Daily Papers

In this technical report, we present Magic 1-For-1 (Magic141), an efficient video generation model with optimized memory consumption and inference latency. The key idea is simple: factorize the text-to-video generation task into two separate easier tasks for diffusion step distillation, namely text-to-image generation and image-to-video generation. We verify that with the same optimization algorithm, the image-to-video task is indeed easier to converge over the text-to-video task. We also explore a bag of optimization tricks to reduce the computational cost of training the image-to-video (I2V) models from three aspects: 1) model convergence speedup by using a multi-modal prior condition injection; 2) inference latency speed up by applying an adversarial step distillation, and 3) inference memory cost optimization with parameter sparsification. With those techniques, we are able to generate 5-second video clips within 3 seconds. By applying a test time sliding window, we are able to generate a minute-long video within one minute with significantly improved visual quality and motion dynamics, spending less than 1 second for generating 1 second video clips on average. We conduct a series of preliminary explorations to find out the optimal tradeoff between computational cost and video quality during diffusion step distillation and hope this could be a good foundation model for open-source explorations. The code and the model weights are available at https://github.com/DA-Group-PKU/Magic-1-For-1.

Despite recent advancements in Large Language Models (LLMs), complex Software Engineering (SE) tasks require more collaborative and specialized approaches. This concept paper systematically reviews the emerging paradigm of LLM-based multi-agent systems, examining their applications across the Software Development Life Cycle (SDLC), from requirements engineering and code generation to static code checking, testing, and debugging. We delve into a wide range of topics such as language model selection, SE evaluation benchmarks, state-of-the-art agentic frameworks and communication protocols. Furthermore, we identify key challenges and outline future research opportunities, with a focus on multi-agent orchestration, human-agent coordination, computational cost optimization, and effective data collection. This work aims to provide researchers and practitioners with valuable insights into the current forefront landscape of agentic systems within the software engineering domain.

Neural architecture search (NAS) for Graph neural networks (GNNs), called NAS-GNNs, has achieved significant performance over manually designed GNN architectures. However, these methods inherit issues from the conventional NAS methods, such as high computational cost and optimization difficulty. More importantly, previous NAS methods have ignored the uniqueness of GNNs, where GNNs possess expressive power without training. With the randomly-initialized weights, we can then seek the optimal architecture parameters via the sparse coding objective and derive a novel NAS-GNNs method, namely neural architecture coding (NAC). Consequently, our NAC holds a no-update scheme on GNNs and can efficiently compute in linear time. Empirical evaluations on multiple GNN benchmark datasets demonstrate that our approach leads to state-of-the-art performance, which is up to 200times faster and 18.8% more accurate than the strong baselines.

Data pruning algorithms are commonly used to reduce the memory and computational cost of the optimization process. Recent empirical results reveal that random data pruning remains a strong baseline and outperforms most existing data pruning methods in the high compression regime, i.e., where a fraction of 30% or less of the data is kept. This regime has recently attracted a lot of interest as a result of the role of data pruning in improving the so-called neural scaling laws; in [Sorscher et al.], the authors showed the need for high-quality data pruning algorithms in order to beat the sample power law. In this work, we focus on score-based data pruning algorithms and show theoretically and empirically why such algorithms fail in the high compression regime. We demonstrate ``No Free Lunch" theorems for data pruning and present calibration protocols that enhance the performance of existing pruning algorithms in this high compression regime using randomization.

Differentially private (DP) optimization is the standard paradigm to learn large neural networks that are accurate and privacy-preserving. The computational cost for DP deep learning, however, is notoriously heavy due to the per-sample gradient clipping. Existing DP implementations are 2-1000times more costly in time and space complexity than the standard (non-private) training. In this work, we develop a novel Book-Keeping (BK) technique that implements existing DP optimizers (thus achieving the same accuracy), with a substantial improvement on the computational cost. Specifically, BK enables DP training on large models and high dimensional data to be roughly as efficient as the standard training, whereas previous DP algorithms can be inefficient or incapable of training due to memory error. The computational advantage of BK is supported by the complexity analysis as well as extensive experiments on vision and language tasks. Our implementation achieves state-of-the-art (SOTA) accuracy with very small extra cost: on GPT2 and at the same memory cost, BK has 1.0times the time complexity of the standard training (0.75times training speed in practice), and 0.6times the time complexity of the most efficient DP implementation (1.24times training speed in practice). We will open-source the codebase for the BK algorithm.

Recent advances in reasoning language models have witnessed a paradigm shift from short to long CoT pattern. Given the substantial computational cost of rollouts in long CoT models, maximizing the utility of fixed training datasets becomes crucial. Our analysis reveals that negative responses contain valuable components such as self-reflection and error-correction steps, yet primary existing methods either completely discard negative samples (RFT) or apply equal penalization across all tokens (RL), failing to leverage these potential learning signals. In light of this, we propose Behavior Constrained Policy Gradient with Negative Sample Augmentation (BCPG-NSA), a fine-grained offline RL framework that encompasses three stages: 1) sample segmentation, 2) consensus-based step correctness assessment combining LLM and PRM judgers, and 3) policy optimization with NSA designed to effectively mine positive steps within negative samples. Experimental results show that BCPG-NSA outperforms baselines on several challenging math/coding reasoning benchmarks using the same training dataset, achieving improved sample efficiency and demonstrating robustness and scalability when extended to multiple iterations.

Automatic algorithm-hardware co-design for DNN has shown great success in improving the performance of DNNs on FPGAs. However, this process remains challenging due to the intractable search space of neural network architectures and hardware accelerator implementation. Differing from existing hardware-aware neural architecture search (NAS) algorithms that rely solely on the expensive learning-based approaches, our work incorporates integer programming into the search algorithm to prune the design space. Given a set of hardware resource constraints, our integer programming formulation directly outputs the optimal accelerator configuration for mapping a DNN subgraph that minimizes latency. We use an accuracy predictor for different DNN subgraphs with different quantization schemes and generate accuracy-latency pareto frontiers. With low computational cost, our algorithm can generate quantized networks that achieve state-of-the-art accuracy and hardware performance on Xilinx Zynq (ZU3EG) FPGA for image classification on ImageNet dataset. The solution searched by our algorithm achieves 72.5% top-1 accuracy on ImageNet at framerate 50, which is 60% faster than MnasNet and 135% faster than FBNet with comparable accuracy.

While long-context large language models (LLMs) exhibit remarkable document processing capabilities, their prohibitively high training costs often hinder customized applications. To mitigate this issue, we propose Sequential Chunk-wise Optimization (SeCO), a memory-efficient training paradigm that partitions lengthy inputs into manageable chunks. Each chunk independently constructs its computational graph and performs localized backpropagation, ensuring that only one chunk's forward activations are stored in memory. Building on SeCO, we further introduce Sparse Chunk-wise Optimization (SpaCO), which reduces computational overhead by selectively propagating gradients to specific chunks and incorporates a carefully designed compensation factor to ensure unbiased gradient estimation. SpaCO decouples the computational cost of backpropagation from the context length, enabling training time to gradually converge to inference time as sequences become longer. Implemented as lightweight training wrappers, both SeCO and SpaCO offer substantial practical benefits. For example, when fine-tuning an 8B model with LoRA on a single RTX 3090 GPU, SeCO expands maximum sequence length from 1K to 16K tokens, while SpaCO demonstrates accelerated training speed -- achieving up to 3x faster than SeCO under the same experimental setup. These innovations provide new insights into optimizing long-context models, making them more accessible for practical applications. We have open-sourced the code at https://github.com/wenhaoli-xmu/seco{here}.

Reinforcement learning (RL) is vital for optimizing large language models (LLMs). Recent Group Relative Policy Optimization (GRPO) estimates advantages using multiple on-policy outputs per prompt, leading to high computational costs and low data efficiency. To address this, we introduce Replay-Enhanced Policy Optimization (RePO), which leverages diverse replay strategies to retrieve off-policy samples from a replay buffer, allowing policy optimization based on a broader and more diverse set of samples for each prompt. Experiments on five LLMs across seven mathematical reasoning benchmarks demonstrate that RePO achieves absolute average performance gains of 18.4 and 4.1 points for Qwen2.5-Math-1.5B and Qwen3-1.7B, respectively, compared to GRPO. Further analysis indicates that RePO increases computational cost by 15% while raising the number of effective optimization steps by 48% for Qwen3-1.7B, with both on-policy and off-policy sample numbers set to 8. The repository can be accessed at https://github.com/SihengLi99/RePO.

This paper presents a practical investigation into fine-tuning model parameters for mathematical reasoning tasks through experimenting with various configurations including randomness control, reasoning depth, and sampling strategies, careful tuning demonstrates substantial improvements in efficiency as well as performance. A holistically optimized framework is introduced for five state-of-the-art models on mathematical reasoning tasks, exhibiting significant performance boosts while maintaining solution correctness. Through systematic parameter optimization across Qwen2.5-72B, Llama-3.1-70B, DeepSeek-V3, Mixtral-8x22B, and Yi-Lightning, consistent efficiency gains are demonstrated with 100% optimization success rate. The methodology achieves an average 29.4% reduction in computational cost and 23.9% improvement in inference speed across all tested models. This framework systematically searches parameter spaces including temperature (0.1-0.5), reasoning steps (4-12), planning periods (1-4), and nucleus sampling (0.85-0.98), determining optimal configurations through testing on mathematical reasoning benchmarks. Critical findings show that lower temperature regimes (0.1-0.4) and reduced reasoning steps (4-6) consistently enhance efficiency without compromising accuracy. DeepSeek-V3 achieves the highest accuracy at 98%, while Mixtral-8x22B delivers the most cost-effective performance at 361.5 tokens per accurate response. Key contributions include: (1) the first comprehensive optimization study for five diverse SOTA models in mathematical reasoning, (2) a standardized production-oriented parameter optimization framework, (3) discovery of universal optimization trends applicable across model architectures, and (4) production-ready configurations with extensive performance characterization.

Computing a Gaussian process (GP) posterior has a computational cost cubical in the number of historical points. A reformulation of the same GP posterior highlights that this complexity mainly depends on how many unique historical points are considered. This can have important implication in active learning settings, where the set of historical points is constructed sequentially by the learner. We show that sequential black-box optimization based on GPs (GP-Opt) can be made efficient by sticking to a candidate solution for multiple evaluation steps and switch only when necessary. Limiting the number of switches also limits the number of unique points in the history of the GP. Thus, the efficient GP reformulation can be used to exactly and cheaply compute the posteriors required to run the GP-Opt algorithms. This approach is especially useful in real-world applications of GP-Opt with high switch costs (e.g. switching chemicals in wet labs, data/model loading in hyperparameter optimization). As examples of this meta-approach, we modify two well-established GP-Opt algorithms, GP-UCB and GP-EI, to switch candidates as infrequently as possible adapting rules from batched GP-Opt. These versions preserve all the theoretical no-regret guarantees while improving practical aspects of the algorithms such as runtime, memory complexity, and the ability of batching candidates and evaluating them in parallel.

In 3D human pose and shape estimation, SMPLify remains a robust baseline that solves inverse kinematics (IK) through iterative optimization. However, its high computational cost limits its practicality. Recent advances across domains have shown that replacing iterative optimization with data-driven neural networks can achieve significant runtime improvements without sacrificing accuracy. Motivated by this trend, we propose Learnable SMPLify, a neural framework that replaces the iterative fitting process in SMPLify with a single-pass regression model. The design of our framework targets two core challenges in neural IK: data construction and generalization. To enable effective training, we propose a temporal sampling strategy that constructs initialization-target pairs from sequential frames. To improve generalization across diverse motions and unseen poses, we propose a human-centric normalization scheme and residual learning to narrow the solution space. Learnable SMPLify supports both sequential inference and plug-in post-processing to refine existing image-based estimators. Extensive experiments demonstrate that our method establishes itself as a practical and simple baseline: it achieves nearly 200x faster runtime compared to SMPLify, generalizes well to unseen 3DPW and RICH, and operates in a model-agnostic manner when used as a plug-in tool on LucidAction. The code is available at https://github.com/Charrrrrlie/Learnable-SMPLify.

Gaussian processes (GP) are one of the most successful frameworks to model uncertainty. However, GP optimization (e.g., GP-UCB) suffers from major scalability issues. Experimental time grows linearly with the number of evaluations, unless candidates are selected in batches (e.g., using GP-BUCB) and evaluated in parallel. Furthermore, computational cost is often prohibitive since algorithms such as GP-BUCB require a time at least quadratic in the number of dimensions and iterations to select each batch. In this paper, we introduce BBKB (Batch Budgeted Kernel Bandits), the first no-regret GP optimization algorithm that provably runs in near-linear time and selects candidates in batches. This is obtained with a new guarantee for the tracking of the posterior variances that allows BBKB to choose increasingly larger batches, improving over GP-BUCB. Moreover, we show that the same bound can be used to adaptively delay costly updates to the sparse GP approximation used by BBKB, achieving a near-constant per-step amortized cost. These findings are then confirmed in several experiments, where BBKB is much faster than state-of-the-art methods.

The alignment of large language models (LLMs) with human preferences remains a key challenge. While post-training techniques like Reinforcement Learning from Human Feedback (RLHF) and Direct Preference Optimization (DPO) have achieved notable success, they often introduce computational inefficiencies and training instability. In this paper, we propose Feature-level constrained Preference Optimization (FPO), a novel method designed to simplify the alignment process while ensuring stability. FPO leverages pre-trained Sparse Autoencoders (SAEs) and introduces feature-level constraints, allowing for efficient, sparsity-enforced alignment. Our approach enjoys efficiency by using sparse features activated in a well-trained sparse autoencoder and the quality of sequential KL divergence by using the feature-level offline reference. Experimental results on benchmark datasets demonstrate that FPO achieves a 5.08% absolute improvement in win rate with much lower computational cost compared to state-of-the-art baselines, making it a promising solution for efficient and controllable LLM alignments.

AI alignment in the shape of Reinforcement Learning from Human Feedback (RLHF) is increasingly treated as a crucial ingredient for high performance large language models. Proximal Policy Optimization (PPO) has been positioned by recent literature as the canonical method for the RL part of RLHF. However, it involves both high computational cost and sensitive hyperparameter tuning. We posit that most of the motivational principles that led to the development of PPO are less of a practical concern in RLHF and advocate for a less computationally expensive method that preserves and even increases performance. We revisit the formulation of alignment from human preferences in the context of RL. Keeping simplicity as a guiding principle, we show that many components of PPO are unnecessary in an RLHF context and that far simpler REINFORCE-style optimization variants outperform both PPO and newly proposed "RL-free" methods such as DPO and RAFT. Our work suggests that careful adaptation to LLMs alignment characteristics enables benefiting from online RL optimization at low cost.

Context: Automated code generation using Foundation Models (FMs) offers promising solutions for enhancing software development efficiency. However, challenges remain in ensuring domain specificity, cost-effectiveness, and security - especially when relying on third-party APIs. This paper introduces CodeLSI, a framework that combines low-rank optimization and domain-specific instruction tuning to address these challenges. Objectives: The aim of this study is to develop and evaluate CodeLSI, a novel approach for generating high-quality code tailored to specific domains, using FMs fine-tuned on company infrastructure without dependence on external APIs. Methods: CodeLSI applies low-rank adaptation techniques to reduce the computational cost of model pre-training and fine-tuning. Domain-specific instruction tuning is employed to align code generation with organizational needs. We implemented and tested the framework on real-world JavaScript coding tasks using datasets drawn from internal software projects. Results: Experimental evaluations show that CodeLSI produces high-quality, context aware code. It outperforms baseline models in terms of relevance, accuracy, and domain fit. The use of low-rank optimization significantly reduced resource requirements, enabling scalable training on company-owned infrastructure. Conclusion: CodeLSI demonstrates that combining low-rank optimization with domain specific tuning can enhance the practicality and performance of FMs for automated code generation. This approach provides a secure, cost-efficient alternative to commercial API based solutions and supports faster, more targeted innovation in software development.

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

Behavior of neural networks is irremediably determined by the specific loss and data used during training. However it is often desirable to tune the model at inference time based on external factors such as preferences of the user or dynamic characteristics of the data. This is especially important to balance the perception-distortion trade-off of ill-posed image-to-image translation tasks. In this work, we propose to optimize a parametric tunable convolutional layer, which includes a number of different kernels, using a parametric multi-loss, which includes an equal number of objectives. Our key insight is to use a shared set of parameters to dynamically interpolate both the objectives and the kernels. During training, these parameters are sampled at random to explicitly optimize all possible combinations of objectives and consequently disentangle their effect into the corresponding kernels. During inference, these parameters become interactive inputs of the model hence enabling reliable and consistent control over the model behavior. Extensive experimental results demonstrate that our tunable convolutions effectively work as a drop-in replacement for traditional convolutions in existing neural networks at virtually no extra computational cost, outperforming state-of-the-art control strategies in a wide range of applications; including image denoising, deblurring, super-resolution, and style transfer.

Existing Reinforcement Learning from Verifiable Rewards (RLVR) methods, such as Group Relative Policy Optimization (GRPO), have achieved remarkable progress in improving the reasoning capabilities of Large Reasoning Models (LRMs). However, they exhibit limited exploration due to reliance on on-policy rollouts where confined to the current policy's distribution, resulting in narrow trajectory diversity. Recent approaches attempt to expand policy coverage by incorporating trajectories generated from stronger expert models, yet this reliance increases computational cost and such advaned models are often inaccessible. To address these issues, we propose In-Context Steered Policy Optimization (ICPO), a unified framework that leverages the inherent in-context learning capability of LRMs to provide expert guidance using existing datasets. ICPO introduces Mixed-Policy GRPO with Implicit Expert Forcing, which expands exploration beyond the current policy distribution without requiring advanced LRM trajectories. To further stabilize optimization, ICPO integrates Expert Region Reject Sampling to filter unreliable off-policy trajectories and Annealed Expert-Bonus Reward Shaping to balance early expert guidance with later autonomous improvement. Results demonstrate that ICPO consistently enhances reinforcement learning performance and training stability on mathematical reasoning benchmarks, revealing a scalable and effective RLVR paradigm for LRMs.

Topology optimization by optimally distributing materials in a given domain requires non-gradient optimizers to solve highly complicated problems. However, with hundreds of design variables or more involved, solving such problems would require millions of Finite Element Method (FEM) calculations whose computational cost is huge and impractical. Here we report Self-directed Online Learning Optimization (SOLO) which integrates Deep Neural Network (DNN) with FEM calculations. A DNN learns and substitutes the objective as a function of design variables. A small number of training data is generated dynamically based on the DNN's prediction of the optimum. The DNN adapts to the new training data and gives better prediction in the region of interest until convergence. The optimum predicted by the DNN is proved to converge to the true global optimum through iterations. Our algorithm was tested by four types of problems including compliance minimization, fluid-structure optimization, heat transfer enhancement and truss optimization. It reduced the computational time by 2 ~ 5 orders of magnitude compared with directly using heuristic methods, and outperformed all state-of-the-art algorithms tested in our experiments. This approach enables solving large multi-dimensional optimization problems.

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.

Recent advancements in timestep-distilled diffusion models have enabled high-quality image generation that rivals non-distilled multi-step models, but with significantly fewer inference steps. While such models are attractive for applications due to the low inference cost and latency, fine-tuning them with a naive diffusion objective would result in degraded and blurry outputs. An intuitive alternative is to repeat the diffusion distillation process with a fine-tuned teacher model, which produces good results but is cumbersome and computationally intensive; the distillation training usually requires magnitude higher of training compute compared to fine-tuning for specific image styles. In this paper, we present an algorithm named pairwise sample optimization (PSO), which enables the direct fine-tuning of an arbitrary timestep-distilled diffusion model. PSO introduces additional reference images sampled from the current time-step distilled model, and increases the relative likelihood margin between the training images and reference images. This enables the model to retain its few-step generation ability, while allowing for fine-tuning of its output distribution. We also demonstrate that PSO is a generalized formulation which can be flexibly extended to both offline-sampled and online-sampled pairwise data, covering various popular objectives for diffusion model preference optimization. We evaluate PSO in both preference optimization and other fine-tuning tasks, including style transfer and concept customization. We show that PSO can directly adapt distilled models to human-preferred generation with both offline and online-generated pairwise preference image data. PSO also demonstrates effectiveness in style transfer and concept customization by directly tuning timestep-distilled diffusion models.

Determining the optimal data mixture for large language model training remains a challenging problem with an outsized impact on performance. In practice, language model developers continue to rely on heuristic exploration since no learning-based approach has emerged as a reliable solution. In this work, we propose to view the selection of training data mixtures as a black-box hyperparameter optimization problem, for which Bayesian Optimization is a well-established class of appropriate algorithms. Firstly, we cast data mixture learning as a sequential decision-making problem, in which we aim to find a suitable trade-off between the computational cost of training exploratory (proxy-) models and final mixture performance. Secondly, we systematically explore the properties of transferring mixtures learned at a small scale to larger-scale experiments, providing insights and highlighting opportunities for research at a modest scale. By proposing Multi-fidelity Bayesian Optimization as a suitable method in this common scenario, we introduce a natural framework to balance experiment cost with model fit, avoiding the risks of overfitting to smaller scales while minimizing the number of experiments at high cost. We present results for pre-training and instruction finetuning across models ranging from 1 million to 7 billion parameters, varying from simple architectures to state-of-the-art models and benchmarks spanning dozens of datasets. We demonstrate consistently strong results relative to a wide range of baselines, resulting inspeed-ups of over 500% in determining the best data mixture on our largest experiments. In addition, we broaden access to research by sharing ADMIRE IFT Runs, a dataset of 460 full training & evaluation runs worth over 13,000 GPU hours, greatly reducing the cost of conducting research in this area.

The DC Optimal Power Flow (DC-OPF) problem is fundamental to power system operations, requiring rapid solutions for real-time grid management. While traditional optimization solvers provide optimal solutions, their computational cost becomes prohibitive for large-scale systems requiring frequent recalculations. Machine learning approaches offer promise for acceleration but often struggle with constraint satisfaction and cost optimality. We present a novel two-stage learning framework that combines physics-informed Graph Neural Networks (GNNs) with Continuous Flow Matching (CFM) for solving DC-OPF problems. Our approach embeds fundamental physical principles--including economic dispatch optimality conditions, Kirchhoff's laws, and Karush-Kuhn-Tucker (KKT) complementarity conditions--directly into the training objectives. The first stage trains a GNN to produce feasible initial solutions by learning from physics-informed losses that encode power system constraints. The second stage employs CFM, a simulation-free continuous normalizing flow technique, to refine these solutions toward optimality through learned vector field regression. Evaluated on the IEEE 30-bus system across five load scenarios ranging from 70\% to 130\% nominal load, our method achieves near-optimal solutions with cost gaps below 0.1\% for nominal loads and below 3\% for extreme conditions, while maintaining 100\% feasibility. Our framework bridges the gap between fast but approximate neural network predictions and optimal but slow numerical solvers, offering a practical solution for modern power systems with high renewable penetration requiring frequent dispatch updates.

We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT and differentiating through optimization, motivating our algorithm. We use the proposed approach to train modern network architectures with millions of weights and millions of hyper-parameters. For example, we learn a data-augmentation network - where every weight is a hyperparameter tuned for validation performance - outputting augmented training examples. Jointly tuning weights and hyperparameters with our approach is only a few times more costly in memory and compute than standard training.

Generative adversarial networks (GANs) have made great success in image inpainting yet still have difficulties tackling large missing regions. In contrast, iterative probabilistic algorithms, such as autoregressive and denoising diffusion models, have to be deployed with massive computing resources for decent effect. To achieve high-quality results with low computational cost, we present a novel pixel spread model (PSM) that iteratively employs decoupled probabilistic modeling, combining the optimization efficiency of GANs with the prediction tractability of probabilistic models. As a result, our model selectively spreads informative pixels throughout the image in a few iterations, largely enhancing the completion quality and efficiency. On multiple benchmarks, we achieve new state-of-the-art performance. Code is released at https://github.com/fenglinglwb/PSM.

Gradient regularization (GR) is a method that penalizes the gradient norm of the training loss during training. While some studies have reported that GR can improve generalization performance, little attention has been paid to it from the algorithmic perspective, that is, the algorithms of GR that efficiently improve the performance. In this study, we first reveal that a specific finite-difference computation, composed of both gradient ascent and descent steps, reduces the computational cost of GR. Next, we show that the finite-difference computation also works better in the sense of generalization performance. We theoretically analyze a solvable model, a diagonal linear network, and clarify that GR has a desirable implicit bias to so-called rich regime and finite-difference computation strengthens this bias. Furthermore, finite-difference GR is closely related to some other algorithms based on iterative ascent and descent steps for exploring flat minima. In particular, we reveal that the flooding method can perform finite-difference GR in an implicit way. Thus, this work broadens our understanding of GR for both practice and theory.

A popular approach to sample a diffusion-based generative model is to solve an ordinary differential equation (ODE). In existing samplers, the coefficients of the ODE solvers are pre-determined by the ODE formulation, the reverse discrete timesteps, and the employed ODE methods. In this paper, we consider accelerating several popular ODE-based sampling processes (including EDM, DDIM, and DPM-Solver) by optimizing certain coefficients via improved integration approximation (IIA). We propose to minimize, for each time step, a mean squared error (MSE) function with respect to the selected coefficients. The MSE is constructed by applying the original ODE solver for a set of fine-grained timesteps, which in principle provides a more accurate integration approximation in predicting the next diffusion state. The proposed IIA technique does not require any change of a pre-trained model, and only introduces a very small computational overhead for solving a number of quadratic optimization problems. Extensive experiments show that considerably better FID scores can be achieved by using IIA-EDM, IIA-DDIM, and IIA-DPM-Solver than the original counterparts when the neural function evaluation (NFE) is small (i.e., less than 25).

Computational Fluid Dynamics (CFD) simulation by the numerical solution of the Navier-Stokes equations is an essential tool in a wide range of applications from engineering design to climate modeling. However, the computational cost and memory demand required by CFD codes may become very high for flows of practical interest, such as in aerodynamic shape optimization. This expense is associated with the complexity of the fluid flow governing equations, which include non-linear partial derivative terms that are of difficult solution, leading to long computational times and limiting the number of hypotheses that can be tested during the process of iterative design. Therefore, we propose DeepCFD: a convolutional neural network (CNN) based model that efficiently approximates solutions for the problem of non-uniform steady laminar flows. The proposed model is able to learn complete solutions of the Navier-Stokes equations, for both velocity and pressure fields, directly from ground-truth data generated using a state-of-the-art CFD code. Using DeepCFD, we found a speedup of up to 3 orders of magnitude compared to the standard CFD approach at a cost of low error rates.

We introduce Virtual Width Networks (VWN), a framework that delivers the benefits of wider representations without incurring the quadratic cost of increasing the hidden size. VWN decouples representational width from backbone width, expanding the embedding space while keeping backbone compute nearly constant. In our large-scale experiment, an 8-times expansion accelerates optimization by over 2 times for next-token and 3 times for next-2-token prediction. The advantage amplifies over training as both the loss gap grows and the convergence-speedup ratio increases, showing that VWN is not only token-efficient but also increasingly effective with scale. Moreover, we identify an approximately log-linear scaling relation between virtual width and loss reduction, offering an initial empirical basis and motivation for exploring virtual-width scaling as a new dimension of large-model efficiency.

Neural network pruning is frequently used to compress over-parameterized networks by large amounts, while incurring only marginal drops in generalization performance. However, the impact of pruning on networks that have been highly optimized for efficient inference has not received the same level of attention. In this paper, we analyze the effect of pruning for computer vision, and study state-of-the-art ConvNets, such as the FBNetV3 family of models. We show that model pruning approaches can be used to further optimize networks trained through NAS (Neural Architecture Search). The resulting family of pruned models can consistently obtain better performance than existing FBNetV3 models at the same level of computation, and thus provide state-of-the-art results when trading off between computational complexity and generalization performance on the ImageNet benchmark. In addition to better generalization performance, we also demonstrate that when limited computation resources are available, pruning FBNetV3 models incur only a fraction of GPU-hours involved in running a full-scale NAS.

A recent approach to neurosymbolic reasoning is to explicitly combine the strengths of large language models (LLMs) and symbolic solvers to tackle complex reasoning tasks. However, current approaches face significant limitations, including poor generalizability due to task-specific prompts, inefficiencies caused by the lack of separation between knowledge and queries, and restricted inferential capabilities. These shortcomings hinder their scalability and applicability across diverse domains. In this paper, we introduce VERUS-LM, a novel framework designed to address these challenges. VERUS-LM employs a generic prompting mechanism, clearly separates domain knowledge from queries, and supports a wide range of different logical reasoning tasks. This framework enhances adaptability, reduces computational cost, and allows for richer forms of reasoning, such as optimization and constraint satisfaction. We show that our approach succeeds in diverse reasoning on a novel dataset, markedly outperforming LLMs. Additionally, our system achieves competitive results on common reasoning benchmarks when compared to other state-of-the-art approaches, and significantly surpasses them on the difficult AR-LSAT dataset. By pushing the boundaries of hybrid reasoning, VERUS-LM represents a significant step towards more versatile neurosymbolic AI systems

The conjugate gradient method is a crucial first-order optimization method that generally converges faster than the steepest descent method, and its computational cost is much lower than that of second-order methods. However, while various types of conjugate gradient methods have been studied in Euclidean spaces and on Riemannian manifolds, there is little study for those in distributed scenarios. This paper proposes a decentralized Riemannian conjugate gradient descent (DRCGD) method that aims at minimizing a global function over the Stiefel manifold. The optimization problem is distributed among a network of agents, where each agent is associated with a local function, and the communication between agents occurs over an undirected connected graph. Since the Stiefel manifold is a non-convex set, a global function is represented as a finite sum of possibly non-convex (but smooth) local functions. The proposed method is free from expensive Riemannian geometric operations such as retractions, exponential maps, and vector transports, thereby reducing the computational complexity required by each agent. To the best of our knowledge, DRCGD is the first decentralized Riemannian conjugate gradient algorithm to achieve global convergence over the Stiefel manifold.

Recent years have witnessed significant advancements in self-supervised learning (SSL) methods for speech-processing tasks. Various speech-based SSL models have been developed and present promising performance on a range of downstream tasks including speech recognition. However, existing speech-based SSL models face a common dilemma in terms of computational cost, which might hinder their potential application and in-depth academic research. To address this issue, we first analyze the computational cost of different modules during HuBERT pre-training and then introduce a stack of efficiency optimizations, which is named Fast-HuBERT in this paper. The proposed Fast-HuBERT can be trained in 1.1 days with 8 V100 GPUs on the Librispeech 960h benchmark, without performance degradation, resulting in a 5.2x speedup, compared to the original implementation. Moreover, we explore two well-studied techniques in the Fast-HuBERT and demonstrate consistent improvements as reported in previous work.

The growing safety concerns surrounding large language models raise an urgent need to align them with diverse human preferences to simultaneously enhance their helpfulness and safety. A promising approach is to enforce safety constraints through Reinforcement Learning from Human Feedback (RLHF). For such constrained RLHF, typical Lagrangian-based primal-dual policy optimization methods are computationally expensive and often unstable. This paper presents a perspective of dualization that reduces constrained alignment to an equivalent unconstrained alignment problem. We do so by pre-optimizing a smooth and convex dual function that has a closed form. This shortcut eliminates the need for cumbersome primal-dual policy iterations, greatly reducing the computational burden and improving training stability. Our strategy leads to two practical algorithms in model-based and preference-based settings (MoCAN and PeCAN, respectively). A broad range of experiments demonstrate the effectiveness and merits of our algorithms.

3D reconstruction, which aims to recover the dense three-dimensional structure of a scene, is a cornerstone technology for numerous applications, including augmented/virtual reality, autonomous driving, and robotics. While traditional pipelines like Structure from Motion (SfM) and Multi-View Stereo (MVS) achieve high precision through iterative optimization, they are limited by complex workflows, high computational cost, and poor robustness in challenging scenarios like texture-less regions. Recently, deep learning has catalyzed a paradigm shift in 3D reconstruction. A new family of models, exemplified by DUSt3R, has pioneered a feed-forward approach. These models employ a unified deep network to jointly infer camera poses and dense geometry directly from an Unconstrained set of images in a single forward pass. This survey provides a systematic review of this emerging domain. We begin by dissecting the technical framework of these feed-forward models, including their Transformer-based correspondence modeling, joint pose and geometry regression mechanisms, and strategies for scaling from two-view to multi-view scenarios. To highlight the disruptive nature of this new paradigm, we contrast it with both traditional pipelines and earlier learning-based methods like MVSNet. Furthermore, we provide an overview of relevant datasets and evaluation metrics. Finally, we discuss the technology's broad application prospects and identify key future challenges and opportunities, such as model accuracy and scalability, and handling dynamic scenes.

Markerless multiview motion capture is often constrained by the need for precise camera calibration, limiting accessibility for non-experts and in-the-wild captures. Existing calibration-free approaches mitigate this requirement but suffer from high computational cost and reduced reconstruction accuracy. We present Kineo, a fully automatic, calibration-free pipeline for markerless motion capture from videos captured by unsynchronized, uncalibrated, consumer-grade RGB cameras. Kineo leverages 2D keypoints from off-the-shelf detectors to simultaneously calibrate cameras, including Brown-Conrady distortion coefficients, and reconstruct 3D keypoints and dense scene point maps at metric scale. A confidence-driven spatio-temporal keypoint sampling strategy, combined with graph-based global optimization, ensures robust calibration at a fixed computational cost independent of sequence length. We further introduce a pairwise reprojection consensus score to quantify 3D reconstruction reliability for downstream tasks. Evaluations on EgoHumans and Human3.6M demonstrate substantial improvements over prior calibration-free methods. Compared to previous state-of-the-art approaches, Kineo reduces camera translation error by approximately 83-85%, camera angular error by 86-92%, and world mean-per-joint error (W-MPJPE) by 83-91%. Kineo is also efficient in real-world scenarios, processing multi-view sequences faster than their duration in specific configuration (e.g., 36min to process 1h20min of footage). The full pipeline and evaluation code are openly released to promote reproducibility and practical adoption at https://liris-xr.github.io/kineo/.

We present ZeroRF, a novel per-scene optimization method addressing the challenge of sparse view 360{\deg} reconstruction in neural field representations. Current breakthroughs like Neural Radiance Fields (NeRF) have demonstrated high-fidelity image synthesis but struggle with sparse input views. Existing methods, such as Generalizable NeRFs and per-scene optimization approaches, face limitations in data dependency, computational cost, and generalization across diverse scenarios. To overcome these challenges, we propose ZeroRF, whose key idea is to integrate a tailored Deep Image Prior into a factorized NeRF representation. Unlike traditional methods, ZeroRF parametrizes feature grids with a neural network generator, enabling efficient sparse view 360{\deg} reconstruction without any pretraining or additional regularization. Extensive experiments showcase ZeroRF's versatility and superiority in terms of both quality and speed, achieving state-of-the-art results on benchmark datasets. ZeroRF's significance extends to applications in 3D content generation and editing. Project page: https://sarahweiii.github.io/zerorf/

Computational efficiency in deep neural networks is critical for object detection, especially as newer models prioritize speed over efficient computation (FLOP). This evolution has somewhat left behind embedded and mobile-oriented AI object detection applications. In this paper, we focus on design choices of neural network architectures for efficient object detection computation based on FLOP and propose several optimizations to enhance the efficiency of YOLO-based models. Firstly, we introduce an efficient backbone scaling inspired by inverted bottlenecks and theoretical insights from the Information Bottleneck principle. Secondly, we present the Fast Pyramidal Architecture Network (FPAN), designed to facilitate fast multiscale feature sharing while reducing computational resources. Lastly, we propose a Decoupled Network-in-Network (DNiN) detection head engineered to deliver rapid yet lightweight computations for classification and regression tasks. Building upon these optimizations and leveraging more efficient backbones, this paper contributes to a new scaling paradigm for object detection and YOLO-centric models called LeYOLO. Our contribution consistently outperforms existing models in various resource constraints, achieving unprecedented accuracy and flop ratio. Notably, LeYOLO-Small achieves a competitive mAP score of 38.2% on the COCOval with just 4.5 FLOP(G), representing a 42% reduction in computational load compared to the latest state-of-the-art YOLOv9-Tiny model while achieving similar accuracy. Our novel model family achieves a FLOP-to-accuracy ratio previously unattained, offering scalability that spans from ultra-low neural network configurations (< 1 GFLOP) to efficient yet demanding object detection setups (> 4 GFLOPs) with 25.2, 31.3, 35.2, 38.2, 39.3 and 41 mAP for 0.66, 1.47, 2.53, 4.51, 5.8 and 8.4 FLOP(G).

Large deep learning models have achieved remarkable success in many scenarios. However, training large models is usually challenging, e.g., due to the high computational cost, the unstable and painfully slow optimization procedure, and the vulnerability to overfitting. To alleviate these problems, this work studies a divide-and-conquer strategy, i.e., dividing a large model into smaller modules, training them independently, and reassembling the trained modules to obtain the target model. This approach is promising since it avoids directly training large models from scratch. Nevertheless, implementing this idea is non-trivial, as it is difficult to ensure the compatibility of the independently trained modules. In this paper, we present an elegant solution to address this issue, i.e., we introduce a global, shared meta model to implicitly link all the modules together. This enables us to train highly compatible modules that collaborate effectively when they are assembled together. We further propose a module incubation mechanism that enables the meta model to be designed as an extremely shallow network. As a result, the additional overhead introduced by the meta model is minimalized. Though conceptually simple, our method significantly outperforms end-to-end (E2E) training in terms of both final accuracy and training efficiency. For example, on top of ViT-Huge, it improves the accuracy by 2.7% compared to the E2E baseline on ImageNet-1K, while saving the training cost by 43% in the meantime. Code is available at https://github.com/LeapLabTHU/Model-Assembling.

Editing illumination in long videos with complex dynamics has significant value in various downstream tasks, including visual content creation and manipulation, as well as data scaling up for embodied AI through sim2real and real2real transfer. Nevertheless, existing video relighting techniques are predominantly limited to portrait videos or fall into the bottleneck of temporal consistency and computation efficiency. In this paper, we propose TC-Light, a novel paradigm characterized by the proposed two-stage post optimization mechanism. Starting from the video preliminarily relighted by an inflated video relighting model, it optimizes appearance embedding in the first stage to align global illumination. Then it optimizes the proposed canonical video representation, i.e., Unique Video Tensor (UVT), to align fine-grained texture and lighting in the second stage. To comprehensively evaluate performance, we also establish a long and highly dynamic video benchmark. Extensive experiments show that our method enables physically plausible relighting results with superior temporal coherence and low computation cost. The code and video demos are available at https://dekuliutesla.github.io/tclight/.

Voxel-based methods have achieved state-of-the-art performance for 3D object detection in autonomous driving. However, their significant computational and memory costs pose a challenge for their application to resource-constrained vehicles. One reason for this high resource consumption is the presence of a large number of redundant background points in Lidar point clouds, resulting in spatial redundancy in both 3D voxel and dense BEV map representations. To address this issue, we propose an adaptive inference framework called Ada3D, which focuses on exploiting the input-level spatial redundancy. Ada3D adaptively filters the redundant input, guided by a lightweight importance predictor and the unique properties of the Lidar point cloud. Additionally, we utilize the BEV features' intrinsic sparsity by introducing the Sparsity Preserving Batch Normalization. With Ada3D, we achieve 40% reduction for 3D voxels and decrease the density of 2D BEV feature maps from 100% to 20% without sacrificing accuracy. Ada3D reduces the model computational and memory cost by 5x, and achieves 1.52x/1.45x end-to-end GPU latency and 1.5x/4.5x GPU peak memory optimization for the 3D and 2D backbone respectively.

The Iterative Closest Point (ICP) algorithm and its variants are a fundamental technique for rigid registration between two point sets, with wide applications in different areas from robotics to 3D reconstruction. The main drawbacks for ICP are its slow convergence as well as its sensitivity to outliers, missing data, and partial overlaps. Recent work such as Sparse ICP achieves robustness via sparsity optimization at the cost of computational speed. In this paper, we propose a new method for robust registration with fast convergence. First, we show that the classical point-to-point ICP can be treated as a majorization-minimization (MM) algorithm, and propose an Anderson acceleration approach to speed up its convergence. In addition, we introduce a robust error metric based on the Welsch's function, which is minimized efficiently using the MM algorithm with Anderson acceleration. On challenging datasets with noises and partial overlaps, we achieve similar or better accuracy than Sparse ICP while being at least an order of magnitude faster. Finally, we extend the robust formulation to point-to-plane ICP, and solve the resulting problem using a similar Anderson-accelerated MM strategy. Our robust ICP methods improve the registration accuracy on benchmark datasets while being competitive in computational time.

Deep neural networks have achieved great success in many data processing applications. However, the high computational complexity and storage cost makes deep learning hard to be used on resource-constrained devices, and it is not environmental-friendly with much power cost. In this paper, we focus on low-rank optimization for efficient deep learning techniques. In the space domain, deep neural networks are compressed by low rank approximation of the network parameters, which directly reduces the storage requirement with a smaller number of network parameters. In the time domain, the network parameters can be trained in a few subspaces, which enables efficient training for fast convergence. The model compression in the spatial domain is summarized into three categories as pre-train, pre-set, and compression-aware methods, respectively. With a series of integrable techniques discussed, such as sparse pruning, quantization, and entropy coding, we can ensemble them in an integration framework with lower computational complexity and storage. Besides of summary of recent technical advances, we have two findings for motivating future works: one is that the effective rank outperforms other sparse measures for network compression. The other is a spatial and temporal balance for tensorized neural networks.

The Retrieval-Augmented Generation (RAG) systems' performance on Thai legal question answering is still limited, especially for questions requiring extensive, complex legal reasoning. To address these limitations, we introduce an approach aligning LLMs toward improved law citation accuracy and better response quality using Group-Relative Policy Optimization (GRPO). Our approach leverages BGE-M3 embeddings as a cost-efficient semantic-similarity reward, significantly reducing computational expenses up to 2.5x compared to large language model judges. Experiments on the NitiBench benchmark demonstrate substantial improvements: GRPO achieves up to 90% citation-F1 gains from the base model and a 31% increase in joint quality metrics over instruction tuning. Crucially, our method shows enhanced robustness on complex legal reasoning tasks compared to instruction tuning, providing an effective and resource-efficient solution for enhancing Thai legal LLMs.

The impressive performance of Large Language Models (LLMs) across various natural language processing tasks comes at the cost of vast computational resources and storage requirements. One-shot pruning techniques offer a way to alleviate these burdens by removing redundant weights without the need for retraining. Yet, the massive scale of LLMs often forces current pruning approaches to rely on heuristics instead of optimization-based techniques, potentially resulting in suboptimal compression. In this paper, we introduce ALPS, an optimization-based framework that tackles the pruning problem using the operator splitting technique and a preconditioned conjugate gradient-based post-processing step. Our approach incorporates novel techniques to accelerate and theoretically guarantee convergence while leveraging vectorization and GPU parallelism for efficiency. ALPS substantially outperforms state-of-the-art methods in terms of the pruning objective and perplexity reduction, particularly for highly sparse models. On the OPT-30B model with 70% sparsity, ALPS achieves a 13% reduction in test perplexity on the WikiText dataset and a 19% improvement in zero-shot benchmark performance compared to existing methods.

Quantization is an effective technique to reduce the deployment cost of large language models (LLMs), and post-training quantization (PTQ) has been widely studied due to its efficiency. However, existing PTQ methods are limited by their inability to fine-tune model parameters and often suffer significant accuracy loss in low-bit scenarios. Quantization-aware training (QAT) provides a more principled solution, but its reliance on backpropagation incurs prohibitive memory costs, limiting its practicality for LLM deployment. To address these challenges, we propose ZeroQAT, a zeroth-order optimization-based QAT framework that supports both weight and activation quantization. ZeroQAT leverages forward-only gradient estimation to eliminate backpropagation, substantially reducing computational and memory overhead while retaining the benefits of end-to-end optimization. We further introduce a lightweight variant of ZeroQAT for quantized fine-tuning, which freezes and pre-quantizes most parameters to further cut memory usage. Experiments show that ZeroQAT consistently outperforms representative PTQ and QAT baselines while requiring significantly less memory. For example, ZeroQAT enables fine-tuning of a 13B model at extremely low bit-widths (e.g., 2-4 bits) on a single 8GB GPU, and even allows fine-tuning a 6.7B model on a OnePlus 12 smartphone, demonstrating its practicality for end-to-end QAT on resource-limited edge devices.

While fine-tuning of pre-trained language models generally helps to overcome the lack of labelled training samples, it also displays model performance instability. This instability mainly originates from randomness in initialisation or data shuffling. To address this, researchers either modify the training process or augment the available samples, which typically results in increased computational costs. We propose a new mitigation strategy, called Delayed Ensemble with Noisy Interpolation (DENI), that leverages the strengths of ensembling, noise regularisation and model interpolation, while retaining computational efficiency. We compare DENI with 9 representative mitigation strategies across 3 models, 4 tuning strategies and 7 text classification datasets. We show that: 1) DENI outperforms the best performing mitigation strategy (Ensemble), while using only a fraction of its cost; 2) the mitigation strategies are beneficial for parameter-efficient fine-tuning (PEFT) methods, outperforming full fine-tuning in specific cases; and 3) combining DENI with data augmentation often leads to even more effective instability mitigation.

Machine learning has emerged as a powerful solution to the modern challenges in accelerator physics. However, the limited availability of beam time, the computational cost of simulations, and the high-dimensionality of optimisation problems pose significant challenges in generating the required data for training state-of-the-art machine learning models. In this work, we introduce Cheetah, a PyTorch-based high-speed differentiable linear-beam dynamics code. Cheetah enables the fast collection of large data sets by reducing computation times by multiple orders of magnitude and facilitates efficient gradient-based optimisation for accelerator tuning and system identification. This positions Cheetah as a user-friendly, readily extensible tool that integrates seamlessly with widely adopted machine learning tools. We showcase the utility of Cheetah through five examples, including reinforcement learning training, gradient-based beamline tuning, gradient-based system identification, physics-informed Bayesian optimisation priors, and modular neural network surrogate modelling of space charge effects. The use of such a high-speed differentiable simulation code will simplify the development of machine learning-based methods for particle accelerators and fast-track their integration into everyday operations of accelerator facilities.

Optimization plays a costly and crucial role in developing machine learning systems. In learned optimizers, the few hyperparameters of commonly used hand-designed optimizers, e.g. Adam or SGD, are replaced with flexible parametric functions. The parameters of these functions are then optimized so that the resulting learned optimizer minimizes a target loss on a chosen class of models. Learned optimizers can both reduce the number of required training steps and improve the final test loss. However, they can be expensive to train, and once trained can be expensive to use due to computational and memory overhead for the optimizer itself. In this work, we identify and quantify the design features governing the memory, compute, and performance trade-offs for many learned and hand-designed optimizers. We further leverage our analysis to construct a learned optimizer that is both faster and more memory efficient than previous work. Our model and training code are open source.

3D Gaussian splatting (3DGS), known for its groundbreaking performance and efficiency, has become a dominant 3D representation and brought progress to many 3D vision tasks. However, in this work, we reveal a significant security vulnerability that has been largely overlooked in 3DGS: the computation cost of training 3DGS could be maliciously tampered by poisoning the input data. By developing an attack named Poison-splat, we reveal a novel attack surface where the adversary can poison the input images to drastically increase the computation memory and time needed for 3DGS training, pushing the algorithm towards its worst computation complexity. In extreme cases, the attack can even consume all allocable memory, leading to a Denial-of-Service (DoS) that disrupts servers, resulting in practical damages to real-world 3DGS service vendors. Such a computation cost attack is achieved by addressing a bi-level optimization problem through three tailored strategies: attack objective approximation, proxy model rendering, and optional constrained optimization. These strategies not only ensure the effectiveness of our attack but also make it difficult to defend with simple defensive measures. We hope the revelation of this novel attack surface can spark attention to this crucial yet overlooked vulnerability of 3DGS systems. Our code is available at https://github.com/jiahaolu97/poison-splat .

Optimization problems with nonlinear cost functions and combinatorial constraints appear in many real-world applications but remain challenging to solve efficiently compared to their linear counterparts. To bridge this gap, we propose SurCo that learns linear text{Sur}rogate costs which can be used in existing text{Co}mbinatorial solvers to output good solutions to the original nonlinear combinatorial optimization problem. The surrogate costs are learned end-to-end with nonlinear loss by differentiating through the linear surrogate solver, combining the flexibility of gradient-based methods with the structure of linear combinatorial optimization. We propose three SurCo variants: SurCo-zero for individual nonlinear problems, SurCo-prior for problem distributions, and SurCo-hybrid to combine both distribution and problem-specific information. We give theoretical intuition motivating SurCo, and evaluate it empirically. Experiments show that SurCo finds better solutions faster than state-of-the-art and domain expert approaches in real-world optimization problems such as embedding table sharding, inverse photonic design, and nonlinear route planning.

While LLMs excel at open-ended reasoning, they often struggle with cost-sensitive planning, either treating all actions as having equal cost or failing to stay within strict budgets. In this paper, we introduce Cost-Augmented Monte Carlo Tree Search (CATS), a novel approach that brings explicit cost-awareness into LLM-guided planning. Tight cost constraints push the planner to quickly identify infeasible solutions, while looser constraints encourage optimization for minimal cost. We benchmark top LLMs such as GPT-4.1, Claude-3.7-Sonnet, and DeepSeek-R1, against our CATS planner to evaluate their performance in cost-sensitive scenarios. Our experiments suggest that raw LLMs such as GPT-4.1 often falter under tight budgets, whereas CATS consistently delivers strong performance, achieving higher task success rates and better cost efficiency. CATS provides an effective solution for budget-aware decision-making by combining the reasoning power of LLMs with structured search.

The deployment constraints in practical applications necessitate the pruning of large-scale deep learning models, i.e., promoting their weight sparsity. As illustrated by the Lottery Ticket Hypothesis (LTH), pruning also has the potential of improving their generalization ability. At the core of LTH, iterative magnitude pruning (IMP) is the predominant pruning method to successfully find 'winning tickets'. Yet, the computation cost of IMP grows prohibitively as the targeted pruning ratio increases. To reduce the computation overhead, various efficient 'one-shot' pruning methods have been developed, but these schemes are usually unable to find winning tickets as good as IMP. This raises the question of how to close the gap between pruning accuracy and pruning efficiency? To tackle it, we pursue the algorithmic advancement of model pruning. Specifically, we formulate the pruning problem from a fresh and novel viewpoint, bi-level optimization (BLO). We show that the BLO interpretation provides a technically-grounded optimization base for an efficient implementation of the pruning-retraining learning paradigm used in IMP. We also show that the proposed bi-level optimization-oriented pruning method (termed BiP) is a special class of BLO problems with a bi-linear problem structure. By leveraging such bi-linearity, we theoretically show that BiP can be solved as easily as first-order optimization, thus inheriting the computation efficiency. Through extensive experiments on both structured and unstructured pruning with 5 model architectures and 4 data sets, we demonstrate that BiP can find better winning tickets than IMP in most cases, and is computationally as efficient as the one-shot pruning schemes, demonstrating 2-7 times speedup over IMP for the same level of model accuracy and sparsity.

We propose an iterative programmatic planning (IPP) framework for solving grid-based tasks by synthesizing interpretable agent policies expressed in code using large language models (LLMs). Instead of relying on traditional search or reinforcement learning, our approach uses code generation as policy synthesis, where the LLM outputs executable programs that map environment states to action sequences. Our proposed architecture incorporates several prompting strategies, including direct code generation, pseudocode-conditioned refinement, and curriculum-based prompting, but also includes an iterative refinement mechanism that updates code based on task performance feedback. We evaluate our approach using six leading LLMs and two challenging grid-based benchmarks (GRASP and MiniGrid). Our IPP framework demonstrates improvements over direct code generation ranging from 10\% to as much as 10x across five of the six models and establishes a new state-of-the-art result for GRASP. IPP is found to significantly outperform direct elicitation of a solution from GPT-o3-mini (by 63\% on MiniGrid to 116\% on GRASP), demonstrating the viability of the overall approach. Computational costs of all code generation approaches are similar. While code generation has a higher initial prompting cost compared to direct solution elicitation (\0.08 per task vs. 0.002 per instance for GPT-o3-mini), the code can be reused for any number of instances, making the amortized cost significantly lower (by 400x on GPT-o3-mini across the complete GRASP benchmark).

Sparse Mixture of Experts (SMoE) has become the key to unlocking unparalleled scalability in deep learning. SMoE has the potential to exponentially increase parameter count while maintaining the efficiency of the model by only activating a small subset of these parameters for a given sample. However, it has been observed that SMoE suffers from unstable training and has difficulty adapting to new distributions, leading to the model's lack of robustness to data contamination. To overcome these limitations, we first establish a connection between the dynamics of the expert representations in SMoEs and gradient descent on a multi-objective optimization problem. Leveraging our framework, we then integrate momentum into SMoE and propose a new family of SMoEs named MomentumSMoE. We theoretically prove and numerically demonstrate that MomentumSMoE is more stable and robust than SMoE. In particular, we verify the advantages of MomentumSMoE over SMoE on a variety of practical tasks including ImageNet-1K object recognition and WikiText-103 language modeling. We demonstrate the applicability of MomentumSMoE to many types of SMoE models, including those in the Sparse MoE model for vision (V-MoE) and the Generalist Language Model (GLaM). We also show that other advanced momentum-based optimization methods, such as Adam, can be easily incorporated into the MomentumSMoE framework for designing new SMoE models with even better performance, almost negligible additional computation cost, and simple implementations.

During early optimization passes, compilers must make predictions for machine-dependent characteristics such as execution unit utilization, number of register spills, latency, throughput etc. to generate better code. Often a hand-written static/analytical hardware cost model is built into the compiler. However, the need for more sophisticated and varied predictions has become more pronounced with the development of deep learning compilers which need to optimize dataflow graphs. Such compilers usually employ a much higher level MLIR form as an IR representation before lowering to traditional LLVM-IR. A static/analytical cost model in such a scenario is cumbersome and error prone as the opcodes represent very high level algebraic/arithmetic operations. Hence, we develop a machine learning-based cost model for high-level MLIR which can predict different target variables of interest such as CPU/GPU/xPU utilization, instructions executed, register usage etc. By considering the incoming MLIR as a text input a la NLP models we can apply well-known techniques from modern NLP research to help predict hardware characteristics more accurately. We expect such precise ML-driven hardware cost models to guide our deep learning compiler in graph level optimizations around operator fusion, local memory allocation, kernel scheduling etc. as well as in many kernel-level optimizations such as loop interchange, LICM and unroll. We report early work-in -progress results of developing such models on high-level MLIR representing dataflow graphs emitted by Pytorch/Tensorflow-like frameworks as well as lower-level dialects like affine. We show that these models can provide reasonably good estimates with low error bounds for various hardware characteristics of interest and can be a go-to mechanism for hardware cost modelling in the future.

This paper presents a distributed algorithm applicable to a wide range of practical multi-robot applications. In such multi-robot applications, the user-defined objectives of the mission can be cast as a general optimization problem, without explicit guidelines of the subtasks per different robot. Owing to the unknown environment, unknown robot dynamics, sensor nonlinearities, etc., the analytic form of the optimization cost function is not available a priori. Therefore, standard gradient-descent-like algorithms are not applicable to these problems. To tackle this, we introduce a new algorithm that carefully designs each robot's subcost function, the optimization of which can accomplish the overall team objective. Upon this transformation, we propose a distributed methodology based on the cognitive-based adaptive optimization (CAO) algorithm, that is able to approximate the evolution of each robot's cost function and to adequately optimize its decision variables (robot actions). The latter can be achieved by online learning only the problem-specific characteristics that affect the accomplishment of mission objectives. The overall, low-complexity algorithm can straightforwardly incorporate any kind of operational constraint, is fault-tolerant, and can appropriately tackle time-varying cost functions. A cornerstone of this approach is that it shares the same convergence characteristics as those of block coordinate descent algorithms. The proposed algorithm is evaluated in three heterogeneous simulation set-ups under multiple scenarios, against both general-purpose and problem-specific algorithms. Source code is available at https://github.com/athakapo/A-distributed-plug-n-play-algorithm-for-multi-robot-applications.

While polyhedral compilers have shown success in implementing advanced code transformations, they still face challenges in selecting the ones that lead to the most profitable speedups. This has motivated the use of machine learning based cost models to guide the search for polyhedral optimizations. State-of-the-art polyhedral compilers have demonstrated a viable proof-of-concept of such an approach. While promising, this approach still faces significant limitations. State-of-the-art polyhedral compilers that use a deep learning cost model only support a small subset of affine transformations, limiting their ability to explore complex code transformations. Furthermore, their applicability does not scale beyond simple programs, thus excluding many program classes from their scope, such as those with non-rectangular iteration domains or multiple loop nests. These limitations significantly impact the generality of such compilers and autoschedulers and put into question the whole approach. In this paper, we introduce LOOPer, the first polyhedral autoscheduler that uses a deep learning based cost model and covers a large space of affine transformations and programs. LOOPer allows the optimization of an extensive set of programs while being effective at applying complex sequences of polyhedral transformations. We implement and evaluate LOOPer and show that it achieves competitive speedups over the state-of-the-art. On the PolyBench benchmarks, LOOPer achieves a geometric mean speedup of 1.84x over Tiramisu and 1.42x over Pluto, two state-of-the-art polyhedral autoschedulers.

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.

Supply chain operations traditionally involve a variety of complex decision making problems. Over the last few decades, supply chains greatly benefited from advances in computation, which allowed the transition from manual processing to automation and cost-effective optimization. Nonetheless, business operators still need to spend substantial efforts in explaining and interpreting the optimization outcomes to stakeholders. Motivated by the recent advances in Large Language Models (LLMs), we study how this disruptive technology can help bridge the gap between supply chain automation and human comprehension and trust thereof. We design -- a framework that accepts as input queries in plain text, and outputs insights about the underlying optimization outcomes. Our framework does not forgo the state-of-the-art combinatorial optimization technology, but rather leverages it to quantitatively answer what-if scenarios (e.g., how would the cost change if we used supplier B instead of supplier A for a given demand?). Importantly, our design does not require sending proprietary data over to LLMs, which can be a privacy concern in some circumstances. We demonstrate the effectiveness of our framework on a real server placement scenario within Microsoft's cloud supply chain. Along the way, we develop a general evaluation benchmark, which can be used to evaluate the accuracy of the LLM output in other scenarios.

We present two different methods for estimating the cost of solving SAT problems. The methods focus on the online behaviour of the backtracking solver, as well as the structure of the problem. Modern SAT solvers present several challenges to estimate search cost including coping with nonchronological backtracking, learning and restarts. Our first method adapt an existing algorithm for estimating the size of a search tree to deal with these challenges. We then suggest a second method that uses a linear model trained on data gathered online at the start of search. We compare the effectiveness of these two methods using random and structured problems. We also demonstrate that predictions made in early restarts can be used to improve later predictions. We conclude by showing that the cost of solving a set of problems can be reduced by selecting a solver from a portfolio based on such cost estimations.

We introduce a novel neural network-based algorithm to compute optimal transport (OT) plans for general cost functionals. In contrast to common Euclidean costs, i.e., ell^1 or ell^2, such functionals provide more flexibility and allow using auxiliary information, such as class labels, to construct the required transport map. Existing methods for general costs are discrete and have limitations in practice, i.e. they do not provide an out-of-sample estimation. We address the challenge of designing a continuous OT approach for general costs that generalizes to new data points in high-dimensional spaces, such as images. Additionally, we provide the theoretical error analysis for our recovered transport plans. As an application, we construct a cost functional to map data distributions while preserving the class-wise structure.

Hyperparameter optimization (HPO) is concerned with the automated search for the most appropriate hyperparameter configuration (HPC) of a parameterized machine learning algorithm. A state-of-the-art HPO method is Hyperband, which, however, has its own parameters that influence its performance. One of these parameters, the maximal budget, is especially problematic: If chosen too small, the budget needs to be increased in hindsight and, as Hyperband is not incremental by design, the entire algorithm must be re-run. This is not only costly but also comes with a loss of valuable knowledge already accumulated. In this paper, we propose incremental variants of Hyperband that eliminate these drawbacks, and show that these variants satisfy theoretical guarantees qualitatively similar to those for the original Hyperband with the "right" budget. Moreover, we demonstrate their practical utility in experiments with benchmark data sets.

In training neural networks, it is common practice to use partial gradients computed over batches, mostly very small subsets of the training set. This approach is motivated by the argument that such a partial gradient is close to the true one, with precision growing only with the square root of the batch size. A theoretical justification is with the help of stochastic approximation theory. However, the conditions for the validity of this theory are not satisfied in the usual learning rate schedules. Batch processing is also difficult to combine with efficient second-order optimization methods. This proposal is based on another hypothesis: the loss minimum of the training set can be expected to be well-approximated by the minima of its subsets. Such subset minima can be computed in a fraction of the time necessary for optimizing over the whole training set. This hypothesis has been tested with the help of the MNIST, CIFAR-10, and CIFAR-100 image classification benchmarks, optionally extended by training data augmentation. The experiments have confirmed that results equivalent to conventional training can be reached. In summary, even small subsets are representative if the overdetermination ratio for the given model parameter set sufficiently exceeds unity. The computing expense can be reduced to a tenth or less.

Test-time compute scaling has emerged as a new axis along which to improve model accuracy, where additional computation is used at inference time to allow the model to think longer for more challenging problems. One promising approach for test-time compute scaling is search against a process reward model, where a model generates multiple potential candidates at each step of the search, and these partial trajectories are then scored by a separate reward model in order to guide the search process. The diversity of trajectories in the tree search process affects the accuracy of the search, since increasing diversity promotes more exploration. However, this diversity comes at a cost, as divergent trajectories have less KV sharing, which means they consume more memory and slow down the search process. Previous search methods either do not perform sufficient exploration, or else explore diverse trajectories but have high latency. We address this challenge by proposing Efficient Tree Search (ETS), which promotes KV sharing by pruning redundant trajectories while maintaining necessary diverse trajectories. ETS incorporates a linear programming cost model to promote KV cache sharing by penalizing the number of nodes retained, while incorporating a semantic coverage term into the cost model to ensure that we retain trajectories which are semantically different. We demonstrate how ETS can achieve 1.8times reduction in average KV cache size during the search process, leading to 1.4times increased throughput relative to prior state-of-the-art methods, with minimal accuracy degradation and without requiring any custom kernel implementation. Code is available at: https://github.com/SqueezeAILab/ETS.

We present an online method for estimating the cost of solving SAT problems. Modern SAT solvers present several challenges to estimate search cost including non-chronological backtracking, learning and restarts. Our method uses a linear model trained on data gathered at the start of search. We show the effectiveness of this method using random and structured problems. We demonstrate that predictions made in early restarts can be used to improve later predictions. We also show that we can use such cost estimations to select a solver from a portfolio.

Large models represent a groundbreaking advancement in multiple application fields, enabling remarkable achievements across various tasks. However, their unprecedented scale comes with significant computational costs. These models, often consisting of billions of parameters, require vast amounts of computational resources for execution. Especially, the expansive scale and computational demands pose considerable challenges when customizing them for particular downstream tasks, particularly over the hardware platforms constrained by computational capabilities. Parameter Efficient Fine-Tuning (PEFT) provides a practical solution by efficiently adapt the large models over the various downstream tasks. In particular, PEFT refers to the process of adjusting the parameters of a pre-trained large models to adapt it to a specific task while minimizing the number of additional parameters introduced or computational resources required. This approach is particularly important when dealing with large language models with high parameter counts, as fine-tuning these models from scratch can be computationally expensive and resource-intensive, posing considerable challenges in the supporting system platform design. In this survey, we present comprehensive studies of various PEFT algorithms, examining their performance and computational overhead. Moreover, we provide an overview of applications developed using different PEFT algorithms and discuss common techniques employed to mitigate computation costs for PEFT. In addition to the algorithmic perspective, we overview various real-world system designs to investigate the implementation costs associated with different PEFT algorithms. This survey serves as an indispensable resource for researchers aiming to understand both the PEFT algorithm and its system implementation, offering detailed insights into recent advancements and practical applications.

Being prompted to engage in reasoning has emerged as a core technique for using large language models (LLMs), deploying additional inference-time compute to improve task performance. However, as LLMs increase in both size and adoption, inference costs are correspondingly becoming increasingly burdensome. How, then, might we optimize reasoning's cost-performance tradeoff? This work introduces a novel approach based on computational models of metareasoning used in cognitive science, training LLMs to selectively use intermediate reasoning steps only when necessary. We first develop a reward function that incorporates the Value of Computation by penalizing unnecessary reasoning, then use this reward function with Expert Iteration to train the LLM. Compared to few-shot chain-of-thought prompting and STaR, our method significantly reduces inference costs (20-37\% fewer tokens generated across three models) while maintaining task performance across diverse datasets.

Large Language Models (LLMs) can self-improve through reinforcement learning, where they generate trajectories to explore and discover better solutions. However, this exploration process is computationally expensive, often forcing current methods to assign limited exploration budgets to each task. This uniform allocation creates problematic edge cases: easy tasks consistently succeed while difficult tasks consistently fail, both producing zero gradients during training updates for the widely used Group Relative Policy Optimization (GRPO). We address this problem from the lens of exploration budget allocation. Viewing each task's exploration as an "item" with a distinct "value" and "cost", we establish a connection to the classical knapsack problem. This formulation allows us to derive an optimal assignment rule that adaptively distributes resources based on the model's current learning status. When applied to GRPO, our method increases the effective ratio of non-zero policy gradients by 20-40% during training. Acting as a computational "free lunch", our approach could reallocate exploration budgets from tasks where learning is saturated to those where it is most impactful. This enables significantly larger budgets (e.g., 93 rollouts) for especially challenging problems, which would be computationally prohibitive under a uniform allocation. These improvements translate to meaningful gains on mathematical reasoning benchmarks, with average improvements of 2-4 points and peak gains of 9 points on specific tasks. Notably, achieving comparable performance with traditional homogeneous allocation would require about 2x the computational resources.

Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are fine-tuned for the application at hand. Although this tuning process can require large computational costs, recent work has shown that these costs can be reduced by line search methods that iteratively adjust the stepsize. We propose an alternative approach to stochastic line search by using a new algorithm based on forward step model building. This model building step incorporates second-order information that allows adjusting not only the stepsize but also the search direction. Noting that deep learning model parameters come in groups (layers of tensors), our method builds its model and calculates a new step for each parameter group. This novel diagonalization approach makes the selected step lengths adaptive. We provide convergence rate analysis, and experimentally show that the proposed algorithm achieves faster convergence and better generalization in well-known test problems. More precisely, SMB requires less tuning, and shows comparable performance to other adaptive methods.

Motivated by the operational problems in click and collect systems, such as curbside pickup programs, we study a joint admission control and capacity allocation problem. We consider a system where arriving customers have preferred service delivery times and gauge the service quality based on the service provider's ability to complete the service as close as possible to the preferred time. Customers can be of different priority classes, and their priority may increase as they wait longer in the queue. The service provider can reject customers upon their arrival if the system is overloaded or outsource the service (alternatively work overtime) when the capacity is not enough. The service provider's goal is to find the minimum-cost admission and capacity allocation policy to dynamically decide when to serve and whom to serve. We model this problem as a Markov Decision Process. Our structural results partially characterize a set of suboptimal solutions, and we develop solution methods using these results. We also develop a problem-specific approximation method that is based on state aggregation to overcome the computational challenges. We present extensive computational results and discuss the impact of problem parameters on the optimal policy.

We propose a novel approach to scaling LLM inference for code generation. We frame code generation as a black box optimization problem within the code space, and employ optimization-inspired techniques to enhance exploration. Specifically, we introduce Scattered Forest Search to enhance solution diversity while searching for solutions. Our theoretical analysis illustrates how these methods avoid local optima during optimization. Extensive experiments on HumanEval, MBPP, APPS, CodeContests, and Leetcode reveal significant performance improvements. For instance, our method achieves a pass@1 rate of 67.1% on HumanEval+ and 87.2% on HumanEval with GPT-3.5, marking improvements of 8.6% and 4.3% over the state-of-the-art, while also halving the iterations needed to find the correct solution. Furthermore, our method scales more efficiently than existing search techniques, including tree search, line search, and repeated sampling.

Efficiently approximating local curvature information of the loss function is a key tool for optimization and compression of deep neural networks. Yet, most existing methods to approximate second-order information have high computational or storage costs, which can limit their practicality. In this work, we investigate matrix-free, linear-time approaches for estimating Inverse-Hessian Vector Products (IHVPs) for the case when the Hessian can be approximated as a sum of rank-one matrices, as in the classic approximation of the Hessian by the empirical Fisher matrix. We propose two new algorithms as part of a framework called M-FAC: the first algorithm is tailored towards network compression and can compute the IHVP for dimension d, if the Hessian is given as a sum of m rank-one matrices, using O(dm^2) precomputation, O(dm) cost for computing the IHVP, and query cost O(m) for any single element of the inverse Hessian. The second algorithm targets an optimization setting, where we wish to compute the product between the inverse Hessian, estimated over a sliding window of optimization steps, and a given gradient direction, as required for preconditioned SGD. We give an algorithm with cost O(dm + m^2) for computing the IHVP and O(dm + m^3) for adding or removing any gradient from the sliding window. These two algorithms yield state-of-the-art results for network pruning and optimization with lower computational overhead relative to existing second-order methods. Implementations are available at [9] and [17].

Computationally intensive decoding procedures--including search, reranking, and self-critique--can improve the quality of language model (LM) outputs in problems spanning code generation, numerical reasoning, and dialog. Existing work typically applies the same decoding procedure for every input to an LM. But not all inputs require the same amount of computation to process. Can we allocate decoding computation adaptively, using more resources to answer questions whose answers will be harder to compute? We present an approach that predicts the distribution of rewards given an input and computation budget, then allocates additional computation to inputs for which it is predicted to be most useful. We apply this approach in two decoding procedures: first, an adaptive best-of-k procedure that dynamically selects the number of samples to generate as input to a reranker; second, a routing procedure that dynamically responds to a query using a decoding procedure that is expensive but accurate, or one that is cheaper but less capable. Across a suite of programming, mathematics, and dialog tasks, we show that accurate computation-allocation procedures can be learned, and reduce computation by up to 50% at no cost to response quality, or improve quality by up to 10% at a fixed computational budget.

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.

The k-means++ seeding algorithm (Arthur & Vassilvitskii, 2007) is widely used in practice for the k-means clustering problem where the goal is to cluster a dataset X subset R ^d into k clusters. The popularity of this algorithm is due to its simplicity and provable guarantee of being O(log k) competitive with the optimal solution in expectation. However, its running time is O(|X|kd), making it expensive for large datasets. In this work, we present a simple and effective rejection sampling based approach for speeding up k-means++. Our first method runs in time O(nnz (X) + beta k^2d) while still being O(log k ) competitive in expectation. Here, beta is a parameter which is the ratio of the variance of the dataset to the optimal k-means cost in expectation and O hides logarithmic factors in k and |X|. Our second method presents a new trade-off between computational cost and solution quality. It incurs an additional scale-invariant factor of k^{-Omega( m/beta)} Var (X) in addition to the O(log k) guarantee of k-means++ improving upon a result of (Bachem et al, 2016a) who get an additional factor of m^{-1}Var(X) while still running in time O(nnz(X) + mk^2d). We perform extensive empirical evaluations to validate our theoretical results and to show the effectiveness of our approach on real datasets.

We consider minimizing functions for which it is expensive to compute the (possibly stochastic) gradient. Such functions are prevalent in reinforcement learning, imitation learning and adversarial training. Our target optimization framework uses the (expensive) gradient computation to construct surrogate functions in a target space (e.g. the logits output by a linear model for classification) that can be minimized efficiently. This allows for multiple parameter updates to the model, amortizing the cost of gradient computation. In the full-batch setting, we prove that our surrogate is a global upper-bound on the loss, and can be (locally) minimized using a black-box optimization algorithm. We prove that the resulting majorization-minimization algorithm ensures convergence to a stationary point of the loss. Next, we instantiate our framework in the stochastic setting and propose the SSO algorithm, which can be viewed as projected stochastic gradient descent in the target space. This connection enables us to prove theoretical guarantees for SSO when minimizing convex functions. Our framework allows the use of standard stochastic optimization algorithms to construct surrogates which can be minimized by any deterministic optimization method. To evaluate our framework, we consider a suite of supervised learning and imitation learning problems. Our experiments indicate the benefits of target optimization and the effectiveness of SSO.

This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural networks, we discuss how optimization problems arise in machine learning and what makes them challenging. A major theme of our study is that large-scale machine learning represents a distinctive setting in which the stochastic gradient (SG) method has traditionally played a central role while conventional gradient-based nonlinear optimization techniques typically falter. Based on this viewpoint, we present a comprehensive theory of a straightforward, yet versatile SG algorithm, discuss its practical behavior, and highlight opportunities for designing algorithms with improved performance. This leads to a discussion about the next generation of optimization methods for large-scale machine learning, including an investigation of two main streams of research on techniques that diminish noise in the stochastic directions and methods that make use of second-order derivative approximations.

Current evaluations of Large Language Model (LLM) agents primarily emphasize task completion, often overlooking resource efficiency and adaptability. This neglects a crucial capability: agents' ability to devise and adjust cost-optimal plans in response to changing environments. To bridge this gap, we introduce CostBench, a scalable, cost-centric benchmark designed to evaluate agents' economic reasoning and replanning abilities. Situated in the travel-planning domain, CostBench comprises tasks solvable via multiple sequences of atomic and composite tools with diverse, customizable costs. It also supports four types of dynamic blocking events, such as tool failures and cost changes, to simulate real-world unpredictability and necessitate agents to adapt in real time. Evaluating leading open-sourced and proprietary models on CostBench reveals a substantial gap in cost-aware planning: agents frequently fail to identify cost-optimal solutions in static settings, with even GPT-5 achieving less than 75% exact match rate on the hardest tasks, and performance further dropping by around 40% under dynamic conditions. By diagnosing these weaknesses, CostBench lays the groundwork for developing future agents that are both economically rational and robust.

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.

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

In this study, we present an model-based approach to recognize full 26 degrees of freedom of a human hand. Input data include RGB-D images acquired from a Kinect camera and a 3D model of the hand constructed from its anatomy and graphical matrices. A cost function is then defined so that its minimum value is achieved when the model and observation images are matched. To solve the optimization problem in 26 dimensional space, the particle swarm optimization algorimth with improvements are used. In addition, parallel computation in graphical processing units (GPU) is utilized to handle computationally expensive tasks. Simulation and experimental results show that the system can recognize 26 degrees of freedom of hands with the processing time of 0.8 seconds per frame. The algorithm is robust to noise and the hardware requirement is simple with a single camera.

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control - potentially with non-smoothness both on the level of the objectives or in the system dynamics. This results in new challenges such as dealing with expensive models (e.g., governed by partial differential equations (PDEs)) and developing dedicated algorithms handling the non-smoothness. Since in contrast to single-objective optimization, the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in the field of multiobjective optimization of non-smooth PDE-constrained problems. In particular we report on the advances achieved within Project 2 "Multiobjective Optimization of Non-Smooth PDE-Constrained Problems - Switches, State Constraints and Model Order Reduction" of the DFG Priority Programm 1962 "Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization".

Combinatorial optimization problems are ubiquitous in science and engineering. Still, learning-based approaches to accelerate combinatorial optimization often require solving a large number of difficult instances to collect training data, incurring significant computational cost. Existing learning-based methods require training dedicated models for each problem distribution, for each downstream task, severely limiting their scalability and generalization. We introduce Forge: Foundational Optimization Representations from Graph Embeddings, a framework that pre-trains a vector-quantized graph autoencoder on a large, diverse collection of mixed-integer programming (MIP) instances in an unsupervised manner, without relying on optimization solvers or optimal solutions. Vector quantization produces discrete code assignments that serve as a vocabulary for representing optimization instances. We evaluate Forge in both unsupervised and supervised settings. In the unsupervised setting, Forge embeddings effectively cluster unseen instances across problem domains and sizes. In the supervised setting, we fine-tune Forge embeddings and show that a single pre-trained model helps predicting both the integrality gap for cut-generation and variable hints for search guidance across multiple problem and size distributions. In both tasks, we improve the performance of a commercial optimization solver and outperform state-of-the-art learning-based methods. Finally, we open-source our training code, pre-trained Forge weights, and embeddings for multiple MIP distributions to foster further research in representation learning for optimization problems.

Despite their remarkable success in complex tasks propelling widespread adoption, large language-model-based agents still face critical deployment challenges due to prohibitive latency and inference costs. While recent work has explored various methods to accelerate inference, existing approaches suffer from significant limitations: they either fail to preserve performance fidelity, require extensive offline training of router modules, or incur excessive operational costs. Moreover, they provide minimal user control over the tradeoff between acceleration and other performance metrics. To address these gaps, we introduce Dynamic Speculative Planning (DSP), an asynchronous online reinforcement learning framework that provides lossless acceleration with substantially reduced costs without requiring additional pre-deployment preparation. DSP explicitly optimizes a joint objective balancing end-to-end latency against dollar cost, allowing practitioners to adjust a single parameter that steers the system toward faster responses, cheaper operation, or any point along this continuum. Experiments on two standard agent benchmarks demonstrate that DSP achieves comparable efficiency to the fastest lossless acceleration method while reducing total cost by 30% and unnecessary cost up to 60%. Our code and data are available through https://github.com/guanyilin428/Dynamic-Speculative-Planning.

Large language models (LLMs) can achieve strong reasoning performance with sufficient computation, but they do not inherently know how much computation a task requires. We study budgeted inference-time reasoning for multiple tasks under a strict global token constraint and formalize it as a Ordered Stochastic Multiple-Choice Knapsack Problem(OS-MCKP). This perspective highlights a meta-cognitive requirement -- anticipating task difficulty, estimating return over investment (ROI), and allocating computation strategically. We propose ROI-Reasoning, a two-stage framework that endows LLMs with intrinsic, budget-aware rationality. In the first stage, Meta-Cognitive Fine-Tuning teaches models to predict reasoning cost and expected utility before generation, enabling explicit solve-or-skip decisions. Next, Rationality-Aware Reinforcement Learning optimizes sequential decision making under a hard token budget, allowing models to learn long-horizon allocation strategies. Across budgeted mathematical reasoning benchmarks, ROI-Reasoning consistently improves overall score while substantially reducing regret under tight computation budgets.

Test-time compute scaling has emerged as a powerful paradigm for enhancing mathematical reasoning in large language models (LLMs) by allocating additional computational resources during inference. However, current methods employ uniform resource distribution across all reasoning sub-problems, creating fundamental bottlenecks where challenging sub-problems receive insufficient attention while routine operations consume disproportionate resources. This uniform allocation creates performance bottlenecks where additional computational resources yield diminishing returns. Inspired by dual-process theory, we propose SCALE (Selective Resource Allocation), a framework that selectively allocates computational resources based on sub-problem difficulty. SCALE operates through four stages: (1) problem decomposition into sequential reasoning sub-problems, (2) difficulty assessment of each sub-problem to distinguish between routine operations and computationally challenging sub-problems, (3) selective processing mode assignment between System 1 for simple sub-problems and System 2 for complex ones, and (4) sequential execution with context propagation. By concentrating resources on challenging sub-problems while processing routine operations efficiently, SCALE achieves substantial performance improvements with superior resource utilization. Extensive experiments demonstrate that SCALE significantly outperforms uniform scaling baselines, achieving accuracy improvements of up to 13.75 percentage points (57.50% to 71.25% on AIME25) while reducing computational costs by 33%-53%, representing a major advance in test-time scaling that addresses fundamental limitations of current approaches.

Using fault-tolerant constructions, computations performed with unreliable components can simulate their noiseless counterparts though the introduction of a modest amount of redundancy. Given the modest overhead required to achieve fault-tolerance, and the fact that increasing the reliability of basic components often comes at a cost, are there situations where fault-tolerance may be more economical? We present a general framework to account for this overhead cost in order to effectively compare fault-tolerant to non-fault-tolerant approaches for computation, in the limit of small logical error rates. Using this detailed accounting, we determine explicit boundaries at which fault-tolerant designs become more efficient than designs that achieve comparable reliability through direct consumption of resources. We find that the fault-tolerant construction is always preferred in the limit of high reliability in cases where the resources required to construct a basic unit grows faster than log(1 / epsilon) asymptotically for small epsilon.

Robust optimization provides a mathematical framework for modeling and solving decision-making problems under worst-case uncertainty. This work addresses two-stage robust optimization (2RO) problems (also called adjustable robust optimization), wherein first-stage and second-stage decisions are made before and after uncertainty is realized, respectively. This results in a nested min-max-min optimization problem which is extremely challenging computationally, especially when the decisions are discrete. We propose Neur2RO, an efficient machine learning-driven instantiation of column-and-constraint generation (CCG), a classical iterative algorithm for 2RO. Specifically, we learn to estimate the value function of the second-stage problem via a novel neural network architecture that is easy to optimize over by design. Embedding our neural network into CCG yields high-quality solutions quickly as evidenced by experiments on two 2RO benchmarks, knapsack and capital budgeting. For knapsack, Neur2RO finds solutions that are within roughly 2% of the best-known values in a few seconds compared to the three hours of the state-of-the-art exact branch-and-price algorithm; for larger and more complex instances, Neur2RO finds even better solutions. For capital budgeting, Neur2RO outperforms three variants of the k-adaptability algorithm, particularly on the largest instances, with a 10 to 100-fold reduction in solution time. Our code and data are available at https://github.com/khalil-research/Neur2RO.

We introduce RL4CO, an extensive reinforcement learning (RL) for combinatorial optimization (CO) benchmark. RL4CO employs state-of-the-art software libraries as well as best practices in implementation, such as modularity and configuration management, to be efficient and easily modifiable by researchers for adaptations of neural network architecture, environments, and algorithms. Contrary to the existing focus on specific tasks like the traveling salesman problem (TSP) for performance assessment, we underline the importance of scalability and generalization capabilities for diverse optimization tasks. We also systematically benchmark sample efficiency, zero-shot generalization, and adaptability to changes in data distributions of various models. Our experiments show that some recent state-of-the-art methods fall behind their predecessors when evaluated using these new metrics, suggesting the necessity for a more balanced view of the performance of neural CO solvers. We hope RL4CO will encourage the exploration of novel solutions to complex real-world tasks, allowing to compare with existing methods through a standardized interface that decouples the science from the software engineering. We make our library publicly available at https://github.com/kaist-silab/rl4co.

We propose a systematic approach to reduce the memory consumption of deep neural network training. Specifically, we design an algorithm that costs O(sqrt(n)) memory to train a n layer network, with only the computational cost of an extra forward pass per mini-batch. As many of the state-of-the-art models hit the upper bound of the GPU memory, our algorithm allows deeper and more complex models to be explored, and helps advance the innovations in deep learning research. We focus on reducing the memory cost to store the intermediate feature maps and gradients during training. Computation graph analysis is used for automatic in-place operation and memory sharing optimizations. We show that it is possible to trade computation for memory - giving a more memory efficient training algorithm with a little extra computation cost. In the extreme case, our analysis also shows that the memory consumption can be reduced to O(log n) with as little as O(n log n) extra cost for forward computation. Our experiments show that we can reduce the memory cost of a 1,000-layer deep residual network from 48G to 7G with only 30 percent additional running time cost on ImageNet problems. Similarly, significant memory cost reduction is observed in training complex recurrent neural networks on very long sequences.

The deployment and training of neural networks on edge computing devices pose many challenges. The low memory nature of edge devices is often one of the biggest limiting factors encountered in the deployment of large neural network models. Tensor rematerialization or recompute is a way to address high memory requirements for neural network training and inference. In this paper we consider the problem of execution time minimization of compute graphs subject to a memory budget. In particular, we develop a new constraint programming formulation called Moccasin with only O(n) integer variables, where n is the number of nodes in the compute graph. This is a significant improvement over the works in the recent literature that propose formulations with O(n^2) Boolean variables. We present numerical studies that show that our approach is up to an order of magnitude faster than recent work especially for large-scale graphs.

We study the problem of using low computational cost to automate the choices of learners and hyperparameters for an ad-hoc training dataset and error metric, by conducting trials of different configurations on the given training data. We investigate the joint impact of multiple factors on both trial cost and model error, and propose several design guidelines. Following them, we build a fast and lightweight library FLAML which optimizes for low computational resource in finding accurate models. FLAML integrates several simple but effective search strategies into an adaptive system. It significantly outperforms top-ranked AutoML libraries on a large open source AutoML benchmark under equal, or sometimes orders of magnitude smaller budget constraints.

Constraint Programming (CP) is a declarative programming paradigm that allows for modeling and solving combinatorial optimization problems, such as the Job-Shop Scheduling Problem (JSSP). While CP solvers manage to find optimal or near-optimal solutions for small instances, they do not scale well to large ones, i.e., they require long computation times or yield low-quality solutions. Therefore, real-world scheduling applications often resort to fast, handcrafted, priority-based dispatching heuristics to find a good initial solution and then refine it using optimization methods. This paper proposes a novel end-to-end approach to solving scheduling problems by means of CP and Reinforcement Learning (RL). In contrast to previous RL methods, tailored for a given problem by including procedural simulation algorithms, complex feature engineering, or handcrafted reward functions, our neural-network architecture and training algorithm merely require a generic CP encoding of some scheduling problem along with a set of small instances. Our approach leverages existing CP solvers to train an agent learning a Priority Dispatching Rule (PDR) that generalizes well to large instances, even from separate datasets. We evaluate our method on seven JSSP datasets from the literature, showing its ability to find higher-quality solutions for very large instances than obtained by static PDRs and by a CP solver within the same time limit.

Machine learning for time-series forecasting remains a key area of research. Despite successful application of many machine learning techniques, relating computational efficiency to forecast error remains an under-explored domain. This paper addresses this topic through a series of real-time experiments to quantify the relationship between computational cost and forecast error using meteorological nowcasting as an example use-case. We employ a variety of popular regression techniques (XGBoost, FC-MLP, Transformer, and LSTM) for multi-horizon, short-term forecasting of three variables (temperature, wind speed, and cloud cover) for multiple locations. During a 5-day live experiment, 4000 data sources were streamed for training and inferencing 144 models per hour. These models were parameterized to explore forecast error for two computational cost minimization methods: a novel auto-adaptive data reduction technique (Variance Horizon) and a performance-based concept drift-detection mechanism. Forecast error of all model variations were benchmarked in real-time against a state-of-the-art numerical weather prediction model. Performance was assessed using classical and novel evaluation metrics. Results indicate that using the Variance Horizon reduced computational usage by more than 50\%, while increasing between 0-15\% in error. Meanwhile, performance-based retraining reduced computational usage by up to 90\% while also improving forecast error by up to 10\%. Finally, the combination of both the Variance Horizon and performance-based retraining outperformed other model configurations by up to 99.7\% when considering error normalized to computational usage.

Resided at the intersection of multi-fidelity optimization (MFO) and Bayesian optimization (BO), MF BO has found a niche in solving expensive engineering design optimization problems, thanks to its advantages in incorporating physical and mathematical understandings of the problems, saving resources, addressing exploitation-exploration trade-off, considering uncertainty, and processing parallel computing. The increasing number of works dedicated to MF BO suggests the need for a comprehensive review of this advanced optimization technique. In this paper, we survey recent developments of two essential ingredients of MF BO: Gaussian process (GP) based MF surrogates and acquisition functions. We first categorize the existing MF modeling methods and MFO strategies to locate MF BO in a large family of surrogate-based optimization and MFO algorithms. We then exploit the common properties shared between the methods from each ingredient of MF BO to describe important GP-based MF surrogate models and review various acquisition functions. By doing so, we expect to provide a structured understanding of MF BO. Finally, we attempt to reveal important aspects that require further research for applications of MF BO in solving intricate yet important design optimization problems, including constrained optimization, high-dimensional optimization, optimization under uncertainty, and multi-objective optimization.

In the realm of deep learning-based recommendation systems, the increasing computational demands, driven by the growing number of users and items, pose a significant challenge to practical deployment. This challenge is primarily twofold: reducing the model size while effectively learning user and item representations for efficient recommendations. Despite considerable advancements in model compression and architecture search, prevalent approaches face notable constraints. These include substantial additional computational costs from pre-training/re-training in model compression and an extensive search space in architecture design. Additionally, managing complexity and adhering to memory constraints is problematic, especially in scenarios with strict time or space limitations. Addressing these issues, this paper introduces a novel learning paradigm, Dynamic Sparse Learning (DSL), tailored for recommendation models. DSL innovatively trains a lightweight sparse model from scratch, periodically evaluating and dynamically adjusting each weight's significance and the model's sparsity distribution during the training. This approach ensures a consistent and minimal parameter budget throughout the full learning lifecycle, paving the way for "end-to-end" efficiency from training to inference. Our extensive experimental results underline DSL's effectiveness, significantly reducing training and inference costs while delivering comparable recommendation performance.

Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is unknown and has to be learned by interacting repeatedly with the environment in the bandit setting. We formalize our learning problem quite generally, as learning how to maximize an unknown modular function on a known polymatroid. We propose a computationally efficient algorithm for solving our problem and bound its expected cumulative regret. Our gap-dependent upper bound is tight up to a constant and our gap-free upper bound is tight up to polylogarithmic factors. Finally, we evaluate our method on three problems and demonstrate that it is practical.

This paper presents a strategy to allocate services on a Cloud system without overloading nodes and maintaining the system stability with minimum cost. We specify an abstract model of cloud resources utilization, including multiple types of resources as well as considerations for the service migration costs. A prototype meta-heuristic load balancer is demonstrated and experimental results are presented and discussed. We also propose a novel genetic algorithm, where population is seeded with the outputs of other meta-heuristic algorithms.

Recent advances show that Neural Architectural Search (NAS) method is able to find state-of-the-art image classification deep architectures. In this paper, we consider the one-shot NAS problem for resource constrained applications. This problem is of great interest because it is critical to choose different architectures according to task complexity when the resource is constrained. Previous techniques are either too slow for one-shot learning or does not take the resource constraint into consideration. In this paper, we propose the resource constrained differentiable architecture search (RC-DARTS) method to learn architectures that are significantly smaller and faster while achieving comparable accuracy. Specifically, we propose to formulate the RC-DARTS task as a constrained optimization problem by adding the resource constraint. An iterative projection method is proposed to solve the given constrained optimization problem. We also propose a multi-level search strategy to enable layers at different depths to adaptively learn different types of neural architectures. Through extensive experiments on the Cifar10 and ImageNet datasets, we show that the RC-DARTS method learns lightweight neural architectures which have smaller model size and lower computational complexity while achieving comparable or better performances than the state-of-the-art methods.

We introduce FrontierCS, a benchmark of 156 open-ended problems across diverse areas of computer science, designed and reviewed by experts, including CS PhDs and top-tier competitive programming participants and problem setters. Unlike existing benchmarks that focus on tasks with known optimal solutions, FrontierCS targets problems where the optimal solution is unknown, but the quality of a solution can be objectively evaluated. Models solve these tasks by implementing executable programs rather than outputting a direct answer. FrontierCS includes algorithmic problems, which are often NP-hard variants of competitive programming problems with objective partial scoring, and research problems with the same property. For each problem we provide an expert reference solution and an automatic evaluator. Combining open-ended design, measurable progress, and expert curation, FrontierCS provides a benchmark at the frontier of computer-science difficulty. Empirically, we find that frontier reasoning models still lag far behind human experts on both the algorithmic and research tracks, that increasing reasoning budgets alone does not close this gap, and that models often over-optimize for generating merely workable code instead of discovering high-quality algorithms and system designs.

We rethink test-time scaling laws from a practical efficiency perspective, revealing that the effectiveness of smaller models is significantly overestimated. Prior work, grounded in compute-optimality, overlooks critical memory access bottlenecks introduced by inference-time strategies (e.g., Best-of-N, long CoTs). Our holistic analysis, spanning models from 0.6B to 32B parameters, reveals a new Kinetics Scaling Law that better guides resource allocation by incorporating both computation and memory access costs. Kinetics Scaling Law suggests that test-time compute is more effective when used on models above a threshold than smaller ones. A key reason is that in TTS, attention, rather than parameter count, emerges as the dominant cost factor. Motivated by this, we propose a new scaling paradigm centered on sparse attention, which lowers per-token cost and enables longer generations and more parallel samples within the same resource budget. Empirically, we show that sparse attention models consistently outperform dense counterparts, achieving over 60 points gains in low-cost regimes and over 5 points gains in high-cost regimes for problem-solving accuracy on AIME, encompassing evaluations on state-of-the-art MoEs. These results suggest that sparse attention is essential for realizing the full potential of test-time scaling because, unlike training, where parameter scaling saturates, test-time accuracy continues to improve through increased generation. The code is available at https://github.com/Infini-AI-Lab/Kinetics.

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.

Combinatorial optimization (CO) problems are often NP-hard and thus out of reach for exact algorithms, making them a tempting domain to apply machine learning methods. The highly structured constraints in these problems can hinder either optimization or sampling directly in the solution space. On the other hand, GFlowNets have recently emerged as a powerful machinery to efficiently sample from composite unnormalized densities sequentially and have the potential to amortize such solution-searching processes in CO, as well as generate diverse solution candidates. In this paper, we design Markov decision processes (MDPs) for different combinatorial problems and propose to train conditional GFlowNets to sample from the solution space. Efficient training techniques are also developed to benefit long-range credit assignment. Through extensive experiments on a variety of different CO tasks with synthetic and realistic data, we demonstrate that GFlowNet policies can efficiently find high-quality solutions.

Bayesian optimization is an approach to optimizing objective functions that take a long time (minutes or hours) to evaluate. It is best-suited for optimization over continuous domains of less than 20 dimensions, and tolerates stochastic noise in function evaluations. It builds a surrogate for the objective and quantifies the uncertainty in that surrogate using a Bayesian machine learning technique, Gaussian process regression, and then uses an acquisition function defined from this surrogate to decide where to sample. In this tutorial, we describe how Bayesian optimization works, including Gaussian process regression and three common acquisition functions: expected improvement, entropy search, and knowledge gradient. We then discuss more advanced techniques, including running multiple function evaluations in parallel, multi-fidelity and multi-information source optimization, expensive-to-evaluate constraints, random environmental conditions, multi-task Bayesian optimization, and the inclusion of derivative information. We conclude with a discussion of Bayesian optimization software and future research directions in the field. Within our tutorial material we provide a generalization of expected improvement to noisy evaluations, beyond the noise-free setting where it is more commonly applied. This generalization is justified by a formal decision-theoretic argument, standing in contrast to previous ad hoc modifications.

When training deep learning models, the performance depends largely on the selected hyperparameters. However, hyperparameter optimization (HPO) is often one of the most expensive parts of model design. Classical HPO methods treat this as a black-box optimization problem. However, gray-box HPO methods, which incorporate more information about the setup, have emerged as a promising direction for more efficient optimization. For example, using intermediate loss evaluations to terminate bad selections. In this work, we propose an HPO method for neural networks using logged checkpoints of the trained weights to guide future hyperparameter selections. Our method, Forecasting Model Search (FMS), embeds weights into a Gaussian process deep kernel surrogate model, using a permutation-invariant graph metanetwork to be data-efficient with the logged network weights. To facilitate reproducibility and further research, we open-source our code at https://github.com/NVlabs/forecasting-model-search.

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.

In this paper, we study the predict-then-optimize problem where the output of a machine learning prediction task is used as the input of some downstream optimization problem, say, the objective coefficient vector of a linear program. The problem is also known as predictive analytics or contextual linear programming. The existing approaches largely suffer from either (i) optimization intractability (a non-convex objective function)/statistical inefficiency (a suboptimal generalization bound) or (ii) requiring strong condition(s) such as no constraint or loss calibration. We develop a new approach to the problem called maximum optimality margin which designs the machine learning loss function by the optimality condition of the downstream optimization. The max-margin formulation enjoys both computational efficiency and good theoretical properties for the learning procedure. More importantly, our new approach only needs the observations of the optimal solution in the training data rather than the objective function, which makes it a new and natural approach to the inverse linear programming problem under both contextual and context-free settings; we also analyze the proposed method under both offline and online settings, and demonstrate its performance using numerical experiments.

Primal-dual safe RL methods commonly perform iterations between the primal update of the policy and the dual update of the Lagrange Multiplier. Such a training paradigm is highly susceptible to the error in cumulative cost estimation since this estimation serves as the key bond connecting the primal and dual update processes. We show that this problem causes significant underestimation of cost when using off-policy methods, leading to the failure to satisfy the safety constraint. To address this issue, we propose conservative policy optimization, which learns a policy in a constraint-satisfying area by considering the uncertainty in cost estimation. This improves constraint satisfaction but also potentially hinders reward maximization. We then introduce local policy convexification to help eliminate such suboptimality by gradually reducing the estimation uncertainty. We provide theoretical interpretations of the joint coupling effect of these two ingredients and further verify them by extensive experiments. Results on benchmark tasks show that our method not only achieves an asymptotic performance comparable to state-of-the-art on-policy methods while using much fewer samples, but also significantly reduces constraint violation during training. Our code is available at https://github.com/ZifanWu/CAL.

The optimal training configurations of large language models (LLMs) with respect to model sizes and compute budgets have been extensively studied. But how to optimally configure LLMs during inference has not been explored in sufficient depth. We study compute-optimal inference: designing models and inference strategies that optimally trade off additional inference-time compute for improved performance. As a first step towards understanding and designing compute-optimal inference methods, we assessed the effectiveness and computational efficiency of multiple inference strategies such as Greedy Search, Majority Voting, Best-of-N, Weighted Voting, and their variants on two different Tree Search algorithms, involving different model sizes and computational budgets. We found that a smaller language model with a novel tree search algorithm typically achieves a Pareto-optimal trade-off. These results highlight the potential benefits of deploying smaller models equipped with more sophisticated decoding algorithms in budget-constrained scenarios, e.g., on end-devices, to enhance problem-solving accuracy. For instance, we show that the Llemma-7B model can achieve competitive accuracy to a Llemma-34B model on MATH500 while using 2times less FLOPs. Our findings could potentially apply to any generation task with a well-defined measure of success.

The Unmanned Aerial Vehicle (UAV) path planning problem is a complex optimization problem in the field of robotics. In this paper, we investigate the possible utilization of this problem in benchmarking global optimization methods. We devise a problem instance generator and pick 56 representative instances, which we compare to established benchmarking suits through Exploratory Landscape Analysis to show their uniqueness. For the computational comparison, we select twelve well-performing global optimization techniques from both subfields of stochastic algorithms (evolutionary computation methods) and deterministic algorithms (Dividing RECTangles, or DIRECT-type methods). The experiments were conducted in settings with varying dimensionality and computational budgets. The results were analyzed through several criteria (number of best-found solutions, mean relative error, Friedman ranks) and utilized established statistical tests. The best-ranking methods for the UAV problems were almost universally the top-performing evolutionary techniques from recent competitions on numerical optimization at the Institute of Electrical and Electronics Engineers Congress on Evolutionary Computation. Lastly, we discussed the variable dimension characteristics of the studied UAV problems that remain still largely under-investigated.

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

The structure learning problem consists of fitting data generated by a Directed Acyclic Graph (DAG) to correctly reconstruct its arcs. In this context, differentiable approaches constrain or regularize the optimization problem using a continuous relaxation of the acyclicity property. The computational cost of evaluating graph acyclicity is cubic on the number of nodes and significantly affects scalability. In this paper we introduce COSMO, a constraint-free continuous optimization scheme for acyclic structure learning. At the core of our method, we define a differentiable approximation of an orientation matrix parameterized by a single priority vector. Differently from previous work, our parameterization fits a smooth orientation matrix and the resulting acyclic adjacency matrix without evaluating acyclicity at any step. Despite the absence of explicit constraints, we prove that COSMO always converges to an acyclic solution. In addition to being asymptotically faster, our empirical analysis highlights how COSMO performance on graph reconstruction compares favorably with competing structure learning methods.

Hyperparameter tuning of deep learning models can lead to order-of-magnitude performance gains for the same amount of compute. Despite this, systematic tuning is uncommon, particularly for large models, which are expensive to evaluate and tend to have many hyperparameters, necessitating difficult judgment calls about tradeoffs, budgets, and search bounds. To address these issues and propose a practical method for robustly tuning large models, we present Cost-Aware Pareto Region Bayesian Search (CARBS), a Bayesian optimization algorithm that performs local search around the performance-cost Pareto frontier. CARBS does well even in unbounded search spaces with many hyperparameters, learns scaling relationships so that it can tune models even as they are scaled up, and automates much of the "black magic" of tuning. Among our results, we effectively solve the entire ProcGen benchmark just by tuning a simple baseline (PPO, as provided in the original ProcGen paper). We also reproduce the model size vs. training tokens scaling result from the Chinchilla project (Hoffmann et al. 2022), while simultaneously discovering scaling laws for every other hyperparameter, via an easy automated process that uses significantly less compute and is applicable to any deep learning problem (not just language models).

We study single-machine scheduling of jobs, each belonging to a job type that determines its duration distribution. We start by analyzing the scenario where the type characteristics are known and then move to two learning scenarios where the types are unknown: non-preemptive problems, where each started job must be completed before moving to another job; and preemptive problems, where job execution can be paused in the favor of moving to a different job. In both cases, we design algorithms that achieve sublinear excess cost, compared to the performance with known types, and prove lower bounds for the non-preemptive case. Notably, we demonstrate, both theoretically and through simulations, how preemptive algorithms can greatly outperform non-preemptive ones when the durations of different job types are far from one another, a phenomenon that does not occur when the type durations are known.

We introduce Evolution Guided General Optimization via Low-rank Learning (EGGROLL), an evolution strategies (ES) algorithm designed to scale backprop-free optimization to large population sizes for modern large neural network architectures with billions of parameters. ES is a set of powerful blackbox optimisation methods that can handle non-differentiable or noisy objectives with excellent scaling potential through parallelisation. Na{ï}ve ES becomes prohibitively expensive at scale due to the computational and memory costs associated with generating matrix perturbations EinR^{mtimes n} and the batched matrix multiplications needed to compute per-member forward passes. EGGROLL overcomes these bottlenecks by generating random matrices Ain R^{mtimes r}, Bin R^{ntimes r} with rll min(m,n) to form a low-rank matrix perturbation A B^top that are used in place of the full-rank perturbation E. As the overall update is an average across a population of N workers, this still results in a high-rank update but with significant memory and computation savings, reducing the auxiliary storage from mn to r(m+n) per layer and the cost of a forward pass from O(mn) to O(r(m+n)) when compared to full-rank ES. A theoretical analysis reveals our low-rank update converges to the full-rank update at a fast Oleft(1{r}right) rate. Our experiments show that (1) EGGROLL does not compromise the performance of ES in tabula-rasa RL settings, despite being faster, (2) it is competitive with GRPO as a technique for improving LLM reasoning, and (3) EGGROLL enables stable pre-training of nonlinear recurrent language models that operate purely in integer datatypes.

Mixture-of-Experts (MoE) Large Language Models (LLMs) suffer from severely sub-optimal expert pathways-our study reveals that naive expert selection learned from pretraining leaves a surprising 10-20% accuracy gap for improvement. Motivated by this observation, we develop a novel class of test-time optimization methods to re-weight or "re-mixing" the experts in different layers jointly for each test sample. Since the test sample's ground truth is unknown, we propose to optimize a surrogate objective defined by the sample's "successful neighbors" from a reference set of samples. We introduce three surrogates and algorithms based on mode-finding, kernel regression, and the average loss of similar reference samples/tasks. To reduce the cost of optimizing whole pathways, we apply our algorithms merely to the core experts' mixing weights in critical layers, which enjoy similar performance but save significant computation. This leads to "Critical-Layer, Core-Expert, Collaborative Pathway Optimization (C3PO)". We apply C3PO to two recent MoE LLMs and examine it on six widely-used benchmarks. It consistently improves the base model by 7-15% in accuracy and outperforms widely used test-time learning baselines, e.g., in-context learning and prompt/prefix tuning, by a large margin. Moreover, C3PO enables MoE LLMs with 1-3B active parameters to outperform LLMs of 7-9B parameters, hence improving MoE's advantages on efficiency. Our thorough ablation study further sheds novel insights on achieving test-time improvement on MoE.

Recent large-scale Vision Language Action (VLA) models have shown superior performance in robotic manipulation tasks guided by natural language. However, their generalization remains limited when applied to novel objects or unfamiliar environments that lie outside the training distribution. To address this, many existing approaches integrate additional components such as depth estimation, segmentation, or even diffusion to improve generalization, at the cost of adding significant computation overhead, resulting in low efficiency. This motivates the exploration of efficient action prediction methods, which are independent of additional high-level visual representations or diffusion techniques. In this work, we propose VOTE, an efficient and general framework for the optimization and acceleration of VLA models. In details, we propose a novel tokenizer-free fine-tuning approach for parallel accurate action prediction, which reduces computational overhead and accelerates inference speed. Additionally, we adopt an ensemble voting strategy for the action sampling, which significantly improves model performance and enhances generalization. Experimental results show that our method achieves state-of-the-art performance with 35x faster inference and 145 Hz throughput. All the details and codes will be open-sourced.

Image denoising is essential for removing noise in images caused by electric device malfunctions or other factors during image acquisition. It helps preserve image quality and interpretation. Many convolutional autoencoder algorithms have proven effective in image denoising. Owing to their promising efficiency, quantum computers have gained popularity. This study introduces a quantum convolutional autoencoder (QCAE) method for improved image denoising. This method was developed by substituting the representative latent space of the autoencoder with a quantum circuit. To enhance efficiency, we leveraged the advantages of the quantum approximate optimization algorithm (QAOA)-incorporated parameter-shift rule to identify an optimized cost function, facilitating effective learning from data and gradient computation on an actual quantum computer. The proposed QCAE method outperformed its classical counterpart as it exhibited lower training loss and a higher structural similarity index (SSIM) value. QCAE also outperformed its classical counterpart in denoising the MNIST dataset by up to 40% in terms of SSIM value, confirming its enhanced capabilities in real-world applications. Evaluation of QAOA performance across different circuit configurations and layer variations showed that our technique outperformed other circuit designs by 25% on average.