoning through reinforcement learning. However, the Group Relative Policy Optimization (GRPO) algorithm, which relies on sparse reward rules, often encounters the issue of identical rewards within groups, leading to the advantage collapse problem. Existing works typically address this challenge from two perspectives: enforcing model reflection to enhance response diversity, and introducing internal feedback to augment the training signal (advantage). In this work, we begin by analyzing the limitations of model reflection and investigating the policy entropy of responses at the fine-grained sample level. Based on our experimental findings, we propose the EDGE-GRPO algorithm, which adopts Entropy-Driven Advantage and Guided Error Correction to effectively mitigate the problem of advantage collapse. Extensive experiments on several main reasoning benchmarks demonstrate the effectiveness and superiority of our approach. It is available at https://github.com/ZhangXJ199/EDGE-GRPO.

We propose a sparsity-aware evolutionary (SAE) framework for model merging that involves iterative pruning-merging cycles to act as a novel mutation operator. We incorporate the sparsity constraints into the score function, which steers the evolutionary process to favor more sparse models, in addition to other conventional performance scores. Interestingly, the by-product of competition for sparsity introduces an extra local attraction and interplay into the evolutionary process: if one competitor has more zero elements, the other competitor's non-zero elements will occupy those positions, even though the less sparse competitor loses to the more sparse competitor in other positions. The proposed pipeline is evaluated on a variety of large-scale LLM benchmarks. Experiments demonstrate that our approach can improve model merging reliability across multiple benchmarks, and is easy to incorporate due to its simplicity and being orthogonal to most existing approaches.

Reinforcement Learning with Verifiable Rewards (RLVR), particularly GRPO, has become the standard for eliciting LLM reasoning. However, its efficiency in exploration and difficulty adaptation remains an open challenge. In this work, we argue that these bottlenecks stem from an implicit advantage symmetry inherent in Group Relative Advantage Estimation (GRAE). This symmetry induces two critical limitations: (i) at the group level, strict symmetry in weights between correct and incorrect trajectories leaves unsampled action logits unchanged, thereby hindering exploration of novel correct solution. (ii) at the sample level, the algorithm implicitly prioritizes medium-difficulty samples, remaining agnostic to the non-stationary demands of difficulty focus. Through controlled experiments, we reveal that this symmetric property is sub-optimal, yielding two pivotal insights: (i) asymmetrically suppressing the advantages of correct trajectories encourages essential exploration. (ii) learning efficiency is maximized by a curriculum-like transition-prioritizing simpler samples initially before gradually shifting to complex ones. Motivated by these findings, we propose Asymmetric GRAE (A-GRAE), which dynamically modulates exploration incentives and sample-difficulty focus. Experiments across seven benchmarks demonstrate that A-GRAE consistently improves GRPO and its variants across both LLMs and MLLMs.

Large Reasoning Models (LRMs) have achieved remarkable success, yet they often suffer from producing unnecessary and verbose reasoning chains. We identify a core aspect of this issue as "invalid thinking" -- models tend to repeatedly double-check their work after having derived the correct answer. To address this specific inefficiency, we move beyond the general principles of Efficacy and Efficiency to propose two new, fine-grained principles: Brevity, which advocates for eliminating redundancy, and Sufficiency, which ensures critical reasoning steps are preserved. Guided by these principles, we introduce LC-R1, a post-training method based on Group Relative Policy Optimization (GRPO). LC-R1 employs a novel combination of a Length Reward for overall conciseness and a Compress Reward that is specifically designed to remove the invalid portion of the thinking process. Extensive experiments on multiple reasoning benchmarks demonstrate that LC-R1 achieves a significant reduction in sequence length (~50%) with only a marginal (~2%) drop in accuracy, achieving a favorable trade-off point on the Pareto frontier that prioritizes high compression. Our analysis further validates the robustness of LC-R1 and provides valuable insights for developing more powerful yet computationally efficient LRMs. Our code is released at https://github.com/zxiangx/LC-R1.

Few-step diffusion models enable efficient high-resolution image synthesis but struggle to align with specific downstream objectives due to limitations of existing reinforcement learning (RL) methods in low-step regimes with limited state spaces and suboptimal sample quality. To address this, we propose Stepwise Diffusion Policy Optimization (SDPO), a novel RL framework tailored for few-step diffusion models. SDPO introduces a dual-state trajectory sampling mechanism, tracking both noisy and predicted clean states at each step to provide dense reward feedback and enable low-variance, mixed-step optimization. For further efficiency, we develop a latent similarity-based dense reward prediction strategy to minimize costly dense reward queries. Leveraging these dense rewards, SDPO optimizes a dense reward difference learning objective that enables more frequent and granular policy updates. Additional refinements, including stepwise advantage estimates, temporal importance weighting, and step-shuffled gradient updates, further enhance long-term dependency, low-step priority, and gradient stability. Our experiments demonstrate that SDPO consistently delivers superior reward-aligned results across diverse few-step settings and tasks. Code is available at https://github.com/ZiyiZhang27/sdpo.

Small, highly trained, open-source large language models are widely used due to their inference efficiency, but further improving their quality remains a challenge. Sparse upcycling is a promising approach that transforms a pretrained dense model into a Mixture-of-Experts (MoE) architecture, increasing the model's parameter count and quality. In this work, we compare the effectiveness of sparse upcycling against continued pretraining (CPT) across different model sizes, compute budgets, and pretraining durations. Our experiments show that sparse upcycling can achieve better quality, with improvements of over 20% relative to CPT in certain scenarios. However, this comes with a significant inference cost, leading to 40% slowdowns in high-demand inference settings for larger models. Our findings highlight the trade-off between model quality and inference efficiency, offering insights for practitioners seeking to balance model quality and deployment constraints.

Historically, the pursuit of efficient inference has been one of the driving forces behind research into new deep learning architectures and building blocks. Some recent examples include: the squeeze-and-excitation module, depthwise separable convolutions in Xception, and the inverted bottleneck in MobileNet v2. Notably, in all of these cases, the resulting building blocks enabled not only higher efficiency, but also higher accuracy, and found wide adoption in the field. In this work, we further expand the arsenal of efficient building blocks for neural network architectures; but instead of combining standard primitives (such as convolution), we advocate for the replacement of these dense primitives with their sparse counterparts. While the idea of using sparsity to decrease the parameter count is not new, the conventional wisdom is that this reduction in theoretical FLOPs does not translate into real-world efficiency gains. We aim to correct this misconception by introducing a family of efficient sparse kernels for ARM and WebAssembly, which we open-source for the benefit of the community as part of the XNNPACK library. Equipped with our efficient implementation of sparse primitives, we show that sparse versions of MobileNet v1, MobileNet v2 and EfficientNet architectures substantially outperform strong dense baselines on the efficiency-accuracy curve. On Snapdragon 835 our sparse networks outperform their dense equivalents by 1.3-2.4times -- equivalent to approximately one entire generation of MobileNet-family improvement. We hope that our findings will facilitate wider adoption of sparsity as a tool for creating efficient and accurate deep learning architectures.

Neural retrievers based on dense representations combined with Approximate Nearest Neighbors search have recently received a lot of attention, owing their success to distillation and/or better sampling of examples for training -- while still relying on the same backbone architecture. In the meantime, sparse representation learning fueled by traditional inverted indexing techniques has seen a growing interest, inheriting from desirable IR priors such as explicit lexical matching. While some architectural variants have been proposed, a lesser effort has been put in the training of such models. In this work, we build on SPLADE -- a sparse expansion-based retriever -- and show to which extent it is able to benefit from the same training improvements as dense models, by studying the effect of distillation, hard-negative mining as well as the Pre-trained Language Model initialization. We furthermore study the link between effectiveness and efficiency, on in-domain and zero-shot settings, leading to state-of-the-art results in both scenarios for sufficiently expressive models.

This paper presents a new approach that integrates deep learning with computational chess, using both the Mixture of Experts (MoE) method and Monte-Carlo Tree Search (MCTS). Our methodology employs a suite of specialized models, each designed to respond to specific changes in the game's input data. This results in a framework with sparsely activated models, which provides significant computational benefits. Our framework combines the MoE method with MCTS, in order to align it with the strategic phases of chess, thus departing from the conventional ``one-for-all'' model. Instead, we utilize distinct game phase definitions to effectively distribute computational tasks across multiple expert neural networks. Our empirical research shows a substantial improvement in playing strength, surpassing the traditional single-model framework. This validates the efficacy of our integrated approach and highlights the potential of incorporating expert knowledge and strategic principles into neural network design. The fusion of MoE and MCTS offers a promising avenue for advancing machine learning architectures.

Pruning is a standard technique for reducing the computational cost of deep networks. Many advances in pruning leverage concepts from the Lottery Ticket Hypothesis (LTH). LTH reveals that inside a trained dense network exists sparse subnetworks (tickets) able to achieve similar accuracy (i.e., win the lottery - winning tickets). Pruning at initialization focuses on finding winning tickets without training a dense network. Studies on these concepts share the trend that subnetworks come from weight or filter pruning. In this work, we investigate LTH and pruning at initialization from the lens of layer pruning. First, we confirm the existence of winning tickets when the pruning process removes layers. Leveraged by this observation, we propose to discover these winning tickets at initialization, eliminating the requirement of heavy computational resources for training the initial (over-parameterized) dense network. Extensive experiments show that our winning tickets notably speed up the training phase and reduce up to 51% of carbon emission, an important step towards democratization and green Artificial Intelligence. Beyond computational benefits, our winning tickets exhibit robustness against adversarial and out-of-distribution examples. Finally, we show that our subnetworks easily win the lottery at initialization while tickets from filter removal (the standard structured LTH) hardly become winning tickets.

This paper presents our latest investigation on Densely Connected Convolutional Networks (DenseNets) for acoustic modelling (AM) in automatic speech recognition. DenseN-ets are very deep, compact convolutional neural networks, which have demonstrated incredible improvements over the state-of-the-art results on several data sets in computer vision. Our experimental results show that DenseNet can be used for AM significantly outperforming other neural-based models such as DNNs, CNNs, VGGs. Furthermore, results on Wall Street Journal revealed that with only a half of the training data DenseNet was able to outperform other models trained with the full data set by a large margin.

How to reduce compute and memory requirements of neural networks (NNs) without sacrificing performance? Many recent works use sparse Mixtures of Experts (MoEs) to build resource-efficient large language models (LMs). Here we introduce several novel perspectives on MoEs, presenting a general framework that unifies various methods to approximate two-layer NNs (e.g., feedforward blocks of Transformers), including product-key memories (PKMs). Leveraging insights from this framework, we propose methods to improve both MoEs and PKMs. Unlike prior work that compares MoEs with dense baselines under the compute-equal condition, our evaluation condition is parameter-equal, which is crucial to properly evaluate LMs. We show that our MoEs are competitive with the dense Transformer-XL on both the WikiText-103 and enwiki8 datasets at two different scales, while being much more resource efficient. This demonstrates that MoEs are relevant not only to extremely large LMs but also to any-scale resource-efficient LMs. Our code is public.

Recently, test-time scaling Large Language Models (LLMs) have demonstrated exceptional reasoning capabilities across scientific and professional tasks by generating long chains-of-thought (CoT). As a crucial component for developing these reasoning models, reinforcement learning (RL), exemplified by Proximal Policy Optimization (PPO) and its variants, allows models to learn through trial and error. However, PPO can be time-consuming due to its inherent on-policy nature, which is further exacerbated by increasing response lengths. In this work, we propose Truncated Proximal Policy Optimization (T-PPO), a novel extension to PPO that improves training efficiency by streamlining policy update and length-restricted response generation. T-PPO mitigates the issue of low hardware utilization, an inherent drawback of fully synchronized long-generation procedures, where resources often sit idle during the waiting periods for complete rollouts. Our contributions are two-folds. First, we propose Extended Generalized Advantage Estimation (EGAE) for advantage estimation derived from incomplete responses while maintaining the integrity of policy learning. Second, we devise a computationally optimized mechanism that allows for the independent optimization of the policy and value models. By selectively filtering prompt and truncated tokens, this mechanism reduces redundant computations and accelerates the training process without sacrificing convergence performance. We demonstrate the effectiveness and efficacy of T-PPO on AIME 2024 with a 32B base model. The experimental results show that T-PPO improves the training efficiency of reasoning LLMs by up to 2.5x and outperforms its existing competitors.

We demonstrate the possibility of what we call sparse learning: accelerated training of deep neural networks that maintain sparse weights throughout training while achieving dense performance levels. We accomplish this by developing sparse momentum, an algorithm which uses exponentially smoothed gradients (momentum) to identify layers and weights which reduce the error efficiently. Sparse momentum redistributes pruned weights across layers according to the mean momentum magnitude of each layer. Within a layer, sparse momentum grows weights according to the momentum magnitude of zero-valued weights. We demonstrate state-of-the-art sparse performance on MNIST, CIFAR-10, and ImageNet, decreasing the mean error by a relative 8%, 15%, and 6% compared to other sparse algorithms. Furthermore, we show that sparse momentum reliably reproduces dense performance levels while providing up to 5.61x faster training. In our analysis, ablations show that the benefits of momentum redistribution and growth increase with the depth and size of the network. Additionally, we find that sparse momentum is insensitive to the choice of its hyperparameters suggesting that sparse momentum is robust and easy to use.

Large Language Models (LLMs) have emerged as a milestone in artificial intelligence, and their performance can improve as the model size increases. However, this scaling brings great challenges to training and inference efficiency, particularly for deploying LLMs in resource-constrained environments, and the scaling trend is becoming increasingly unsustainable. This paper introduces the concept of ``capacity density'' as a new metric to evaluate the quality of the LLMs across different scales and describes the trend of LLMs in terms of both effectiveness and efficiency. To calculate the capacity density of a given target LLM, we first introduce a set of reference models and develop a scaling law to predict the downstream performance of these reference models based on their parameter sizes. We then define the effective parameter size of the target LLM as the parameter size required by a reference model to achieve equivalent performance, and formalize the capacity density as the ratio of the effective parameter size to the actual parameter size of the target LLM. Capacity density provides a unified framework for assessing both model effectiveness and efficiency. Our further analysis of recent open-source base LLMs reveals an empirical law (the densing law)that the capacity density of LLMs grows exponentially over time. More specifically, using some widely used benchmarks for evaluation, the capacity density of LLMs doubles approximately every three months. The law provides new perspectives to guide future LLM development, emphasizing the importance of improving capacity density to achieve optimal results with minimal computational overhead.

Reasoning training incentivizes LLMs to produce long chains of thought (long CoT), which among other things, allows them to explore solution strategies with self-checking. This results in higher accuracy, but inflates context length, token/compute cost, and answer latency. We ask: Can current models leverage their metacognition to provide other combinations on this Pareto frontier, e.g., better accuracy with lower context length and/or latency? Abstractly, we view the model as an improvement operator on its own "thoughts" with a continuum of possible strategies. We identify an interesting inference family Parallel-Distill-Refine (PDR), which performs the following: (i) generate diverse drafts in parallel; (ii) distill them into a bounded, textual workspace; and (iii) refine conditioned on this workspace, producing an output that seeds the next round. Importantly, context length (hence compute cost) is controllable via degree of parallelism, and is no longer conflated with the total number of generated tokens. We report PDR instantiations of current models that give better accuracy than long CoT while incurring lower latency. Setting degree of parallelism to 1 yields an interesting subcase, Sequential Refinement (SR) (iteratively improve a single candidate answer) which provides performance superior to long CoT. Success of such model orchestrations raises the question whether further training could shift the Pareto frontier. To this end, we train an 8B thinking model with Reinforcement Learning (RL) to make it consistent with PDR as the inference method. On math tasks with verifiable answers, iterative pipelines surpass single-pass baselines at matched sequential budgets, with PDR delivering the largest gains (e.g., +11% on AIME 2024 and +9% on AIME 2025).

Effective decision-making in Large Language Models (LLMs) is essential for handling intricate tasks. However, existing approaches prioritize performance but often overlook the balance between effectiveness and computational cost. To address this, we first introduce the 3E Criteria to systematically assess the cost-effectiveness of search strategies, revealing that existing methods often trade significant efficiency for marginal performance gains. To improve LLM decision-making while maintaining efficiency, we propose the Speculative Reward Model (SRM), a plug-and-play framework that seamlessly integrates with existing search strategies. Specifically, SRM employs an external reward assigner to predict optimal actions, reducing reliance on LLMs' internal self-evaluation. And a speculative verification mechanism is used to prune suboptimal choices and guide the search toward more promising steps. We evaluate SRM on several complex decision-making tasks including mathematical reasoning, planning and numerical reasoning in specialized domains. Experimental results show that SRM reduces costs to 1/10 of the original search framework on average while maintaining effectiveness.

In this work, we investigate how explicitly modeling problem's difficulty prior information shapes the effectiveness of reinforcement learning based fine-tuning for multimodal reasoning. Our exploration mainly comprises of following three perspective: First, through offline data curation, we analyze the U-shaped difficulty distribution of two given datasets using the base model by multi-round sampling, and then filter out prompts that are either too simple or extremely difficult to provide meaningful gradients and perform subsequent two-stage training. Second, we implement an online advantage differentiation, computing group-wise empirical accuracy as a difficulty proxy to adaptively reweight advantages estimation, providing stronger learning signals for more challenging problems. Finally, we introduce difficulty hints as explicit prompts for more complex samples in the second training stage, encouraging the model to calibrate its reasoning depth and perform reflective validation checks. Our comprehensive approach demonstrates significant performances across various multi-modal mathematical reasoning benchmarks with only 2K+0.6K two-stage training data.

Recent work has shown that convolutional networks can be substantially deeper, more accurate, and efficient to train if they contain shorter connections between layers close to the input and those close to the output. In this paper, we embrace this observation and introduce the Dense Convolutional Network (DenseNet), which connects each layer to every other layer in a feed-forward fashion. Whereas traditional convolutional networks with L layers have L connections - one between each layer and its subsequent layer - our network has L(L+1)/2 direct connections. For each layer, the feature-maps of all preceding layers are used as inputs, and its own feature-maps are used as inputs into all subsequent layers. DenseNets have several compelling advantages: they alleviate the vanishing-gradient problem, strengthen feature propagation, encourage feature reuse, and substantially reduce the number of parameters. We evaluate our proposed architecture on four highly competitive object recognition benchmark tasks (CIFAR-10, CIFAR-100, SVHN, and ImageNet). DenseNets obtain significant improvements over the state-of-the-art on most of them, whilst requiring less computation to achieve high performance. Code and pre-trained models are available at https://github.com/liuzhuang13/DenseNet .

Reinforcement Learning with Verifiable Rewards (RLVR) can elicit strong multi-step reasoning, yet it often encourages overly verbose traces. Moreover, naive length penalties in group-relative optimization can severely hurt accuracy. We attribute this failure to two structural issues: (i) Dilution of Length Baseline, where incorrect responses (with zero length reward) depress the group baseline and over-penalize correct solutions; and (ii) Difficulty-Penalty Mismatch, where a static penalty cannot adapt to problem difficulty, suppressing necessary reasoning on hard instances while leaving redundancy on easy ones. We propose Dynamic Decoupled Conditional Advantage (DDCA) to decouple efficiency optimization from correctness. DDCA computes length advantages conditionally within the correct-response cluster to eliminate baseline dilution, and dynamically scales the penalty strength using the group pass rate as a proxy for difficulty. Experiments on GSM8K, MATH500, AMC23, and AIME25 show that DDCA consistently improves the efficiency--accuracy trade-off relative to adaptive baselines, reducing generated tokens by approximately 60% on simpler tasks (e.g., GSM8K) versus over 20% on harder benchmarks (e.g., AIME25), thereby maintaining or improving accuracy. Code is available at https://github.com/alphadl/DDCA.

Large language model (LLM)-based agents are increasingly trained with reinforcement learning (RL) to enhance their ability to interact with external environments through tool use, particularly in search-based settings that require multi-turn reasoning and knowledge acquisition. However, existing approaches typically rely on outcome-based rewards that are only provided at the final answer. This reward sparsity becomes particularly problematic in multi-turn settings, where long trajectories exacerbate two critical issues: (i) advantage collapse, where all rollouts receive identical rewards and provide no useful learning signals, and (ii) lack of fine-grained credit assignment, where dependencies between turns are obscured, especially in long-horizon tasks. In this paper, we propose Information Gain-based Policy Optimization (IGPO), a simple yet effective RL framework that provides dense and intrinsic supervision for multi-turn agent training. IGPO models each interaction turn as an incremental process of acquiring information about the ground truth, and defines turn-level rewards as the marginal increase in the policy's probability of producing the correct answer. Unlike prior process-level reward approaches that depend on external reward models or costly Monte Carlo estimation, IGPO derives intrinsic rewards directly from the model's own belief updates. These intrinsic turn-level rewards are combined with outcome-level supervision to form dense reward trajectories. Extensive experiments on both in-domain and out-of-domain benchmarks demonstrate that IGPO consistently outperforms strong baselines in multi-turn scenarios, achieving higher accuracy and improved sample efficiency.

This paper investigates the problem of ensembling multiple strategies for sequential portfolios to outperform individual strategies in terms of long-term wealth. Due to the uncertainty of strategies' performances in the future market, which are often based on specific models and statistical assumptions, investors often mitigate risk and enhance robustness by combining multiple strategies, akin to common approaches in collective learning prediction. However, the absence of a distribution-free and consistent preference framework complicates decisions of combination due to the ambiguous objective. To address this gap, we introduce a novel framework for decision-making in combining strategies, irrespective of market conditions, by establishing the investor's preference between decisions and then forming a clear objective. Through this framework, we propose a combinatorial strategy construction, free from statistical assumptions, for any scale of component strategies, even infinite, such that it meets the determined criterion. Finally, we test the proposed strategy along with its accelerated variant and some other multi-strategies. The numerical experiments show results in favor of the proposed strategies, albeit with small tradeoffs in their Sharpe ratios, in which their cumulative wealths eventually exceed those of the best component strategies while the accelerated strategy significantly improves performance.

Reasoning language models such as OpenAI-o1, DeepSeek-R1, and Qwen achieve strong performance via extended chains of thought but often generate unnecessarily long outputs. Maximizing intelligence per token--accuracy relative to response length--remains an open problem. We revisit reinforcement learning (RL) with the simplest length penalty--truncation--and show that accuracy degradation arises not from the lack of sophisticated penalties but from inadequate RL optimization. We identify three key challenges: (i) large bias in advantage estimation, (ii) entropy collapse, and (iii) sparse reward signal. We address them with Doing Length pEnalty Right (DLER), a training recipe combining batch-wise reward normalization, higher clipping, dynamic sampling, and a simple truncation length penalty. DLER achieves state-of-the-art accuracy--efficiency trade-offs, cutting output length by over 70 percent while surpassing all previous baseline accuracy. It also improves test-time scaling: compared to DeepSeek-R1-7B, DLER-7B generates multiple concise responses in parallel with 28 percent higher accuracy and lower latency. We further introduce Difficulty-Aware DLER, which adaptively tightens truncation on easier questions for additional efficiency gains. We also propose an update-selective merging method that preserves baseline accuracy while retaining the concise reasoning ability of the DLER model, which is useful for scenarios where RL training data is scarce.

Dense retrieval systems have been widely used in various NLP applications. However, their vulnerabilities to potential attacks have been underexplored. This paper investigates a novel attack scenario where the attackers aim to mislead the retrieval system into retrieving the attacker-specified contents. Those contents, injected into the retrieval corpus by attackers, can include harmful text like hate speech or spam. Unlike prior methods that rely on model weights and generate conspicuous, unnatural outputs, we propose a covert backdoor attack triggered by grammar errors. Our approach ensures that the attacked models can function normally for standard queries while covertly triggering the retrieval of the attacker's contents in response to minor linguistic mistakes. Specifically, dense retrievers are trained with contrastive loss and hard negative sampling. Surprisingly, our findings demonstrate that contrastive loss is notably sensitive to grammatical errors, and hard negative sampling can exacerbate susceptibility to backdoor attacks. Our proposed method achieves a high attack success rate with a minimal corpus poisoning rate of only 0.048\%, while preserving normal retrieval performance. This indicates that the method has negligible impact on user experience for error-free queries. Furthermore, evaluations across three real-world defense strategies reveal that the malicious passages embedded within the corpus remain highly resistant to detection and filtering, underscoring the robustness and subtlety of the proposed attack Codes of this work are available at https://github.com/ruyue0001/Backdoor_DPR..

Reinforcement Learning from Verifier Rewards (RLVR) has emerged as a widely used approach for post-training large language models on reasoning tasks, with group-based methods such as GRPO and its variants gaining broad adoption. These methods rely on group-relative advantage estimation to avoid learned critics, yet its theoretical properties remain poorly understood. In this work, we uncover a fundamental issue of group-based RL: the group-relative advantage estimator is inherently biased relative to the true (expected) advantage. We provide the first theoretical analysis showing that it systematically underestimates advantages for hard prompts and overestimates them for easy prompts, leading to imbalanced exploration and exploitation. To address this issue, we propose History-Aware Adaptive Difficulty Weighting (HA-DW), an adaptive reweighting scheme that adjusts advantage estimates based on an evolving difficulty anchor and training dynamics. Both theoretical analysis and experiments on five mathematical reasoning benchmarks demonstrate that HA-DW consistently improves performance when integrated into GRPO and its variants. Our results suggest that correcting biased advantage estimation is critical for robust and efficient RLVR training.

Large neural networks excel in many domains, but they are expensive to train and fine-tune. A popular approach to reduce their compute or memory requirements is to replace dense weight matrices with structured ones (e.g., sparse, low-rank, Fourier transform). These methods have not seen widespread adoption (1) in end-to-end training due to unfavorable efficiency--quality tradeoffs, and (2) in dense-to-sparse fine-tuning due to lack of tractable algorithms to approximate a given dense weight matrix. To address these issues, we propose a class of matrices (Monarch) that is hardware-efficient (they are parameterized as products of two block-diagonal matrices for better hardware utilization) and expressive (they can represent many commonly used transforms). Surprisingly, the problem of approximating a dense weight matrix with a Monarch matrix, though nonconvex, has an analytical optimal solution. These properties of Monarch matrices unlock new ways to train and fine-tune sparse and dense models. We empirically validate that Monarch can achieve favorable accuracy-efficiency tradeoffs in several end-to-end sparse training applications: speeding up ViT and GPT-2 training on ImageNet classification and Wikitext-103 language modeling by 2x with comparable model quality, and reducing the error on PDE solving and MRI reconstruction tasks by 40%. In sparse-to-dense training, with a simple technique called "reverse sparsification," Monarch matrices serve as a useful intermediate representation to speed up GPT-2 pretraining on OpenWebText by 2x without quality drop. The same technique brings 23% faster BERT pretraining than even the very optimized implementation from Nvidia that set the MLPerf 1.1 record. In dense-to-sparse fine-tuning, as a proof-of-concept, our Monarch approximation algorithm speeds up BERT fine-tuning on GLUE by 1.7x with comparable accuracy.

Large reasoning models (LRMs) are commonly trained with reinforcement learning (RL) to explore long chain-of-thought reasoning, achieving strong performance at high computational cost. Recent methods add multi-reward objectives to jointly optimize correctness and brevity, but these complex extensions often destabilize training and yield suboptimal trade-offs. We revisit this objective and challenge the necessity of such complexity. Through principled analysis, we identify fundamental misalignments in this paradigm: KL regularization loses its intended role when correctness and length are directly verifiable, and group-wise normalization becomes ambiguous under multiple reward signals. By removing these two items and simplifying the reward to a truncation-based length penalty, we show that the optimization problem reduces to supervised fine-tuning on self-generated data filtered for both correctness and conciseness. We term this simplified training strategy on-policy SFT. Despite its simplicity, on-policy SFT consistently defines the accuracy-efficiency Pareto frontier. It reduces CoT length by up to 80 while maintaining original accuracy, surpassing more complex RL-based methods across five benchmarks. Furthermore, it significantly enhances training efficiency, reducing GPU memory usage by 50% and accelerating convergence by 70%. Our code is available at https://github.com/EIT-NLP/On-Policy-SFT.

Dense retrieval overcome the lexical gap and has shown great success in ad-hoc information retrieval (IR). Despite their success, dense retrievers are expensive to serve across practical use cases. For use cases requiring to search from millions of documents, the dense index becomes bulky and requires high memory usage for storing the index. More recently, learning-to-hash (LTH) techniques, for e.g., BPR and JPQ, produce binary document vectors, thereby reducing the memory requirement to efficiently store the dense index. LTH techniques are supervised and finetune the retriever using a ranking loss. They outperform their counterparts, i.e., traditional out-of-the-box vector compression techniques such as PCA or PQ. A missing piece from prior work is that existing techniques have been evaluated only in-domain, i.e., on a single dataset such as MS MARCO. In our work, we evaluate LTH and vector compression techniques for improving the downstream zero-shot retrieval accuracy of the TAS-B dense retriever while maintaining efficiency at inference. Our results demonstrate that, unlike prior work, LTH strategies when applied naively can underperform the zero-shot TAS-B dense retriever on average by up to 14% nDCG@10 on the BEIR benchmark. To solve this limitation, in our work, we propose an easy yet effective solution of injecting domain adaptation with existing supervised LTH techniques. We experiment with two well-known unsupervised domain adaptation techniques: GenQ and GPL. Our domain adaptation injection technique can improve the downstream zero-shot retrieval effectiveness for both BPR and JPQ variants of the TAS-B model by on average 11.5% and 8.2% nDCG@10 while both maintaining 32times memory efficiency and 14times and 2times speedup respectively in CPU retrieval latency on BEIR. All our code, models, and data are publicly available at https://github.com/thakur-nandan/income.

For a two-player imperfect-information extensive-form game (IIEFG) with K time steps and a player action space of size U, the game tree complexity is U^{2K}, causing existing IIEFG solvers to struggle with large or infinite (U,K), e.g., differential games with continuous action spaces. To partially address this scalability challenge, we focus on an important class of 2p0s games where the informed player (P1) knows the payoff while the uninformed player (P2) only has a belief over the set of I possible payoffs. Such games encompass a wide range of scenarios in sports, defense, cybersecurity, and finance. We prove that under mild conditions, P1's (resp. P2's) equilibrium strategy at any infostate concentrates on at most I (resp. I+1) action prototypes. When Ill U, this equilibrium structure causes the game tree complexity to collapse to I^K for P1 when P2 plays pure best responses, and (I+1)^K for P2 in a dual game where P1 plays pure best responses. We then show that exploiting this structure in standard learning modes, i.e., model-free multiagent reinforcement learning and model predictive control, is straightforward, leading to significant improvements in learning accuracy and efficiency from SOTA IIEFG solvers. Our demonstration solves a 22-player football game (K=10, U=infty) where the attacking team has to strategically conceal their intention until a critical moment in order to exploit information advantage. Code is available at https://github.com/ghimiremukesh/cams/tree/iclr

Recent years have witnessed increasing interest in extending large language models into agentic systems. While the effectiveness of agents has continued to improve, efficiency, which is crucial for real-world deployment, has often been overlooked. This paper therefore investigates efficiency from three core components of agents: memory, tool learning, and planning, considering costs such as latency, tokens, steps, etc. Aimed at conducting comprehensive research addressing the efficiency of the agentic system itself, we review a broad range of recent approaches that differ in implementation yet frequently converge on shared high-level principles including but not limited to bounding context via compression and management, designing reinforcement learning rewards to minimize tool invocation, and employing controlled search mechanisms to enhance efficiency, which we discuss in detail. Accordingly, we characterize efficiency in two complementary ways: comparing effectiveness under a fixed cost budget, and comparing cost at a comparable level of effectiveness. This trade-off can also be viewed through the Pareto frontier between effectiveness and cost. From this perspective, we also examine efficiency oriented benchmarks by summarizing evaluation protocols for these components and consolidating commonly reported efficiency metrics from both benchmark and methodological studies. Moreover, we discuss the key challenges and future directions, with the goal of providing promising insights.

Reinforcement learning (RL) agents often face challenges in balancing exploration and exploitation, particularly in environments where sparse or dense rewards bias learning. Biological systems, such as human toddlers, naturally navigate this balance by transitioning from free exploration with sparse rewards to goal-directed behavior guided by increasingly dense rewards. Inspired by this natural progression, we investigate the Toddler-Inspired Reward Transition in goal-oriented RL tasks. Our study focuses on transitioning from sparse to potential-based dense (S2D) rewards while preserving optimal strategies. Through experiments on dynamic robotic arm manipulation and egocentric 3D navigation tasks, we demonstrate that effective S2D reward transitions significantly enhance learning performance and sample efficiency. Additionally, using a Cross-Density Visualizer, we show that S2D transitions smooth the policy loss landscape, resulting in wider minima that improve generalization in RL models. In addition, we reinterpret Tolman's maze experiments, underscoring the critical role of early free exploratory learning in the context of S2D rewards.

We study why Tool-Integrated Reasoning (TIR) makes Large Language Models (LLMs) more capable. While LLMs integrated with tools like Python code interpreters show great promise, a principled theory explaining why this paradigm is effective has been missing. This work provides the first formal proof that TIR fundamentally expands an LLM's capabilities. We demonstrate that tools enable a strict expansion of the model's empirical and feasible support, breaking the capability ceiling of pure-text models by unlocking problem-solving strategies that are otherwise impossible or intractably verbose. To guide model behavior without compromising training stability and performance, we also introduce Advantage Shaping Policy Optimization (ASPO), a novel algorithm that directly modifies the advantage function to guide the policy behavior. We conduct comprehensive experiments on challenging mathematical benchmarks, leveraging a Python interpreter as the external tool. Our results show that the TIR model decisively outperforms its pure-text counterpart on the pass@k metric. Crucially, this advantage is not confined to computationally-intensive problems but extends to those requiring significant abstract insight. We further identify the emergent cognitive patterns that illustrate how models learn to think with tools. Finally, we report improved tool usage behavior with early code invocation and much more interactive turns with ASPO. Overall, our work provides the first principled explanation for TIR's success, shifting the focus from the mere fact that tools work to why and how they enable more powerful reasoning.

We model Mixture-of-Experts (MoE) token routing as a congestion game with a single effective parameter, the congestion coefficient gamma_eff, that quantifies the balance-quality tradeoff. Tracking gamma_eff across training checkpoints of two open-source MoE models, OLMoE-1B-7B (20 checkpoints, with dense sampling in the surge region) and OpenMoE-8B (6 checkpoints), reveals a three-phase trajectory: a surge phase where the router learns to balance load (gamma_eff: 14 to 36-39, peaking in the step 30K-40K region), a stabilization phase where experts specialize under steady balance (B_0: 2.4 to 2.3, steps 100K-400K), and a relaxation phase where the router trades balance for quality as experts differentiate (gamma_eff: 27 to 9, steps 400K-1.2M). This non-monotone trajectory, invisible to post-hoc analysis of converged models, reveals that early MoE training prioritizes balance while late training prioritizes quality. The theoretical framework is honest about its limits: the single-type equilibrium reduces to temperature-scaled softmax (held-out L1: MFG = 0.199 vs. softmax = 0.200). The game is not a better predictor; it reveals what the temperature means and, critically, how that temperature evolves. We complement the dynamics with an effective congestion decomposition, a multi-type extension that improves load prediction via token clustering on all 16 layers (mean: 30%), scope diagnostics (K/M, epsilon_l), and robustness verification across four independent quality estimators (r >= 0.89). All confidence intervals are from bootstrap resampling over 50 independent text batches.

Multi-objective reinforcement learning (MORL) excels at handling rapidly changing preferences in tasks that involve multiple criteria, even for unseen preferences. However, previous dominating MORL methods typically generate a fixed policy set or preference-conditioned policy through multiple training iterations exclusively for sampled preference vectors, and cannot ensure the efficient discovery of the Pareto front. Furthermore, integrating preferences into the input of policy or value functions presents scalability challenges, in particular as the dimension of the state and preference space grow, which can complicate the learning process and hinder the algorithm's performance on more complex tasks. To address these issues, we propose a two-stage Pareto front discovery algorithm called Constrained MORL (C-MORL), which serves as a seamless bridge between constrained policy optimization and MORL. Concretely, a set of policies is trained in parallel in the initialization stage, with each optimized towards its individual preference over the multiple objectives. Then, to fill the remaining vacancies in the Pareto front, the constrained optimization steps are employed to maximize one objective while constraining the other objectives to exceed a predefined threshold. Empirically, compared to recent advancements in MORL methods, our algorithm achieves more consistent and superior performances in terms of hypervolume, expected utility, and sparsity on both discrete and continuous control tasks, especially with numerous objectives (up to nine objectives in our experiments).

Recent works have successfully demonstrated that sparse deep reinforcement learning agents can be competitive against their dense counterparts. This opens up opportunities for reinforcement learning applications in fields where inference time and memory requirements are cost-sensitive or limited by hardware. Until now, dense-to-sparse methods have relied on hand-designed sparsity schedules that are not synchronized with the agent's learning pace. Crucially, the final sparsity level is chosen as a hyperparameter, which requires careful tuning as setting it too high might lead to poor performances. In this work, we address these shortcomings by crafting a dense-to-sparse algorithm that we name Eau De Q-Network (EauDeQN). To increase sparsity at the agent's learning pace, we consider multiple online networks with different sparsity levels, where each online network is trained from a shared target network. At each target update, the online network with the smallest loss is chosen as the next target network, while the other networks are replaced by a pruned version of the chosen network. We evaluate the proposed approach on the Atari 2600 benchmark and the MuJoCo physics simulator, showing that EauDeQN reaches high sparsity levels while keeping performances high.

Tool-using agents based on Large Language Models (LLMs) excel in tasks such as mathematical reasoning and multi-hop question answering. However, in long trajectories, agents often trigger excessive and low-quality tool calls, increasing latency and degrading inference performance, making managing tool-use behavior challenging. In this work, we conduct entropy-based pilot experiments and observe a strong positive correlation between entropy reduction and high-quality tool calls. Building on this finding, we propose using entropy reduction as a supervisory signal and design two reward strategies to address the differing needs of optimizing tool-use behavior. Sparse outcome rewards provide coarse, trajectory-level guidance to improve efficiency, while dense process rewards offer fine-grained supervision to enhance performance. Experiments across diverse domains show that both reward designs improve tool-use behavior: the former reduces tool calls by 72.07% compared to the average of baselines, while the latter improves performance by 22.27%. These results position entropy reduction as a key mechanism for enhancing tool-use behavior, enabling agents to be more adaptive in real-world applications.

Pseudo-Relevance Feedback (PRF) utilises the relevance signals from the top-k passages from the first round of retrieval to perform a second round of retrieval aiming to improve search effectiveness. A recent research direction has been the study and development of PRF methods for deep language models based rankers, and in particular in the context of dense retrievers. Dense retrievers, compared to more complex neural rankers, provide a trade-off between effectiveness, which is often reduced compared to more complex neural rankers, and query latency, which also is reduced making the retrieval pipeline more efficient. The introduction of PRF methods for dense retrievers has been motivated as an attempt to further improve their effectiveness. In this paper, we reproduce and study a recent method for PRF with dense retrievers, called ANCE-PRF. This method concatenates the query text and that of the top-k feedback passages to form a new query input, which is then encoded into a dense representation using a newly trained query encoder based on the original dense retriever used for the first round of retrieval. While the method can potentially be applied to any of the existing dense retrievers, prior work has studied it only in the context of the ANCE dense retriever. We study the reproducibility of ANCE-PRF in terms of both its training (encoding of the PRF signal) and inference (ranking) steps. We further extend the empirical analysis provided in the original work to investigate the effect of the hyper-parameters that govern the training process and the robustness of the method across these different settings. Finally, we contribute a study of the generalisability of the ANCE-PRF method when dense retrievers other than ANCE are used for the first round of retrieval and for encoding the PRF signal.

While fusing the capacities and advantages of various large language models (LLMs) offers a pathway to construct more powerful and versatile models, a fundamental challenge is to properly select advantageous model during the training. Existing fusion methods primarily focus on the training mode that uses cross entropy on ground truth in a teacher-forcing setup to measure a model's advantage, which may provide limited insight towards model advantage. In this paper, we introduce a novel approach that enhances the fusion process by incorporating both the training and inference modes. Our method evaluates model advantage not only through cross entropy during training but also by considering inference outputs, providing a more comprehensive assessment. To combine the two modes effectively, we introduce ProFuser to progressively transition from inference mode to training mode. To validate ProFuser's effectiveness, we fused three models, including vicuna-7b-v1.5, Llama-2-7b-chat, and mpt-7b-8k-chat, and demonstrated the improved performance in knowledge, reasoning, and safety compared to baseline methods.

Recent developments in representational learning for information retrieval can be organized in a conceptual framework that establishes two pairs of contrasts: sparse vs. dense representations and unsupervised vs. learned representations. Sparse learned representations can further be decomposed into expansion and term weighting components. This framework allows us to understand the relationship between recently proposed techniques such as DPR, ANCE, DeepCT, DeepImpact, and COIL, and furthermore, gaps revealed by our analysis point to "low hanging fruit" in terms of techniques that have yet to be explored. We present a novel technique dubbed "uniCOIL", a simple extension of COIL that achieves to our knowledge the current state-of-the-art in sparse retrieval on the popular MS MARCO passage ranking dataset. Our implementation using the Anserini IR toolkit is built on the Lucene search library and thus fully compatible with standard inverted indexes.

Query expansion plays a crucial role in information retrieval, which aims to bridge the semantic gap between queries and documents to improve matching performance. This paper introduces LLM-QE, a novel approach that leverages Large Language Models (LLMs) to generate document-based query expansions, thereby enhancing dense retrieval models. Unlike traditional methods, LLM-QE designs both rank-based and answer-based rewards and uses these reward models to optimize LLMs to align with the ranking preferences of both retrievers and LLMs, thus mitigating the hallucination of LLMs during query expansion. Our experiments on the zero-shot dense retrieval model, Contriever, demonstrate the effectiveness of LLM-QE, achieving an improvement of over 8%. Furthermore, by incorporating answer-based reward modeling, LLM-QE generates more relevant and precise information related to the documents, rather than simply producing redundant tokens to maximize rank-based rewards. Notably, LLM-QE also improves the training process of dense retrievers, achieving a more than 5% improvement after fine-tuning. All codes are available at https://github.com/NEUIR/LLM-QE.

Steering Large Language Models (LLMs) through activation interventions has emerged as a lightweight alternative to fine-tuning for alignment and personalization. Recent work on Bi-directional Preference Optimization (BiPO) shows that dense steering vectors can be learned directly from preference data in a Direct Preference Optimization (DPO) fashion, enabling control over truthfulness, hallucinations, and safety behaviors. However, dense steering vectors often entangle multiple latent factors due to neuron multi-semanticity, limiting their effectiveness and stability in fine-grained settings such as cultural alignment, where closely related values and behaviors (e.g., among Middle Eastern cultures) must be distinguished. In this paper, we propose Yet another Policy Optimization (YaPO), a reference-free method that learns sparse steering vectors in the latent space of a Sparse Autoencoder (SAE). By optimizing sparse codes, YaPO produces disentangled, interpretable, and efficient steering directions. Empirically, we show that YaPO converges faster, achieves stronger performance, and exhibits improved training stability compared to dense steering baselines. Beyond cultural alignment, YaPO generalizes to a range of alignment-related behaviors, including hallucination, wealth-seeking, jailbreak, and power-seeking. Importantly, YaPO preserves general knowledge, with no measurable degradation on MMLU. Overall, our results show that YaPO provides a general recipe for efficient, stable, and fine-grained alignment of LLMs, with broad applications to controllability and domain adaptation. The associated code and data are publicly availablehttps://github.com/MBZUAI-Paris/YaPO.

The theories of offline and online reinforcement learning, despite having evolved in parallel, have begun to show signs of the possibility for a unification, with algorithms and analysis techniques for one setting often having natural counterparts in the other. However, the notion of density ratio modeling, an emerging paradigm in offline RL, has been largely absent from online RL, perhaps for good reason: the very existence and boundedness of density ratios relies on access to an exploratory dataset with good coverage, but the core challenge in online RL is to collect such a dataset without having one to start. In this work we show -- perhaps surprisingly -- that density ratio-based algorithms have online counterparts. Assuming only the existence of an exploratory distribution with good coverage, a structural condition known as coverability (Xie et al., 2023), we give a new algorithm (GLOW) that uses density ratio realizability and value function realizability to perform sample-efficient online exploration. GLOW addresses unbounded density ratios via careful use of truncation, and combines this with optimism to guide exploration. GLOW is computationally inefficient; we complement it with a more efficient counterpart, HyGLOW, for the Hybrid RL setting (Song et al., 2022) wherein online RL is augmented with additional offline data. HyGLOW is derived as a special case of a more general meta-algorithm that provides a provable black-box reduction from hybrid RL to offline RL, which may be of independent interest.

Training dense LLMs requires enormous amounts of data and centralized compute, which introduces fundamental bottlenecks and ever-growing costs for large models. Several studies aim to reduce this dependency on centralization by reducing the communication overhead of training dense models. Taking this idea of reducing communication overhead to a natural extreme, by training embarrassingly parallelizable ensembles of small independent experts, has been shown to outperform large dense models trained in traditional centralized settings. However, existing studies do not take into account underlying differences amongst data domains and treat them as monolithic, regardless of their underlying complexity, size, or distribution. In this paper, we explore the effects of introducing heterogeneity to these ensembles of domain expert models. Specifically, by allowing models within the ensemble to vary in size--as well as the number of training steps taken depending on the training data's domain--we study the effect heterogeneity has on these ensembles when evaluated against domains included in, and excluded from, the training set. We use the same compute budget to train heterogeneous ensembles and homogeneous baselines for comparison. We show that the heterogeneous ensembles achieve the lowest perplexity scores in 20 out of the 21 data domains used in the evaluation. Our code is available at https://github.com/gensyn-ai/hdee.

In neural Information Retrieval, ongoing research is directed towards improving the first retriever in ranking pipelines. Learning dense embeddings to conduct retrieval using efficient approximate nearest neighbors methods has proven to work well. Meanwhile, there has been a growing interest in learning sparse representations for documents and queries, that could inherit from the desirable properties of bag-of-words models such as the exact matching of terms and the efficiency of inverted indexes. In this work, we present a new first-stage ranker based on explicit sparsity regularization and a log-saturation effect on term weights, leading to highly sparse representations and competitive results with respect to state-of-the-art dense and sparse methods. Our approach is simple, trained end-to-end in a single stage. We also explore the trade-off between effectiveness and efficiency, by controlling the contribution of the sparsity regularization.

Recent sparse detectors with multiple, e.g. six, decoder layers achieve promising performance but much inference time due to complex heads. Previous works have explored using dense priors as initialization and built one-decoder-layer detectors. Although they gain remarkable acceleration, their performance still lags behind their six-decoder-layer counterparts by a large margin. In this work, we aim to bridge this performance gap while retaining fast speed. We find that the architecture discrepancy between dense and sparse detectors leads to feature conflict, hampering the performance of one-decoder-layer detectors. Thus we propose Adaptive Sparse Anchor Generator (ASAG) which predicts dynamic anchors on patches rather than grids in a sparse way so that it alleviates the feature conflict problem. For each image, ASAG dynamically selects which feature maps and which locations to predict, forming a fully adaptive way to generate image-specific anchors. Further, a simple and effective Query Weighting method eases the training instability from adaptiveness. Extensive experiments show that our method outperforms dense-initialized ones and achieves a better speed-accuracy trade-off. The code is available at https://github.com/iSEE-Laboratory/ASAG.

In this paper we study how to effectively exploit implicit feedback in Dense Retrievers (DRs). We consider the specific case in which click data from a historic click log is available as implicit feedback. We then exploit such historic implicit interactions to improve the effectiveness of a DR. A key challenge that we study is the effect that biases in the click signal, such as position bias, have on the DRs. To overcome the problems associated with the presence of such bias, we propose the Counterfactual Rocchio (CoRocchio) algorithm for exploiting implicit feedback in Dense Retrievers. We demonstrate both theoretically and empirically that dense query representations learnt with CoRocchio are unbiased with respect to position bias and lead to higher retrieval effectiveness. We make available the implementations of the proposed methods and the experimental framework, along with all results at https://github.com/ielab/Counterfactual-DR.

Reasoning in large language models is typically trained via supervised fine-tuning (SFT) on expert traces, often framed as knowledge distillation, or reinforcement learning (RL) with outcome-based verifiable rewards. However, SFT focuses on imitation rather than optimisation, while outcome-based RL requires a well-defined reward function. We propose an inverse reinforcement learning (IRL) framework that learns (partially) dense token-level reasoning reward models directly from expert demonstrations. We show that this learned reward serves a dual purpose: (1) as a dense training signal that optimises policies to reason more effectively, outperforming SFT baselines on GSM8K (79\% vs. 56\%) and MedReason (74\% vs. 65\%); and (2) as an inference-time assistant that improves performance via reward-guided reranking, yielding gains of up to 12 percentage points on Llama3 architectures. Furthermore, our dense rewards provide interpretable, step-wise diagnostics that can indicate the location of logical errors. This work proposes a process-level reasoning learning framework from data, bridging the gap between imitation and reinforcement learning for reasoning.

Imposing known physical constraints, such as conservation laws, during neural network training introduces an inductive bias that can improve accuracy, reliability, convergence, and data efficiency for modeling physical dynamics. While such constraints can be softly imposed via loss function penalties, recent advancements in differentiable physics and optimization improve performance by incorporating PDE-constrained optimization as individual layers in neural networks. This enables a stricter adherence to physical constraints. However, imposing hard constraints significantly increases computational and memory costs, especially for complex dynamical systems. This is because it requires solving an optimization problem over a large number of points in a mesh, representing spatial and temporal discretizations, which greatly increases the complexity of the constraint. To address this challenge, we develop a scalable approach to enforce hard physical constraints using Mixture-of-Experts (MoE), which can be used with any neural network architecture. Our approach imposes the constraint over smaller decomposed domains, each of which is solved by an "expert" through differentiable optimization. During training, each expert independently performs a localized backpropagation step by leveraging the implicit function theorem; the independence of each expert allows for parallelization across multiple GPUs. Compared to standard differentiable optimization, our scalable approach achieves greater accuracy in the neural PDE solver setting for predicting the dynamics of challenging non-linear systems. We also improve training stability and require significantly less computation time during both training and inference stages.

Saliency post-hoc explainability methods are important tools for understanding increasingly complex NLP models. While these methods can reflect the model's reasoning, they may not align with human intuition, making the explanations not plausible. In this work, we present a methodology for incorporating rationales, which are text annotations explaining human decisions, into text classification models. This incorporation enhances the plausibility of post-hoc explanations while preserving their faithfulness. Our approach is agnostic to model architectures and explainability methods. We introduce the rationales during model training by augmenting the standard cross-entropy loss with a novel loss function inspired by contrastive learning. By leveraging a multi-objective optimization algorithm, we explore the trade-off between the two loss functions and generate a Pareto-optimal frontier of models that balance performance and plausibility. Through extensive experiments involving diverse models, datasets, and explainability methods, we demonstrate that our approach significantly enhances the quality of model explanations without causing substantial (sometimes negligible) degradation in the original model's performance.

Direct Preference Optimization (DPO) has recently been applied as a post-training technique for text-to-video diffusion models. To obtain training data, annotators are asked to provide preferences between two videos generated from independent noise. However, this approach prohibits fine-grained comparisons, and we point out that it biases the annotators towards low-motion clips as they often contain fewer visual artifacts. In this work, we introduce DenseDPO, a method that addresses these shortcomings by making three contributions. First, we create each video pair for DPO by denoising corrupted copies of a ground truth video. This results in aligned pairs with similar motion structures while differing in local details, effectively neutralizing the motion bias. Second, we leverage the resulting temporal alignment to label preferences on short segments rather than entire clips, yielding a denser and more precise learning signal. With only one-third of the labeled data, DenseDPO greatly improves motion generation over vanilla DPO, while matching it in text alignment, visual quality, and temporal consistency. Finally, we show that DenseDPO unlocks automatic preference annotation using off-the-shelf Vision Language Models (VLMs): GPT accurately predicts segment-level preferences similar to task-specifically fine-tuned video reward models, and DenseDPO trained on these labels achieves performance close to using human labels.

While reinforcement learning (RL) shows promise in training tool-use large language models (LLMs) using verifiable outcome rewards, existing methods largely overlook the potential of explicit reasoning rewards to bolster reasoning and tool utilization. Furthermore, natively combining reasoning and outcome rewards may yield suboptimal performance or conflict with the primary optimization objective. To address this, we propose advantage-weighted policy optimization (AWPO) -- a principled RL framework that effectively integrates explicit reasoning rewards to enhance tool-use capability. AWPO incorporates variance-aware gating and difficulty-aware weighting to adaptively modulate advantages from reasoning signals based on group-relative statistics, alongside a tailored clipping mechanism for stable optimization. Extensive experiments demonstrate that AWPO achieves state-of-the-art performance across standard tool-use benchmarks, significantly outperforming strong baselines and leading closed-source models in challenging multi-turn scenarios. Notably, with exceptional parameter efficiency, our 4B model surpasses Grok-4 by 16.0 percent in multi-turn accuracy while preserving generalization capability on the out-of-distribution MMLU-Pro benchmark.

Information Retrieval using dense low-dimensional representations recently became popular and showed out-performance to traditional sparse-representations like BM25. However, no previous work investigated how dense representations perform with large index sizes. We show theoretically and empirically that the performance for dense representations decreases quicker than sparse representations for increasing index sizes. In extreme cases, this can even lead to a tipping point where at a certain index size sparse representations outperform dense representations. We show that this behavior is tightly connected to the number of dimensions of the representations: The lower the dimension, the higher the chance for false positives, i.e. returning irrelevant documents.

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

Reinforcement Learning (RL) for Large Language Models (LLMs) often suffers from training collapse in long-horizon tasks due to exploding gradient variance. To mitigate this, a baseline is commonly introduced for advantage computation; however, traditional value models remain difficult to optimize, and standard group-based baselines overlook sequence heterogeneity. Although classic optimal baseline theory can achieve global variance reduction, it neglects token heterogeneity and requires prohibitive gradient-based computation. In this work, we derive the Optimal Token Baseline (OTB) from first principles, proving that gradient updates should be weighted inversely to their cumulative gradient norm. To ensure efficiency, we propose the Logit-Gradient Proxy that approximates the gradient norm using only forward-pass probabilities. Our method achieves training stability and matches the performance of large group sizes (N=32) with only N=4, reducing token consumption by over 65% across single-turn and tool-integrated reasoning tasks.

Automatically synthesizing dense rewards from natural language descriptions is a promising paradigm in reinforcement learning (RL), with applications to sparse reward problems, open-ended exploration, and hierarchical skill design. Recent works have made promising steps by exploiting the prior knowledge of large language models (LLMs). However, these approaches suffer from important limitations: they are either not scalable to problems requiring billions of environment samples, due to requiring LLM annotations for each observation, or they require a diverse offline dataset, which may not exist or be impossible to collect. In this work, we address these limitations through a combination of algorithmic and systems-level contributions. We propose \oni, a distributed architecture that simultaneously learns an RL policy and an intrinsic reward function using LLM feedback. Our approach annotates the agent's collected experience via an asynchronous LLM server, which is then distilled into an intrinsic reward model. We explore a range of algorithmic choices for reward modeling with varying complexity, including hashing, classification, and ranking models. By studying their relative tradeoffs, we shed light on questions regarding intrinsic reward design for sparse reward problems. Our approach achieves state-of-the-art performance across a range of challenging, sparse reward tasks from the NetHack Learning Environment in a simple unified process, solely using the agent's gathered experience, without requiring external datasets. We make our code available at https://github.com/facebookresearch/oni.

This work introduces MultiTRON, an approach that adapts Pareto front approximation techniques to multi-objective session-based recommender systems using a transformer neural network. Our approach optimizes trade-offs between key metrics such as click-through and conversion rates by training on sampled preference vectors. A significant advantage is that after training, a single model can access the entire Pareto front, allowing it to be tailored to meet the specific requirements of different stakeholders by adjusting an additional input vector that weights the objectives. We validate the model's performance through extensive offline and online evaluation. For broader application and research, the source code is made available at https://github.com/otto-de/MultiTRON. The results confirm the model's ability to manage multiple recommendation objectives effectively, offering a flexible tool for diverse business needs.

Text retrieval is a long-standing research topic on information seeking, where a system is required to return relevant information resources to user's queries in natural language. From classic retrieval methods to learning-based ranking functions, the underlying retrieval models have been continually evolved with the ever-lasting technical innovation. To design effective retrieval models, a key point lies in how to learn the text representation and model the relevance matching. The recent success of pretrained language models (PLMs) sheds light on developing more capable text retrieval approaches by leveraging the excellent modeling capacity of PLMs. With powerful PLMs, we can effectively learn the representations of queries and texts in the latent representation space, and further construct the semantic matching function between the dense vectors for relevance modeling. Such a retrieval approach is referred to as dense retrieval, since it employs dense vectors (a.k.a., embeddings) to represent the texts. Considering the rapid progress on dense retrieval, in this survey, we systematically review the recent advances on PLM-based dense retrieval. Different from previous surveys on dense retrieval, we take a new perspective to organize the related work by four major aspects, including architecture, training, indexing and integration, and summarize the mainstream techniques for each aspect. We thoroughly survey the literature, and include 300+ related reference papers on dense retrieval. To support our survey, we create a website for providing useful resources, and release a code repertory and toolkit for implementing dense retrieval models. This survey aims to provide a comprehensive, practical reference focused on the major progress for dense text retrieval.

Reinforcement Learning from Human Feedback (RLHF) has emerged as a dominant approach for aligning LLM outputs with human preferences. Inspired by the success of RLHF, we study the performance of multiple algorithms that learn from feedback (Expert Iteration, Proximal Policy Optimization (PPO), Return-Conditioned RL) on improving LLM reasoning capabilities. We investigate both sparse and dense rewards provided to the LLM both heuristically and via a learned reward model. We additionally start from multiple model sizes and initializations both with and without supervised fine-tuning (SFT) data. Overall, we find all algorithms perform comparably, with Expert Iteration performing best in most cases. Surprisingly, we find the sample complexity of Expert Iteration is similar to that of PPO, requiring at most on the order of 10^6 samples to converge from a pretrained checkpoint. We investigate why this is the case, concluding that during RL training models fail to explore significantly beyond solutions already produced by SFT models. Additionally, we discuss a trade off between maj@1 and pass@96 metric performance during SFT training and how conversely RL training improves both simultaneously. We then conclude by discussing the implications of our findings for RLHF and the future role of RL in LLM fine-tuning.

Analyzing large-scale text corpora is a core challenge in machine learning, crucial for tasks like identifying undesirable model behaviors or biases in training data. Current methods often rely on costly LLM-based techniques (e.g. annotating dataset differences) or dense embedding models (e.g. for clustering), which lack control over the properties of interest. We propose using sparse autoencoders (SAEs) to create SAE embeddings: representations whose dimensions map to interpretable concepts. Through four data analysis tasks, we show that SAE embeddings are more cost-effective and reliable than LLMs and more controllable than dense embeddings. Using the large hypothesis space of SAEs, we can uncover insights such as (1) semantic differences between datasets and (2) unexpected concept correlations in documents. For instance, by comparing model responses, we find that Grok-4 clarifies ambiguities more often than nine other frontier models. Relative to LLMs, SAE embeddings uncover bigger differences at 2-8x lower cost and identify biases more reliably. Additionally, SAE embeddings are controllable: by filtering concepts, we can (3) cluster documents along axes of interest and (4) outperform dense embeddings on property-based retrieval. Using SAE embeddings, we study model behavior with two case studies: investigating how OpenAI model behavior has changed over time and finding "trigger" phrases learned by Tulu-3 (Lambert et al., 2024) from its training data. These results position SAEs as a versatile tool for unstructured data analysis and highlight the neglected importance of interpreting models through their data.

Multi-objective reinforcement learning (MORL) seeks to learn policies that balance multiple, often conflicting objectives. Although a single preference-conditioned policy is the most flexible and scalable solution, existing approaches remain brittle in practice, frequently failing to recover complete Pareto fronts. We show that this failure stems from two structural issues in current methods: destructive gradient interference caused by premature scalarization and representational collapse across the preference space. We introduce D^3PO, a PPO-based framework that reorganizes multi-objective policy optimization to address these issues directly. D^3PO preserves per-objective learning signals through a decomposed optimization pipeline and integrates preferences only after stabilization, enabling reliable credit assignment. In addition, a scaled diversity regularizer enforces sensitivity of policy behavior to preference changes, preventing collapse. Across standard MORL benchmarks, including high-dimensional and many-objective control tasks, D^3PO consistently discovers broader and higher-quality Pareto fronts than prior single- and multi-policy methods, matching or exceeding state-of-the-art hypervolume and expected utility while using a single deployable policy.

As machine learning tasks continue to evolve, the trend has been to gather larger datasets and train increasingly larger models. While this has led to advancements in accuracy, it has also escalated computational costs to unsustainable levels. Addressing this, our work aims to strike a delicate balance between computational efficiency and model accuracy, a persisting challenge in the field. We introduce a novel method that employs core subset selection for reweighting, effectively optimizing both computational time and model performance. By focusing on a strategically selected coreset, our approach offers a robust representation, as it efficiently minimizes the influence of outliers. The re-calibrated weights are then mapped back to and propagated across the entire dataset. Our experimental results substantiate the effectiveness of this approach, underscoring its potential as a scalable and precise solution for model training.

We seek to understand fundamental tradeoffs between the accuracy of prior information that a learner has on a given problem and its learning performance. We introduce the notion of prioritized risk, which differs from traditional notions of minimax and Bayes risk by allowing us to study such fundamental tradeoffs in settings where reality does not necessarily conform to the learner's prior. We present a general reduction-based approach for extending classical minimax lower-bound techniques in order to lower bound the prioritized risk for statistical estimation problems. We also introduce a novel generalization of Fano's inequality (which may be of independent interest) for lower bounding the prioritized risk in more general settings involving unbounded losses. We illustrate the ability of our framework to provide insights into tradeoffs between prior information and learning performance for problems in estimation, regression, and reinforcement learning.

The performance of the reward model (RM) is a critical factor in improving the effectiveness of the large language model (LLM) during alignment fine-tuning. There remain two challenges in RM training: 1) training the same RM using various categories of data may cause its generalization performance to suffer from multi-task disturbance, and 2) the human annotation consistency rate is generally only 60% to 75%, causing training data to contain a lot of noise. To tackle these two challenges, we introduced the idea of Mixture-of-Experts (MoE) into the field of RM for the first time. We propose the Double-Layer MoE RM (DMoERM). The outer layer MoE is a sparse model. After classifying an input into task categories, we route it to the corresponding inner layer task-specific model. The inner layer MoE is a dense model. We decompose the specific task into multiple capability dimensions and individually fine-tune a LoRA expert on each one. Their outputs are then synthesized by an MLP to compute the final rewards. To minimize costs, we call a public LLM API to obtain the capability preference labels. The validation on manually labeled datasets confirms that our model attains superior consistency with human preference and outstrips advanced generative approaches. Meanwhile, through BoN sampling and RL experiments, we demonstrate that our model outperforms state-of-the-art ensemble methods of RM and mitigates the overoptimization problem. Our code and dataset are available at: https://github.com/quanshr/DMoERM-v1.

Multi-agent systems play a central role in area coverage tasks across search-and-rescue, environmental monitoring, and precision agriculture. Achieving non-uniform coverage, where spatial priorities vary across the domain, requires coordinating agents while respecting dynamic and communication constraints. Density-driven approaches can distribute agents according to a prescribed reference density, but existing methods do not ensure connectivity. This limitation often leads to communication loss, reduced coordination, and degraded coverage performance. This letter introduces a connectivity-preserving extension of the Density-Driven Optimal Control (D2OC) framework. The coverage objective, defined using the Wasserstein distance between the agent distribution and the reference density, admits a convex quadratic program formulation. Communication constraints are incorporated through a smooth connectivity penalty, which maintains strict convexity, supports distributed implementation, and preserves inter-agent communication without imposing rigid formations. Simulation studies show that the proposed method consistently maintains connectivity, improves convergence speed, and enhances non-uniform coverage quality compared with density-driven schemes that do not incorporate explicit connectivity considerations.

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.

Large foundation models have become central to modern machine learning, with performance scaling predictably with model size and data. However, training and deploying such models incur substantial computational and memory costs, motivating the development of low-precision training techniques. Recent work has demonstrated that 4-bit floating-point (FP4) formats--such as MXFP4 and NVFP4--can be successfully applied to linear GEMM operations in large language models (LLMs), achieving up to 4x improvements in compute throughput and memory efficiency compared to higher-precision baselines. In this work, we investigate the recently proposed HiFloat4 FP4 format for Huawei Ascend NPUs and systematically compare it with MXFP4 in large-scale training settings. All experiments are conducted on Ascend NPU clusters, with linear and expert GEMM operations performed entirely in FP4 precision. We evaluate both dense architectures (e.g., Pangu and LLaMA-style models) and mixture-of-experts (MoE) models, where both standard linear layers and expert-specific GEMMs operate in FP4. Furthermore, we explore stabilization techniques tailored to FP4 training that significantly reduce numerical degradation, maintaining relative error within 1% of full-precision baselines while preserving the efficiency benefits of 4-bit computation. Our results provide a comprehensive empirical study of FP4 training on NPUs and highlight the practical trade-offs between FP4 formats in large-scale dense and MoE models.

We introduce a new balanced assignment of experts (BASE) layer for large language models that greatly simplifies existing high capacity sparse layers. Sparse layers can dramatically improve the efficiency of training and inference by routing each token to specialized expert modules that contain only a small fraction of the model parameters. However, it can be difficult to learn balanced routing functions that make full use of the available experts; existing approaches typically use routing heuristics or auxiliary expert-balancing loss functions. In contrast, we formulate token-to-expert allocation as a linear assignment problem, allowing an optimal assignment in which each expert receives an equal number of tokens. This optimal assignment scheme improves efficiency by guaranteeing balanced compute loads, and also simplifies training by not requiring any new hyperparameters or auxiliary losses. Code is publicly released at https://github.com/pytorch/fairseq/