Daily Papers

Recent Large Reasoning Models (LRMs) have achieved remarkable performance in solving complex problems via supervised fine-tuning (SFT) and reinforcement learning (RL). Although existing RL algorithms significantly enhance model accuracy, they still suffer from excessively lengthy responses and overthinking issues, resulting in increased inference latency and computational consumption, especially for simple tasks that require minimal reasoning. To address this, we propose a novel RL framework, DEPO, to reduce inefficient reasoning for models. Our method mainly consists of three core components: (1) an innovative advantage decoupled algorithm to guide model reduction of inefficient tokens; (2) a difficulty-aware length penalty to lower the overall length of model responses; (3) an advantage clipping method to prevent bias in policy optimization. In our experiments, applied to DeepSeek-Distill-Qwen-7B and DeepSeek-Distill-Qwen-1.5B as base models, DEPO achieves a significant reduction in sequence length by 39% and reduces excessive reasoning paths in inefficient tokens, while outperforming the base model in overall accuracy.

Research on applications of Reinforcement Learning (RL) to Large Language Models (LLMs) has mostly been focused on single-turn problems, such as mathematical reasoning or single-shot code generation. While these problems can be viewed as token-level multi-turn MDPs, this view corresponds to a degenerate case of multi-turn interaction where the environment provides no feedback. This contrasts with many real-world domains, such as software engineering (SWE), which require rich multi-turn interactions with a stateful environment that responds to each action with a non-trivial observation. To bridge this gap, we demonstrate the successful application of RL to this general regime. Using a modified Decoupled Advantage Policy Optimization (DAPO) algorithm, we train an agent based on Qwen2.5-72B-Instruct to solve real-world software engineering tasks. Our approach increases the agent's success rate on the SWE-bench Verified benchmark from a 20% rejection fine-tuned baseline to 39%, without relying on any teacher models. On SWE-rebench, our agent matches or outperforms leading open-weight models such as DeepSeek-V3-0324 and Qwen3-235B-A22B using an identical scaffolding, offering a viable path toward building more capable autonomous agents for complex real-world problems based on open models.

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.

Parallel test-time scaling typically trains separate generation and verification models, incurring high training and inference costs. We propose Advantage Decoupled Preference Optimization (ADPO), a unified reinforcement learning framework that jointly learns answer generation and self-verification within a single policy. ADPO introduces two innovations: a preference verification reward improving verification capability and a decoupled optimization mechanism enabling synergistic optimization of generation and verification. Specifically, the preference verification reward computes mean verification scores from positive and negative samples as decision thresholds, providing positive feedback when prediction correctness aligns with answer correctness. Meanwhile, the advantage decoupled optimization computes separate advantages for generation and verification, applies token masks to isolate gradients, and combines masked GRPO objectives, preserving generation quality while calibrating verification scores. ADPO achieves up to +34.1% higher verification AUC and -53.5% lower inference time, with significant gains of +2.8%/+1.4% accuracy on MathVista/MMMU, +1.9 cIoU on ReasonSeg, and +1.7%/+1.0% step success rate on AndroidControl/GUI Odyssey.

One of the challenges in online reinforcement learning (RL) is that the agent needs to trade off the exploration of the environment and the exploitation of the samples to optimize its behavior. Whether we optimize for regret, sample complexity, state-space coverage or model estimation, we need to strike a different exploration-exploitation trade-off. In this paper, we propose to tackle the exploration-exploitation problem following a decoupled approach composed of: 1) An "objective-specific" algorithm that (adaptively) prescribes how many samples to collect at which states, as if it has access to a generative model (i.e., a simulator of the environment); 2) An "objective-agnostic" sample collection exploration strategy responsible for generating the prescribed samples as fast as possible. Building on recent methods for exploration in the stochastic shortest path problem, we first provide an algorithm that, given as input the number of samples b(s,a) needed in each state-action pair, requires O(B D + D^{3/2} S^2 A) time steps to collect the B=sum_{s,a} b(s,a) desired samples, in any unknown communicating MDP with S states, A actions and diameter D. Then we show how this general-purpose exploration algorithm can be paired with "objective-specific" strategies that prescribe the sample requirements to tackle a variety of settings -- e.g., model estimation, sparse reward discovery, goal-free cost-free exploration in communicating MDPs -- for which we obtain improved or novel sample complexity guarantees.

Decoupled loss has been a successful reinforcement learning (RL) algorithm to deal with the high data staleness under the asynchronous RL setting. Decoupled loss improves coupled-loss style of algorithms' (e.g., PPO, GRPO) learning stability by introducing a proximal policy to decouple the off-policy corrections (importance weight) from the controlling policy updates (trust region). However, the proximal policy requires an extra forward pass through the network at each training step, creating a computational bottleneck for large language models. We observe that since the proximal policy only serves as a trust region anchor between the behavior and target policies, we can approximate it through simple interpolation without explicit computation. We call this approach A-3PO (APproximated Proximal Policy Optimization). A-3PO eliminates this overhead, reducing training time by 18% while maintaining comparable performance. Code & off-the-shelf example are available at: https://github.com/inclusionAI/AReaL/blob/main/docs/algorithms/prox_approx.md

Decoupled weight decay, solely responsible for the performance advantage of AdamW over Adam, has long been set to proportional to learning rate γ without questioning. Some researchers have recently challenged such assumption and argued that decoupled weight decay should be set propto γ^2 instead based on orthogonality arguments at steady state. To the contrary, we find that eliminating the contribution of the perpendicular component of the update to the weight norm leads to little change to the training dynamics. Instead, we derive that decoupled weight decay propto γ^2 results in stable weight norm based on the simple assumption that updates become independent of the weights at steady state, regardless of the nature of the optimizer. Based on the same assumption, we derive and empirically verify that the Total Update Contribution (TUC) of a minibatch under the Scion optimizer is better characterized by the momentum-dependent effective learning rate whose optimal value transfers and we show that decoupled weight decay propto γ^2 leads to stable weight and gradient norms and allows us to better control the training dynamics and improve the model performance.

Quantization emerges as one of the most promising compression technologies for deploying efficient large models for various real time application in recent years. Considering that the storage and IO of weights take up the vast majority of the overhead inside a large model, weight only quantization can lead to large gains. However, existing quantization schemes suffer from significant accuracy degradation at very low bits, or require some additional computational overhead when deployed, making it difficult to be applied to large-scale applications in industry. In this paper, we propose decoupleQ, achieving a substantial increase in model accuracy, especially at very low bits. decoupleQ abandons the traditional heuristic quantization paradigm and decouples the model parameters into integer and floating-point parts, thus transforming the quantization problem into a traditional mathematical optimization problem with constraints, which is then solved alternatively by off-the-shelf optimization methods. Quantization via decoupleQ is linear and uniform, making it hardware-friendlier than non-uniform counterpart, and enabling the idea to be migrated to high-bit quantization to enhance its robustness. Our method has achieved well on-line accuracy near fp16/bf16 on the 2-bit quantization of large speech models in ByteDance. The code is available at https://github.com/bytedance/decoupleQ

Post-training of large language models routinely interleaves supervised fine-tuning (SFT) with reinforcement learning (RL). These two methods have different objectives: SFT minimizes the cross-entropy loss between model outputs and expert responses, while RL maximizes reward signals derived from human preferences or rule-based verifiers. Modern reasoning models have widely adopted the practice of alternating SFT and RL training. However, there is no theoretical account of whether they can be decoupled. We prove that decoupling is impossible in either order: (1) SFT-then-RL coupling: RL increases SFT loss under SFT optimality and (2) RL-then-SFT coupling: SFT lowers the reward achieved by RL. Experiments on Qwen3-0.6B confirm the predicted degradation, verifying that SFT and RL cannot be separated without loss of prior performance in the post-training

We identity a by-far-unrecognized problem of Adam-style optimizers which results from unnecessary coupling between momentum and adaptivity. The coupling leads to instability and divergence when the momentum and adaptivity parameters are mismatched. In this work, we propose a method, Laprop, which decouples momentum and adaptivity in the Adam-style methods. We show that the decoupling leads to greater flexibility in the hyperparameters and allows for a straightforward interpolation between the signed gradient methods and the adaptive gradient methods. We experimentally show that Laprop has consistently improved speed and stability over Adam on a variety of tasks. We also bound the regret of Laprop on a convex problem and show that our bound differs from that of Adam by a key factor, which demonstrates its advantage.

We study multi-agent reinforcement learning (MARL) for the general-sum Markov Games (MGs) under the general function approximation. In order to find the minimum assumption for sample-efficient learning, we introduce a novel complexity measure called the Multi-Agent Decoupling Coefficient (MADC) for general-sum MGs. Using this measure, we propose the first unified algorithmic framework that ensures sample efficiency in learning Nash Equilibrium, Coarse Correlated Equilibrium, and Correlated Equilibrium for both model-based and model-free MARL problems with low MADC. We also show that our algorithm provides comparable sublinear regret to the existing works. Moreover, our algorithm combines an equilibrium-solving oracle with a single objective optimization subprocedure that solves for the regularized payoff of each deterministic joint policy, which avoids solving constrained optimization problems within data-dependent constraints (Jin et al. 2020; Wang et al. 2023) or executing sampling procedures with complex multi-objective optimization problems (Foster et al. 2023), thus being more amenable to empirical implementation.

L_2 regularization and weight decay regularization are equivalent for standard stochastic gradient descent (when rescaled by the learning rate), but as we demonstrate this is not the case for adaptive gradient algorithms, such as Adam. While common implementations of these algorithms employ L_2 regularization (often calling it "weight decay" in what may be misleading due to the inequivalence we expose), we propose a simple modification to recover the original formulation of weight decay regularization by decoupling the weight decay from the optimization steps taken w.r.t. the loss function. We provide empirical evidence that our proposed modification (i) decouples the optimal choice of weight decay factor from the setting of the learning rate for both standard SGD and Adam and (ii) substantially improves Adam's generalization performance, allowing it to compete with SGD with momentum on image classification datasets (on which it was previously typically outperformed by the latter). Our proposed decoupled weight decay has already been adopted by many researchers, and the community has implemented it in TensorFlow and PyTorch; the complete source code for our experiments is available at https://github.com/loshchil/AdamW-and-SGDW

Is the standard weight decay in AdamW truly optimal? Although AdamW decouples weight decay from adaptive gradient scaling, a fundamental conflict remains: the Radial Tug-of-War. In deep learning, gradients tend to increase parameter norms to expand effective capacity while steering directions to learn features, whereas weight decay indiscriminately suppresses norm growth. This push--pull interaction induces radial oscillations, injecting noise into Adam's second-moment estimates and potentially degrading delicate tangential feature learning. We argue that magnitude and direction play distinct roles and should be decoupled in optimizer dynamics. We propose Orthogonal Dynamics Decoupling and instantiate it as AdamO: an SGD-style update handles the one-dimensional norm control, while Adam's adaptive preconditioning is confined to the tangential subspace. AdamO further incorporates curvature-adaptive radial step sizing and architecture-aware rules and projections for scale-invariant layers and low-dimensional parameters. Experiments on vision and language tasks show that AdamO improves generalization and stability over AdamW without introducing additional complex constraints.

Temporal credit assignment in reinforcement learning is often approached by introducing value estimates at multiple discount factors. A natural next step is to let the actor dynamically route among these temporal heads, using either differentiable attention or heuristic uncertainty weights. This paper argues that such routing can create a numerical shortcut rather than a reliable temporal abstraction. We study this issue in a controlled PPO setting on LunarLander-v2, using the environment as a visual sandbox for diagnosing failure modes. First, we formalize Surrogate Objective Hacking: a differentiable softmax router exposed to the PPO surrogate receives a direct gradient toward advantage heads that are numerically favorable for the current update, even when this routing change does not correspond to improved physical control. Because unnormalized advantages at different discount factors have different effective scales, this creates a scale-discrepancy vulnerability. Second, we identify the Paradox of Temporal Uncertainty in gradient-free error-based routing: short-horizon heads can receive the largest routing share because their prediction targets are easier, even when they are less aligned with delayed task success. As a structural response, we study Target Decoupling: the critic may retain multi-timescale auxiliary heads, but the actor is updated only with the long-horizon advantage. Target Decoupling is not presented as a broad performance booster; in this run set it removes the exploitable actor-side routing pathway and improves the observed worst-seed return. Code is available at https://github.com/ben-dlwlrma/Representation-Over-Routing.

We present a class of novel optimisers for training neural networks that makes use of the Riemannian metric naturally induced when the loss landscape is embedded in higher-dimensional space. This is the same metric that underlies common visualisations of loss landscapes. By taking this geometric perspective literally and using the induced metric, we develop a new optimiser and compare it to existing methods, namely: SGD, Adam, AdamW, and Muon, across a range of tasks and architectures. Empirically, we conclude that this new class of optimisers is highly effective in low dimensional examples, and provides slight improvement over state-of-the-art methods for training neural networks. These new optimisers have theoretically desirable properties. In particular, the effective learning rate is automatically decreased in regions of high curvature acting as a smoothed out form of gradient clipping. Similarly, one variant of these optimisers can also be viewed as inducing an effective scheduled learning rate and decoupled weight decay is the natural choice from our geometric perspective. The basic method can be used to modify any existing preconditioning method. The new optimiser has a computational complexity comparable to that of Adam.

With more open-source models available for diverse tasks, model merging has gained attention by combining models into one, reducing training, storage, and inference costs. Current research mainly focuses on model merging for full fine-tuning, overlooking the popular LoRA. However, our empirical analysis reveals that: a) existing merging methods designed for full fine-tuning perform poorly on LoRA; b) LoRA modules show much larger parameter magnitude variance than full fine-tuned weights; c) greater parameter magnitude variance correlates with worse merging performance. Considering that large magnitude variances cause deviations in the distribution of the merged parameters, resulting in information loss and performance degradation, we propose a Decoupled and Orthogonal merging approach(DO-Merging). By separating parameters into magnitude and direction components and merging them independently, we reduce the impact of magnitude differences on the directional alignment of the merged models, thereby preserving task information. Furthermore, we introduce a data-free, layer-wise gradient descent method with orthogonal constraints to mitigate interference during the merging of direction components. We provide theoretical guarantees for both the decoupling and orthogonal components. And we validate through extensive experiments across vision, language, and multi-modal domains that our proposed DO-Merging can achieve significantly higher performance than existing merging methods at a minimal cost. Notably, each component can be flexibly integrated with existing methods, offering near free-lunch improvements across tasks.

This work breaks through the Base-New Tradeoff (BNT)dilemma in prompt tuning, i.e., the better the tuned model generalizes to the base (or target) task, the worse it generalizes to new tasks, and vice versa. Specifically, through an in-depth analysis of the learned features of the base and new tasks, we observe that the BNT stems from a channel bias issue, i.e., the vast majority of feature channels are occupied by base-specific knowledge, resulting in the collapse of taskshared knowledge important to new tasks. To address this, we propose the Decoupled Prompt Tuning (DePT) framework, which decouples base-specific knowledge from feature channels into an isolated feature space during prompt tuning, so as to maximally preserve task-shared knowledge in the original feature space for achieving better zero-shot generalization on new tasks. Importantly, our DePT is orthogonal to existing prompt tuning methods, hence it can improve all of them. Extensive experiments on 11 datasets show the strong flexibility and effectiveness of DePT. Our code and pretrained models are available at https://github.com/Koorye/DePT.

Diffusion transformers have demonstrated remarkable generation quality, albeit requiring longer training iterations and numerous inference steps. In each denoising step, diffusion transformers encode the noisy inputs to extract the lower-frequency semantic component and then decode the higher frequency with identical modules. This scheme creates an inherent optimization dilemma: encoding low-frequency semantics necessitates reducing high-frequency components, creating tension between semantic encoding and high-frequency decoding. To resolve this challenge, we propose a new \color{ddtD}ecoupled \color{ddtD}iffusion \color{ddtT}ransformer~(\color{ddtDDT}), with a decoupled design of a dedicated condition encoder for semantic extraction alongside a specialized velocity decoder. Our experiments reveal that a more substantial encoder yields performance improvements as model size increases. For ImageNet 256times256, Our DDT-XL/2 achieves a new state-of-the-art performance of {1.31 FID}~(nearly 4times faster training convergence compared to previous diffusion transformers). For ImageNet 512times512, Our DDT-XL/2 achieves a new state-of-the-art FID of 1.28. Additionally, as a beneficial by-product, our decoupled architecture enhances inference speed by enabling the sharing self-condition between adjacent denoising steps. To minimize performance degradation, we propose a novel statistical dynamic programming approach to identify optimal sharing strategies.

Interactive multimodal agents must convert raw visual observations into coherent sequences of language-conditioned actions -- a capability that current vision-language models (VLMs) still lack. Earlier reinforcement-learning (RL) efforts could, in principle, endow VLMs with such skills, but they have seldom tested whether the learned behaviours generalize beyond their training simulators, and they depend either on brittle hyperparameter tuning or on dense-reward environments with low state variability. We introduce Vision-Language Decoupled Actor-Critic (VL-DAC), a lightweight, hyperparameter-free RL algorithm. VL-DAC applies PPO updates to action tokens while learning value only at the environment-step level: an arrangement, to our knowledge, not previously explored for large VLMs or LLMs. This simple decoupling removes unstable weighting terms and yields faster, more reliable convergence. Training a single VLM with VL-DAC in one inexpensive simulator at a time (MiniWorld, Gym-Cards, ALFWorld, or WebShop) already produces policies that generalize widely: +50\% relative on BALROG (game-centric agentic control), +5\% relative on the hardest part of VSI-Bench (spatial planning), and +2\% on VisualWebBench (web navigation), all without degrading general image understanding accuracy. These results provide the first evidence that a simple RL algorithm can train VLMs entirely in cheap synthetic worlds while delivering measurable gains on real-image agentic, spatial-reasoning, and web-navigation benchmarks.

Training large neural networks typically requires sharing gradients between accelerators through specialized high-speed interconnects. Drawing from the signal processing principles of frequency decomposition and energy compaction, we demonstrate that synchronizing full optimizer states and model parameters during training is unnecessary. By decoupling momentum updates and allowing controlled divergence in optimizer states across accelerators, we achieve improved convergence compared to state-of-the-art optimizers. We introduce {De}coupled {Mo}mentum (DeMo), a fused optimizer and data parallel algorithm that reduces inter-accelerator communication requirements by several orders of magnitude. This enables training of large neural networks even with limited network bandwidth and heterogeneous hardware. Our method is topology-agnostic and architecture-independent and supports scalable clock-synchronous distributed training with negligible compute and memory overhead. Empirical results show that models trained with DeMo match or exceed the performance of equivalent models trained with AdamW, while eliminating the need for high-speed interconnects when pre-training large scale foundation models. An open source reference PyTorch implementation is published on GitHub at https://github.com/bloc97/DeMo

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

Model fairness is an essential element for Trustworthy AI. While many techniques for model fairness have been proposed, most of them assume that the training and deployment data distributions are identical, which is often not true in practice. In particular, when the bias between labels and sensitive groups changes, the fairness of the trained model is directly influenced and can worsen. We make two contributions for solving this problem. First, we analytically show that existing in-processing fair algorithms have fundamental limits in accuracy and group fairness. We introduce the notion of correlation shifts, which can explicitly capture the change of the above bias. Second, we propose a novel pre-processing step that samples the input data to reduce correlation shifts and thus enables the in-processing approaches to overcome their limitations. We formulate an optimization problem for adjusting the data ratio among labels and sensitive groups to reflect the shifted correlation. A key benefit of our approach lies in decoupling the roles of pre- and in-processing approaches: correlation adjustment via pre-processing and unfairness mitigation on the processed data via in-processing. Experiments show that our framework effectively improves existing in-processing fair algorithms w.r.t. accuracy and fairness, both on synthetic and real datasets.

Diffusion models have shown strong competitiveness in offline reinforcement learning tasks by formulating decision-making as sequential generation. However, the practicality of these methods is limited due to the lengthy inference processes they require. In this paper, we address this problem by decomposing the sampling process of diffusion models into two decoupled subprocesses: 1) generating a feasible trajectory, which is a time-consuming process, and 2) optimizing the trajectory. With this decomposition approach, we are able to partially separate efficiency and quality factors, enabling us to simultaneously gain efficiency advantages and ensure quality assurance. We propose the Trajectory Diffuser, which utilizes a faster autoregressive model to handle the generation of feasible trajectories while retaining the trajectory optimization process of diffusion models. This allows us to achieve more efficient planning without sacrificing capability. To evaluate the effectiveness and efficiency of the Trajectory Diffuser, we conduct experiments on the D4RL benchmarks. The results demonstrate that our method achieves it 3-it 10 times faster inference speed compared to previous sequence modeling methods, while also outperforming them in terms of overall performance. https://github.com/RenMing-Huang/TrajectoryDiffuser Keywords: Reinforcement Learning and Efficient Planning and Diffusion Model

As the use of artificial intelligence rapidly increases, the development of trustworthy artificial intelligence has become important. However, recent studies have shown that deep neural networks are susceptible to learn spurious correlations present in datasets. To improve the reliability, we propose a simple yet effective framework called controllable feature whitening. We quantify the linear correlation between the target and bias features by the covariance matrix, and eliminate it through the whitening module. Our results systemically demonstrate that removing the linear correlations between features fed into the last linear classifier significantly mitigates the bias, while avoiding the need to model intractable higher-order dependencies. A particular advantage of the proposed method is that it does not require regularization terms or adversarial learning, which often leads to unstable optimization in practice. Furthermore, we show that two fairness criteria, demographic parity and equalized odds, can be effectively handled by whitening with the re-weighted covariance matrix. Consequently, our method controls the trade-off between the utility and fairness of algorithms by adjusting the weighting coefficient. Finally, we validate that our method outperforms existing approaches on four benchmark datasets: Corrupted CIFAR-10, Biased FFHQ, WaterBirds, and Celeb-A.

The Base-New Trade-off (BNT) problem universally exists during the optimization of CLIP-based prompt tuning, where continuous fine-tuning on base (target) classes leads to a simultaneous decrease of generalization ability on new (unseen) classes. Existing approaches attempt to regulate the prompt tuning process to balance BNT by appending constraints. However, imposed on the same target prompt, these constraints fail to fully avert the mutual exclusivity between the optimization directions for base and new. As a novel solution to this challenge, we propose the plug-and-play Dual-Prompt Collaboration (DPC) framework, the first that decoupling the optimization processes of base and new tasks at the prompt level. Specifically, we clone a learnable parallel prompt based on the backbone prompt, and introduce a variable Weighting-Decoupling framework to independently control the optimization directions of dual prompts specific to base or new tasks, thus avoiding the conflict in generalization. Meanwhile, we propose a Dynamic Hard Negative Optimizer, utilizing dual prompts to construct a more challenging optimization task on base classes for enhancement. For interpretability, we prove the feature channel invariance of the prompt vector during the optimization process, providing theoretical support for the Weighting-Decoupling of DPC. Extensive experiments on multiple backbones demonstrate that DPC can significantly improve base performance without introducing any external knowledge beyond the base classes, while maintaining generalization to new classes. Code is available at: https://github.com/JREion/DPC.

Lion (Evolved Sign Momentum), a new optimizer discovered through program search, has shown promising results in training large AI models. It performs comparably or favorably to AdamW but with greater memory efficiency. As we can expect from the results of a random search program, Lion incorporates elements from several existing algorithms, including signed momentum, decoupled weight decay, Polak, and Nesterov momentum, but does not fit into any existing category of theoretically grounded optimizers. Thus, even though Lion appears to perform well as a general-purpose optimizer for a wide range of tasks, its theoretical basis remains uncertain. This lack of theoretical clarity limits opportunities to further enhance and expand Lion's efficacy. This work aims to demystify Lion. Based on both continuous-time and discrete-time analysis, we demonstrate that Lion is a theoretically novel and principled approach for minimizing a general loss function f(x) while enforcing a bound constraint |x|_infty leq 1/lambda. Lion achieves this through the incorporation of decoupled weight decay, where lambda represents the weight decay coefficient. Our analysis is made possible by the development of a new Lyapunov function for the Lion updates. It applies to a broader family of Lion-kappa algorithms, where the sign(cdot) operator in Lion is replaced by the subgradient of a convex function kappa, leading to the solution of a general composite optimization problem of min_x f(x) + kappa^*(x). Our findings provide valuable insights into the dynamics of Lion and pave the way for further improvements and extensions of Lion-related algorithms.

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

Learning from off-policy data is essential for sample-efficient reinforcement learning. In the present work, we build on the insight that the advantage function can be understood as the causal effect of an action on the return, and show that this allows us to decompose the return of a trajectory into parts caused by the agent's actions (skill) and parts outside of the agent's control (luck). Furthermore, this decomposition enables us to naturally extend Direct Advantage Estimation (DAE) to off-policy settings (Off-policy DAE). The resulting method can learn from off-policy trajectories without relying on importance sampling techniques or truncating off-policy actions. We draw connections between Off-policy DAE and previous methods to demonstrate how it can speed up learning and when the proposed off-policy corrections are important. Finally, we use the MinAtar environments to illustrate how ignoring off-policy corrections can lead to suboptimal policy optimization performance.

A prevailing view in Reinforcement Learning for Verifiable Rewards (RLVR) interprets recent progress through the lens of an exploration-exploitation trade-off, a perspective largely shaped by token-level metrics. We re-examine this perspective, proposing that this perceived trade-off may not be a fundamental constraint but rather an artifact of the measurement level. To investigate this, we shift the analysis to the semantically rich hidden-state space, adopting Effective Rank (ER) to quantify exploration and proposing its novel first- and second-order derivatives, named Effective Rank Velocity (ERV) and Effective Rank Acceleration (ERA), to capture exploitation dynamics. Our analysis reveals that at the hidden-state level, exploration and exploitation could be decoupled (Sec. 4). This finding reveals an opportunity to enhance both capacities simultaneously. This insight motivates our method, Velocity-Exploiting Rank-Learning (VERL), the first to operationalize the principle of synergistic exploration-exploitation enhancement by directly shaping the RL advantage function. The key innovation is leveraging the theoretically stable ERA as a predictive meta-controller to create a synergistic, dual-channel incentive structure. Instead of forcing a trade-off, VERL prospectively amplifies rewards for exploration to preempt overconfidence and reinforces exploitative gains to consolidate reasoning. Experiments across diverse LLMs and reasoning benchmarks show consistent gains, including up to 21.4% absolute accuracy improvement on the challenging Gaokao 2024 dataset.

We say an algorithm is batch size-invariant if changes to the batch size can largely be compensated for by changes to other hyperparameters. Stochastic gradient descent is well-known to have this property at small batch sizes, via the learning rate. However, some policy optimization algorithms (such as PPO) do not have this property, because of how they control the size of policy updates. In this work we show how to make these algorithms batch size-invariant. Our key insight is to decouple the proximal policy (used for controlling policy updates) from the behavior policy (used for off-policy corrections). Our experiments help explain why these algorithms work, and additionally show how they can make more efficient use of stale data.

Multimodal Large Language Models (MLLMs) have achieved strong performance across many tasks, yet most systems remain limited to offline inference, requiring complete inputs before generating outputs. Recent streaming methods reduce latency by interleaving perception and generation, but still enforce a sequential perception-generation cycle, limiting real-time interaction. In this work, we target a fundamental bottleneck that arises when extending MLLMs to real-time video understanding: the global positional continuity constraint imposed by standard positional encoding schemes. While natural in offline inference, this constraint tightly couples perception and generation, preventing effective input-output parallelism. To address this limitation, we propose a parallel streaming framework that relaxes positional continuity through three designs: Overlapped, Group-Decoupled, and Gap-Isolated. These designs enable simultaneous perception and generation, allowing the model to process incoming inputs while producing responses in real time. Extensive experiments reveal that Group-Decoupled achieves the best efficiency-performance balance, maintaining high fluency and accuracy while significantly reducing latency. We further show that the proposed framework yields up to 2x acceleration under balanced perception-generation workloads, establishing a principled pathway toward speak-while-watching real-time systems. We make all our code publicly available: https://github.com/EIT-NLP/Speak-While-Watching.

Speculative decoding can significantly accelerate LLM serving, yet most deployments today disentangle speculator training from serving, treating speculator training as a standalone offline modeling problem. We show that this decoupled formulation introduces substantial deployment and adaptation lag: (1) high time-to-serve, since a speculator must be trained offline for a considerable period before deployment; (2) delayed utility feedback, since the true end-to-end decoding speedup is only known after training and cannot be inferred reliably from acceptance rate alone due to model-architecture and system-level overheads; and (3) domain-drift degradation, as the target model is repurposed to new domains and the speculator becomes stale and less effective. To address these issues, we present Aurora, a unified training-serving system that closes the loop by continuously learning a speculator directly from live inference traces. Aurora reframes online speculator learning as an asynchronous reinforcement-learning problem: accepted tokens provide positive feedback, while rejected speculator proposals provide implicit negative feedback that we exploit to improve sample efficiency. Our design integrates an SGLang-based inference server with an asynchronous training server, enabling hot-swapped speculator updates without service interruption. Crucially, Aurora supports day-0 deployment: a speculator can be served immediately and rapidly adapted to live traffic, improving system performance while providing immediate utility feedback. Across experiments, Aurora achieves a 1.5x day-0 speedup on recently released frontier models (e.g., MiniMax M2.1 229B and Qwen3-Coder-Next 80B). Aurora also adapts effectively to distribution shifts in user traffic, delivering an additional 1.25x speedup over a well-trained but static speculator on widely used models (e.g., Qwen3 and Llama3).

We propose Decoupled Residual Denoising Diffusion models (DRDD) for unified and data-efficient image-to-image (I2I) translation. While diffusion models have advanced I2I translation in terms of quality and diversity, we uncover a previously under-explored property in diffusion models. Crucially, beyond its conventional role of manifold lifting (i.e., moving data off low-dimensional manifolds), injecting Gaussian noise facilitates domain harmonization by implicitly aligning feature distributions across domains, a property particularly advantageous for unified I2I translation. However, existing diffusion models prematurely erode this harmonization effect, as noise and residuals are simultaneously removed in a single coupled diffusion process. To address this, DRDD decouples the diffusion process into two sequential and independent diffusion stages: (1) a stochastic noise diffusion for domain harmonization and manifold lifting, and (2) a deterministic residual diffusion that learns the core semantic mapping entirely within the fixed-noise domain. This decoupling preserves harmonization and manifold lifting effects throughout the transformation, substantially simplifying the learning of unified mappings across diverse tasks and domains. Notably, the noise diffusion stage is trained exclusively on abundant, unpaired target-domain images, greatly improving data efficiency. Comprehensive theoretical and empirical analysis demonstrates that DRDD is broadly compatible with mainstream diffusion models and consistently delivers robust, unified I2I translation, even under limited paired data. Our code is available at https://github.com/HKU-HealthAI/DRDD.

The advent of agentic multimodal models has empowered systems to actively interact with external environments. However, current agents suffer from a profound meta-cognitive deficit: they struggle to arbitrate between leveraging internal knowledge and querying external utilities. Consequently, they frequently fall prey to blind tool invocation, resorting to reflexive tool execution even when queries are resolvable from the raw visual context. This pathological behavior precipitates severe latency bottlenecks and injects extraneous noise that derails sound reasoning. Existing reinforcement learning protocols attempt to mitigate this via a scalarized reward that penalizes tool usage. Yet, this coupled formulation creates an irreconcilable optimization dilemma: an aggressive penalty suppresses essential tool use, whereas a mild penalty is entirely subsumed by the variance of the accuracy reward during advantage normalization, rendering it impotent against tool overuse. To transcend this bottleneck, we propose HDPO, a framework that reframes tool efficiency from a competing scalar objective to a strictly conditional one. By eschewing reward scalarization, HDPO maintains two orthogonal optimization channels: an accuracy channel that maximizes task correctness, and an efficiency channel that enforces execution economy exclusively within accurate trajectories via conditional advantage estimation. This decoupled architecture naturally induces a cognitive curriculum-compelling the agent to first master task resolution before refining its self-reliance. Extensive evaluations demonstrate that our resulting model, Metis, reduces tool invocations by orders of magnitude while simultaneously elevating reasoning accuracy.

In multi-fidelity optimization, biased approximations of varying costs of the target function are available. This paper studies the problem of optimizing a locally smooth function with a limited budget, where the learner has to make a tradeoff between the cost and the bias of these approximations. We first prove lower bounds for the simple regret under different assumptions on the fidelities, based on a cost-to-bias function. We then present the Kometo algorithm which achieves, with additional logarithmic factors, the same rates without any knowledge of the function smoothness and fidelity assumptions, and improves previously proven guarantees. We finally empirically show that our algorithm outperforms previous multi-fidelity optimization methods without the knowledge of problem-dependent parameters.

Differentially Private methods for training Deep Neural Networks (DNNs) have progressed recently, in particular with the use of massive batches and aggregated data augmentations for a large number of training steps. These techniques require much more computing resources than their non-private counterparts, shifting the traditional privacy-accuracy trade-off to a privacy-accuracy-compute trade-off and making hyper-parameter search virtually impossible for realistic scenarios. In this work, we decouple privacy analysis and experimental behavior of noisy training to explore the trade-off with minimal computational requirements. We first use the tools of R\'enyi Differential Privacy (RDP) to highlight that the privacy budget, when not overcharged, only depends on the total amount of noise (TAN) injected throughout training. We then derive scaling laws for training models with DP-SGD to optimize hyper-parameters with more than a 100times reduction in computational budget. We apply the proposed method on CIFAR-10 and ImageNet and, in particular, strongly improve the state-of-the-art on ImageNet with a +9 points gain in top-1 accuracy for a privacy budget epsilon=8.

A complex system with cluttered observations may be a coupled mixture of multiple simple sub-systems corresponding to latent entities. Such sub-systems may hold distinct dynamics in the continuous-time domain; therein, complicated interactions between sub-systems also evolve over time. This setting is fairly common in the real world but has been less considered. In this paper, we propose a sequential learning approach under this setting by decoupling a complex system for handling irregularly sampled and cluttered sequential observations. Such decoupling brings about not only subsystems describing the dynamics of each latent entity but also a meta-system capturing the interaction between entities over time. Specifically, we argue that the meta-system evolving within a simplex is governed by projected differential equations (ProjDEs). We further analyze and provide neural-friendly projection operators in the context of Bregman divergence. Experimental results on synthetic and real-world datasets show the advantages of our approach when facing complex and cluttered sequential data compared to the state-of-the-art.

This article reviews modern optimization methods for training neural networks with an emphasis on efficiency and scale. We present state-of-the-art optimization algorithms under a unified algorithmic template that highlights the importance of adapting to the structures in the problem. We then cover how to make these algorithms agnostic to the scale of the problem. Our exposition is intended as an introduction for both practitioners and researchers who wish to be involved in these exciting new developments.

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.

Dynamic multi-objective optimization requires continuous tracking of moving Pareto fronts. Existing methods struggle with irregular mutations and data sparsity, primarily facing three challenges: the non-linear coupling of dynamic modes, negative transfer from outdated historical data, and the cold-start problem during environmental switches. To address these issues, this paper proposes a decoupled basis-vector-driven generative framework (DB-GEN). First, to resolve non-linear coupling, the framework employs the discrete wavelet transform to separate evolutionary trajectories into low-frequency trends and high-frequency details. Second, to mitigate negative transfer, it learns transferable basis vectors via sparse dictionary learning rather than directly memorizing historical instances. Recomposing these bases under a topology-aware contrastive constraint constructs a structured latent manifold. Finally, to overcome the cold-start problem, a surrogate-assisted search paradigm samples initial populations from this manifold. Pre-trained on 120 million solutions, DB-GEN performs direct online inference without retraining or fine-tuning. This zero-shot generation process executes in milliseconds, requiring approximately 0.2 seconds per environmental change. Experimental results demonstrate that DB-GEN improves tracking accuracy across various dynamic benchmarks compared to existing algorithms.

We identify and formalize a fundamental gradient descent phenomenon resulting in a learning proclivity in over-parameterized neural networks. Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of features relevant for the task, despite the presence of other predictive features that fail to be discovered. This work provides a theoretical explanation for the emergence of such feature imbalance in neural networks. Using tools from Dynamical Systems theory, we identify simple properties of learning dynamics during gradient descent that lead to this imbalance, and prove that such a situation can be expected given certain statistical structure in training data. Based on our proposed formalism, we develop guarantees for a novel regularization method aimed at decoupling feature learning dynamics, improving accuracy and robustness in cases hindered by gradient starvation. We illustrate our findings with simple and real-world out-of-distribution (OOD) generalization experiments.

Reinforcement learning with Verifiable Rewards (RLVR) has emerged as a powerful paradigm for eliciting reasoning capabilities in large language models, particularly in mathematics and coding. While recent efforts have extended this paradigm to broader general scientific (STEM) domains, the complex interplay between supervised fine-tuning (SFT) and RL in these contexts remains underexplored. In this paper, we conduct controlled experiments revealing a critical challenge: for general STEM domains, RL applied directly to base models is highly sample-inefficient and is consistently surpassed by supervised fine-tuning (SFT) on moderate-quality responses. Yet sequential SFT followed by RL can further improve performance, suggesting that the two stages play complementary roles, and that how training data is allocated between them matters. Therefore, we propose DeReason, a difficulty-based data decoupling strategy for general reasoning. DeReason partitions training data by reasoning intensity estimated via LLM-based scoring into reasoning-intensive and non-reasoning-intensive subsets. It allocates broad-coverage, non-reasoning-intensive problems to SFT to establish foundational domain knowledge, and reserves a focused subset of difficult problems for RL to cultivate complex reasoning. We demonstrate that this principled decoupling yields better performance than randomly splitting the data for sequential SFT and RL. Extensive experiments on general STEM and mathematical benchmarks demonstrate that our decoupled curriculum training significantly outperforms SFT-only, RL-only, and random-split baselines. Our work provides a systematic study of the interplay between SFT and RL for general reasoning, offering a highly effective and generalized post-training recipe.

Reinforcement learning (RL) with verifiable rewards has recently catalyzed a wave of "MLLM-r1" approaches that bring RL to vision language models. Most representative paradigms begin with a cold start, typically employing supervised fine-tuning (SFT), to initialize the policy before RL. However, SFT-based cold start adopts the reasoning paradigm intertwined with task solution and output format, which may induce instruction-style overfitting, weakens out-of-distribution generalization, and ultimately affects downstream RL. We revisit the cold start along two views, its training method and data construction, and introduce the Generalization Factor (GF) coefficient to quantify the generalization capability under different methods. Our empirical study finds that preference-based training methods (e.g. DPO) generalizes better than SFT-based methods in cold start. Motivated by this, we propose SPECS-a Self-distilled, Preference-based Cold Start framework that decouples multimodal learning: (1) generates introspective preference data pairs via self-distillation, avoiding reliance on larger teachers or manual annotation; (2) performs preference-based training to learn, focusing on shallow, transferable surface-form criteria (format, structure, style) rather than memorizing content; and (3) hands off to RL with verifiable rewards for deep reasoning results. Experimental results across multiple multimodal benchmarks show that our decoupling learning framework yields consistent performance gains over strong baselines, improving MEGA-Bench by 4.1% and MathVista by 12.2%. Additional experiments indicate that SPECS contributes to reducing in-distribution "stuckness," improving exploration, stabilizing training, and raising the performance ceiling.

We propose a meta-ability decoupling (MAD) paradigm, which brings together various object navigation methods in an architecture system, allowing them to mutually enhance each other and evolve together. Based on the MAD paradigm, we design a multiple thinking (MT) model that leverages distinct thinking to abstract various meta-abilities. Our method decouples meta-abilities from three aspects: input, encoding, and reward while employing the multiple thinking collaboration (MTC) module to promote mutual cooperation between thinking. MAD introduces a novel qualitative and quantitative interpretability system for object navigation. Through extensive experiments on AI2-Thor and RoboTHOR, we demonstrate that our method outperforms state-of-the-art (SOTA) methods on both typical and zero-shot object navigation tasks.

Second-order optimizers, maintaining a matrix termed a preconditioner, are superior to first-order optimizers in both theory and practice. The states forming the preconditioner and its inverse root restrict the maximum size of models trained by second-order optimizers. To address this, compressing 32-bit optimizer states to lower bitwidths has shown promise in reducing memory usage. However, current approaches only pertain to first-order optimizers. In this paper, we propose the first 4-bit second-order optimizers, exemplified by 4-bit Shampoo, maintaining performance similar to that of 32-bit ones. We show that quantizing the eigenvector matrix of the preconditioner in 4-bit Shampoo is remarkably better than quantizing the preconditioner itself both theoretically and experimentally. By rectifying the orthogonality of the quantized eigenvector matrix, we enhance the approximation of the preconditioner's eigenvector matrix, which also benefits the computation of its inverse 4-th root. Besides, we find that linear square quantization slightly outperforms dynamic tree quantization when quantizing second-order optimizer states. Evaluation on various networks for image classification demonstrates that our 4-bit Shampoo achieves comparable test accuracy to its 32-bit counterpart while being more memory-efficient. The source code will be made available.

Sparse Mixture-of-Experts (SMoE) language models achieve strong capability at low per-token compute, yet deployment remains memory- and throughput-bound because the full expert pool must be stored and served. Post-training expert pruning reduces this cost, but most methods focus on which experts to prune within each layer and default to a uniform layer-wise sparsity allocation, even though the allocation can strongly affect performance. We decouple pruning into within-layer expert ranking and across-layer budget allocation, and introduce Expected Speculative Acceptance Proxy (ESAP), a speculative-decoding-inspired, teacher-forced metric that measures how well a pruned model matches the full model. ESAP is bounded and stable, enabling cheap comparison of many candidates without costly autoregressive decoding. Building on ESAP, we propose EvoESAP, an evolutionary searching framework that optimizes a non-uniform layer-wise sparsity allocation under a fixed global budget while holding the within-layer pruning order fixed, making it a plug-and-play method with criteria such as Frequency, EAN, SEER, and REAP. Across 7B--30B SMoE LLMs at 25\% and 50\% sparsity, EvoESAP consistently discovers non-uniform allocations that improve open-ended generation (up to +19.6\% on MATH-500 at 50\% sparsity) while preserving competitive multiple-choice accuracy compared with uniform pruning at the same sparsity.

This paper proposes a novel approach to address the challenge that pretrained VLA models often fail to effectively improve performance and reduce adaptation costs during standard supervised finetuning (SFT). Some advanced finetuning methods with auxiliary training objectives can improve performance and reduce the number of convergence steps. However, they typically incur significant computational overhead due to the additional losses from auxiliary objectives. To simultaneously achieve the enhanced capabilities of auxiliary training with the simplicity of standard SFT, we decouple the two objectives of auxiliary-objective SFT within the parameter space, namely, enhancing general capabilities and fitting task-specific action distributions. To deliver the goal, we only need to train the model to converge on a small-scale task set using two distinct training strategies, resulting in two finetuned models. The parameters' difference between the two models can then be interpreted as capability vectors provided by auxiliary objectives. These vectors are then merged with pretrained parameters to form a capability-enhanced meta model. Moreover, when standard SFT is augmented with a lightweight orthogonal regularization loss, the merged model attains performance comparable to auxiliary finetuned baselines with reduced computational overhead. Internal and external experiments demonstrate that our capability vectors (1) are effective and versatile across diverse models, (2) can generalize to novel environments and embodiments out of the box.

High-quality power flow datasets are essential for training machine learning models in power systems. However, security and privacy concerns restrict access to real-world data, making statistically accurate and physically consistent synthetic datasets a viable alternative. We develop a diffusion model for generating synthetic power flow datasets from real-world power grids that both replicate the statistical properties of the real-world data and ensure AC power flow feasibility. To enforce the constraints, we incorporate gradient guidance based on the power flow constraints to steer diffusion sampling toward feasible samples. For computational efficiency, we further leverage insights from the fast decoupled power flow method and propose a variable decoupling strategy for the training and sampling of the diffusion model. These solutions lead to a physics-informed diffusion model, generating power flow datasets that outperform those from the standard diffusion in terms of feasibility and statistical similarity, as shown in experiments across IEEE benchmark systems.

Masked Diffusion Models (MDMs) offer greater flexibility in decoding order than autoregressive models but require careful planning to achieve high-quality generation. Existing samplers typically adopt greedy heuristics, prioritizing positions with the highest local certainty to decode at each step. Through failure case analysis, we identify a fundamental limitation of this approach: it neglects the downstream impact of current decoding choices on subsequent steps and fails to minimize cumulative uncertainty. In particular, these methods do not fully exploit the non-causal nature of MDMs, which enables evaluating how a decoding decision reshapes token probabilities/uncertainty across all remaining masked positions. To bridge this gap, we propose the Info-Gain Sampler, a principled decoding framework that balances immediate uncertainty with information gain over future masked tokens. Extensive evaluations across diverse architectures and tasks (reasoning, coding, creative writing, and image generation) demonstrate that Info-Gain Sampler consistently outperforms existing samplers for MDMs. For instance, it achieves a 3.6% improvement in average accuracy on reasoning tasks and a 63.1% win-rate in creative writing. Notably, on reasoning tasks it reduces cumulative uncertainty from 78.4 to 48.6, outperforming the best baseline by a large margin. The code will be available at https://github.com/yks23/Information-Gain-Sampler.

We study the problem of learning in zero-sum matrix games with repeated play and bandit feedback. Specifically, we focus on developing uncoupled algorithms that guarantee, without communication between players, the convergence of the last-iterate to a Nash equilibrium. Although the non-bandit case has been studied extensively, this setting has only been explored recently, with a bound of O(T^{-1/8}) on the exploitability gap. We show that, for uncoupled algorithms, guaranteeing convergence of the policy profiles to a Nash equilibrium is detrimental to the performance, with the best attainable rate being Ω(T^{-1/4}) in contrast to the usual Ω(T^{-1/2}) rate for convergence of the average iterates. We then propose two algorithms that achieve this optimal rate up to constant and logarithmic factors. The first algorithm leverages a straightforward trade-off between exploration and exploitation, while the second employs a regularization technique based on a two-step mirror descent approach.

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

Large reasoning models improve with more test-time computation, but often overthink, producing unnecessarily long chains-of-thought that raise cost without improving accuracy. Prior reinforcement learning approaches typically rely on a single outcome reward with trajectory-level length penalties, which cannot distinguish essential from redundant reasoning steps and therefore yield blunt compression. Although recent work incorporates step-level signals, such as offline pruning, supervised data construction, or verifier-based intermediate rewards, reasoning length is rarely treated as an explicit step-level optimization objective during RL. We propose Step-wise Adaptive Penalization (SWAP), a fine-grained framework that allocates length reduction across steps based on intrinsic contribution. We estimate step importance from the model's on-policy log-probability improvement toward the correct answer, then treat excess length as a penalty mass redistributed to penalize low-importance steps more heavily while preserving high-importance reasoning. We optimize with a unified outcome-process advantage within group-relative policy optimization. Extensive experiments demonstrate that SWAP reduces reasoning length by 64.3% on average while improving accuracy by 5.7% relative to the base model.

We study the problem of optimizing a function under a budgeted number of evaluations. We only assume that the function is locally smooth around one of its global optima. The difficulty of optimization is measured in terms of 1) the amount of noise b of the function evaluation and 2) the local smoothness, d, of the function. A smaller d results in smaller optimization error. We come with a new, simple, and parameter-free approach. First, for all values of b and d, this approach recovers at least the state-of-the-art regret guarantees. Second, our approach additionally obtains these results while being agnostic to the values of both b and d. This leads to the first algorithm that naturally adapts to an unknown range of noise b and leads to significant improvements in a moderate and low-noise regime. Third, our approach also obtains a remarkable improvement over the state-of-the-art SOO algorithm when the noise is very low which includes the case of optimization under deterministic feedback (b=0). There, under our minimal local smoothness assumption, this improvement is of exponential magnitude and holds for a class of functions that covers the vast majority of functions that practitioners optimize (d=0). We show that our algorithmic improvement is borne out in experiments as we empirically show faster convergence on common benchmarks.

We consider function optimization as a sequential decision making problem under budget constraint. This constraint limits the number of objective function evaluations allowed during the optimization. We consider an algorithm inspired by a continuous version of a multi-armed bandit problem which attacks this optimization problem by solving the tradeoff between exploration (initial quasi-uniform search of the domain) and exploitation (local optimization around the potentially global maxima). We introduce the so-called Simultaneous Optimistic Optimization (SOO), a deterministic algorithm that works by domain partitioning. The benefit of such approach are the guarantees on the returned solution and the numerical efficiency of the algorithm. We present this machine learning approach to optimization, and provide the empirical assessment of SOO on the CEC'2014 competition on single objective real-parameter numerical optimization test-suite.

Modern large-scale language model pre-training relies heavily on the single program multiple data (SPMD) paradigm, which requires tight coupling across accelerators. Due to this coupling, transient slowdowns, hardware failures, and synchronization overhead stall the entire computation, wasting significant compute time at scale. While recent distributed methods like DiLoCo reduced communication bandwidth, they remained fundamentally synchronous and vulnerable to these system stalls. To address this, we introduce Decoupled DiLoCo, an evolution of the DiLoCo framework designed to break the lock-step synchronization barrier and go beyond SPMD to maximize training goodput. Decoupled DiLoCo partitions compute across multiple independent ``learners'' that execute local inner optimization steps. These learners asynchronously communicate parameter fragments to a central synchronizer, which circumvents failed or straggling learners by aggregating updates using a minimum quorum, an adaptive grace window, and dynamic token-weighted merging. Inspired by ``chaos engineering'', we achieve significantly improved training efficiency in failure-prone environments with millions of simulated chips with strictly zero global downtime, while maintaining competitive model performance across text and vision tasks, for both dense and mixture-of-expert architectures.

Offline optimization has recently emerged as an increasingly popular approach to mitigate the prohibitively expensive cost of online experimentation. The key idea is to learn a surrogate of the black-box function that underlines the target experiment using a static (offline) dataset of its previous input-output queries. Such an approach is, however, fraught with an out-of-distribution issue where the learned surrogate becomes inaccurate outside the offline data regimes. To mitigate this, existing offline optimizers have proposed numerous conditioning techniques to prevent the learned surrogate from being too erratic. Nonetheless, such conditioning strategies are often specific to particular surrogate or search models, which might not generalize to a different model choice. This motivates us to develop a model-agnostic approach instead, which incorporates a notion of model sharpness into the training loss of the surrogate as a regularizer. Our approach is supported by a new theoretical analysis demonstrating that reducing surrogate sharpness on the offline dataset provably reduces its generalized sharpness on unseen data. Our analysis extends existing theories from bounding generalized prediction loss (on unseen data) with loss sharpness to bounding the worst-case generalized surrogate sharpness with its empirical estimate on training data, providing a new perspective on sharpness regularization. Our extensive experimentation on a diverse range of optimization tasks also shows that reducing surrogate sharpness often leads to significant improvement, marking (up to) a noticeable 9.6% performance boost. Our code is publicly available at https://github.com/cuong-dm/IGNITE

Recent deep-learning-based approaches to single-image reflection removal have shown promising advances, primarily for two reasons: 1) the utilization of recognition-pretrained features as inputs, and 2) the design of dual-stream interaction networks. However, according to the Information Bottleneck principle, high-level semantic clues tend to be compressed or discarded during layer-by-layer propagation. Additionally, interactions in dual-stream networks follow a fixed pattern across different layers, limiting overall performance. To address these limitations, we propose a novel architecture called Reversible Decoupling Network (RDNet), which employs a reversible encoder to secure valuable information while flexibly decoupling transmission- and reflection-relevant features during the forward pass. Furthermore, we customize a transmission-rate-aware prompt generator to dynamically calibrate features, further boosting performance. Extensive experiments demonstrate the superiority of RDNet over existing SOTA methods on five widely-adopted benchmark datasets. Our code will be made publicly available.

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.

In this paper, we propose a novel factored agent architecture designed to overcome the limitations of traditional single-agent systems in agentic AI. Our approach decomposes the agent into two specialized components: (1) a large language model (LLM) that serves as a high level planner and in-context learner, which may use dynamically available information in user prompts, (2) a smaller language model which acts as a memorizer of tool format and output. This decoupling addresses prevalent issues in monolithic designs, including malformed, missing, and hallucinated API fields, as well as suboptimal planning in dynamic environments. Empirical evaluations demonstrate that our factored architecture significantly improves planning accuracy and error resilience, while elucidating the inherent trade-off between in-context learning and static memorization. These findings suggest that a factored approach is a promising pathway for developing more robust and adaptable agentic AI systems.

Neural Memory Networks (NMNs) have received increased attention in recent years compared to deep architectures that use a constrained memory. Despite their new appeal, the success of NMNs hinges on the ability of the gradient-based optimiser to perform incremental training of the NMN controllers, determining how to leverage their high capacity for knowledge retrieval. This means that while excellent performance can be achieved when the training data is consistent and well distributed, rare data samples are hard to learn from as the controllers fail to incorporate them effectively during model training. Drawing inspiration from the human cognition process, in particular the utilisation of neuromodulators in the human brain, we propose to decouple the learning process of the NMN controllers to allow them to achieve flexible, rapid adaptation in the presence of new information. This trait is highly beneficial for meta-learning tasks where the memory controllers must quickly grasp abstract concepts in the target domain, and adapt stored knowledge. This allows the NMN controllers to quickly determine which memories are to be retained and which are to be erased, and swiftly adapt their strategy to the new task at hand. Through both quantitative and qualitative evaluations on multiple public benchmarks, including classification and regression tasks, we demonstrate the utility of the proposed approach. Our evaluations not only highlight the ability of the proposed NMN architecture to outperform the current state-of-the-art methods, but also provide insights on how the proposed augmentations help achieve such superior results. In addition, we demonstrate the practical implications of the proposed learning strategy, where the feedback path can be shared among multiple neural memory networks as a mechanism for knowledge sharing.

In many applications of machine learning, like drug discovery and material design, the goal is to generate candidates that simultaneously maximize a set of objectives. As these objectives are often conflicting, there is no single candidate that simultaneously maximizes all objectives, but rather a set of Pareto-optimal candidates where one objective cannot be improved without worsening another. Moreover, in practice, these objectives are often under-specified, making the diversity of candidates a key consideration. The existing multi-objective optimization methods focus predominantly on covering the Pareto front, failing to capture diversity in the space of candidates. Motivated by the success of GFlowNets for generation of diverse candidates in a single objective setting, in this paper we consider Multi-Objective GFlowNets (MOGFNs). MOGFNs consist of a novel Conditional GFlowNet which models a family of single-objective sub-problems derived by decomposing the multi-objective optimization problem. Our work is the first to empirically demonstrate conditional GFlowNets. Through a series of experiments on synthetic and benchmark tasks, we empirically demonstrate that MOGFNs outperform existing methods in terms of Hypervolume, R2-distance and candidate diversity. We also demonstrate the effectiveness of MOGFNs over existing methods in active learning settings. Finally, we supplement our empirical results with a careful analysis of each component of MOGFNs.

Offline preference optimization allows fine-tuning large models directly from offline data, and has proved effective in recent alignment practices. We propose generalized preference optimization (GPO), a family of offline losses parameterized by a general class of convex functions. GPO enables a unified view over preference optimization, encompassing existing algorithms such as DPO, IPO and SLiC as special cases, while naturally introducing new variants. The GPO framework also sheds light on how offline algorithms enforce regularization, through the design of the convex function that defines the loss. Our analysis and experiments reveal the connections and subtle differences between the offline regularization and the KL divergence regularization intended by the canonical RLHF formulation. In a controlled setting akin to Gao et al 2023, we also show that different GPO variants achieve similar trade-offs between regularization and performance, though the optimal values of hyper-parameter might differ as predicted by theory. In all, our results present new algorithmic toolkits and empirical insights to alignment practitioners.

We prove rich algebraic structures of the solution space for 2-layer neural networks with quadratic activation and L_2 loss, trained on reasoning tasks in Abelian group (e.g., modular addition). Such a rich structure enables analytical construction of global optimal solutions from partial solutions that only satisfy part of the loss, despite its high nonlinearity. We coin the framework as CoGO (Composing Global Optimizers). Specifically, we show that the weight space over different numbers of hidden nodes of the 2-layer network is equipped with a semi-ring algebraic structure, and the loss function to be optimized consists of monomial potentials, which are ring homomorphism, allowing partial solutions to be composed into global ones by ring addition and multiplication. Our experiments show that around 95% of the solutions obtained by gradient descent match exactly our theoretical constructions. Although the global optimizers constructed only required a small number of hidden nodes, our analysis on gradient dynamics shows that over-parameterization asymptotically decouples training dynamics and is beneficial. We further show that training dynamics favors simpler solutions under weight decay, and thus high-order global optimizers such as perfect memorization are unfavorable.

This paper proposes a novel approach to address the challenge that pretrained VLA models often fail to effectively improve performance and reduce adaptation costs during standard supervised finetuning (SFT). Some advanced finetuning methods with auxiliary training objectives can improve performance and reduce the number of convergence steps. However, they typically incur significant computational overhead due to the additional losses from auxiliary tasks. To simultaneously achieve the enhanced capabilities of auxiliary training with the simplicity of standard SFT, we decouple the two objectives of auxiliary task training within the parameter space, namely, enhancing general capabilities and fitting task-specific action distributions. To deliver this goal, we only need to train the model to converge on a small-scale task set using two distinct training strategies. The difference between the resulting model parameters can then be interpreted as capability vectors provided by auxiliary tasks. These vectors are then merged with pretrained parameters to form a capability-enhanced meta model. Moreover, when standard SFT is augmented with a lightweight orthogonal regularization loss, the merged model attains performance comparable to auxiliary finetuned baselines with reduced computational overhead. Experimental results demonstrate that this approach is highly effective across diverse robot tasks. Project page: https://chris1220313648.github.io/Fast-dVLA/

In the field of algorithmic fairness, significant attention has been put on group fairness criteria, such as Demographic Parity and Equalized Odds. Nevertheless, these objectives, measured as global averages, have raised concerns about persistent local disparities between sensitive groups. In this work, we address the problem of local fairness, which ensures that the predictor is unbiased not only in terms of expectations over the whole population, but also within any subregion of the feature space, unknown at training time. To enforce this objective, we introduce ROAD, a novel approach that leverages the Distributionally Robust Optimization (DRO) framework within a fair adversarial learning objective, where an adversary tries to infer the sensitive attribute from the predictions. Using an instance-level re-weighting strategy, ROAD is designed to prioritize inputs that are likely to be locally unfair, i.e. where the adversary faces the least difficulty in reconstructing the sensitive attribute. Numerical experiments demonstrate the effectiveness of our method: it achieves Pareto dominance with respect to local fairness and accuracy for a given global fairness level across three standard datasets, and also enhances fairness generalization under distribution shift.

Preconditioned gradient methods are among the most general and powerful tools in optimization. However, preconditioning requires storing and manipulating prohibitively large matrices. We describe and analyze a new structure-aware preconditioning algorithm, called Shampoo, for stochastic optimization over tensor spaces. Shampoo maintains a set of preconditioning matrices, each of which operates on a single dimension, contracting over the remaining dimensions. We establish convergence guarantees in the stochastic convex setting, the proof of which builds upon matrix trace inequalities. Our experiments with state-of-the-art deep learning models show that Shampoo is capable of converging considerably faster than commonly used optimizers. Although it involves a more complex update rule, Shampoo's runtime per step is comparable to that of simple gradient methods such as SGD, AdaGrad, and Adam.

Proximal Policy Optimization (PPO)-based Reinforcement Learning from Human Feedback (RLHF) is essential for aligning large language models (LLMs) with human preferences. It requires joint training of an actor and critic with a pretrained, fixed reward model for guidance. This approach increases computational complexity and instability due to actor-critic interdependence. Additionally, PPO lacks access to true environment rewards in LLM tasks, limiting its adaptability. Under such conditions, pretraining a value model or a reward model becomes equivalent, as both provide fixed supervisory signals without new ground-truth feedback. To address these issues, we propose Decoupled Value Policy Optimization (DVPO), a lean framework that replaces traditional reward modeling with a pretrained global value model (GVM). The GVM is conditioned on policy trajectories and predicts token-level return-to-go estimates. By decoupling value model from policy training (via frozen GVM-driven RL objectives), DVPO eliminates actor-critic interdependence, reducing GPU memory usage by 40\% and training time by 35\% compared to conventional RLHF. Experiments across benchmarks show DVPO outperforms efficient RLHF methods (e.g., DPO) while matching state-of-the-art PPO in performance.

The online knapsack problem is a classic problem in the field of online algorithms. Its canonical version asks how to pack items of different values and weights arriving online into a capacity-limited knapsack so as to maximize the total value of the admitted items. Although optimal competitive algorithms are known for this problem, they may be fundamentally unfair, i.e., individual items may be treated inequitably in different ways. We formalize a practically-relevant notion of time fairness which effectively models a trade off between static and dynamic pricing in a motivating application such as cloud resource allocation, and show that existing algorithms perform poorly under this metric. We propose a parameterized deterministic algorithm where the parameter precisely captures the Pareto-optimal trade-off between fairness (static pricing) and competitiveness (dynamic pricing). We show that randomization is theoretically powerful enough to be simultaneously competitive and fair; however, it does not work well in experiments. To further improve the trade-off between fairness and competitiveness, we develop a nearly-optimal learning-augmented algorithm which is fair, consistent, and robust (competitive), showing substantial performance improvements in numerical experiments.

Recent vision-language models (VLMs) achieve remarkable reasoning through reinforcement learning (RL), which provides a feasible solution for realizing continuous self-evolving large vision-language models (LVLMs) in the era of experience. However, RL for VLMs requires abundant high-quality multimodal data, especially challenging in specialized domains like chemistry, earth sciences, and multimodal mathematics. Existing strategies such as synthetic data and self-rewarding mechanisms suffer from limited distributions and alignment difficulties, ultimately causing reward hacking: models exploit high-reward patterns, collapsing policy entropy and destabilizing training. We propose DoGe (Decouple to Generalize), a dual-decoupling framework that guides models to first learn from context rather than problem solving by refocusing on the problem context scenarios overlooked by synthetic data methods. By decoupling learning process into dual components (Thinker and Solver), we reasonably quantify the reward signals of this process and propose a two-stage RL post-training approach from freely exploring context to practically solving tasks. Second, to increase the diversity of training data, DoGe constructs an evolving curriculum learning pipeline: an expanded native domain knowledge corpus and an iteratively evolving seed problems pool. Experiments show that our method consistently outperforms the baseline across various benchmarks, providing a scalable pathway for realizing self-evolving LVLMs.

Automatic differentiation (autodiff) has revolutionized machine learning. It allows to express complex computations by composing elementary ones in creative ways and removes the burden of computing their derivatives by hand. More recently, differentiation of optimization problem solutions has attracted widespread attention with applications such as optimization layers, and in bi-level problems such as hyper-parameter optimization and meta-learning. However, so far, implicit differentiation remained difficult to use for practitioners, as it often required case-by-case tedious mathematical derivations and implementations. In this paper, we propose automatic implicit differentiation, an efficient and modular approach for implicit differentiation of optimization problems. In our approach, the user defines directly in Python a function F capturing the optimality conditions of the problem to be differentiated. Once this is done, we leverage autodiff of F and the implicit function theorem to automatically differentiate the optimization problem. Our approach thus combines the benefits of implicit differentiation and autodiff. It is efficient as it can be added on top of any state-of-the-art solver and modular as the optimality condition specification is decoupled from the implicit differentiation mechanism. We show that seemingly simple principles allow to recover many existing implicit differentiation methods and create new ones easily. We demonstrate the ease of formulating and solving bi-level optimization problems using our framework. We also showcase an application to the sensitivity analysis of molecular dynamics.

High-level autonomous driving requires motion planners capable of modeling multimodal future uncertainties while remaining robust in closed-loop interactions. Although diffusion-based planners are effective at modeling complex trajectory distributions, they often suffer from stochastic instabilities and the lack of corrective negative feedback when trained purely with imitation learning. To address these issues, we propose RAD-2, a unified generator-discriminator framework for closed-loop planning. Specifically, a diffusion-based generator is used to produce diverse trajectory candidates, while an RL-optimized discriminator reranks these candidates according to their long-term driving quality. This decoupled design avoids directly applying sparse scalar rewards to the full high-dimensional trajectory space, thereby improving optimization stability. To further enhance reinforcement learning, we introduce Temporally Consistent Group Relative Policy Optimization, which exploits temporal coherence to alleviate the credit assignment problem. In addition, we propose On-policy Generator Optimization, which converts closed-loop feedback into structured longitudinal optimization signals and progressively shifts the generator toward high-reward trajectory manifolds. To support efficient large-scale training, we introduce BEV-Warp, a high-throughput simulation environment that performs closed-loop evaluation directly in Bird's-Eye View feature space via spatial warping. RAD-2 reduces the collision rate by 56% compared with strong diffusion-based planners. Real-world deployment further demonstrates improved perceived safety and driving smoothness in complex urban traffic.

Multi-agent systems perform well on general reasoning tasks. However, the lack of training in specialized areas hinders their accuracy. Current training methods train a unified large language model (LLM) for all agents in the system. This may limit the performances due to different distributions underlying for different agents. Therefore, training multi-agent systems with distinct LLMs should be the next step to solve. However, this approach introduces optimization challenges. For example, agents operate at different frequencies, rollouts involve varying sub-agent invocations, and agents are often deployed across separate servers, disrupting end-to-end gradient flow. To address these issues, we propose M-GRPO, a hierarchical extension of Group Relative Policy Optimization designed for vertical Multi-agent systems with a main agent (planner) and multiple sub-agents (multi-turn tool executors). M-GRPO computes group-relative advantages for both main and sub-agents, maintaining hierarchical credit assignment. It also introduces a trajectory-alignment scheme that generates fixed-size batches despite variable sub-agent invocations. We deploy a decoupled training pipeline in which agents run on separate servers and exchange minimal statistics via a shared store. This enables scalable training without cross-server backpropagation. In experiments on real-world benchmarks (e.g., GAIA, XBench-DeepSearch, and WebWalkerQA), M-GRPO consistently outperforms both single-agent GRPO and multi-agent GRPO with frozen sub-agents, demonstrating improved stability and sample efficiency. These results show that aligning heterogeneous trajectories and decoupling optimization across specialized agents enhances tool-augmented reasoning tasks.

This paper tackles optimization problems whose objective and constraints involve a trained Neural Network (NN), where the goal is to maximize f(Phi(x)) subject to c(Phi(x)) leq 0, with f smooth, c general and non-stringent, and Phi an already trained and possibly nonwhite-box NN. We address two challenges regarding this problem: identifying ascent directions for local search, and ensuring reliable convergence towards relevant local solutions. To this end, we re-purpose the notion of directional NN attacks as efficient optimization subroutines, since directional NN attacks use the neural structure of Phi to compute perturbations of x that steer Phi(x) in prescribed directions. Precisely, we develop an attack operator that computes attacks of Phi at any x along the direction nabla f(Phi(x)). Then, we propose a hybrid algorithm combining the attack operator with derivative-free optimization (DFO) techniques, designed for numerical reliability by remaining oblivious to the structure of the problem. We consider the cDSM algorithm, which offers asymptotic guarantees to converge to a local solution under mild assumptions on the problem. The resulting method alternates between attack-based steps for heuristic yet fast local intensification and cDSM steps for certified convergence and numerical reliability. Experiments on three problems show that this hybrid approach consistently outperforms standard DFO baselines.

In recent years, multiple notions of algorithmic fairness have arisen. One such notion is individual fairness (IF), which requires that individuals who are similar receive similar treatment. In parallel, matrix estimation (ME) has emerged as a natural paradigm for handling noisy data with missing values. In this work, we connect the two concepts. We show that pre-processing data using ME can improve an algorithm's IF without sacrificing performance. Specifically, we show that using a popular ME method known as singular value thresholding (SVT) to pre-process the data provides a strong IF guarantee under appropriate conditions. We then show that, under analogous conditions, SVT pre-processing also yields estimates that are consistent and approximately minimax optimal. As such, the ME pre-processing step does not, under the stated conditions, increase the prediction error of the base algorithm, i.e., does not impose a fairness-performance trade-off. We verify these results on synthetic and real data.

Learned optimizers are powerful alternatives to hand-designed update rules like Adam, yet they have seen limited practical adoption since they often fail to meta-generalize beyond their training distribution and incur high meta-training cost. For instance, prior work, VeLO, scaled meta-training to 4,000 TPU months (sim10times GPT-3 compute) to meta-train a general-purpose optimizer but it failed to generalize beyond 600M parameters tasks. In this work, we present a surprising finding: by crafting a simple normalized optimizer architecture and augmenting meta-training, it becomes feasible to meta-train a performant general-purpose learned update rule on a tiny fraction of VeLO compute, 4.5 GPU hours to be precise. Our learned update rule scales stably to a billion-scale pretraining task (GPT-3 XL 1.3B) which is six orders of magnitude larger than its meta-training distribution. Furthermore, it shows strong performance across diverse out-of-distribution tasks and is compatible with modern optimization harness that includes orthogonalization, distinct update rules for input-output and hidden weights, and decoupled weight decay. In all, this work paves the way for practically applicable learnable optimization algorithms, unlocking exploration of richer meta-training and data curation recipes to further improve performance.

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

Orthogonality-based optimizers, such as Muon, have recently shown strong performance across large-scale training and community-driven efficiency challenges. However, these methods rely on a costly gradient orthogonalization step. Even efficient iterative approximations such as Newton-Schulz remain expensive, typically requiring dozens of matrix multiplications to converge. We introduce a preconditioning procedure that accelerates Newton-Schulz convergence and reduces its computational cost. We evaluate its impact and show that the overhead of our preconditioning can be made negligible. Furthermore, the faster convergence it enables allows us to remove one iteration out of the usual five without degrading approximation quality. Our publicly available implementation achieves up to a 2.8x speedup in the Newton-Schulz approximation. We also show that this has a direct impact on end-to-end training runtime with 5-10% improvement in realistic training scenarios across two efficiency-focused tasks. On challenging language or vision tasks, we validate that our method maintains equal or superior model performance while improving runtime. Crucially, these improvements require no hyperparameter tuning and can be adopted as a simple drop-in replacement. Our code is publicly available on github.

Decoding sits between a language model and everything we do with it, yet it is still treated as a heuristic knob-tuning exercise. We argue decoding should be understood as a principled optimisation layer: at each token, we solve a regularised problem over the probability simplex that trades off model score against structural preferences and constraints. This single template recovers greedy decoding, Softmax sampling, Top-K, Top-P, and Sparsemax-style sparsity as special cases, and explains their common structure through optimality conditions. More importantly, the framework makes it easy to invent new decoders without folklore. We demonstrate this by designing Best-of-K (BoK), a KL-anchored coverage objective aimed at multi-sample pipelines (self-consistency, reranking, verifier selection). BoK targets the probability of covering good alternatives within a fixed K-sample budget and improves empirical performance. We show that such samples can improve accuracy by, for example, +18.6% for Qwen2.5-Math-7B on MATH500 at high sampling temperatures.

As Large Language Model (LLM) capabilities advance, locally deployed personal agents relying on API-based remote models and external skills have emerged as a novel paradigm. With the rapid expansion of available skills, enabling personal agents to learn and adapt to implicit user preferences becomes a critical challenge. However, local deployment constraints preclude complex centralized selection algorithms, creating an urgent need for a lightweight local preference harness. This paper explores the implementation of such a harness through a novel architecture that strictly decouples statistical preference learning from semantic intent parsing. Specifically, we leverage localized statistical results to influence and modulate the selection decisions of the remote LLM. Extensive evaluations demonstrate that our decoupled approach achieves the lowest cumulative regret and highest test accuracy, significantly outperforming traditional memory-augmented agents.

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.

We revisit Group Relative Policy Optimization (GRPO) in both on-policy and off-policy optimization regimes. Our motivation comes from recent work on off-policy Proximal Policy Optimization (PPO), which improves training stability, sampling efficiency, and memory usage. In addition, a recent analysis of GRPO suggests that estimating the advantage function with off-policy samples could be beneficial. Building on these observations, we adapt GRPO to the off-policy setting. We show that both on-policy and off-policy GRPO objectives yield an improvement in the reward. This result motivates the use of clipped surrogate objectives in the off-policy version of GRPO. We then compare the empirical performance of reinforcement learning with verifiable rewards in post-training using both GRPO variants. Our results show that off-policy GRPO either significantly outperforms or performs on par with its on-policy counterpart.

Training large neural network models requires extensive computational resources, often distributed across several nodes and accelerators. Recent findings suggest that it may be sufficient to only exchange the fast moving components of the gradients, while accumulating momentum locally (Decoupled Momentum, or DeMo). However, DeMo assumes that models fit on a single accelerator. We relax this assumption and introduce FlexDeMo, whereby nodes fully shard model parameters locally between different accelerators, while inter-node communication is reduced by synchronizing only fast-moving components instead of the full gradients -- resulting in a hybrid sharded data parallel training strategy. We further introduce a framework, denoted as DeToNATION, that generalizes DeMo, FlexDeMo, and other popular distributed training schemes such as DiLoCo -- introducing new variations of replication schemes and challenging choices made in DeMo. Our results across language and vision domains show that FlexDeMo attains similar validation loss as hybrid sharded data parallel training employing AdamW and full gradient synchronization, while being substantially faster. FlexDeMo is thus a promising distributed training scheme for the largest machine learning models.

Merging finetuned Large Language Models (LLMs) has become increasingly important for integrating diverse capabilities into a single unified model. However, prevailing model merging methods rely on linear arithmetic in Euclidean space, which often destroys the intrinsic geometric properties of pretrained weights, such as hyperspherical energy. To address this, we propose Orthogonal Model Merging (OrthoMerge), a method that performs merging operations on the Riemannian manifold formed by the orthogonal group to preserve the geometric structure of the model's weights. By mapping task-specific orthogonal matrices learned by Orthogonal Finetuning (OFT) to the Lie algebra, OrthoMerge enables a principled yet efficient integration that takes into account both the direction and intensity of adaptations. In addition to directly leveraging orthogonal matrices obtained by OFT, we further extend this approach to general models finetuned with non-OFT methods (i.e., low-rank finetuning, full finetuning) via an Orthogonal-Residual Decoupling strategy. This technique extracts the orthogonal components of expert models by solving the orthogonal Procrustes problem, which are then merged on the manifold of the orthogonal group, while the remaining linear residuals are processed through standard additive merging. Extensive empirical results demonstrate the effectiveness of OrthoMerge in mitigating catastrophic forgetting and maintaining model performance across diverse tasks.

Training stability is a persistent challenge in the pre-training of large language models (LLMs), particularly for architectures such as Post-Norm Transformers, which are prone to gradient explosion and dissipation. In this paper, we propose Scale-Distribution Decoupling (SDD), a novel approach that stabilizes training by explicitly decoupling the scale and distribution of the weight matrix in fully-connected layers. SDD applies a normalization mechanism to regulate activations and a learnable scaling vector to maintain well-conditioned gradients, effectively preventing gradient explosion and dissipation. This separation improves optimization efficiency, particularly in deep networks, by ensuring stable gradient propagation. Experimental results demonstrate that our method stabilizes training across various LLM architectures and outperforms existing techniques in different normalization configurations. Furthermore, the proposed method is lightweight and compatible with existing frameworks, making it a practical solution for stabilizing LLM training. Code is available at https://github.com/kaihemo/SDD.

A unified framework for first-order optimization algorithms fornonconvex unconstrained optimization is proposed that uses adaptivelypreconditioned gradients and includes popular methods such as full anddiagonal AdaGrad, AdaNorm, as well as adpative variants of Shampoo andMuon. This framework also allows combining heterogeneous geometriesacross different groups of variables while preserving a unifiedconvergence analysis. A fully stochastic global rate-of-convergenceanalysis is conducted for all methods in the framework, with andwithout two types of momentum, using reasonable assumptions on thevariance of the gradient oracle and without assuming boundedstochastic gradients or small enough stepsize.

Reasoning Language Models, capable of extended chain-of-thought reasoning, have demonstrated remarkable performance on tasks requiring complex logical inference. However, applying elaborate reasoning for all queries often results in substantial computational inefficiencies, particularly when many problems admit straightforward solutions. This motivates an open question: Can LLMs learn when to think? To answer this, we propose Thinkless, a learnable framework that empowers an LLM to adaptively select between short-form and long-form reasoning, based on both task complexity and the model's ability. Thinkless is trained under a reinforcement learning paradigm and employs two control tokens, <short> for concise responses and <think> for detailed reasoning. At the core of our method is a Decoupled Group Relative Policy Optimization (DeGRPO) algorithm, which decomposes the learning objective of hybrid reasoning into two components: (1) a control token loss that governs the selection of the reasoning mode, and (2) a response loss that improves the accuracy of the generated answers. This decoupled formulation enables fine-grained control over the contributions of each objective, stabilizing training and effectively preventing collapse observed in vanilla GRPO. Empirically, on several benchmarks such as Minerva Algebra, MATH-500, and GSM8K, Thinkless is able to reduce the usage of long-chain thinking by 50% - 90%, significantly improving the efficiency of Reasoning Language Models. The code is available at https://github.com/VainF/Thinkless

We compare the (1,lambda)-EA and the (1 + lambda)-EA on the recently introduced benchmark DisOM, which is the OneMax function with randomly planted local optima. Previous work showed that if all local optima have the same relative height, then the plus strategy never loses more than a factor O(nlog n) compared to the comma strategy. Here we show that even small random fluctuations in the heights of the local optima have a devastating effect for the plus strategy and lead to super-polynomial runtimes. On the other hand, due to their ability to escape local optima, comma strategies are unaffected by the height of the local optima and remain efficient. Our results hold for a broad class of possible distortions and show that the plus strategy, but not the comma strategy, is generally deceived by sparse unstructured fluctuations of a smooth landscape.

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of ell predictors, we obtain a competitive ratio of O(ell^2), and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a (1+epsilon)-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the k-server problem.

Offline paired preference optimization algorithms have become a popular approach for fine-tuning on preference data, outperforming traditional supervised fine-tuning in various tasks. However, traditional implementations often involve redundant computations, especially for tasks with long shared prompts. We introduce prefix sharing for preference tuning, a novel technique that processes chosen and rejected responses as one sequence with a shared prefix. To prevent cross-response contamination, we use a custom block-sparse attention mask. Our method achieves 1.1-1.5times improvement in training throughput on popular DPO datasets, without any effect on convergence. When combined with sequence packing, we observe consistent 1.3-1.6times speedups, benefiting even datasets with smaller sequence lengths. While we focus on Direct Preference Optimization (DPO), our approach is applicable to other paired preference tuning methods. By enhancing computational efficiency, our work contributes to making preference-based fine-tuning more accessible for a wider range of applications and model sizes. We open-source our code at https://github.com/frankxwang/dpo-prefix-sharing.

We study first-order methods with preconditioning for solving structured nonlinear convex optimization problems. We propose a new family of preconditioners generated by symmetric polynomials. They provide first-order optimization methods with a provable improvement of the condition number, cutting the gaps between highest eigenvalues, without explicit knowledge of the actual spectrum. We give a stochastic interpretation of this preconditioning in terms of coordinate volume sampling and compare it with other classical approaches, including the Chebyshev polynomials. We show how to incorporate a polynomial preconditioning into the Gradient and Fast Gradient Methods and establish the corresponding global complexity bounds. Finally, we propose a simple adaptive search procedure that automatically chooses the best possible polynomial preconditioning for the Gradient Method, minimizing the objective along a low-dimensional Krylov subspace. Numerical experiments confirm the efficiency of our preconditioning strategies for solving various machine learning problems.

Learning decompositions of expensive-to-evaluate black-box functions promises to scale Bayesian optimisation (BO) to high-dimensional problems. However, the success of these techniques depends on finding proper decompositions that accurately represent the black-box. While previous works learn those decompositions based on data, we investigate data-independent decomposition sampling rules in this paper. We find that data-driven learners of decompositions can be easily misled towards local decompositions that do not hold globally across the search space. Then, we formally show that a random tree-based decomposition sampler exhibits favourable theoretical guarantees that effectively trade off maximal information gain and functional mismatch between the actual black-box and its surrogate as provided by the decomposition. Those results motivate the development of the random decomposition upper-confidence bound algorithm (RDUCB) that is straightforward to implement - (almost) plug-and-play - and, surprisingly, yields significant empirical gains compared to the previous state-of-the-art on a comprehensive set of benchmarks. We also confirm the plug-and-play nature of our modelling component by integrating our method with HEBO, showing improved practical gains in the highest dimensional tasks from Bayesmark.

We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global Optimization), a simple and effective algorithm to solve it. Under certain regularity assumptions, we show that our algorithm enjoys the same cumulative regret bound as that in the unconstrained case and similar cumulative constraint violation upper bounds. For commonly used Matern and Squared Exponential kernels, our bounds are sublinear and allow us to derive a convergence rate to the optimal solution of the original constrained problem. In addition, our method naturally provides a scheme to declare infeasibility when the original black-box optimization problem is infeasible. Numerical experiments on sampled instances from the Gaussian process, artificial numerical problems, and a black-box building controller tuning problem all demonstrate the competitive performance of our algorithm. Compared to the other state-of-the-art methods, our algorithm significantly improves the theoretical guarantees, while achieving competitive empirical performance.

Inference-time optimization scales computation to derive deliberate reasoning steps for effective performance. While previous search-based strategies address the short-sightedness of auto-regressive generation, the vast search space leads to excessive exploration and insufficient exploitation. To strike an efficient balance to derive the optimal step, we frame the decoding strategy as foresight sampling, leveraging simulated future steps to obtain globally optimal step estimation. Built on it, we propose a novel decoding strategy, named phi-Decoding. To provide a precise and expressive estimation of step value, phi-Decoding approximates two distributions via foresight and clustering. Sampling from the joint distribution, the optimal steps can be selected for exploitation. To support adaptive computation allocation, we propose in-width and in-depth pruning strategies, featuring a light-weight solution to achieve inference efficiency. Extensive experiments across seven benchmarks show phi-Decoding outperforms strong baselines in both performance and efficiency. Additional analysis demonstrates its generalization across various LLMs and scalability across a wide range of computing budgets. The code will be released at https://github.com/xufangzhi/phi-Decoding, and the open-source PyPI package is coming soon.

The evolution of Retrieval-Augmented Generation (RAG) has shifted from static retrieval pipelines to dynamic, agentic workflows where a central planner orchestrates multi-turn reasoning. However, existing paradigms face a critical dichotomy: they either optimize modules jointly within rigid, fixed-graph architectures, or empower dynamic planning while treating executors as frozen, black-box tools. We identify that this decoupled optimization creates a ``strategic-operational mismatch,'' where sophisticated planning strategies fail to materialize due to unadapted local executors, often leading to negative performance gains despite increased system complexity. In this paper, we propose JADE (Joint Agentic Dynamic Execution), a unified framework for the joint optimization of planning and execution within dynamic, multi-turn workflows. By modeling the system as a cooperative multi-agent team unified under a single shared backbone, JADE enables end-to-end learning driven by outcome-based rewards. This approach facilitates co-adaptation: the planner learns to operate within the capability boundaries of the executors, while the executors evolve to align with high-level strategic intent. Empirical results demonstrate that JADE transforms disjoint modules into a synergistic system, yielding remarkable performance improvements via joint optimization and enabling a flexible balance between efficiency and effectiveness through dynamic workflow orchestration.

Recent advances in large language models (LLMs) have enabled agents to autonomously execute complex, long-horizon tasks, yet planning remains a primary bottleneck for reliable task execution. Existing methods typically fall into two paradigms: step-wise planning, which is reactive but often short-sighted; and one-shot planning, which generates a complete plan upfront yet is brittle to execution errors. Crucially, both paradigms suffer from entangled contexts, where the agent must reason over a monolithic history spanning multiple sub-tasks. This entanglement increases cognitive load and lets local errors propagate across otherwise independent decisions, making recovery computationally expensive. To address this, we propose Task-Decoupled Planning (TDP), a training-free framework that replaces entangled reasoning with task decoupling. TDP decomposes tasks into a directed acyclic graph (DAG) of sub-goals via a Supervisor. Using a Planner and Executor with scoped contexts, TDP confines reasoning and replanning to the active sub-task. This isolation prevents error propagation and corrects deviations locally without disrupting the workflow. Results on TravelPlanner, ScienceWorld, and HotpotQA show that TDP outperforms strong baselines while reducing token consumption by up to 82%, demonstrating that sub-task decoupling improves both robustness and efficiency for long-horizon agents.

Multi-step learning applies lookahead over multiple time steps and has proved valuable in policy evaluation settings. However, in the optimal control case, the impact of multi-step learning has been relatively limited despite a number of prior efforts. Fundamentally, this might be because multi-step policy improvements require operations that cannot be approximated by stochastic samples, hence hindering the widespread adoption of such methods in practice. To address such limitations, we introduce doubly multi-step off-policy VI (DoMo-VI), a novel oracle algorithm that combines multi-step policy improvements and policy evaluations. DoMo-VI enjoys guaranteed convergence speed-up to the optimal policy and is applicable in general off-policy learning settings. We then propose doubly multi-step off-policy actor-critic (DoMo-AC), a practical instantiation of the DoMo-VI algorithm. DoMo-AC introduces a bias-variance trade-off that ensures improved policy gradient estimates. When combined with the IMPALA architecture, DoMo-AC has showed improvements over the baseline algorithm on Atari-57 game benchmarks.

Exploiting partial first-order information in a cyclic way is arguably the most natural strategy to obtain scalable first-order methods. However, despite their wide use in practice, cyclic schemes are far less understood from a theoretical perspective than their randomized counterparts. Motivated by a recent success in analyzing an extrapolated cyclic scheme for generalized variational inequalities, we propose an Accelerated Cyclic Coordinate Dual Averaging with Extrapolation (A-CODER) method for composite convex optimization, where the objective function can be expressed as the sum of a smooth convex function accessible via a gradient oracle and a convex, possibly nonsmooth, function accessible via a proximal oracle. We show that A-CODER attains the optimal convergence rate with improved dependence on the number of blocks compared to prior work. Furthermore, for the setting where the smooth component of the objective function is expressible in a finite sum form, we introduce a variance-reduced variant of A-CODER, VR-A-CODER, with state-of-the-art complexity guarantees. Finally, we demonstrate the effectiveness of our algorithms through numerical experiments.

Consistency-based generative models like Shortcut and MeanFlow achieve impressive results via a target-aware design for solving the Probability Flow ODE (PF-ODE). Typically, such methods introduce a target time r alongside the current time t to modulate outputs between a local multi-step derivative (r = t) and a global few-step integral (r = 0). However, the conventional "one input, one output" paradigm enforces a partition of the training budget, often allocating a significant portion (e.g., 75% in MeanFlow) solely to the multi-step objective for stability. This separation forces a trade-off: allocating sufficient samples to the multi-step objective leaves the few-step generation undertrained, which harms convergence and limits scalability. To this end, we propose Duality Models (DuMo) via a "one input, dual output" paradigm. Using a shared backbone with dual heads, DuMo simultaneously predicts velocity v_t and flow-map u_t from a single input x_t. This applies geometric constraints from the multi-step objective to every sample, bounding the few-step estimation without separating training objectives, thereby significantly improving stability and efficiency. On ImageNet 256 times 256, a 679M Diffusion Transformer with SD-VAE achieves a state-of-the-art (SOTA) FID of 1.79 in just 2 steps. Code is available at: https://github.com/LINs-lab/DuMo

Synthesizing optimal controllers for dynamical systems often involves solving optimization problems with hard real-time constraints. These constraints determine the class of numerical methods that can be applied: computationally expensive but accurate numerical routines are replaced by fast and inaccurate methods, trading inference time for solution accuracy. This paper provides techniques to improve the quality of optimized control policies given a fixed computational budget. We achieve the above via a hypersolvers approach, which hybridizes a differential equation solver and a neural network. The performance is evaluated in direct and receding-horizon optimal control tasks in both low and high dimensions, where the proposed approach shows consistent Pareto improvements in solution accuracy and control performance.

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.

Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance tradeoffs. We theoretically show that, under some conditions, estimators such as MINE exhibit variance that could grow exponentially with the true amount of underlying MI. We also empirically demonstrate that existing estimators fail to satisfy basic self-consistency properties of MI, such as data processing and additivity under independence. Based on a unified perspective of variational approaches, we develop a new estimator that focuses on variance reduction. Empirical results on standard benchmark tasks demonstrate that our proposed estimator exhibits improved bias-variance trade-offs on standard benchmark tasks.

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.

The key-value (KV) cache dominates memory bandwidth and footprint in long-context autoregressive inference. Recent rotation-preconditioned codecs (TurboQuant, PolarQuant) show that a structured random rotation followed by a per-coordinate scalar quantizer matched to an analytically tractable marginal is a near-optimal recipe for KV compression. OCTOPUS advances this paradigm through joint quantization of rotated coordinate triplets. Each triplet's direction is mapped to a square via an octahedral parameterization, and the two resulting coordinates and the triplet norm are Lloyd-Max quantized against implementation-matched marginals. Optimizing the per-triplet squared error gives a strictly non-uniform bit allocation depending only on the total dimensionality of the keys. We find the finite-dimensional quality optimum with sweeps to be constant on every real decoder we test. The codec is data-oblivious, online, and deterministic given a seed. Across text, video, and audio, OCTOPUS matches or beats every prior rotation codec at every reported bit width and metric, with a lead that grows as bits drop for extreme compression. Furthermore, a fused Triton implementation reconstructs keys on the fly without materializing the uncompressed key, so the codec adds no decode-time bandwidth or latency over the existing dequantization. Project Page: https://octopus-quant.github.io/

Model-agnostic meta-reinforcement learning requires estimating the Hessian matrix of value functions. This is challenging from an implementation perspective, as repeatedly differentiating policy gradient estimates may lead to biased Hessian estimates. In this work, we provide a unifying framework for estimating higher-order derivatives of value functions, based on off-policy evaluation. Our framework interprets a number of prior approaches as special cases and elucidates the bias and variance trade-off of Hessian estimates. This framework also opens the door to a new family of estimates, which can be easily implemented with auto-differentiation libraries, and lead to performance gains in practice.

While most autoregressive LLMs are constrained to one-by-one decoding, diffusion LLMs (dLLMs) have attracted growing interest for their potential to dramatically accelerate inference through parallel decoding. Despite this promise, the conditional independence assumption in dLLMs causes parallel decoding to ignore token dependencies, inevitably degrading generation quality when these dependencies are strong. However, existing works largely overlook these inherent challenges, and evaluations on standard benchmarks (e.g., math and coding) are not sufficient to capture the quality degradation caused by parallel decoding. To address this gap, we first provide an information-theoretic analysis of parallel decoding. We then conduct case studies on analytically tractable synthetic list operations from both data distribution and decoding strategy perspectives, offering quantitative insights that highlight the fundamental limitations of parallel decoding. Building on these insights, we propose ParallelBench, the first benchmark specifically designed for dLLMs, featuring realistic tasks that are trivial for humans and autoregressive LLMs yet exceptionally challenging for dLLMs under parallel decoding. Using ParallelBench, we systematically analyze both dLLMs and autoregressive LLMs, revealing that: (i) dLLMs under parallel decoding can suffer dramatic quality degradation in real-world scenarios, and (ii) current parallel decoding strategies struggle to adapt their degree of parallelism based on task difficulty, thus failing to achieve meaningful speedup without compromising quality. Our findings underscore the pressing need for innovative decoding methods that can overcome the current speed-quality trade-off. We release our benchmark to help accelerate the development of truly efficient dLLMs.

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.

As language models become increasingly capable, users expect them to provide not only accurate responses but also behaviors aligned with diverse human preferences across a variety of scenarios. To achieve this, Reinforcement learning (RL) pipelines have begun incorporating multiple rewards, each capturing a distinct preference, to guide models toward these desired behaviors. However, recent work has defaulted to apply Group Relative Policy Optimization (GRPO) under multi-reward setting without examining its suitability. In this paper, we demonstrate that directly applying GRPO to normalize distinct rollout reward combinations causes them to collapse into identical advantage values, reducing the resolution of the training signal and resulting in suboptimal convergence and, in some cases, early training failure. We then introduce Group reward-Decoupled Normalization Policy Optimization (GDPO), a new policy optimization method to resolve these issues by decoupling the normalization of individual rewards, more faithfully preserving their relative differences and enabling more accurate multi-reward optimization, along with substantially improved training stability. We compare GDPO with GRPO across three tasks: tool calling, math reasoning, and coding reasoning, evaluating both correctness metrics (accuracy, bug ratio) and constraint adherence metrics (format, length). Across all settings, GDPO consistently outperforms GRPO, demonstrating its effectiveness and generalizability for multi-reward reinforcement learning optimization.

We study online reinforcement learning in linear Markov decision processes with adversarial losses and bandit feedback, without prior knowledge on transitions or access to simulators. We introduce two algorithms that achieve improved regret performance compared to existing approaches. The first algorithm, although computationally inefficient, ensures a regret of mathcal{O}left(Kright), where K is the number of episodes. This is the first result with the optimal K dependence in the considered setting. The second algorithm, which is based on the policy optimization framework, guarantees a regret of mathcal{O}left(K^{3{4}} right) and is computationally efficient. Both our results significantly improve over the state-of-the-art: a computationally inefficient algorithm by Kong et al. [2023] with mathcal{O}left(K^{4{5}}+polyleft(1{lambda_{min}}right) right) regret, for some problem-dependent constant lambda_{min} that can be arbitrarily close to zero, and a computationally efficient algorithm by Sherman et al. [2023b] with mathcal{O}left(K^{6{7}} right) regret.

This paper presents a novel information-theoretic perspective on generalization in machine learning by framing the learning problem within the context of lossy compression and applying finite blocklength analysis. In our approach, the sampling of training data formally corresponds to an encoding process, and the model construction to a decoding process. By leveraging finite blocklength analysis, we derive lower bounds on sample complexity and generalization error for a fixed randomized learning algorithm and its associated optimal sampling strategy. Our bounds explicitly characterize the degree of overfitting of the learning algorithm and the mismatch between its inductive bias and the task as distinct terms. This separation provides a significant advantage over existing frameworks. Additionally, we decompose the overfitting term to show its theoretical connection to existing metrics found in information-theoretic bounds and stability theory, unifying these perspectives under our proposed framework.

In offline multi-objective optimization (MOO), we leverage an offline dataset of designs and their associated labels to simultaneously minimize multiple objectives. This setting more closely mirrors complex real-world problems compared to single-objective optimization. Recent works mainly employ evolutionary algorithms and Bayesian optimization, with limited attention given to the generative modeling capabilities inherent in such data. In this study, we explore generative modeling in offline MOO through flow matching, noted for its effectiveness and efficiency. We introduce ParetoFlow, specifically designed to guide flow sampling to approximate the Pareto front. Traditional predictor (classifier) guidance is inadequate for this purpose because it models only a single objective. In response, we propose a multi-objective predictor guidance module that assigns each sample a weight vector, representing a weighted distribution across multiple objective predictions. A local filtering scheme is introduced to address non-convex Pareto fronts. These weights uniformly cover the entire objective space, effectively directing sample generation towards the Pareto front. Since distributions with similar weights tend to generate similar samples, we introduce a neighboring evolution module to foster knowledge sharing among neighboring distributions. This module generates offspring from these distributions, and selects the most promising one for the next iteration. Our method achieves state-of-the-art performance across various tasks.

Multi-agent reinforcement learning shines as the pinnacle of multi-agent systems, conquering intricate real-world challenges, fostering collaboration and coordination among agents, and unleashing the potential for intelligent decision-making across domains. However, training a multi-agent reinforcement learning network is a formidable endeavor, demanding substantial computational resources to interact with diverse environmental variables, extract state representations, and acquire decision-making knowledge. The recent breakthroughs in large-scale pre-trained models ignite our curiosity: Can we uncover shared knowledge in multi-agent reinforcement learning and leverage pre-trained models to expedite training for future tasks? Addressing this issue, we present an innovative multi-task learning approach that aims to extract and harness common decision-making knowledge, like cooperation and competition, across different tasks. Our approach involves concurrent training of multiple multi-agent tasks, with each task employing independent front-end perception layers while sharing back-end decision-making layers. This effective decoupling of state representation extraction from decision-making allows for more efficient training and better transferability. To evaluate the efficacy of our proposed approach, we conduct comprehensive experiments in two distinct environments: the StarCraft Multi-agent Challenge (SMAC) and the Google Research Football (GRF) environments. The experimental results unequivocally demonstrate the smooth transferability of the shared decision-making network to other tasks, thereby significantly reducing training costs and improving final performance. Furthermore, visualizations authenticate the presence of general multi-agent decision-making knowledge within the shared network layers, further validating the effectiveness of our approach.

As first-order optimization methods become the method of choice for solving large-scale optimization problems, optimization solvers based on first-order algorithms are being built. Such general-purpose solvers must robustly detect infeasible or misspecified problem instances, but the computational complexity of first-order methods for doing so has yet to be formally studied. In this work, we characterize the optimal accelerated rate of infeasibility detection. We show that the standard fixed-point iteration achieves a O(1/k^2) and O(1/k) rates, respectively, on the normalized iterates and the fixed-point residual converging to the infimal displacement vector, while the accelerated fixed-point iteration achieves O(1/k^2) and mathcal{O}(1/k^2) rates. We then provide a matching complexity lower bound to establish that Theta(1/k^2) is indeed the optimal accelerated rate.

Orthogonalized-update optimizers such as Muon improve training of matrix-valued parameters, but existing extensions typically either rescale updates after orthogonalization or use heavier whitening-based preconditioners before it. We introduce {\method}, a lightweight family of pre-orthogonalization equilibration schemes for Muon with three forms: two-sided row/column normalization (RC), row normalization (R), and column normalization (C). By rebalancing the momentum matrix before finite-step Newton--Schulz orthogonalization, {\method} improves the geometry seen by orthogonalization. We show that finite-step orthogonalization is governed by the input spectrum, especially stable rank and condition number, and that row/column normalization acts as a zeroth-order surrogate for whitening. For hidden matrix weights, R is the default variant. Theoretically, {\method} (R) retains the standard mathcal O(T^{-1/4}) Muon-type nonconvex stationarity guarantee with decoupled weight decay and a horizon-free diminishing learning-rate schedule, and extends it to finite-step NS5 up to an explicit inexactness constant. In LLaMA2 pretraining on C4, {\method} (R) consistently outperforms Muon on 130M, 350M, and 1B models, with faster convergence and lower validation perplexity. The code is available at the https://github.com/MaeChd/muon-eq{MuonEq codebase}.

We study the algorithm configuration (AC) problem, in which one seeks to find an optimal parameter configuration of a given target algorithm in an automated way. Recently, there has been significant progress in designing AC approaches that satisfy strong theoretical guarantees. However, a significant gap still remains between the practical performance of these approaches and state-of-the-art heuristic methods. To this end, we introduce AC-Band, a general approach for the AC problem based on multi-armed bandits that provides theoretical guarantees while exhibiting strong practical performance. We show that AC-Band requires significantly less computation time than other AC approaches providing theoretical guarantees while still yielding high-quality configurations.

Efficient numerical solvers for partial differential equations empower science and engineering. One of the commonly employed numerical solvers is the preconditioned conjugate gradient (PCG) algorithm which can solve large systems to a given precision level. One challenge in PCG solvers is the selection of preconditioners, as different problem-dependent systems can benefit from different preconditioners. We present a new method to introduce inductive bias in preconditioning conjugate gradient algorithm. Given a system matrix and a set of solution vectors arise from an underlying distribution, we train a graph neural network to obtain an approximate decomposition to the system matrix to be used as a preconditioner in the context of PCG solvers. We conduct extensive experiments to demonstrate the efficacy and generalizability of our proposed approach in solving various 2D and 3D linear second-order PDEs.

We present a non-asymptotic theory of generalization in deep learning where the empirical neural tangent kernel partitions the output space. In directions corresponding to signal, error dissipates rapidly; in the vast orthogonal dimensions corresponding to noise, the kernel's near-zero eigenvalues trap residual error in a test-invisible reservoir. Within the signal channel, minibatch SGD ensures that coherent population signal accumulates via fast linear drift, while idiosyncratic memorization is suppressed into a slow, diffusive random walk. We prove generalization survives even when the kernel evolves O(1) in operator norm, the full feature-learning regime. This theory naturally explains disparate phenomena in deep learning theory, such as benign overfitting, double descent, implicit bias, and grokking. Lastly, we derive an exact population-risk objective from a single training run with no validation data, for any architecture, loss, or optimizer, and prove that it measures precisely the noise in the signal channel. This objective reduces in practice to an SNR preconditioner on top of Adam, adding one state vector at no extra cost; it accelerates grokking by 5 times, suppresses memorization in PINNs and implicit neural representations, and improves DPO fine-tuning under noisy preferences while staying 3 times closer to the reference policy.

We consider a family of convex quadratic programs in which the coefficients of the linear objective term and the righthand side of the constraints are affine functions of a parameter. It is well known that the solution of such a parametrized quadratic program is a piecewise affine function of the parameter. The number of (polyhedral) regions in the solution map can grow exponentially in problem size, but when the number of regions is moderate, a so-called explicit solver is practical. Such a solver computes the coefficients of the affine functions and the linear inequalities defining the polyhedral regions offline; to solve a problem instance online it simply evaluates this explicit solution map. Potential advantages of an explicit solver over a more general purpose iterative solver can include transparency, interpretability, reliability, and speed. In this paper we describe how code generation can be used to automatically generate an explicit solver from a high level description of a parametrized quadratic program. Our method has been implemented in the open-source software CVXPYgen, which is part of CVXPY, a domain specific language for general convex optimization.

We propose a method that achieves near-optimal rates for smooth stochastic convex optimization and requires essentially no prior knowledge of problem parameters. This improves on prior work which requires knowing at least the initial distance to optimality d0. Our method, U-DoG, combines UniXGrad (Kavis et al., 2019) and DoG (Ivgi et al., 2023) with novel iterate stabilization techniques. It requires only loose bounds on d0 and the noise magnitude, provides high probability guarantees under sub-Gaussian noise, and is also near-optimal in the non-smooth case. Our experiments show consistent, strong performance on convex problems and mixed results on neural network 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 optimal bit-width for achieving the best trade-off between quantized model size and accuracy has been a subject of ongoing debate. While some advocate for 4-bit quantization, others propose that 1.58-bit offers superior results. However, the lack of a cohesive framework for different bits has left such conclusions relatively tenuous. We present ParetoQ, the first unified framework that facilitates rigorous comparisons across 1-bit, 1.58-bit, 2-bit, 3-bit, and 4-bit quantization settings. Our findings reveal a notable learning transition between 2 and 3 bits: For 3-bits and above, the fine-tuned models stay close to their original pre-trained distributions, whereas for learning 2-bit networks or below, the representations change drastically. By optimizing training schemes and refining quantization functions, ParetoQ surpasses all previous methods tailored to specific bit widths. Remarkably, our ParetoQ ternary 600M-parameter model even outperforms the previous SoTA ternary 3B-parameter model in accuracy, using only one-fifth of the parameters. Extensive experimentation shows that ternary, 2-bit, and 3-bit quantization maintains comparable performance in the size-accuracy trade-off and generally exceeds 4-bit and binary quantization. Considering hardware constraints, 2-bit quantization offers promising potential for memory reduction and speedup.