Daily Papers

In machine learning applications, it is well known that carefully designed learning rate (step size) schedules can significantly improve the convergence of commonly used first-order optimization algorithms. Therefore how to set step size adaptively becomes an important research question. A popular and effective method is the Polyak step size, which sets step size adaptively for gradient descent or stochastic gradient descent without the need to estimate the smoothness parameter of the objective function. However, there has not been a principled way to generalize the Polyak step size for algorithms with momentum accelerations. This paper presents a general framework to set the learning rate adaptively for first-order optimization methods with momentum, motivated by the derivation of Polyak step size. It is shown that the resulting methods are much less sensitive to the choice of momentum parameter and may avoid the oscillation of the heavy-ball method on ill-conditioned problems. These adaptive step sizes are further extended to the stochastic settings, which are attractive choices for stochastic gradient descent with momentum. Our methods are demonstrated to be more effective for stochastic gradient methods than prior adaptive step size algorithms in large-scale machine learning tasks.

We showcase important features of the dynamics of the Stochastic Gradient Descent (SGD) in the training of neural networks. We present empirical observations that commonly used large step sizes (i) lead the iterates to jump from one side of a valley to the other causing loss stabilization, and (ii) this stabilization induces a hidden stochastic dynamics orthogonal to the bouncing directions that biases it implicitly toward sparse predictors. Furthermore, we show empirically that the longer large step sizes keep SGD high in the loss landscape valleys, the better the implicit regularization can operate and find sparse representations. Notably, no explicit regularization is used so that the regularization effect comes solely from the SGD training dynamics influenced by the step size schedule. Therefore, these observations unveil how, through the step size schedules, both gradient and noise drive together the SGD dynamics through the loss landscape of neural networks. We justify these findings theoretically through the study of simple neural network models as well as qualitative arguments inspired from stochastic processes. Finally, this analysis allows us to shed a new light on some common practice and observed phenomena when training neural networks. The code of our experiments is available at https://github.com/tml-epfl/sgd-sparse-features.

We propose a tuning-free dynamic SGD step size formula, which we call Distance over Gradients (DoG). The DoG step sizes depend on simple empirical quantities (distance from the initial point and norms of gradients) and have no ``learning rate'' parameter. Theoretically, we show that a slight variation of the DoG formula enjoys strong parameter-free convergence guarantees for stochastic convex optimization assuming only locally bounded stochastic gradients. Empirically, we consider a broad range of vision and language transfer learning tasks, and show that DoG's performance is close to that of SGD with tuned learning rate. We also propose a per-layer variant of DoG that generally outperforms tuned SGD, approaching the performance of tuned Adam. A PyTorch implementation is available at https://github.com/formll/dog

Masked diffusion language models (MDLMs) have recently emerged as a promising alternative to autoregressive (AR) language models, offering properties such as parallel decoding, flexible generation orders, and the potential for fewer inference steps. Despite these advantages, decoding strategies and reinforcement learning (RL) algorithms tailored for MDLMs remain underexplored. A naive approach is to directly transfer techniques well-established for AR models to MDLMs. However, this raises an immediate question: Is such a naive transfer truly optimal? For example, 1) Block-wise and semi-AR decoding strategies are not employed during the training of MDLMs, so why do they outperform full diffusion-style decoding during inference? 2) Applying RL algorithms designed for AR models directly to MDLMs exhibits a training-inference inconsistency, since MDLM decoding are non-causal (parallel). This results in inconsistencies between the rollout trajectory and the optimization trajectory. To address these challenges, we propose EOS Early Rejection (EOSER) and Ascending Step-Size (ASS) decoding scheduler, which unlock the potential of MDLMs to perform full diffusion-style decoding, achieving competitive performance with fewer decoding steps. Additionally, we introduce Consistency Trajectory Group Relative Policy Optimization (CJ-GRPO) for taming MDLMs, which emphasizes the consistency between rollout trajectory and optimization trajectory, and reduces the optimization errors caused by skip-step optimization. We conduct extensive experiments on reasoning tasks, such as mathematical and planning benchmarks, using LLaDA-8B-Instruct. The results demonstrate that the proposed EOSER and ASS mechanisms, together with CJ-GRPO, hold significant promise for effectively and efficiently taming MDLMs. Code: https://github.com/yjyddq/EOSER-ASS-RL.

Diffusion models achieve remarkable generation quality but suffer from computational intensive sampling due to suboptimal step discretization. While existing works focus on optimizing denoising directions, we address the principled design of stepsize schedules. This paper proposes Optimal Stepsize Distillation, a dynamic programming framework that extracts theoretically optimal schedules by distilling knowledge from reference trajectories. By reformulating stepsize optimization as recursive error minimization, our method guarantees global discretization bounds through optimal substructure exploitation. Crucially, the distilled schedules demonstrate strong robustness across architectures, ODE solvers, and noise schedules. Experiments show 10x accelerated text-to-image generation while preserving 99.4% performance on GenEval. Our code is available at https://github.com/bebebe666/OptimalSteps.

This paper investigates the global convergence of stepsized Newton methods for convex functions. We propose several simple stepsize schedules with fast global convergence guarantees, up to O (k^{-3}), nearly matching lower complexity bounds Omega (k^{-3.5}) of second-order methods. For cases with multiple plausible smoothness parameterizations or an unknown smoothness constant, we introduce a stepsize backtracking procedure that ensures convergence as if the optimal smoothness parameters were known.

The expanding computational costs and limited resources underscore the critical need for budgeted-iteration training, which aims to achieve optimal learning within predetermined iteration budgets.While learning rate schedules fundamentally govern the performance of different networks and tasks, particularly in budgeted-iteration scenarios, their design remains largely heuristic, lacking theoretical foundations.In addition, the optimal learning rate schedule requires extensive trial-and-error selection, making the training process inefficient.In this work, we propose the Unified Budget-Aware (UBA) schedule, a theoretically grounded learning rate schedule that consistently outperforms commonly-used schedules among diverse architectures and tasks under different constrained training budgets.First, we bridge the gap by constructing a novel training budget-aware optimization framework, which explicitly accounts for the robustness to landscape curvature variations.From this framework, we derive the UBA schedule, controlled by a single hyper-parameter varphi that provides a trade-off between flexibility and simplicity, eliminating the need for per-network numerical optimization. Moreover, we establish a theoretical connection between varphi and the condition number, adding interpretation and justification to our approach. Besides, we prove the convergence for different values of varphi.We offer practical guidelines for its selection via theoretical analysis and empirical results.xtensive experimental results show that UBA consistently surpasses the commonly-used schedules across diverse vision and language tasks, spanning network architectures (e.g., ResNet, OLMo) and scales, under different training-iteration budgets.

Text-to-image diffusion models are computationally intensive, often requiring dozens of forward passes through large transformer backbones. For instance, Stable Diffusion XL generates high-quality images with 50 evaluations of a 2.6B-parameter model, an expensive process even for a single batch. Few-step diffusion models reduce this cost to 2-8 denoising steps but still depend on large, uncompressed U-Net or diffusion transformer backbones, which are often too costly for full-precision inference without datacenter GPUs. These requirements also limit existing post-training quantization methods that rely on full-precision calibration. We introduce Q-Sched, a new paradigm for post-training quantization that modifies the diffusion model scheduler rather than model weights. By adjusting the few-step sampling trajectory, Q-Sched achieves full-precision accuracy with a 4x reduction in model size. To learn quantization-aware pre-conditioning coefficients, we propose the JAQ loss, which combines text-image compatibility with an image quality metric for fine-grained optimization. JAQ is reference-free and requires only a handful of calibration prompts, avoiding full-precision inference during calibration. Q-Sched delivers substantial gains: a 15.5% FID improvement over the FP16 4-step Latent Consistency Model and a 16.6% improvement over the FP16 8-step Phased Consistency Model, showing that quantization and few-step distillation are complementary for high-fidelity generation. A large-scale user study with more than 80,000 annotations further confirms Q-Sched's effectiveness on both FLUX.1[schnell] and SDXL-Turbo.

Deep learning practitioners often operate on a computational and monetary budget. Thus, it is critical to design optimization algorithms that perform well under any budget. The linear learning rate schedule is considered the best budget-aware schedule, as it outperforms most other schedules in the low budget regime. On the other hand, learning rate schedules -- such as the 30-60-90 step schedule -- are known to achieve high performance when the model can be trained for many epochs. Yet, it is often not known a priori whether one's budget will be large or small; thus, the optimal choice of learning rate schedule is made on a case-by-case basis. In this paper, we frame the learning rate schedule selection problem as a combination of i) selecting a profile (i.e., the continuous function that models the learning rate schedule), and ii) choosing a sampling rate (i.e., how frequently the learning rate is updated/sampled from this profile). We propose a novel profile and sampling rate combination called the Reflected Exponential (REX) schedule, which we evaluate across seven different experimental settings with both SGD and Adam optimizers. REX outperforms the linear schedule in the low budget regime, while matching or exceeding the performance of several state-of-the-art learning rate schedules (linear, step, exponential, cosine, step decay on plateau, and OneCycle) in both high and low budget regimes. Furthermore, REX requires no added computation, storage, or hyperparameters.

Policy gradient is a widely utilized and foundational algorithm in the field of reinforcement learning (RL). Renowned for its convergence guarantees and stability compared to other RL algorithms, its practical application is often hindered by sensitivity to hyper-parameters, particularly the step-size. In this paper, we introduce the integration of the Polyak step-size in RL, which automatically adjusts the step-size without prior knowledge. To adapt this method to RL settings, we address several issues, including unknown f* in the Polyak step-size. Additionally, we showcase the performance of the Polyak step-size in RL through experiments, demonstrating faster convergence and the attainment of more stable policies.

The learning rate (LR) schedule is one of the most important hyper-parameters needing careful tuning in training DNNs. However, it is also one of the least automated parts of machine learning systems and usually costs significant manual effort and computing. Though there are pre-defined LR schedules and optimizers with adaptive LR, they introduce new hyperparameters that need to be tuned separately for different tasks/datasets. In this paper, we consider the question: Can we automatically tune the LR over the course of training without human involvement? We propose an efficient method, AutoLRS, which automatically optimizes the LR for each training stage by modeling training dynamics. AutoLRS aims to find an LR applied to every tau steps that minimizes the resulted validation loss. We solve this black-box optimization on the fly by Bayesian optimization (BO). However, collecting training instances for BO requires a system to evaluate each LR queried by BO's acquisition function for tau steps, which is prohibitively expensive in practice. Instead, we apply each candidate LR for only tau'lltau steps and train an exponential model to predict the validation loss after tau steps. This mutual-training process between BO and the loss-prediction model allows us to limit the training steps invested in the BO search. We demonstrate the advantages and the generality of AutoLRS through extensive experiments of training DNNs for tasks from diverse domains using different optimizers. The LR schedules auto-generated by AutoLRS lead to a speedup of 1.22times, 1.43times, and 1.5times when training ResNet-50, Transformer, and BERT, respectively, compared to the LR schedules in their original papers, and an average speedup of 1.31times over state-of-the-art heavily-tuned LR schedules.

Performing tasks on the web presents fundamental challenges to large language models (LLMs), including combinatorially large open-world tasks and variations across web interfaces. Simply specifying a large prompt to handle all possible behaviors and states is extremely complex, and results in behavior leaks between unrelated behaviors. Decomposition to distinct policies can address this challenge, but requires carefully handing off control between policies. We propose Stacked LLM Policies for Web Actions (SteP), an approach to dynamically compose policies to solve a diverse set of web tasks. SteP defines a Markov Decision Process where the state is a stack of policies representing the control state, i.e., the chain of policy calls. Unlike traditional methods that are restricted to static hierarchies, SteP enables dynamic control that adapts to the complexity of the task. We evaluate SteP against multiple baselines and web environments including WebArena, MiniWoB++, and a CRM. On WebArena, SteP improves (14.9\% to 33.5\%) over SOTA that use GPT-4 policies, while on MiniWob++, SteP is competitive with prior works while using significantly less data. Our code and data are available at https://asappresearch.github.io/webagents-step.

Many problems in astrophysics cover multiple orders of magnitude in spatial and temporal scales. While simulating systems that experience rapid changes in these conditions, it is essential to adapt the (time-) step size to capture the behavior of the system during those rapid changes and use a less accurate time step at other, less demanding, moments. We encounter three problems with traditional methods. Firstly, making such changes requires expert knowledge of the astrophysics as well as of the details of the numerical implementation. Secondly, some parameters that determine the time-step size are fixed throughout the simulation, which means that they do not adapt to the rapidly changing conditions of the problem. Lastly, we would like the choice of time-step size to balance accuracy and computation effort. We address these challenges with Reinforcement Learning by training it to select the time-step size dynamically. We use the integration of a system of three equal-mass bodies that move due to their mutual gravity as an example of its application. With our method, the selected integration parameter adapts to the specific requirements of the problem, both in terms of computation time and accuracy while eliminating the expert knowledge needed to set up these simulations. Our method produces results competitive to existing methods and improve the results found with the most commonly-used values of time-step parameter. This method can be applied to other integrators without further retraining. We show that this extrapolation works for variable time-step integrators but does not perform to the desired accuracy for fixed time-step integrators.

Learning rate schedules used in practice bear little resemblance to those recommended by theory. We close much of this theory/practice gap, and as a consequence are able to derive new problem-adaptive learning rate schedules. Our key technical contribution is a refined analysis of learning rate schedules for a wide class of optimization algorithms (including SGD). In contrast to most prior works that study the convergence of the average iterate, we study the last iterate, which is what most people use in practice. When considering only worst-case analysis, our theory predicts that the best choice is the linear decay schedule: a popular choice in practice that sets the stepsize proportionally to 1 - t/T, where t is the current iteration and T is the total number of steps. To go beyond this worst-case analysis, we use the observed gradient norms to derive schedules refined for any particular task. These refined schedules exhibit learning rate warm-up and rapid learning rate annealing near the end of training. Ours is the first systematic approach to automatically yield both of these properties. We perform the most comprehensive evaluation of learning rate schedules to date, evaluating across 10 diverse deep learning problems, a series of LLMs, and a suite of logistic regression problems. We validate that overall, the linear-decay schedule matches or outperforms all commonly used default schedules including cosine annealing, and that our schedule refinement method gives further improvements.

Computer use agents (CUAs) can operate real-world digital interfaces but remain difficult to train due to the high cost of graphical user interface (GUI) interaction and the scarcity of high-quality trajectory data. Existing datasets rely on human demonstrations, limiting scalability. A natural alternative is to synthesize data from strong CUAs, yet their rollouts are highly noisy, with incorrect or suboptimal actions consisting a large proportion of the steps, making naive imitation ineffective. To tackle this challenge, we introduce a scalable data synthesis pipeline that transforms noisy rollouts into reliable supervision without human annotation. The core idea is step-level filtering, which evaluates actions individually to retain only correct steps, complemented by reasoning augmentation for improved planning. Using this pipeline, we construct WebSTAR, a dataset of 13.3K trajectories and 100K graded, reasoning-rich steps synthesized from OpenAI's computer-use-preview model. We train Qwen-2.5-VL-Instruct models (7B and 32B) on WebSTAR. On WebVoyager, our 7B model surpasses SoTA open-source CUA model UI-TARS-1.5-7B by more than 15% with only supervised finetuning. Building on step-level grading, we further create WebSCORE, a dataset of graded step-level actions, and train StepRM, a 7B multimodal reward model distilled from o4-mini, which matches its grading quality while being far more efficient to deploy at scale. Our results establish step-level filtering as a key principle for scalable CUA training and construct two new datasets (WebSTAR, WebSCORE) and a lightweight reward model (StepRM) as practical tools to advance robust and efficient CUAs.

The concept of Critical Batch Size, as pioneered by OpenAI, has long served as a foundational principle for large-scale pre-training. However, with the paradigm shift towards the Warmup-Stable-Decay (WSD) learning rate scheduler, we observe that the original theoretical framework and its underlying mechanisms fail to align with new pre-training dynamics. To bridge this gap between theory and practice, this paper derives a revised E(S) relationship tailored for WSD scheduler, characterizing the trade-off between training data consumption E and steps S during pre-training. Our theoretical analysis reveals two fundamental properties of WSD-based pre-training: 1) B_min, the minimum batch size threshold required to achieve a target loss, and 2) B_opt, the optimal batch size that maximizes data efficiency by minimizing total tokens. Building upon these properties, we propose a dynamic Batch Size Scheduler. Extensive experiments demonstrate that our revised formula precisely captures the dynamics of large-scale pre-training, and the resulting scheduling strategy significantly enhances both training efficiency and final model quality.

Many existing reinforcement learning (RL) methods employ stochastic gradient iteration on the back end, whose stability hinges upon a hypothesis that the data-generating process mixes exponentially fast with a rate parameter that appears in the step-size selection. Unfortunately, this assumption is violated for large state spaces or settings with sparse rewards, and the mixing time is unknown, making the step size inoperable. In this work, we propose an RL methodology attuned to the mixing time by employing a multi-level Monte Carlo estimator for the critic, the actor, and the average reward embedded within an actor-critic (AC) algorithm. This method, which we call Multi-level Actor-Critic (MAC), is developed especially for infinite-horizon average-reward settings and neither relies on oracle knowledge of the mixing time in its parameter selection nor assumes its exponential decay; it, therefore, is readily applicable to applications with slower mixing times. Nonetheless, it achieves a convergence rate comparable to the state-of-the-art AC algorithms. We experimentally show that these alleviated restrictions on the technical conditions required for stability translate to superior performance in practice for RL problems with sparse rewards.

Deep reinforcement learning (RL) based controllers for legged robots have demonstrated impressive robustness for walking in different environments for several robot platforms. To enable the application of RL policies for humanoid robots in real-world settings, it is crucial to build a system that can achieve robust walking in any direction, on 2D and 3D terrains, and be controllable by a user-command. In this paper, we tackle this problem by learning a policy to follow a given step sequence. The policy is trained with the help of a set of procedurally generated step sequences (also called footstep plans). We show that simply feeding the upcoming 2 steps to the policy is sufficient to achieve omnidirectional walking, turning in place, standing, and climbing stairs. Our method employs curriculum learning on the complexity of terrains, and circumvents the need for reference motions or pre-trained weights. We demonstrate the application of our proposed method to learn RL policies for 2 new robot platforms - HRP5P and JVRC-1 - in the MuJoCo simulation environment. The code for training and evaluation is available online.

When training neural networks, it has been widely observed that a large step size is essential in stochastic gradient descent (SGD) for obtaining superior models. However, the effect of large step sizes on the success of SGD is not well understood theoretically. Several previous works have attributed this success to the stochastic noise present in SGD. However, we show through a novel set of experiments that the stochastic noise is not sufficient to explain good non-convex training, and that instead the effect of a large learning rate itself is essential for obtaining best performance.We demonstrate the same effects also in the noise-less case, i.e. for full-batch GD. We formally prove that GD with large step size -- on certain non-convex function classes -- follows a different trajectory than GD with a small step size, which can lead to convergence to a global minimum instead of a local one. Our settings provide a framework for future analysis which allows comparing algorithms based on behaviors that can not be observed in the traditional settings.

Language agents have shown promising adaptability in dynamic environments to perform complex tasks. However, despite the versatile knowledge embedded in large language models, these agents still fall short when it comes to tasks that require planning. We introduce STEP, a novel framework designed to efficiently learn from previous experiences to enhance the planning capabilities of language agents in future steps. Concretely, STEP functions through four interconnected components. First, the Planner takes on the task, breaks it down into subtasks and provides relevant insights. Then the Executor generates action candidates, while the Evaluator ensures the actions align with learned rules from previous experiences. Lastly, Memory stores experiences to inform future decisions. In the ScienceWorld benchmark, our results show that STEP consistently outperforms state-of-the-art models, achieving an overall score of 67.4 and successfully completing 12 out of 18 tasks. These findings highlight STEP's potential as a framework for enhancing planning capabilities in language agents, paving the way for more sophisticated task-solving in dynamic environments.

Deep networks run with low precision operations at inference time offer power and space advantages over high precision alternatives, but need to overcome the challenge of maintaining high accuracy as precision decreases. Here, we present a method for training such networks, Learned Step Size Quantization, that achieves the highest accuracy to date on the ImageNet dataset when using models, from a variety of architectures, with weights and activations quantized to 2-, 3- or 4-bits of precision, and that can train 3-bit models that reach full precision baseline accuracy. Our approach builds upon existing methods for learning weights in quantized networks by improving how the quantizer itself is configured. Specifically, we introduce a novel means to estimate and scale the task loss gradient at each weight and activation layer's quantizer step size, such that it can be learned in conjunction with other network parameters. This approach works using different levels of precision as needed for a given system and requires only a simple modification of existing training code.

Recent hardware developments have dramatically increased the scale of data parallelism available for neural network training. Among the simplest ways to harness next-generation hardware is to increase the batch size in standard mini-batch neural network training algorithms. In this work, we aim to experimentally characterize the effects of increasing the batch size on training time, as measured by the number of steps necessary to reach a goal out-of-sample error. We study how this relationship varies with the training algorithm, model, and data set, and find extremely large variation between workloads. Along the way, we show that disagreements in the literature on how batch size affects model quality can largely be explained by differences in metaparameter tuning and compute budgets at different batch sizes. We find no evidence that larger batch sizes degrade out-of-sample performance. Finally, we discuss the implications of our results on efforts to train neural networks much faster in the future. Our experimental data is publicly available as a database of 71,638,836 loss measurements taken over the course of training for 168,160 individual models across 35 workloads.

Existing learning rate schedules that do not require specification of the optimization stopping step T are greatly out-performed by learning rate schedules that depend on T. We propose an approach that avoids the need for this stopping time by eschewing the use of schedules entirely, while exhibiting state-of-the-art performance compared to schedules across a wide family of problems ranging from convex problems to large-scale deep learning problems. Our Schedule-Free approach introduces no additional hyper-parameters over standard optimizers with momentum. Our method is a direct consequence of a new theory we develop that unifies scheduling and iterate averaging. An open source implementation of our method is available (https://github.com/facebookresearch/schedule_free).

Stochastic Gradient Descent (SGD) is one of the many iterative optimization methods that are widely used in solving machine learning problems. These methods display valuable properties and attract researchers and industrial machine learning engineers with their simplicity. However, one of the weaknesses of this type of methods is the necessity to tune learning rate (step-size) for every loss function and dataset combination to solve an optimization problem and get an efficient performance in a given time budget. Stochastic Gradient Descent with Polyak Step-size (SPS) is a method that offers an update rule that alleviates the need of fine-tuning the learning rate of an optimizer. In this paper, we propose an extension of SPS that employs preconditioning techniques, such as Hutchinson's method, Adam, and AdaGrad, to improve its performance on badly scaled and/or ill-conditioned datasets.

Hamiltonian Monte Carlo provides efficient Markov transitions at the expense of introducing two free parameters: a step size and total integration time. Because the step size controls discretization error it can be readily tuned to achieve certain accuracy criteria, but the total integration time is left unconstrained. Recently Hoffman and Gelman proposed a criterion for tuning the integration time in certain systems with their No U-Turn Sampler, or NUTS. In this paper I investigate the dynamical basis for the success of NUTS and generalize it to Riemannian Manifold Hamiltonian Monte Carlo.

Best-of-N decoding methods instruct large language models (LLMs) to generate multiple solutions, score each using a scoring function, and select the highest scored as the final answer to mathematical reasoning problems. However, this repeated independent process often leads to the same mistakes, making the selected solution still incorrect. We propose a novel prompting method named Stepwise Correction (StepCo) that helps LLMs identify and revise incorrect steps in their generated reasoning paths. It iterates verification and revision phases that employ a process-supervised verifier. The verify-then-revise process not only improves answer correctness but also reduces token consumption with fewer paths needed to generate. With StepCo, a series of LLMs demonstrate exceptional performance. Notably, using GPT-4o as the backend LLM, StepCo achieves an average accuracy of 94.1 across eight datasets, significantly outperforming the state-of-the-art Best-of-N method by +2.4, while reducing token consumption by 77.8%.

Following step-by-step procedures is an essential component of various activities carried out by individuals in their daily lives. These procedures serve as a guiding framework that helps to achieve goals efficiently, whether it is assembling furniture or preparing a recipe. However, the complexity and duration of procedural activities inherently increase the likelihood of making errors. Understanding such procedural activities from a sequence of frames is a challenging task that demands an accurate interpretation of visual information and the ability to reason about the structure of the activity. To this end, we collect a new egocentric 4D dataset, CaptainCook4D, comprising 384 recordings (94.5 hours) of people performing recipes in real kitchen environments. This dataset consists of two distinct types of activity: one in which participants adhere to the provided recipe instructions and another in which they deviate and induce errors. We provide 5.3K step annotations and 10K fine-grained action annotations and benchmark the dataset for the following tasks: supervised error recognition, multistep localization, and procedure learning

We focus on the classification problem with a separable dataset, one of the most important and classical problems from machine learning. The standard approach to this task is logistic regression with gradient descent (LR+GD). Recent studies have observed that LR+GD can find a solution with arbitrarily large step sizes, defying conventional optimization theory. Our work investigates this phenomenon and makes three interconnected key observations about LR+GD with large step sizes. First, we find a remarkably simple explanation of why LR+GD with large step sizes solves the classification problem: LR+GD reduces to a batch version of the celebrated perceptron algorithm when the step size gamma to infty. Second, we observe that larger step sizes lead LR+GD to higher logistic losses when it tends to the perceptron algorithm, but larger step sizes also lead to faster convergence to a solution for the classification problem, meaning that logistic loss is an unreliable metric of the proximity to a solution. Surprisingly, high loss values can actually indicate faster convergence. Third, since the convergence rate in terms of loss function values of LR+GD is unreliable, we examine the iteration complexity required by LR+GD with large step sizes to solve the classification problem and prove that this complexity is suboptimal. To address this, we propose a new method, Normalized LR+GD - based on the connection between LR+GD and the perceptron algorithm - with much better theoretical guarantees.

Normalization techniques are a boon for modern deep learning. They let weights converge more quickly with often better generalization performances. It has been argued that the normalization-induced scale invariance among the weights provides an advantageous ground for gradient descent (GD) optimizers: the effective step sizes are automatically reduced over time, stabilizing the overall training procedure. It is often overlooked, however, that the additional introduction of momentum in GD optimizers results in a far more rapid reduction in effective step sizes for scale-invariant weights, a phenomenon that has not yet been studied and may have caused unwanted side effects in the current practice. This is a crucial issue because arguably the vast majority of modern deep neural networks consist of (1) momentum-based GD (e.g. SGD or Adam) and (2) scale-invariant parameters. In this paper, we verify that the widely-adopted combination of the two ingredients lead to the premature decay of effective step sizes and sub-optimal model performances. We propose a simple and effective remedy, SGDP and AdamP: get rid of the radial component, or the norm-increasing direction, at each optimizer step. Because of the scale invariance, this modification only alters the effective step sizes without changing the effective update directions, thus enjoying the original convergence properties of GD optimizers. Given the ubiquity of momentum GD and scale invariance in machine learning, we have evaluated our methods against the baselines on 13 benchmarks. They range from vision tasks like classification (e.g. ImageNet), retrieval (e.g. CUB and SOP), and detection (e.g. COCO) to language modelling (e.g. WikiText) and audio classification (e.g. DCASE) tasks. We verify that our solution brings about uniform gains in those benchmarks. Source code is available at https://github.com/clovaai/AdamP.

Understanding human mobility through Point-of-Interest (POI) recommendation is increasingly important for applications such as urban planning, personalized services, and generative agent simulation. However, progress in this field is hindered by two key challenges: the over-reliance on older datasets from 2012-2013 and the lack of reproducible, city-level check-in datasets that reflect diverse global regions. To address these gaps, we present Massive-STEPS (Massive Semantic Trajectories for Understanding POI Check-ins), a large-scale, publicly available benchmark dataset built upon the Semantic Trails dataset and enriched with semantic POI metadata. Massive-STEPS spans 12 geographically and culturally diverse cities and features more recent (2017-2018) and longer-duration (24 months) check-in data than prior datasets. We benchmarked a wide range of POI recommendation models on Massive-STEPS using both supervised and zero-shot approaches, and evaluated their performance across multiple urban contexts. By releasing Massive-STEPS, we aim to facilitate reproducible and equitable research in human mobility and POI recommendation. The dataset and benchmarking code are available at: https://github.com/cruiseresearchgroup/Massive-STEPS

Online resources such as WikiHow compile a wide range of scripts for performing everyday tasks, which can assist models in learning to reason about procedures. However, the scripts are always presented in a linear manner, which does not reflect the flexibility displayed by people executing tasks in real life. For example, in the CrossTask Dataset, 64.5% of consecutive step pairs are also observed in the reverse order, suggesting their ordering is not fixed. In addition, each step has an average of 2.56 frequent next steps, demonstrating "branching". In this paper, we propose the new challenging task of non-sequential graph script induction, aiming to capture optional and interchangeable steps in procedural planning. To automate the induction of such graph scripts for given tasks, we propose to take advantage of loosely aligned videos of people performing the tasks. In particular, we design a multimodal framework to ground procedural videos to WikiHow textual steps and thus transform each video into an observed step path on the latent ground truth graph script. This key transformation enables us to train a script knowledge model capable of both generating explicit graph scripts for learnt tasks and predicting future steps given a partial step sequence. Our best model outperforms the strongest pure text/vision baselines by 17.52% absolute gains on F1@3 for next step prediction and 13.8% absolute gains on Acc@1 for partial sequence completion. Human evaluation shows our model outperforming the WikiHow linear baseline by 48.76% absolute gains in capturing sequential and non-sequential step relationships.

We introduce two complementary techniques for efficient adaptive optimization that reduce memory requirements while accelerating training of large-scale neural networks. The first technique, Subset-Norm adaptive step size, generalizes AdaGrad-Norm and AdaGrad(-Coordinate) by reducing the second moment term's memory footprint from O(d) to O(d) through step-size sharing, where d is the model size. For non-convex smooth objectives under coordinate-wise sub-gaussian gradient noise, we prove a noise-adapted high-probability convergence guarantee showing improved dimensional dependence over existing methods. Our second technique, Subspace-Momentum, reduces the momentum state's memory footprint by operating in a low-dimensional subspace while applying standard SGD in the orthogonal complement. We establish high-probability convergence rates under similar relaxed assumptions. Empirical evaluation on LLaMA models from 60M to 1B parameters demonstrates the effectiveness of our methods, where combining subset-norm with subspace-momentum achieves Adam's validation perplexity in approximately half the training tokens (6.8B vs 13.1B) while using only 20% of the Adam's optimizer-states memory footprint and requiring minimal additional hyperparameter tuning.

In Large Language Model (LLM) inference, the output length of an LLM request is typically regarded as not known a priori. Consequently, most LLM serving systems employ a simple First-come-first-serve (FCFS) scheduling strategy, leading to Head-Of-Line (HOL) blocking and reduced throughput and service quality. In this paper, we reexamine this assumption -- we show that, although predicting the exact generation length of each request is infeasible, it is possible to predict the relative ranks of output lengths in a batch of requests, using learning to rank. The ranking information offers valuable guidance for scheduling requests. Building on this insight, we develop a novel scheduler for LLM inference and serving that can approximate the shortest-job-first (SJF) schedule better than existing approaches. We integrate this scheduler with the state-of-the-art LLM serving system and show significant performance improvement in several important applications: 2.8x lower latency in chatbot serving and 6.5x higher throughput in synthetic data generation. Our code is available at https://github.com/hao-ai-lab/vllm-ltr.git

We focus on agile, continuous, and terrain-adaptive jumping of quadrupedal robots in discontinuous terrains such as stairs and stepping stones. Unlike single-step jumping, continuous jumping requires accurately executing highly dynamic motions over long horizons, which is challenging for existing approaches. To accomplish this task, we design a hierarchical learning and control framework, which consists of a learned heightmap predictor for robust terrain perception, a reinforcement-learning-based centroidal-level motion policy for versatile and terrain-adaptive planning, and a low-level model-based leg controller for accurate motion tracking. In addition, we minimize the sim-to-real gap by accurately modeling the hardware characteristics. Our framework enables a Unitree Go1 robot to perform agile and continuous jumps on human-sized stairs and sparse stepping stones, for the first time to the best of our knowledge. In particular, the robot can cross two stair steps in each jump and completes a 3.5m long, 2.8m high, 14-step staircase in 4.5 seconds. Moreover, the same policy outperforms baselines in various other parkour tasks, such as jumping over single horizontal or vertical discontinuities. Experiment videos can be found at https://yxyang.github.io/jumping\_cod/.

The exploration and application of Large Language Models (LLMs) is thriving. To reduce deployment costs, continuous batching has become an essential feature in current service frameworks. The effectiveness of continuous batching relies on an accurate estimate of the memory requirements of requests. However, due to the diversity in request output lengths, existing frameworks tend to adopt aggressive or conservative schedulers, which often result in significant overestimation or underestimation of memory consumption. Consequently, they suffer from harmful request evictions or prolonged queuing times, failing to achieve satisfactory throughput under strict Service Level Agreement (SLA) guarantees (a.k.a. goodput), across various LLM application scenarios with differing input-output length distributions. To address this issue, we propose a novel Past-Future scheduler that precisely estimates the peak memory resources required by the running batch via considering the historical distribution of request output lengths and calculating memory occupancy at each future time point. It adapts to applications with all types of input-output length distributions, balancing the trade-off between request queuing and harmful evictions, thereby consistently achieving better goodput. Furthermore, to validate the effectiveness of the proposed scheduler, we developed a high-performance LLM serving framework, LightLLM, that implements the Past-Future scheduler. Compared to existing aggressive or conservative schedulers, LightLLM demonstrates superior goodput, achieving up to 2-3times higher goodput than other schedulers under heavy loads. LightLLM is open source to boost the research in such direction (https://github.com/ModelTC/lightllm).

Training large models is both resource-intensive and time-consuming, making it crucial to understand the quantitative relationship between model performance and hyperparameters. In this paper, we present an empirical law that describes how the pretraining loss of large language models evolves under different learning rate schedules, such as constant, cosine, and step decay schedules. Our proposed law takes a multi-power form, combining a power law based on the sum of learning rates and additional power laws to account for a loss reduction effect induced by learning rate decay. We extensively validate this law on various model sizes and architectures, and demonstrate that after fitting on a few learning rate schedules, the law accurately predicts the loss curves for unseen schedules of different shapes and horizons. Moreover, by minimizing the predicted final pretraining loss across learning rate schedules, we are able to find a schedule that outperforms the widely used cosine learning rate schedule. Interestingly, this automatically discovered schedule bears some resemblance to the recently proposed Warmup-Stable-Decay (WSD) schedule (Hu et al, 2024) but achieves a slightly lower final loss. We believe these results could offer valuable insights for understanding the dynamics of pretraining and designing learning rate schedules to improve efficiency.

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.

The deployment of agent systems in an enterprise environment is often hindered by several challenges: common models lack domain-specific process knowledge, leading to disorganized plans, missing key tools, and poor execution stability. To address this, this paper introduces Routine, a multi-step agent planning framework designed with a clear structure, explicit instructions, and seamless parameter passing to guide the agent's execution module in performing multi-step tool-calling tasks with high stability. In evaluations conducted within a real-world enterprise scenario, Routine significantly increases the execution accuracy in model tool calls, increasing the performance of GPT-4o from 41.1% to 96.3%, and Qwen3-14B from 32.6% to 83.3%. We further constructed a Routine-following training dataset and fine-tuned Qwen3-14B, resulting in an accuracy increase to 88.2% on scenario-specific evaluations, indicating improved adherence to execution plans. In addition, we employed Routine-based distillation to create a scenario-specific, multi-step tool-calling dataset. Fine-tuning on this distilled dataset raised the model's accuracy to 95.5%, approaching GPT-4o's performance. These results highlight Routine's effectiveness in distilling domain-specific tool-usage patterns and enhancing model adaptability to new scenarios. Our experimental results demonstrate that Routine provides a practical and accessible approach to building stable agent workflows, accelerating the deployment and adoption of agent systems in enterprise environments, and advancing the technical vision of AI for Process.