Daily Papers

The ever-growing availability of unlabeled data presents both opportunities and challenges for training artificial intelligence systems. While self-supervised learning (SSL) has emerged as a powerful paradigm for extracting meaningful representations from vast amounts of unlabeled data, existing methods still struggle to adapt to the non-stationary, non-IID nature of real-world data streams without forgetting previously learned knowledge. Recent works have adopted a repeated cosine annealing schedule for large-scale continual pre-training; however, these schedules (1) inherently cause forgetting during the re-warming phase and (2) have not been systematically compared to existing continual SSL methods. In this work, we systematically compare the widely used cosine schedule with the recently proposed infinite learning rate schedule and empirically find the latter to be a more effective alternative. Our extensive empirical evaluation across diverse image and language datasets demonstrates that the infinite learning rate schedule consistently enhances continual pre-training performance compared to a repeated cosine decay without being restricted to a fixed iteration budget. For instance, in a small-scale MAE pre-training setup, it outperforms several strong baselines from the literature. We then scale up our experiments to larger MAE pre-training and autoregressive language model pre-training. Our results show that the infinite learning rate schedule remains effective at scale, surpassing repeated cosine decay for both MAE pre-training and zero-shot LM benchmarks.

Ultrasound (US) imaging exhibits substantial heterogeneity across anatomical structures and acquisition protocols, posing significant challenges to the development of generalizable analysis models. Most existing methods are task-specific, limiting their suitability as clinically deployable foundation models. To address this limitation, the Foundation Model Challenge for Ultrasound Image Analysis (FM\_UIA~2026) introduces a large-scale multi-task benchmark comprising 27 subtasks across segmentation, classification, detection, and regression. In this paper, we present the official baseline for FM\_UIA~2026 based on a unified Multi-Head Multi-Task Learning (MH-MTL) framework that supports all tasks within a single shared network. The model employs an ImageNet-pretrained EfficientNet--B4 backbone for robust feature extraction, combined with a Feature Pyramid Network (FPN) to capture multi-scale contextual information. A task-specific routing strategy enables global tasks to leverage high-level semantic features, while dense prediction tasks exploit spatially detailed FPN representations. Training incorporates a composite loss with task-adaptive learning rate scaling and a cosine annealing schedule. Validation results demonstrate the feasibility and robustness of this unified design, establishing a strong and extensible baseline for ultrasound foundation model research. The code and dataset are publicly available at https://github.com/lijiake2408/Foundation-Model-Challenge-for-Ultrasound-Image-Analysis{GitHub}.

Federated learning (FL) is a distributed machine learning method where multiple devices collaboratively train a model under the management of a central server without sharing underlying data. One of the key challenges of FL is the communication bottleneck caused by variations in connection speed and bandwidth across devices. Therefore, it is essential to reduce the size of transmitted data during training. Additionally, there is a potential risk of exposing sensitive information through the model or gradient analysis during training. To address both privacy and communication efficiency, we combine differential privacy (DP) and adaptive quantization methods. We use Laplacian-based DP to preserve privacy, which is relatively underexplored in FL and offers tighter privacy guarantees than Gaussian-based DP. We propose a simple and efficient global bit-length scheduler using round-based cosine annealing, along with a client-based scheduler that dynamically adapts based on client contribution estimated through dataset entropy analysis. We evaluate our approach through extensive experiments on CIFAR10, MNIST, and medical imaging datasets, using non-IID data distributions across varying client counts, bit-length schedulers, and privacy budgets. The results show that our adaptive quantization methods reduce total communicated data by up to 52.64% for MNIST, 45.06% for CIFAR10, and 31% to 37% for medical imaging datasets compared to 32-bit float training while maintaining competitive model accuracy and ensuring robust privacy through differential privacy.

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

Neural Architecture Search (NAS) has been a source of dramatic improvements in neural network design, with recent results meeting or exceeding the performance of hand-tuned architectures. However, our understanding of how to represent the search space for neural net architectures and how to search that space efficiently are both still in their infancy. We have performed an in-depth analysis to identify limitations in a widely used search space and a recent architecture search method, Differentiable Architecture Search (DARTS). These findings led us to introduce novel network blocks with a more general, balanced, and consistent design; a better-optimized Cosine Power Annealing learning rate schedule; and other improvements. Our resulting sharpDARTS search is 50% faster with a 20-30% relative improvement in final model error on CIFAR-10 when compared to DARTS. Our best single model run has 1.93% (1.98+/-0.07) validation error on CIFAR-10 and 5.5% error (5.8+/-0.3) on the recently released CIFAR-10.1 test set. To our knowledge, both are state of the art for models of similar size. This model also generalizes competitively to ImageNet at 25.1% top-1 (7.8% top-5) error. We found improvements for existing search spaces but does DARTS generalize to new domains? We propose Differentiable Hyperparameter Grid Search and the HyperCuboid search space, which are representations designed to leverage DARTS for more general parameter optimization. Here we find that DARTS fails to generalize when compared against a human's one shot choice of models. We look back to the DARTS and sharpDARTS search spaces to understand why, and an ablation study reveals an unusual generalization gap. We finally propose Max-W regularization to solve this problem, which proves significantly better than the handmade design. Code will be made available.

Any optimization algorithm programming interface can be seen as a black-box function with additional free parameters. In this spirit, simulated annealing (SA) can be implemented in pseudo-code within the dimensions of a single slide with free parameters relating to the annealing schedule. Such an implementation, however, necessarily neglects much of the structure necessary to take advantage of advances in computing resources and algorithmic breakthroughs. Simulated annealing is often introduced in myriad disciplines, from discrete examples like the Traveling Salesman Problem (TSP) to molecular cluster potential energy exploration or even explorations of a protein's configurational space. Theoretical guarantees also demand a stricter structure in terms of statistical quantities, which cannot simply be left to the user. We will introduce several standard paradigms and demonstrate how these can be "lifted" into a unified framework using object-oriented programming in Python. We demonstrate how clean, interoperable, reproducible programming libraries can be used to access and rapidly iterate on variants of Simulated Annealing in a manner which can be extended to serve as a best practices blueprint or design pattern for a data-driven optimization library.

Simulated annealing (SA) is a stochastic global optimisation technique applicable to a wide range of discrete and continuous variable problems. Despite its simplicity, the development of an effective SA optimiser for a given problem hinges on a handful of carefully handpicked components; namely, neighbour proposal distribution and temperature annealing schedule. In this work, we view SA from a reinforcement learning perspective and frame the proposal distribution as a policy, which can be optimised for higher solution quality given a fixed computational budget. We demonstrate that this Neural SA with such a learnt proposal distribution, parametrised by small equivariant neural networks, outperforms SA baselines on a number of problems: Rosenbrock's function, the Knapsack problem, the Bin Packing problem, and the Travelling Salesperson problem. We also show that Neural SA scales well to large problems - generalising to significantly larger problems than the ones seen during training - while achieving comparable performance to popular off-the-shelf solvers and other machine learning methods in terms of solution quality and wall-clock time.

Denoising diffusion models excel at generating high-quality images conditioned on text prompts, yet their effectiveness heavily relies on careful guidance during the sampling process. Classifier-Free Guidance (CFG) provides a widely used mechanism for steering generation by setting the guidance scale, which balances image quality and prompt alignment. However, the choice of the guidance scale has a critical impact on the convergence toward a visually appealing and prompt-adherent image. In this work, we propose an annealing guidance scheduler which dynamically adjusts the guidance scale over time based on the conditional noisy signal. By learning a scheduling policy, our method addresses the temperamental behavior of CFG. Empirical results demonstrate that our guidance scheduler significantly enhances image quality and alignment with the text prompt, advancing the performance of text-to-image generation. Notably, our novel scheduler requires no additional activations or memory consumption, and can seamlessly replace the common classifier-free guidance, offering an improved trade-off between prompt alignment and quality.

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

Specialized hardware accelerators have been extensively used for Deep Neural Networks (DNNs) to provide power/performance benefits. These accelerators contain specialized hardware that supports DNN operators, and scratchpad memory for storing the tensor operands. Often, the size of the scratchpad is insufficient to store all the tensors needed for the computation, and additional data accesses are needed to move tensors back and forth from host memory during the computation with significant power/performance overhead. The volume of these additional data accesses depends on the operator schedule, and memory allocation (specific locations selected for the tensors in the scratchpad). We propose an optimization framework, named COSMA, for mapping DNNs to an accelerator that finds the optimal operator schedule, memory allocation and tensor replacement that minimizes the additional data accesses. COSMA provides an Integer Linear Programming (ILP) formulation to generate the optimal solution for mapping a DNN to the accelerator for a given scratchpad size. We demonstrate that, using an off-the-shelf ILP solver, COSMA obtains the optimal solution in seconds for a wide-range of state-of-the-art DNNs for different applications. Further, it out-performs existing methods by reducing on average 84% of the non-compulsory data accesses. We further propose a divide-and-conquer heuristic to scale up to certain complex DNNs generated by Neural Architecture Search, and this heuristic solution reduces on average 85% data accesses compared with other works.

Scale has become a main ingredient in obtaining strong machine learning models. As a result, understanding a model's scaling properties is key to effectively designing both the right training setup as well as future generations of architectures. In this work, we argue that scale and training research has been needlessly complex due to reliance on the cosine schedule, which prevents training across different lengths for the same model size. We investigate the training behavior of a direct alternative - constant learning rate and cooldowns - and find that it scales predictably and reliably similar to cosine. Additionally, we show that stochastic weight averaging yields improved performance along the training trajectory, without additional training costs, across different scales. Importantly, with these findings we demonstrate that scaling experiments can be performed with significantly reduced compute and GPU hours by utilizing fewer but reusable training runs.

In this article, we describe an algorithm for solving Quadratic Unconstrained Binary Optimization problems on the Intel Loihi 2 neuromorphic processor. The solver is based on a hardware-aware fine-grained parallel simulated annealing algorithm developed for Intel's neuromorphic research chip Loihi 2. Preliminary results show that our approach can generate feasible solutions in as little as 1 ms and up to 37x more energy efficient compared to two baseline solvers running on a CPU. These advantages could be especially relevant for size-, weight-, and power-constrained edge computing applications.

Despite significant advances in optimizers for training, most research works use common scheduler choices like Cosine or exponential decay. In this paper, we study GreedyLR, a novel scheduler that adaptively adjusts the learning rate during training based on the current loss. To validate the effectiveness of our proposed scheduler, we conduct experiments on several NLP, CV, and LLM tasks with up to 7B parameters, including both fine-tuning and pre-training experiments. The results show that our approach outperforms several state-of-the-art schedulers in terms of accuracy, speed, and convergence. We also provide a theoretical analysis of the GreedyLR algorithm, including a proof of convergence and derivation of the optimal scaling factor F that maximizes the convergence rate, along with experiments to show robustness of the algorithm to realistic noisy landscapes. Our scheduler is easy to implement, computationally efficient, and could be considered a good default scheduler for training.

We design learning rate schedules that minimize regret for SGD-based online learning in the presence of a changing data distribution. We fully characterize the optimal learning rate schedule for online linear regression via a novel analysis with stochastic differential equations. For general convex loss functions, we propose new learning rate schedules that are robust to distribution shift, and we give upper and lower bounds for the regret that only differ by constants. For non-convex loss functions, we define a notion of regret based on the gradient norm of the estimated models and propose a learning schedule that minimizes an upper bound on the total expected regret. Intuitively, one expects changing loss landscapes to require more exploration, and we confirm that optimal learning rate schedules typically increase in the presence of distribution shift. Finally, we provide experiments for high-dimensional regression models and neural networks to illustrate these learning rate schedules and their cumulative regret.

We introduce NeuroSA, a neuromorphic architecture specifically designed to ensure asymptotic convergence to the ground state of an Ising problem using an annealing process that is governed by the physics of quantum mechanical tunneling using Fowler-Nordheim (FN). The core component of NeuroSA consists of a pair of asynchronous ON-OFF neurons, which effectively map classical simulated annealing (SA) dynamics onto a network of integrate-and-fire (IF) neurons. The threshold of each ON-OFF neuron pair is adaptively adjusted by an FN annealer which replicates the optimal escape mechanism and convergence of SA, particularly at low temperatures. To validate the effectiveness of our neuromorphic Ising machine, we systematically solved various benchmark MAX-CUT combinatorial optimization problems. Across multiple runs, NeuroSA consistently generates solutions that approach the state-of-the-art level with high accuracy (greater than 99%), and without any graph-specific hyperparameter tuning. For practical illustration, we present results from an implementation of NeuroSA on the SpiNNaker2 platform, highlighting the feasibility of mapping our proposed architecture onto a standard neuromorphic accelerator platform.

This paper describes the design and simulation of an 8-bit dedicated processor for calculating the Sine and Cosine of an Angle using CORDIC Algorithm (COordinate Rotation DIgital Computer), a simple and efficient algorithm to calculate hyperbolic and trigonometric functions. We have proposed a dedicated processor system, modeled by writing appropriate programs in VHDL, for calculating the Sine and Cosine of an angle. System simulation was carried out using ModelSim 6.3f and Xilinx ISE Design Suite 12.3. A maximum frequency of 81.353 MHz was reached with a minimum period of 12.292 ns. 126 (3%) slices were used. This paper attempts to survey the existing CORDIC algorithm with an eye towards implementation in Field Programmable Gate Arrays (FPGAs). A brief description of the theory behind the algorithm and the derivation of the Sine and Cosine of an angle using the CORDIC algorithm has been presented. The system can be implemented using Spartan3 XC3S400 with Xilinx ISE 12.3 and VHDL.

Diffusion models have emerged as the de facto choice for generating visual signals. However, training a single model to predict noise across various levels poses significant challenges, necessitating numerous iterations and incurring significant computational costs. Various approaches, such as loss weighting strategy design and architectural refinements, have been introduced to expedite convergence. In this study, we propose a novel approach to design the noise schedule for enhancing the training of diffusion models. Our key insight is that the importance sampling of the logarithm of the Signal-to-Noise ratio (logSNR), theoretically equivalent to a modified noise schedule, is particularly beneficial for training efficiency when increasing the sample frequency around log SNR=0. We empirically demonstrate the superiority of our noise schedule over the standard cosine schedule. Furthermore, we highlight the advantages of our noise schedule design on the ImageNet benchmark, showing that the designed schedule consistently benefits different prediction targets.

In this paper, we~present a novel scheduling solution for a class of System-on-Chip (SoC) systems where heterogeneous chip resources (DSP, FPGA, GPU, etc.) must be efficiently scheduled for continuously arriving hierarchical jobs with their tasks represented by a directed acyclic graph. Traditionally, heuristic algorithms have been widely used for many resource scheduling domains, and Heterogeneous Earliest Finish Time (HEFT) has been a dominating state-of-the-art technique across a broad range of heterogeneous resource scheduling domains over many years. Despite their long-standing popularity, HEFT-like algorithms are known to be vulnerable to a small amount of noise added to the environment. Our Deep Reinforcement Learning (DRL)-based SoC Scheduler (DeepSoCS), capable of learning the "best" task ordering under dynamic environment changes, overcomes the brittleness of rule-based schedulers such as HEFT with significantly higher performance across different types of jobs. We~describe a DeepSoCS design process using a real-time heterogeneous SoC scheduling emulator, discuss major challenges, and present two novel neural network design features that lead to outperforming HEFT: (i) hierarchical job- and task-graph embedding; and (ii) efficient use of real-time task information in the state space. Furthermore, we~introduce effective techniques to address two fundamental challenges present in our environment: delayed consequences and joint actions. Through an extensive simulation study, we~show that our DeepSoCS exhibits the significantly higher performance of job execution time than that of HEFT with a higher level of robustness under realistic noise conditions. We~conclude with a discussion of the potential improvements for our DeepSoCS neural scheduler.

Diffusion models (DMs) have established themselves as the state-of-the-art generative modeling approach in the visual domain and beyond. A crucial drawback of DMs is their slow sampling speed, relying on many sequential function evaluations through large neural networks. Sampling from DMs can be seen as solving a differential equation through a discretized set of noise levels known as the sampling schedule. While past works primarily focused on deriving efficient solvers, little attention has been given to finding optimal sampling schedules, and the entire literature relies on hand-crafted heuristics. In this work, for the first time, we propose a general and principled approach to optimizing the sampling schedules of DMs for high-quality outputs, called Align Your Steps. We leverage methods from stochastic calculus and find optimal schedules specific to different solvers, trained DMs and datasets. We evaluate our novel approach on several image, video as well as 2D toy data synthesis benchmarks, using a variety of different samplers, and observe that our optimized schedules outperform previous hand-crafted schedules in almost all experiments. Our method demonstrates the untapped potential of sampling schedule optimization, especially in the few-step synthesis regime.

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

We find that the cross-entropy loss curves of neural language models empirically adhere to a scaling law with learning rate (LR) annealing over training steps (s): $L(s) = L_0 + Acdot S_1^{-alpha} - Ccdot S_2 Where S_1 is forward area and S_2$ is learning rate annealing area. This formulation takes into account two factors: (1) The forward scaling defined as typical scaling law, and (2) the additional loss drop brought by LR annealing. Therefore, this formulation can describe the full loss curve at each step, rather than the single loss point at the end of training. Applying the scaling law with LR annealing and fitting only one or two training curves, we can accurately predict the loss of language model training at any given step and across any learning rate scheduler (LRS). Furthermore, this equation accurately describes the dynamics during training process, and provides a theoretical verification and explanation for numerous experimental findings of previous studies, particularly those focusing on LR schedule and LR annealing. The resulting insights, also serve as a guide for researchers to select critical LRS in advance by prediction using our equation. Most significantly, since all the points in a full training curve follow the equation, we can achieve accurate loss prediction at any given step across any learning rate scheduler, while expending less than 1\% of the computational cost required by the chinchilla scaling law to fit language modeling loss. This approach extremely democratizes scaling law fitting and predicting in developing large language models.

In VLSI physical design, many algorithms require the solution of difficult combinatorial optimization problems such as max/min-cut, max-flow problems etc. Due to the vast number of elements typically found in this problem domain, these problems are computationally intractable leading to the use of approximate solutions. In this work, we explore the Ising spin glass model as a solution methodology for hard combinatorial optimization problems using the general purpose GPU (GPGPU). The Ising model is a mathematical model of ferromagnetism in statistical mechanics. Ising computing finds a minimum energy state for the Ising model which essentially corresponds to the expected optimal solution of the original problem. Many combinatorial optimization problems can be mapped into the Ising model. In our work, we focus on the max-cut problem as it is relevant to many VLSI physical design problems. Our method is inspired by the observation that Ising annealing process is very amenable to fine-grain massive parallel GPU computing. We will illustrate how the natural randomness of GPU thread scheduling can be exploited during the annealing process to create random update patterns and allow better GPU resource utilization. Furthermore, the proposed GPU-based Ising computing can handle any general Ising graph with arbitrary connections, which was shown to be difficult for existing FPGA and other hardware based implementation methods. Numerical results show that the proposed GPU Ising max-cut solver can deliver more than 2000X speedup over the CPU version of the algorithm on some large examples, which shows huge performance improvement for addressing many hard optimization algorithms for practical VLSI physical design.

Our study contributes to the scheduling and combinatorial optimization literature with new heuristics discovered by leveraging the power of Large Language Models (LLMs). We focus on the single-machine total tardiness (SMTT) problem, which aims to minimize total tardiness by sequencing n jobs on a single processor without preemption, given processing times and due dates. We develop and benchmark two novel LLM-discovered heuristics, the EDD Challenger (EDDC) and MDD Challenger (MDDC), inspired by the well-known Earliest Due Date (EDD) and Modified Due Date (MDD) rules. In contrast to prior studies that employed simpler rule-based heuristics, we evaluate our LLM-discovered algorithms using rigorous criteria, including optimality gaps and solution time derived from a mixed-integer programming (MIP) formulation of SMTT. We compare their performance against state-of-the-art heuristics and exact methods across various job sizes (20, 100, 200, and 500 jobs). For instances with more than 100 jobs, exact methods such as MIP and dynamic programming become computationally intractable. Up to 500 jobs, EDDC improves upon the classic EDD rule and another widely used algorithm in the literature. MDDC consistently outperforms traditional heuristics and remains competitive with exact approaches, particularly on larger and more complex instances. This study shows that human-LLM collaboration can produce scalable, high-performing heuristics for NP-hard constrained combinatorial optimization, even under limited resources when effectively configured.

In this paper, we explore the potential for quantum annealing to solve realistic routing problems. We focus on two NP-Hard problems, including the Traveling Salesman Problem with Time Windows and the Capacitated Vehicle Routing Problem with Time Windows. We utilize D-Wave's Quantum Annealer and Constrained Quadratic Model (CQM) solver within a hybrid framework to solve these problems. We demonstrate that while the CQM solver effectively minimizes route costs, it struggles to maintain time window feasibility as the problem size increases. To address this limitation, we implement a heuristic method that fixes infeasible solutions through a series of swapping operations. Testing on benchmark instances shows our method achieves promising results with an average optimality gap of 3.86%.

Active learning (AL) algorithms may achieve better performance with fewer data because the model guides the data selection process. While many algorithms have been proposed, there is little study on what the optimal AL algorithm looks like, which would help researchers understand where their models fall short and iterate on the design. In this paper, we present a simulated annealing algorithm to search for this optimal oracle and analyze it for several tasks. We present qualitative and quantitative insights into the behaviors of this oracle, comparing and contrasting them with those of various heuristics. Moreover, we are able to consistently improve the heuristics using one particular insight. We hope that our findings can better inform future active learning research. The code is available at https://github.com/YilunZhou/optimal-active-learning.

Our work presents extensive empirical evidence that layer rotation, i.e. the evolution across training of the cosine distance between each layer's weight vector and its initialization, constitutes an impressively consistent indicator of generalization performance. In particular, larger cosine distances between final and initial weights of each layer consistently translate into better generalization performance of the final model. Interestingly, this relation admits a network independent optimum: training procedures during which all layers' weights reach a cosine distance of 1 from their initialization consistently outperform other configurations -by up to 30% test accuracy. Moreover, we show that layer rotations are easily monitored and controlled (helpful for hyperparameter tuning) and potentially provide a unified framework to explain the impact of learning rate tuning, weight decay, learning rate warmups and adaptive gradient methods on generalization and training speed. In an attempt to explain the surprising properties of layer rotation, we show on a 1-layer MLP trained on MNIST that layer rotation correlates with the degree to which features of intermediate layers have been trained.

This paper introduces bucket calculus, a novel mathematical framework that fundamentally transforms the computational complexity landscape of parallel machine scheduling optimization. We address the strongly NP-hard problem P2|r_j|C_{max} through an innovative adaptive temporal discretization methodology that achieves exponential complexity reduction from O(T^n) to O(B^n) where B ll T, while maintaining near-optimal solution quality. Our bucket-indexed mixed-integer linear programming (MILP) formulation exploits dimensional complexity heterogeneity through precision-aware discretization, reducing decision variables by 94.4\% and achieving a theoretical speedup factor 2.75 times 10^{37} for 20-job instances. Theoretical contributions include partial discretization theory, fractional bucket calculus operators, and quantum-inspired mechanisms for temporal constraint modeling. Empirical validation on instances with 20--400 jobs demonstrates 97.6\% resource utilization, near-perfect load balancing (σ/μ= 0.006), and sustained performance across problem scales with optimality gaps below 5.1\%. This work represents a paradigm shift from fine-grained temporal discretization to multi-resolution precision allocation, bridging the fundamental gap between exact optimization and computational tractability for industrial-scale NP-hard scheduling problems.

Multi-Agent Deep Reinforcement Learning (MADRL) has emerged as a powerful tool for optimizing decentralized decision-making systems in complex settings, such as Dynamic Spectrum Access (DSA). However, deploying deep learning models on resource-constrained edge devices remains challenging due to their high computational cost. To address this challenge, in this paper, we present a novel sparse recurrent MARL framework integrating gradual neural network pruning into the independent actor global critic paradigm. Additionally, we introduce a harmonic annealing sparsity scheduler, which achieves comparable, and in certain cases superior, performance to standard linear and polynomial pruning schedulers at large sparsities. Our experimental investigation demonstrates that the proposed DSA framework can discover superior policies, under diverse training conditions, outperforming conventional DSA, MADRL baselines, and state-of-the-art pruning techniques.

We develop a robust quaternion recurrent neural network (QRNN) for real-time processing of 3D and 4D data with outliers. This is achieved by combining the real-time recurrent learning (RTRL) algorithm and the maximum correntropy criterion (MCC) as a loss function. While both the mean square error and maximum correntropy criterion are viable cost functions, it is shown that the non-quadratic maximum correntropy loss function is less sensitive to outliers, making it suitable for applications with multidimensional noisy or uncertain data. Both algorithms are derived based on the novel generalised HR (GHR) calculus, which allows for the differentiation of real functions of quaternion variables and offers the product and chain rules, thus enabling elegant and compact derivations. Simulation results in the context of motion prediction of chest internal markers for lung cancer radiotherapy, which includes regular and irregular breathing sequences, support the analysis.

Generative posterior sampling using diffusion models has emerged as a dominant paradigm for solving inverse problems in imaging, which usually consists of three main components: data consistency (DC) guidance, classifier-free guidance (CFG) and stochasticity. While prior arts have focused on how to develop each or all components, less attention has given to how to schedule them, leading to heuristically fixed or partially adjusted suboptimal schedules. In this work, we argue that the interactions among all three components in terms of scheduling are crucial for significantly improved performance in solving inverse problems in imaging. Our analysis shows that aggressive CFG early in sampling conflict with DC guidance, while stochasticity brings the trajectory back to higher-probability regions. Based on these findings, we propose Triadic Dynamics Aware Posterior Sampling (TriPS), which reformulates posterior sampling as a time-varying control problem and optimizes schedules following a triadic trend of decreasing DC and stochasticity scales alongside increasing CFG scale. TriPS achieves this through two strategies: template-based search over functional priors for reliable baseline schedules, and Group Relative Policy Optimization (GRPO)-based reinforcement learning for more flexible temporal curves. Experiments demonstrate TriPS outperforms state-of-the-art baselines in data fidelity and perceptual realism.

Learning rate scheduling is essential in transformer training, where the final annealing plays a crucial role in getting the best performance. However, the mechanisms behind this cooldown phase, with its characteristic drop in loss, remain poorly understood. To address this, we provide a comprehensive analysis focusing solely on the cooldown phase in the Warmup-Stable-Decay (WSD) learning rate scheduler. Our analysis reveals that different cooldown shapes reveal a fundamental bias-variance trade-off in the resulting models, with shapes that balance exploration and exploitation consistently outperforming alternatives. Similarly, we find substantial performance variations x2013 comparable to those from cooldown shape selection x2013 when tuning AdamW hyperparameters. Notably, we observe consistent improvements with higher values of beta_2 during cooldown. From a loss landscape perspective, we provide visualizations of the landscape during cooldown, supporting the river valley loss perspective empirically. These findings offer practical recommendations for configuring the WSD scheduler in transformer training, emphasizing the importance of optimizing the cooldown phase alongside traditional hyperparameter tuning.

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

Time series play a fundamental role in many domains, capturing a plethora of information about the underlying data-generating processes. When a process generates multiple synchronized signals we are faced with multidimensional time series. In this context a fundamental problem is that of motif mining, where we seek patterns repeating twice with minor variations, spanning some of the dimensions. State of the art exact solutions for this problem run in time quadratic in the length of the input time series. We provide a scalable method to find the top-k motifs in multidimensional time series with probabilistic guarantees on the quality of the results. Our algorithm runs in time subquadratic in the length of the input, and returns the exact solution with probability at least 1-δ, where δ is a user-defined parameter. The algorithm is designed to be adaptive to the input distribution, self-tuning its parameters while respecting user-defined limits on the memory to use. Our theoretical analysis is complemented by an extensive experimental evaluation, showing that our algorithm is orders of magnitude faster than the state of the art.

Large language models (LLMs) are routinely pre-trained on billions of tokens, only to start the process over again once new data becomes available. A much more efficient solution is to continually pre-train these models, saving significant compute compared to re-training. However, the distribution shift induced by new data typically results in degraded performance on previous data or poor adaptation to the new data. In this work, we show that a simple and scalable combination of learning rate (LR) re-warming, LR re-decaying, and replay of previous data is sufficient to match the performance of fully re-training from scratch on all available data, as measured by final loss and language model (LM) evaluation benchmarks. Specifically, we show this for a weak but realistic distribution shift between two commonly used LLM pre-training datasets (EnglishrightarrowEnglish) and a stronger distribution shift (EnglishrightarrowGerman) at the 405M parameter model scale with large dataset sizes (hundreds of billions of tokens). Selecting the weak but realistic shift for larger-scale experiments, we also find that our continual learning strategies match the re-training baseline for a 10B parameter LLM. Our results demonstrate that LLMs can be successfully updated via simple and scalable continual learning strategies, matching the re-training baseline using only a fraction of the compute. Finally, inspired by previous work, we propose alternatives to the cosine learning rate schedule that help circumvent forgetting induced by LR re-warming and that are not bound to a fixed token budget.

Efficient operator scheduling is a fundamental challenge in software compilation and hardware synthesis. While recent differentiable approaches have sought to replace traditional ones like exact solvers or heuristics with gradient-based search, they typically rely on categorical distributions that fail to capture the ordinal nature of time and suffer from a parameter space that scales poorly. In this paper, we propose a novel differentiable framework, GauS, that models operator scheduling as a stochastic relaxation using Gaussian distributions, which fully utilize modern parallel computing devices like GPUs. By representing schedules as continuous Gaussian variables, we successfully capture the ordinal nature of time and reduce the optimization space by orders of magnitude. Our method is highly flexible to represent various objectives and constraints, which provides the first differentiable formulation for the complex pipelined scheduling problem. We evaluate our method on a range of benchmarks, demonstrating that Gaus achieves Pareto-optimal results.

Background: Recursive reasoning models achieve strong performance through iterative refinement, allowing small networks to match large language models. However, training is computationally expensive, often requiring 36 GPU-hours for Sudoku extreme. Existing models use fixed recursion depth and uniform supervision weighting, leading to inefficient training. Objectives: We propose CGAR (Curriculum-Guided Adaptive Recursion), applying curriculum learning to architectural depth. CGAR introduces Progressive Depth Curriculum (PDC) to dynamically adjust recursion depth and Hierarchical Supervision Weighting (HSW) to apply exponentially decaying importance to supervision steps. Methods: PDC implements a three-stage schedule transitioning from shallow (2, 1) to full depth (6, 3) configurations, providing 41.4% FLOPs reduction. HSW applies exponential decay to supervision steps, achieving 40% gradient variance reduction and accelerated convergence. Results: On Sudoku-Extreme, CGAR achieves 1.71x training speedup (10.93 to 6.38 hours) with only a 0.63% accuracy drop (86.65% to 86.02%). PDC alone achieves 2.26x speedup with 85.47% accuracy, showing a Pareto improvement in efficiency and quality. HSW provides 1.61x speedup. CGAR-trained models show superior inference efficiency with 100% halting accuracy and 11% fewer reasoning steps. Conclusions: CGAR enables efficient training of recursive models on modest hardware. By treating depth as a scheduled parameter, it achieves substantial savings and prevents overfitting, making these models practical for neurosymbolic AI and program synthesis. https://github.com/Kaleemullahqasim/CGAR and huggingface.co/Kaleemullah/trm-cgar-sudoku.

GPU architectures have continued to grow in complexity, with recent incarnations introducing increasingly powerful fixed-function units for matrix multiplication and data movement to accompany highly parallel general-purpose cores. To fully leverage these machines, software must use sophisticated schedules that maximally utilize all hardware resources. Since realizing such schedules is complex, both programmers and compilers routinely employ program transformations, such as software pipelining (SWP) and warp specialization (WS), to do so in practice. However, determining how best to use SWP and WS in combination is a challenging problem that is currently handled through a mix of brittle compilation heuristics and fallible human intuition, with little insight into the space of solutions. To remedy this situation, we introduce a novel formulation of SWP and WS as a joint optimization problem that can be solved holistically by off-the-shelf constraint solvers. We reify our approach in Twill, the first system that automatically derives optimal SWP and WS schedules for a large class of iterative programs. Twill is heuristic-free, easily extensible to new GPU architectures, and guaranteed to produce optimal schedules. We show that Twill can rediscover, and thereby prove optimal, the SWP and WS schedules manually developed by experts for Flash Attention on both the NVIDIA Hopper and Blackwell GPU architectures.

Periodic signals play an important role in daily lives. Although conventional sequential models have shown remarkable success in various fields, they still come short in modeling periodicity; they either collapse, diverge or ignore details. In this paper, we introduce a novel framework inspired by Fourier series to generate periodic signals. We first decompose the given signals into multiple sines and cosines and then conditionally generate periodic signals with the output components. We have shown our model efficacy on three tasks: reconstruction, imputation and conditional generation. Our model outperforms baselines in all tasks and shows more stable and refined results.

Training competitive deep video models is an order of magnitude slower than training their counterpart image models. Slow training causes long research cycles, which hinders progress in video understanding research. Following standard practice for training image models, video model training assumes a fixed mini-batch shape: a specific number of clips, frames, and spatial size. However, what is the optimal shape? High resolution models perform well, but train slowly. Low resolution models train faster, but they are inaccurate. Inspired by multigrid methods in numerical optimization, we propose to use variable mini-batch shapes with different spatial-temporal resolutions that are varied according to a schedule. The different shapes arise from resampling the training data on multiple sampling grids. Training is accelerated by scaling up the mini-batch size and learning rate when shrinking the other dimensions. We empirically demonstrate a general and robust grid schedule that yields a significant out-of-the-box training speedup without a loss in accuracy for different models (I3D, non-local, SlowFast), datasets (Kinetics, Something-Something, Charades), and training settings (with and without pre-training, 128 GPUs or 1 GPU). As an illustrative example, the proposed multigrid method trains a ResNet-50 SlowFast network 4.5x faster (wall-clock time, same hardware) while also improving accuracy (+0.8% absolute) on Kinetics-400 compared to the baseline training method. Code is available online.

Recent years have witnessed the rapid progress and broad application of diffusion probabilistic models (DPMs). Sampling from DPMs can be viewed as solving an ordinary differential equation (ODE). Despite the promising performance, the generation of DPMs usually consumes much time due to the large number of function evaluations (NFE). Though recent works have accelerated the sampling to around 20 steps with high-order solvers, the sample quality with less than 10 NFE can still be improved. In this paper, we propose a unified sampling framework (USF) to study the optional strategies for solver. Under this framework, we further reveal that taking different solving strategies at different timesteps may help further decrease the truncation error, and a carefully designed solver schedule has the potential to improve the sample quality by a large margin. Therefore, we propose a new sampling framework based on the exponential integral formulation that allows free choices of solver strategy at each step and design specific decisions for the framework. Moreover, we propose S^3, a predictor-based search method that automatically optimizes the solver schedule to get a better time-quality trade-off of sampling. We demonstrate that S^3 can find outstanding solver schedules which outperform the state-of-the-art sampling methods on CIFAR-10, CelebA, ImageNet, and LSUN-Bedroom datasets. Specifically, we achieve 2.69 FID with 10 NFE and 6.86 FID with 5 NFE on CIFAR-10 dataset, outperforming the SOTA method significantly. We further apply S^3 to Stable-Diffusion model and get an acceleration ratio of 2times, showing the feasibility of sampling in very few steps without retraining the neural network.

This work proposes a simple yet effective sampling framework for combinatorial optimization (CO). Our method builds on discrete Langevin dynamics (LD), an efficient gradient-guided generative paradigm. However, we observe that directly applying LD often leads to limited exploration. To overcome this limitation, we propose the Regularized Langevin Dynamics (RLD), which enforces an expected distance between the sampled and current solutions, effectively avoiding local minima. We develop two CO solvers on top of RLD, one based on simulated annealing (SA), and the other one based on neural network (NN). Empirical results on three classic CO problems demonstrate that both of our methods can achieve comparable or better performance against the previous state-of-the-art (SOTA) SA- and NN-based solvers. In particular, our SA algorithm reduces the runtime of the previous SOTA SA method by up to 80\%, while achieving equal or superior performance. In summary, RLD offers a promising framework for enhancing both traditional heuristics and NN models to solve CO problems. Our code is available at https://github.com/Shengyu-Feng/RLD4CO.

Text-guided diffusion models have significantly advanced image editing, enabling high-quality and diverse modifications driven by text prompts. However, effective editing requires inverting the source image into a latent space, a process often hindered by prediction errors inherent in DDIM inversion. These errors accumulate during the diffusion process, resulting in inferior content preservation and edit fidelity, especially with conditional inputs. We address these challenges by investigating the primary contributors to error accumulation in DDIM inversion and identify the singularity problem in traditional noise schedules as a key issue. To resolve this, we introduce the Logistic Schedule, a novel noise schedule designed to eliminate singularities, improve inversion stability, and provide a better noise space for image editing. This schedule reduces noise prediction errors, enabling more faithful editing that preserves the original content of the source image. Our approach requires no additional retraining and is compatible with various existing editing methods. Experiments across eight editing tasks demonstrate the Logistic Schedule's superior performance in content preservation and edit fidelity compared to traditional noise schedules, highlighting its adaptability and effectiveness.

Diffusion large language models (dLLMs) have emerged as a promising alternative for text generation, distinguished by their native support for parallel decoding. In practice, block inference is crucial for avoiding order misalignment in global bidirectional decoding and improving output quality. However, the widely-used fixed, predefined block (naive) schedule is agnostic to semantic difficulty, making it a suboptimal strategy for both quality and efficiency: it can force premature commitments to uncertain positions while delaying easy positions near block boundaries. In this work, we analyze the limitations of naive block scheduling and disclose the importance of dynamically adapting the schedule to semantic difficulty for reliable and efficient inference. Motivated by this, we propose Dynamic Sliding Block (DSB), a training-free block scheduling method that uses a sliding block with a dynamic size to overcome the rigidity of the naive block. To further improve efficiency, we introduce DSB Cache, a training-free KV-cache mechanism tailored to DSB. Extensive experiments across multiple models and benchmarks demonstrate that DSB, together with DSB Cache, consistently improves both generation quality and inference efficiency for dLLMs. Code is released at https://github.com/lizhuo-luo/DSB.

Diffusion models have gradually gained prominence in the field of image synthesis, showcasing remarkable generative capabilities. Nevertheless, the slow inference and complex networks, resulting from redundancy at both temporal and structural levels, hinder their low-latency applications in real-world scenarios. Current acceleration methods for diffusion models focus separately on temporal and structural levels. However, independent optimization at each level to further push the acceleration limits results in significant performance degradation. On the other hand, integrating optimizations at both levels can compound the acceleration effects. Unfortunately, we find that the optimizations at these two levels are not entirely orthogonal. Performing separate optimizations and then simply integrating them results in unsatisfactory performance. To tackle this issue, we propose CacheQuant, a novel training-free paradigm that comprehensively accelerates diffusion models by jointly optimizing model caching and quantization techniques. Specifically, we employ a dynamic programming approach to determine the optimal cache schedule, in which the properties of caching and quantization are carefully considered to minimize errors. Additionally, we propose decoupled error correction to further mitigate the coupled and accumulated errors step by step. Experimental results show that CacheQuant achieves a 5.18 speedup and 4 compression for Stable Diffusion on MS-COCO, with only a 0.02 loss in CLIP score. Our code are open-sourced: https://github.com/BienLuky/CacheQuant .

QUBO formulations of combinatorial optimization problems allow for solving them using various quantum heuristics. While large-scale quantum computations are currently still out of reach, we can already numerically test such QUBO formulations on a perhaps surprisingly large scale. In this work, we benchmark Fujitsu's Digital Annealer (DA) on the Max-Cut problem, which captures the main complexity of the QUBO problem. We make a comprehensive benchmark against leading other heuristic algorithms on graphs with up to 53,000 variables by focusing on the wall-clock time. Moreover, we compare the DA performance against published performance results of the D-Wave hybrid quantum-classical annealer and the recently proposed QIS3 heuristic. Based on performance statistics for over 2,000 graphs from the MQLib, we find that the DA yields competitive results. We hope that this benchmark demonstrates the extent to which large QUBO instances can be heuristically solved today, yielding consistent results across different solvers.

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

Modern deep residual networks perform substantial redundant computation by evaluating all residual blocks for every input, even when identity mappings suffice. We introduce CosineGate, an end-to-end differentiable architecture for dynamic routing in residual networks that uses cosine incompatibility between identity and residual feature representations as a self-supervised skip signal. CosineGate measures semantic redundancy through the Cosine Incompatibility Ratio (CIR), defined as 1 - cos(x, F(x)), and uses Gumbel-Softmax relaxation to enable per-sample, per-block gating during training. A progressive FLOPs regularization term controls average compute usage without destabilizing optimization. On CIFAR-10, CosineGate spans the accuracy-efficiency Pareto frontier: an aggressive configuration achieves 89.9 percent accuracy with 24.1 percent FLOPs savings, a balanced configuration achieves 91.3 percent accuracy with 28.5 percent savings at epoch 160, and a conservative configuration reaches a peak of 93.2 percent accuracy with minimal compute reduction. These results match or exceed ResNet-20 (91.3 percent) while reducing computation, without auxiliary supervision, distillation, or task-specific heuristics. Our results demonstrate that simple geometric measures of feature incompatibility provide a principled and effective signal for dynamic residual routing.

Global placement is a critical step with high computational complexity in VLSI physical design. Modern analytical placers formulate the placement problem as a nonlinear optimization, where initialization strongly affects both convergence behavior and final placement quality. However, existing initialization methods exhibit a trade-off: area-aware initializers account for cell areas but are computationally expensive and can dominate total runtime, while fast point-based initializers ignore cell area, leading to a modeling gap that impairs convergence and solution quality. We propose a lightweight co-optimization framework that bridges this initialization gap through two strategies. First, an area-hint refinement initializer incorporates heuristic cell area information into a signed graph signal by augmenting the netlist graph with virtual nodes and negative-weight edges, yielding an area-aware and spectrally smooth placement initialization. Second, a macro-schedule placement procedure progressively restores area constraints, enabling a smooth transition from the refined initializer to the full area-aware objective and producing high-quality placement results. We evaluate the framework on macro-heavy ISPD2005 academic benchmarks and two real-world industrial designs across two technology nodes (12 cases in total). Experimental results show that our method consistently improves half-perimeter wirelength (HPWL) over point-based initializers in 11 out of 12 cases, achieving up to 2.2% HPWL reduction, while running approximately 100 times faster than the state-of-the-art area-aware initializer.

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

We empirically study the effect of noise scheduling strategies for denoising diffusion generative models. There are three findings: (1) the noise scheduling is crucial for the performance, and the optimal one depends on the task (e.g., image sizes), (2) when increasing the image size, the optimal noise scheduling shifts towards a noisier one (due to increased redundancy in pixels), and (3) simply scaling the input data by a factor of b while keeping the noise schedule function fixed (equivalent to shifting the logSNR by log b) is a good strategy across image sizes. This simple recipe, when combined with recently proposed Recurrent Interface Network (RIN), yields state-of-the-art pixel-based diffusion models for high-resolution images on ImageNet, enabling single-stage, end-to-end generation of diverse and high-fidelity images at 1024times1024 resolution (without upsampling/cascades).

Training language models currently requires pre-determining a fixed compute budget because the typical cosine learning rate schedule depends on the total number of steps. In contrast, the Warmup-Stable-Decay (WSD) schedule uses a constant learning rate to produce a main branch of iterates that can in principle continue indefinitely without a pre-specified compute budget. Then, given any compute budget, one can branch out from the main branch at a proper time with a rapidly decaying learning rate to produce a strong model. Empirically, WSD generates a non-traditional loss curve: the loss remains elevated during the stable phase but sharply declines during the decay phase. Towards explaining this phenomenon, we conjecture that pretraining loss exhibits a river valley landscape, which resembles a deep valley with a river at its bottom. Under this assumption, we show that during the stable phase, the iterate undergoes large oscillations due to the high learning rate, yet it progresses swiftly along the river. During the decay phase, the rapidly dropping learning rate minimizes the iterate's oscillations, moving it closer to the river and revealing true optimization progress. Therefore, the sustained high learning rate phase and fast decaying phase are responsible for progress in the river and the mountain directions respectively, and are both critical. Our analysis predicts phenomenons consistent with empirical observations and shows that this landscape can emerge from pretraining on a simple bi-gram dataset. Inspired by the theory, we introduce WSD-S, a variant of WSD that reuses previous checkpoints' decay phases and keeps only one main branch, where we resume from a decayed checkpoint. WSD-S empirically outperforms WSD and Cyclic-Cosine in obtaining multiple language model checkpoints across various compute budgets in a single run for parameters scaling from 0.1B to 1.2B.

Approximate Nearest Neighbor Search (ANNS) plays a critical role in applications such as search engines, recommender systems, and RAG for LLMs. Vector quantization (VQ), a crucial technique for ANNS, is commonly used to reduce space overhead and accelerate distance computations. However, despite significant research advances, state-of-the-art VQ methods still face challenges in balancing encoding efficiency and quantization accuracy. To address these limitations, we propose a novel VQ method called SAQ. To improve accuracy, SAQ employs a new dimension segmentation technique to strategically partition PCA-projected vectors into segments along their dimensions. By prioritizing leading dimension segments with larger magnitudes, SAQ allocates more bits to high-impact segments, optimizing the use of the available space quota. An efficient dynamic programming algorithm is developed to optimize dimension segmentation and bit allocation, ensuring minimal quantization error. To speed up vector encoding, SAQ devises a code adjustment technique to first quantize each dimension independently and then progressively refine quantized vectors using a coordinate-descent-like approach to avoid exhaustive enumeration. Extensive experiments demonstrate SAQ's superiority over classical methods (e.g., PQ, PCA) and recent state-of-the-art approaches (e.g., LVQ, Extended RabitQ). SAQ achieves up to 80% reduction in quantization error and accelerates encoding speed by over 80x compared to Extended RabitQ.

Coarse-guided visual generation, which synthesizes fine visual samples from degraded or low-fidelity coarse references, is essential for various real-world applications. While training-based approaches are effective, they are inherently limited by high training costs and restricted generalization due to paired data collection. Accordingly, recent training-free works propose to leverage pretrained diffusion models and incorporate guidance during the sampling process. However, these training-free methods either require knowing the forward (fine-to-coarse) transformation operator, e.g., bicubic downsampling, or are difficult to balance between guidance and synthetic quality. To address these challenges, we propose a novel guided method by using the h-transform, a tool that can constrain stochastic processes (e.g., sampling process) under desired conditions. Specifically, we modify the transition probability at each sampling timestep by adding to the original differential equation with a drift function, which approximately steers the generation toward the ideal fine sample. To address unavoidable approximation errors, we introduce a noise-level-aware schedule that gradually de-weights the term as the error increases, ensuring both guidance adherence and high-quality synthesis. Extensive experiments across diverse image and video generation tasks demonstrate the effectiveness and generalization of our method.

Sparse training is emerging as a promising avenue for reducing the computational cost of training neural networks. Several recent studies have proposed pruning methods using learnable thresholds to efficiently explore the non-uniform distribution of sparsity inherent within the models. In this paper, we propose Gradient Annealing (GA), where gradients of masked weights are scaled down in a non-linear manner. GA provides an elegant trade-off between sparsity and accuracy without the need for additional sparsity-inducing regularization. We integrated GA with the latest learnable pruning methods to create an automated sparse training algorithm called AutoSparse, which achieves better accuracy and/or training/inference FLOPS reduction than existing learnable pruning methods for sparse ResNet50 and MobileNetV1 on ImageNet-1K: AutoSparse achieves (2x, 7x) reduction in (training,inference) FLOPS for ResNet50 on ImageNet at 80% sparsity. Finally, AutoSparse outperforms sparse-to-sparse SotA method MEST (uniform sparsity) for 80% sparse ResNet50 with similar accuracy, where MEST uses 12% more training FLOPS and 50% more inference FLOPS.

Recent large language models (LLMs) have tended to leverage sparsity to reduce computations, employing the sparsely activated mixture-of-experts (MoE) technique. MoE introduces four modules, including token routing, token communication, expert computation, and expert parallelism, that impact model quality and training efficiency. To enable versatile usage of MoE models, we introduce FSMoE, a flexible training system optimizing task scheduling with three novel techniques: 1) Unified abstraction and online profiling of MoE modules for task scheduling across various MoE implementations. 2) Co-scheduling intra-node and inter-node communications with computations to minimize communication overheads. 3) To support near-optimal task scheduling, we design an adaptive gradient partitioning method for gradient aggregation and a schedule to adaptively pipeline communications and computations. We conduct extensive experiments with configured MoE layers and real-world MoE models on two GPU clusters. Experimental results show that 1) our FSMoE supports four popular types of MoE routing functions and is more efficient than existing implementations (with up to a 1.42times speedup), and 2) FSMoE outperforms the state-of-the-art MoE training systems (DeepSpeed-MoE and Tutel) by 1.18times-1.22times on 1458 MoE layers and 1.19times-3.01times on real-world MoE models based on GPT-2 and Mixtral using a popular routing function.

Metric-induced discrete flow matching (MI-DFM) exploits token-latent geometry for discrete generation, but its practical use is limited by two issues: heuristic schedulers requiring hyperparameter search, and finite-step path-tracking error from its first-order continuous-time Markov chain (CTMC) solver. We address both issues. First, we derive a kinetic-optimal scheduler for prescribed scalar-parameterized probability paths, and instantiate it for MI-DFM as a training-free numerical schedule that traverses the path at constant Fisher-Rao speed. Second, we introduce a finite-step moment correction that adjusts the jump probability while preserving the CTMC jump destination distribution. We validate the resulting method, GibbsTTS, on codec-based zero-shot text-to-speech (TTS). Under controlled comparisons with a unified architecture and large-scale dataset, GibbsTTS achieves the best objective naturalness and is preferred in subjective evaluations over masked discrete generative baselines. Additionally, in comparison with the evaluated state-of-the-art TTS systems, GibbsTTS shows strong speaker similarity, achieving the highest similarity on three of four test sets and ranking second on the fourth. Project page: https://ydqmkkx.github.io/GibbsTTSProject

Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic solutions and their good mathematical properties. Despite their success, an important drawback of diffusion models is their sensitivity to the choice of variance schedule, which controls the dynamics of the diffusion process. Fine-tuning this schedule for specific applications is crucial but time-costly and does not guarantee an optimal result. We propose a novel approach for learning the schedule as part of the training process. Our method supports probabilistic conditioning on data, provides high-quality solutions, and is flexible, proving able to adapt to different applications with minimum overhead. This approach is tested in two unrelated inverse problems: super-resolution microscopy and quantitative phase imaging, yielding comparable or superior results to previous methods and fine-tuned diffusion models. We conclude that fine-tuning the schedule by experimentation should be avoided because it can be learned during training in a stable way that yields better results.

An increasing number of autoregressive models, such as MAR, FlowAR, xAR, and Harmon adopt diffusion sampling to improve the quality of image generation. However, this strategy leads to low inference efficiency, because it usually takes 50 to 100 steps for diffusion to sample a token. This paper explores how to effectively address this issue. Our key motivation is that as more tokens are generated during the autoregressive process, subsequent tokens follow more constrained distributions and are easier to sample. To intuitively explain, if a model has generated part of a dog, the remaining tokens must complete the dog and thus are more constrained. Empirical evidence supports our motivation: at later generation stages, the next tokens can be well predicted by a multilayer perceptron, exhibit low variance, and follow closer-to-straight-line denoising paths from noise to tokens. Based on our finding, we introduce diffusion step annealing (DiSA), a training-free method which gradually uses fewer diffusion steps as more tokens are generated, e.g., using 50 steps at the beginning and gradually decreasing to 5 steps at later stages. Because DiSA is derived from our finding specific to diffusion in autoregressive models, it is complementary to existing acceleration methods designed for diffusion alone. DiSA can be implemented in only a few lines of code on existing models, and albeit simple, achieves 5-10times faster inference for MAR and Harmon and 1.4-2.5times for FlowAR and xAR, while maintaining the generation quality.

Diffusion models have shown promising generative capabilities across diverse domains, yet aligning their outputs with desired reward functions remains a challenge, particularly in cases where reward functions are non-differentiable. Some gradient-free guidance methods have been developed, but they often struggle to achieve optimal inference-time alignment. In this work, we newly frame inference-time alignment in diffusion as a search problem and propose Dynamic Search for Diffusion (DSearch), which subsamples from denoising processes and approximates intermediate node rewards. It also dynamically adjusts beam width and tree expansion to efficiently explore high-reward generations. To refine intermediate decisions, DSearch incorporates adaptive scheduling based on noise levels and a lookahead heuristic function. We validate DSearch across multiple domains, including biological sequence design, molecular optimization, and image generation, demonstrating superior reward optimization compared to existing approaches.

This paper presents Randomized AutoRegressive modeling (RAR) for visual generation, which sets a new state-of-the-art performance on the image generation task while maintaining full compatibility with language modeling frameworks. The proposed RAR is simple: during a standard autoregressive training process with a next-token prediction objective, the input sequence-typically ordered in raster form-is randomly permuted into different factorization orders with a probability r, where r starts at 1 and linearly decays to 0 over the course of training. This annealing training strategy enables the model to learn to maximize the expected likelihood over all factorization orders and thus effectively improve the model's capability of modeling bidirectional contexts. Importantly, RAR preserves the integrity of the autoregressive modeling framework, ensuring full compatibility with language modeling while significantly improving performance in image generation. On the ImageNet-256 benchmark, RAR achieves an FID score of 1.48, not only surpassing prior state-of-the-art autoregressive image generators but also outperforming leading diffusion-based and masked transformer-based methods. Code and models will be made available at https://github.com/bytedance/1d-tokenizer

Timestep sampling p(t) is a central design choice in Flow Matching models, yet common practice increasingly favors static middle-biased distributions (e.g., Logit-Normal). We show that this choice induces a speed--quality trade-off: middle-biased sampling accelerates early convergence but yields worse asymptotic fidelity than Uniform sampling. By analyzing per-timestep training losses, we identify a U-shaped difficulty profile with persistent errors near the boundary regimes, implying that under-sampling the endpoints leaves fine details unresolved. Guided by this insight, we propose Curriculum Sampling, a two-phase schedule that begins with middle-biased sampling for rapid structure learning and then switches to Uniform sampling for boundary refinement. On CIFAR-10, Curriculum Sampling improves the best FID from 3.85 (Uniform) to 3.22 while reaching peak performance at 100k rather than 150k training steps. Our results highlight that timestep sampling should be treated as an evolving curriculum rather than a fixed hyperparameter.

Effective learning rate (LR) scheduling is crucial for training deep neural networks. However, popular pre-defined and adaptive schedulers can still lead to suboptimal generalization. This paper introduces VolSched, a novel adaptive LR scheduler inspired by the concept of volatility in stochastic processes like Geometric Brownian Motion to dynamically adjust the learning rate. By calculating the ratio between long-term and short-term accuracy volatility, VolSched increases the LR to escape plateaus and decreases it to stabilize training, allowing the model to explore the loss landscape more effectively. We evaluate VolSched on the CIFAR-100 dataset against a strong baseline using a standard augmentation pipeline. When paired with ResNet-18 and ResNet-34, our scheduler delivers consistent performance gains, improving top-1 accuracy by 1.4 and 1.3 percentage points respectively. Analysis of the loss curves reveals that VolSched promotes a longer exploration phase. A quantitative analysis of the Hessian shows that VolSched finds a final solution that is 38% flatter than the next-best baseline, allowing the model to obtain wider minima and hence better generalization performance.

3D Gaussian Splatting (3DGS) enables real-time, photorealistic novel view synthesis, making it a highly attractive representation for model-based video tracking. However, leveraging the differentiability of the 3DGS renderer "in the wild" remains notoriously fragile. A fundamental bottleneck lies in the compact, local support of the Gaussian primitives. Standard photometric objectives implicitly rely on spatial overlap; if severe camera misalignment places the rendered object outside the target's local footprint, gradients strictly vanish, leaving the optimizer stranded. We introduce SpectralSplats, a robust tracking framework that resolves this "vanishing gradient" problem by shifting the optimization objective from the spatial to the frequency domain. By supervising the rendered image via a set of global complex sinusoidal features (Spectral Moments), we construct a global basin of attraction, ensuring that a valid, directional gradient toward the target exists across the entire image domain, even when pixel overlap is completely nonexistent. To harness this global basin without introducing periodic local minima associated with high frequencies, we derive a principled Frequency Annealing schedule from first principles, gracefully transitioning the optimizer from global convexity to precise spatial alignment. We demonstrate that SpectralSplats acts as a seamless, drop-in replacement for spatial losses across diverse deformation parameterizations (from MLPs to sparse control points), successfully recovering complex deformations even from severely misaligned initializations where standard appearance-based tracking catastrophically fails.

Recent advances in learning rate (LR) scheduling have demonstrated the effectiveness of decay-free approaches that eliminate the traditional decay phase while maintaining competitive performance. Model merging techniques have emerged as particularly promising solutions in this domain. We present Warmup-Stable and Merge (WSM), a general framework that establishes a formal connection between learning rate decay and model merging. WSM provides a unified theoretical foundation for emulating various decay strategies-including cosine decay, linear decay and inverse square root decay-as principled model averaging schemes, while remaining fully compatible with diverse optimization methods. Through extensive experiments, we identify merge duration-the training window for checkpoint aggregation-as the most critical factor influencing model performance, surpassing the importance of both checkpoint interval and merge quantity. Our framework consistently outperforms the widely-adopted Warmup-Stable-Decay (WSD) approach across multiple benchmarks, achieving significant improvements of +3.5% on MATH, +2.9% on HumanEval, and +5.5% on MMLU-Pro. The performance advantages extend to supervised fine-tuning scenarios, highlighting WSM's potential for long-term model refinement.

In recent years, diffusion models have become the most popular and powerful methods in the field of image synthesis, even rivaling human artists in artistic creativity. However, the key issue currently limiting the application of diffusion models is its extremely slow generation process. Although several methods were proposed to speed up the generation process, there still exists a trade-off between efficiency and quality. In this paper, we first provide a detailed theoretical and empirical analysis of the generation process of the diffusion models based on schedulers. We transform the designing problem of schedulers into the determination of several parameters, and further transform the accelerated generation process into an expansion process of the linear subspace. Based on these analyses, we consequently propose a novel method called Optimal Linear Subspace Search (OLSS), which accelerates the generation process by searching for the optimal approximation process of the complete generation process in the linear subspaces spanned by latent variables. OLSS is able to generate high-quality images with a very small number of steps. To demonstrate the effectiveness of our method, we conduct extensive comparative experiments on open-source diffusion models. Experimental results show that with a given number of steps, OLSS can significantly improve the quality of generated images. Using an NVIDIA A100 GPU, we make it possible to generate a high-quality image by Stable Diffusion within only one second without other optimization techniques.

While diffusion-based image restoration (IR) methods have achieved remarkable success, they are still limited by the low inference speed attributed to the necessity of executing hundreds or even thousands of sampling steps. Existing acceleration sampling techniques, though seeking to expedite the process, inevitably sacrifice performance to some extent, resulting in over-blurry restored outcomes. To address this issue, this study proposes a novel and efficient diffusion model for IR that significantly reduces the required number of diffusion steps. Our method avoids the need for post-acceleration during inference, thereby avoiding the associated performance deterioration. Specifically, our proposed method establishes a Markov chain that facilitates the transitions between the high-quality and low-quality images by shifting their residuals, substantially improving the transition efficiency. A carefully formulated noise schedule is devised to flexibly control the shifting speed and the noise strength during the diffusion process. Extensive experimental evaluations demonstrate that the proposed method achieves superior or comparable performance to current state-of-the-art methods on three classical IR tasks, namely image super-resolution, image inpainting, and blind face restoration, \textbf{even only with four sampling steps}. Our code and model are publicly available at https://github.com/zsyOAOA/ResShift.

Although Large Language Models have advanced Automated Heuristic Design, treating algorithm evolution as a monolithic text generation task overlooks the coupling between discrete algorithmic structures and continuous numerical parameters. Consequently, existing methods often discard promising algorithms due to uncalibrated constants and suffer from premature convergence resulting from simple similarity metrics. To address these limitations, we propose TIDE, a Tuning-Integrated Dynamic Evolution framework designed to decouple structural reasoning from parameter optimization. TIDE features a nested architecture where an outer parallel island model utilizes Tree Similarity Edit Distance to drive structural diversity, while an inner loop integrates LLM-based logic generation with a differential mutation operator for parameter tuning. Additionally, a UCB-based scheduler dynamically prioritizes high-yield prompt strategies to optimize resource allocation. Extensive experiments across nine combinatorial optimization problems demonstrate that TIDE discovers heuristics that significantly outperform state-of-the-art baselines in solution quality while achieving improved search efficiency and reduced computational costs.

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

We present LeMiCa, a training-free and efficient acceleration framework for diffusion-based video generation. While existing caching strategies primarily focus on reducing local heuristic errors, they often overlook the accumulation of global errors, leading to noticeable content degradation between accelerated and original videos. To address this issue, we formulate cache scheduling as a directed graph with error-weighted edges and introduce a Lexicographic Minimax Path Optimization strategy that explicitly bounds the worst-case path error. This approach substantially improves the consistency of global content and style across generated frames. Extensive experiments on multiple text-to-video benchmarks demonstrate that LeMiCa delivers dual improvements in both inference speed and generation quality. Notably, our method achieves a 2.9x speedup on the Latte model and reaches an LPIPS score of 0.05 on Open-Sora, outperforming prior caching techniques. Importantly, these gains come with minimal perceptual quality degradation, making LeMiCa a robust and generalizable paradigm for accelerating diffusion-based video generation. We believe this approach can serve as a strong foundation for future research on efficient and reliable video synthesis. Our code is available at :https://github.com/UnicomAI/LeMiCa

Diffusion models (DMs) have demonstrated remarkable success in real-world image super-resolution (SR), yet their reliance on time-consuming multi-step sampling largely hinders their practical applications. While recent efforts have introduced few- or single-step solutions, existing methods either inefficiently model the process from noisy input or fail to fully exploit iterative generative priors, compromising the fidelity and quality of the reconstructed images. To address this issue, we propose FlowSR, a novel approach that reformulates the SR problem as a rectified flow from low-resolution (LR) to high-resolution (HR) images. Our method leverages an improved consistency learning strategy to enable high-quality SR in a single step. Specifically, we refine the original consistency distillation process by incorporating HR regularization, ensuring that the learned SR flow not only enforces self-consistency but also converges precisely to the ground-truth HR target. Furthermore, we introduce a fast-slow scheduling strategy, where adjacent timesteps for consistency learning are sampled from two distinct schedulers: a fast scheduler with fewer timesteps to improve efficiency, and a slow scheduler with more timesteps to capture fine-grained texture details. Extensive experiments demonstrate that FlowSR achieves outstanding performance in both efficiency and image quality.

Diffusion Large Language Models (dLLMs) have emerged as a competitive alternative to autoregressive (AR) models, offering better hardware utilization and bidirectional context through parallel block-level decoding. However, as dLLMs continue to scale up with mixture-of-experts (MoE) architectures, their deployment on resource-constrained devices remains an open challenge. Existing AR-based methods often incur either prohibitive I/O overhead or significant compute bottlenecks. In this work, we propose TIDE, a novel resource-efficient inference system that leverages the temporal stability of expert activations during the diffusion process within the block. Specifically, we leverage the temporal stability of expert activations during the diffusion process within the block and introduce an interval-based expert refresh strategy that updates the expert placement in an I/O-aware fashion. To ensure optimal performance, we formulate the inference scheduling as a mathematical programming problem, solving for the optimal interval that minimizes I/O traffic and CPU computation. Most importantly, TIDE is a lossless optimization that requires no model training, providing a "free lunch" acceleration for dLLM inference. In a single GPU-CPU system, we demonstrate that TIDE achieves up to 1.4times and 1.5times throughput improvements over prior baselines on LLaDA2.0-mini and LLaDA2.0-flash models, respectively.

Learning-based methods have gained attention as general-purpose solvers due to their ability to automatically learn problem-specific heuristics, reducing the need for manually crafted heuristics. However, these methods often face scalability challenges. To address these issues, the improved Sampling algorithm for Combinatorial Optimization (iSCO), using discrete Langevin dynamics, has been proposed, demonstrating better performance than several learning-based solvers. This study proposes a different approach that integrates gradient-based update through continuous relaxation, combined with Quasi-Quantum Annealing (QQA). QQA smoothly transitions the objective function, starting from a simple convex function, minimized at half-integral values, to the original objective function, where the relaxed variables are minimized only in the discrete space. Furthermore, we incorporate parallel run communication leveraging GPUs to enhance exploration capabilities and accelerate convergence. Numerical experiments demonstrate that our method is a competitive general-purpose solver, achieving performance comparable to iSCO and learning-based solvers across various benchmark problems. Notably, our method exhibits superior speed-quality trade-offs for large-scale instances compared to iSCO, learning-based solvers, commercial solvers, and specialized algorithms.

Diffusion models have proven to be highly effective in image and video generation; however, they still face composition challenges when generating images of varying sizes due to single-scale training data. Adapting large pre-trained diffusion models for higher resolution demands substantial computational and optimization resources, yet achieving a generation capability comparable to low-resolution models remains elusive. This paper proposes a novel self-cascade diffusion model that leverages the rich knowledge gained from a well-trained low-resolution model for rapid adaptation to higher-resolution image and video generation, employing either tuning-free or cheap upsampler tuning paradigms. Integrating a sequence of multi-scale upsampler modules, the self-cascade diffusion model can efficiently adapt to a higher resolution, preserving the original composition and generation capabilities. We further propose a pivot-guided noise re-schedule strategy to speed up the inference process and improve local structural details. Compared to full fine-tuning, our approach achieves a 5X training speed-up and requires only an additional 0.002M tuning parameters. Extensive experiments demonstrate that our approach can quickly adapt to higher resolution image and video synthesis by fine-tuning for just 10k steps, with virtually no additional inference time.

Converting raster floorplans into engineering-grade vector graphics is challenging due to complex topology and strict geometric constraints. To address this, we present FloorplanVLM, a unified framework that reformulates floorplan vectorization as an image-conditioned sequence modeling task. Unlike pixel-based methods that rely on fragile heuristics or query-based transformers that generate fragmented rooms, our model directly outputs structured JSON sequences representing the global topology. This 'pixels-to-sequence' paradigm enables the precise and holistic constraint satisfaction of complex geometries, such as slanted walls and curved arcs. To support this data-hungry approach, we introduce a scalable data engine: we construct a large-scale dataset (Floorplan-2M) and a high-fidelity subset (Floorplan-HQ-300K) to balance geometric diversity and pixel-level precision. We then employ a progressive training strategy, using Supervised Fine-Tuning (SFT) for structural grounding and quality annealing, followed by Group Relative Policy Optimization (GRPO) for strict geometric alignment. To standardize evaluation on complex layouts, we establish and open-source FPBench-2K. Evaluated on this rigorous benchmark, FloorplanVLM demonstrates exceptional structural validity, achieving 92.52% external-wall IoU and robust generalization across non-Manhattan architectures.

Predictive coding networks are neuroscience-inspired models with roots in both Bayesian statistics and neuroscience. Training such models, however, is quite inefficient and unstable. In this work, we show how by simply changing the temporal scheduling of the update rule for the synaptic weights leads to an algorithm that is much more efficient and stable than the original one, and has theoretical guarantees in terms of convergence. The proposed algorithm, that we call incremental predictive coding (iPC) is also more biologically plausible than the original one, as it it fully automatic. In an extensive set of experiments, we show that iPC constantly performs better than the original formulation on a large number of benchmarks for image classification, as well as for the training of both conditional and masked language models, in terms of test accuracy, efficiency, and convergence with respect to a large set of hyperparameters.

We present COS(M+O)S, a System 2-inspired framework for open-ended plot development that systematically explores the vast space of possible story expansions, enabling a 3B-parameter language model to approach the plot quality of a 70B model on select short-story tasks. The method accomplishes this by combining Monte Carlo Tree Search (MCTS), guided by a step-level value model that rewards moderate surprisal (curiosity) while penalizing incoherence, and Odds Ratio Preference Optimization (ORPO) to fine-tune the policy on high-value plot expansions. This iterative reinforcement learning loop systematically explores multiple candidate plot branches, backpropagates quality signals, and adapts the policy for faster convergence, notably shifting the policy from puzzle-based Chain-of-Thought to more character-driven storytelling. In small-scale tests with short-story prompts, 67%-77% of participants favored COS(M+O)S's highest-rated expansions over lower-rated ones, suggesting that our learned value function aligns. GPT-4o ratings further show that COS(M+O)S surpasses naive single-pass decoding from Llama 3.2 3B by 0.59 SD, coming within 0.06 SD of Llama 3.1 70B (no significant difference, p=0.93). Pairwise comparisons with o1 place COS(M+O)S 1.5 SD above the 3B baseline and find no statistically significant gap from 70B. Nevertheless, absolute story quality remains modest, constrained by the small model's capacity and limited training data.

Classifier-free guidance (CFG) is a cornerstone of text-to-image diffusion models, yet its effectiveness is limited by the use of static guidance scales. This "one-size-fits-all" approach fails to adapt to the diverse requirements of different prompts; moreover, prior solutions like gradient-based correction or fixed heuristic schedules introduce additional complexities and fail to generalize. In this work, we challeng this static paradigm by introducing a framework for dynamic CFG scheduling. Our method leverages online feedback from a suite of general-purpose and specialized small-scale latent-space evaluations, such as CLIP for alignment, a discriminator for fidelity and a human preference reward model, to assess generation quality at each step of the reverse diffusion process. Based on this feedback, we perform a greedy search to select the optimal CFG scale for each timestep, creating a unique guidance schedule tailored to every prompt and sample. We demonstrate the effectiveness of our approach on both small-scale models and the state-of-the-art Imagen 3, showing significant improvements in text alignment, visual quality, text rendering and numerical reasoning. Notably, when compared against the default Imagen 3 baseline, our method achieves up to 53.8% human preference win-rate for overall preference, a figure that increases up to to 55.5% on prompts targeting specific capabilities like text rendering. Our work establishes that the optimal guidance schedule is inherently dynamic and prompt-dependent, and provides an efficient and generalizable framework to achieve it.

While conditional diffusion models are known to have good coverage of the data distribution, they still face limitations in output diversity, particularly when sampled with a high classifier-free guidance scale for optimal image quality or when trained on small datasets. We attribute this problem to the role of the conditioning signal in inference and offer an improved sampling strategy for diffusion models that can increase generation diversity, especially at high guidance scales, with minimal loss of sample quality. Our sampling strategy anneals the conditioning signal by adding scheduled, monotonically decreasing Gaussian noise to the conditioning vector during inference to balance diversity and condition alignment. Our Condition-Annealed Diffusion Sampler (CADS) can be used with any pretrained model and sampling algorithm, and we show that it boosts the diversity of diffusion models in various conditional generation tasks. Further, using an existing pretrained diffusion model, CADS achieves a new state-of-the-art FID of 1.70 and 2.31 for class-conditional ImageNet generation at 256times256 and 512times512 respectively.

A long standing challenge in computational chemistry and biophysics is efficiently sampling the Boltzmann distribution of molecules. Advances in generative modeling have been proposed to address the limitations of conventional sampling techniques by eliminating the computational cost of simulation. A promising direction is iteratively finetuning diffusion models along a temperature ladder whereby training data is generated via importance sampling during inference-time annealing. Unfortunately, these methods require computing a divergence over the score field to estimate importance weights, rendering them intractable for larger systems. Here we present scalable inference-time annealing (SITA), which retrains flow-based models to generate samples at progressively lower temperatures using an energy-based model to facilitate fast surrogate likelihoods. We demonstrate state-of-the-art performance on both Alanine Dipeptide and Alanine Tripeptide while avoiding costly divergence terms. Our code is available at https://github.com/countrsignal/sita.git

Generating realistic animated videos from static images is an important area of research in computer vision. Methods based on physical simulation and motion prediction have achieved notable advances, but they are often limited to specific object textures and motion trajectories, failing to exhibit highly complex environments and physical dynamics. In this paper, we introduce an open-domain controllable image animation method using motion priors with video diffusion models. Our method achieves precise control over the direction and speed of motion in the movable region by extracting the motion field information from videos and learning moving trajectories and strengths. Current pretrained video generation models are typically limited to producing very short videos, typically less than 30 frames. In contrast, we propose an efficient long-duration video generation method based on noise reschedule specifically tailored for image animation tasks, facilitating the creation of videos over 100 frames in length while maintaining consistency in content scenery and motion coordination. Specifically, we decompose the denoise process into two distinct phases: the shaping of scene contours and the refining of motion details. Then we reschedule the noise to control the generated frame sequences maintaining long-distance noise correlation. We conducted extensive experiments with 10 baselines, encompassing both commercial tools and academic methodologies, which demonstrate the superiority of our method. Our project page: https://wangqiang9.github.io/Controllable.github.io/

Resource scheduling and allocation is a critical component of many high impact systems ranging from congestion control to cloud computing. Finding more optimal solutions to these problems often has significant impact on resource and time savings, reducing device wear-and-tear, and even potentially improving carbon emissions. In this paper, we focus on a specific instance of a scheduling problem, namely the memory mapping problem that occurs during compilation of machine learning programs: That is, mapping tensors to different memory layers to optimize execution time. We introduce an approach for solving the memory mapping problem using Reinforcement Learning. RL is a solution paradigm well-suited for sequential decision making problems that are amenable to planning, and combinatorial search spaces with high-dimensional data inputs. We formulate the problem as a single-player game, which we call the mallocGame, such that high-reward trajectories of the game correspond to efficient memory mappings on the target hardware. We also introduce a Reinforcement Learning agent, mallocMuZero, and show that it is capable of playing this game to discover new and improved memory mapping solutions that lead to faster execution times on real ML workloads on ML accelerators. We compare the performance of mallocMuZero to the default solver used by the Accelerated Linear Algebra (XLA) compiler on a benchmark of realistic ML workloads. In addition, we show that mallocMuZero is capable of improving the execution time of the recently published AlphaTensor matrix multiplication model.

Scheduling precedence-constrained tasks under shared renewable resources is central to modern computing platforms. The Resource Investment Problem (RIP) models this setting by minimizing the cost of provisioned renewable resources under precedence and timing constraints. Exact mixed-integer programming and constraint programming become impractically slow on large instances, and dynamic updates require schedule revisions under tight latency budgets. We present iScheduler, a reinforcement-learning-driven iterative scheduling framework that formulates RIP solving as a Markov decision process over decomposed subproblems and constructs schedules through sequential process selection. The framework accelerates optimization and supports reconfiguration by reusing unchanged process schedules and rescheduling only affected processes. We also release L-RIPLIB, an industrial-scale benchmark derived from cloud-platform workloads with 1,000 instances of 2,500-10,000 tasks. Experiments show that iScheduler attains competitive resource costs while reducing time to feasibility by up to 43times against strong commercial baselines.

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

Fast Weight Programmers (FWPs) encode temporal dependencies through dynamically updated parameters rather than recurrent hidden states. Quantum FWPs (QFWPs) extend this idea with variational quantum circuits (VQCs), but existing implementations rely on multi-qubit architectures that are difficult to scale on noisy intermediate-scale quantum (NISQ) devices and expensive to simulate classically. We propose gated QKAN-FWP, a fast-weight framework that integrates FWP with Quantum-inspired Kolmogorov-Arnold Network (QKAN) using single-qubit data re-uploading circuits as learnable nonlinear activation, known as DatA Re-Uploading ActivatioN (DARUAN). We further introduce a scalar-gated fast-weight update rule that stabilizes parameter evolution, supported by a theoretical analysis of its adaptive memory kernel, geometric boundedness, and parallelizable gradient paths. We evaluate the framework across time-series benchmarks, MiniGrid reinforcement learning, and highlight real-world solar cycle forecasting as our main practical result. In the long-horizon setting with 528-month input window and 132-month forecast horizon, our 12.5k-parameter model achieves lower scaled Mean Square Error (MSE), peak amplitude error, and peak timing error than a suite of classical recurrent baselines with up to 13x more parameters, including Long Short-Term Memory (LSTM) networks (25.9k-89.1k parameters), WaveNet-LSTM (167k), Vanilla recurrent neural network (11.5k), and a Modified Echo State Network (132k). To validate NISQ compatibility, we further deploy the trained fast programmer on IonQ and IBM Quantum processors, recovering forecasting accuracy within 0.1% relative MSE of the noiseless simulator at 1024 shots. These results position gated QKAN-FWP as a scalable, parameter-efficient, and NISQ-compatible approach to quantum-inspired sequence modeling.

Visual generation has witnessed remarkable progress in single-image tasks, yet extending these capabilities to temporal sequences remains challenging. Current approaches either build specialized video models from scratch with enormous computational costs or add separate motion modules to image generators, both requiring learning temporal dynamics anew. We observe that modern image generation models possess underutilized potential in handling structured layouts with implicit temporal understanding. Building on this insight, we introduce GRID, which reformulates temporal sequences as grid layouts, enabling holistic processing of visual sequences while leveraging existing model capabilities. Through a parallel flow-matching training strategy with coarse-to-fine scheduling, our approach achieves up to 67 faster inference speeds while using <1/1000 of the computational resources compared to specialized models. Extensive experiments demonstrate that GRID not only excels in temporal tasks from Text-to-Video to 3D Editing but also preserves strong performance in image generation, establishing itself as an efficient and versatile omni-solution for visual generation.

Scaling multi-dimensional transformers to long sequences is indispensable across various domains. However, the challenges of large memory requirements and slow speeds of such sequences necessitate sequence parallelism. All existing approaches fall under the category of embedded sequence parallelism, which are limited to shard along a single sequence dimension, thereby introducing significant communication overhead. However, the nature of multi-dimensional transformers involves independent calculations across multiple sequence dimensions. To this end, we propose Dynamic Sequence Parallelism (DSP) as a novel abstraction of sequence parallelism. DSP dynamically switches the parallel dimension among all sequences according to the computation stage with efficient resharding strategy. DSP offers significant reductions in communication costs, adaptability across modules, and ease of implementation with minimal constraints. Experimental evaluations demonstrate DSP's superiority over state-of-the-art embedded sequence parallelism methods by remarkable throughput improvements ranging from 32.2% to 10x, with less than 25% communication volume.

Diffusion-based image generation models excel at producing high-quality synthetic content, but suffer from slow and computationally expensive inference. Prior work has attempted to mitigate this by caching and reusing features within diffusion transformers across inference steps. These methods, however, often rely on rigid heuristics that result in limited acceleration or poor generalization across architectures. We propose Evolutionary Caching to Accelerate Diffusion models (ECAD), a genetic algorithm that learns efficient, per-model, caching schedules forming a Pareto frontier, using only a small set of calibration prompts. ECAD requires no modifications to network parameters or reference images. It offers significant inference speedups, enables fine-grained control over the quality-latency trade-off, and adapts seamlessly to different diffusion models. Notably, ECAD's learned schedules can generalize effectively to resolutions and model variants not seen during calibration. We evaluate ECAD on PixArt-alpha, PixArt-Sigma, and FLUX-1.dev using multiple metrics (FID, CLIP, Image Reward) across diverse benchmarks (COCO, MJHQ-30k, PartiPrompts), demonstrating consistent improvements over previous approaches. On PixArt-alpha, ECAD identifies a schedule that outperforms the previous state-of-the-art method by 4.47 COCO FID while increasing inference speedup from 2.35x to 2.58x. Our results establish ECAD as a scalable and generalizable approach for accelerating diffusion inference. Our project website is available at https://aniaggarwal.github.io/ecad and our code is available at https://github.com/aniaggarwal/ecad.

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

Group Relative Policy Optimisation (GRPO) enhances large language models by estimating advantages across a group of sampled trajectories. However, mapping these trajectory-level advantages to policy updates requires aggregating token-level probabilities within each sequence. Relying on a fixed aggregation mechanism for this step fundamentally limits the algorithm's adaptability. Empirically, we observe a critical trade-off: certain fixed aggregations frequently suffer from training collapse, while others fail to yield satisfactory performance. To resolve this, we propose HölderPO, a generalised policy optimisation framework unifying token-level probability aggregation via the Hölder mean. By explicitly modulating the parameter p, our framework provides continuous control over the trade-off between gradient concentration and variance bounds. Theoretically, we prove that a larger p concentrates the gradient to amplify sparse learning signals, whereas a smaller p strictly bounds gradient variance. Because no static configuration can universally resolve this concentration-stability trade-off, we instantiate the framework with a dynamic annealing algorithm that progressively schedules p across the training lifecycle. Extensive evaluations demonstrate superior stability and convergence over existing baselines. Specifically, our approach achieves a state-of-the-art average accuracy of 54.9% across multiple mathematical benchmarks, yielding a substantial 7.2% relative gain over standard GRPO and secures an exceptional 93.8% success rate on ALFWorld.

Denoising diffusion models are widely used for high-quality image and video generation. Their performance depends on noise schedules, which define the distribution of noise levels applied during training and the sequence of noise levels traversed during sampling. Noise schedules are typically handcrafted and require manual tuning across different resolutions. In this work, we propose a principled way to design per-instance noise schedules for pixel diffusion, based on the image's spectral properties. By deriving theoretical bounds on the efficacy of minimum and maximum noise levels, we design ``tight'' noise schedules that eliminate redundant steps. During inference, we propose to conditionally sample such noise schedules. Experiments show that our noise schedules improve generative quality of single-stage pixel diffusion models, particularly in the low-step regime.

Portfolio optimization has been a broad and intense area of interest for quantitative and statistical finance researchers and financial analysts. It is a challenging task to design a portfolio of stocks to arrive at the optimized values of the return and risk. This paper presents an algorithmic approach for designing optimum risk and eigen portfolios for five thematic sectors of the NSE of India. The prices of the stocks are extracted from the web from Jan 1, 2016, to Dec 31, 2020. Optimum risk and eigen portfolios for each sector are designed based on ten critical stocks from the sector. An LSTM model is designed for predicting future stock prices. Seven months after the portfolios were formed, on Aug 3, 2021, the actual returns of the portfolios are compared with the LSTM-predicted returns. The predicted and the actual returns indicate a very high-level accuracy of the LSTM model.

Smart home energy management systems help the distribution grid operate more efficiently and reliably, and enable effective penetration of distributed renewable energy sources. These systems rely on robust forecasting, optimization, and control/scheduling algorithms that can handle the uncertain nature of demand and renewable generation. This paper proposes an advanced ML algorithm, called Recurrent Trend Predictive Neural Network based Forecast Embedded Scheduling (rTPNN-FES), to provide efficient residential demand control. rTPNN-FES is a novel neural network architecture that simultaneously forecasts renewable energy generation and schedules household appliances. By its embedded structure, rTPNN-FES eliminates the utilization of separate algorithms for forecasting and scheduling and generates a schedule that is robust against forecasting errors. This paper also evaluates the performance of the proposed algorithm for an IoT-enabled smart home. The evaluation results reveal that rTPNN-FES provides near-optimal scheduling 37.5 times faster than the optimization while outperforming state-of-the-art forecasting techniques.

We propose AdaMuon, a novel optimizer that combines element-wise adaptivity with orthogonal updates for large-scale neural network training. AdaMuon incorporates two tightly coupled mechanisms: (1) an element-wise second momentum estimator applied to orthogonalized update directions, and (2) a sign-stabilized orthogonal update, where the momentum is first sign-transformed before orthogonalization. These two components jointly enable variance-adaptive scaling while maintaining stable update geometry. In addition, AdaMuon employs an RMS-aligned rescaling strategy to match the root-mean-square update magnitude to Adam, allowing direct reuse of existing learning rate schedules without extra tuning. Experiments demonstrate that AdaMuon not only maintains stability but can surpass Adam by more than 40% training efficiency in large-scale scenarios.

In this paper, we study a class of composite optimization problems whose objective function is given by the summation of a general smooth and nonsmooth component, together with a relatively simple nonsmooth term. While restart strategies are commonly employed in first-order methods to achieve optimal convergence under strong convexity, they introduce structural complexity and practical overhead, making algorithm design and nesting cumbersome. To address this, we propose a restart-free stochastic gradient sliding algorithm that eliminates the need for explicit restart phases when the simple nonsmooth component is strongly convex. Through a novel and carefully designed parameter selection strategy, we prove that the proposed algorithm achieves an ε-solution with only O(log(1ε)) gradient evaluations for the smooth component and O(1ε) stochastic subgradient evaluations for the nonsmooth component, matching the optimal complexity of existing multi-phase (restart-based) methods. Moreover, for the case where the nonsmooth component is structured, allowing the overall problem to be reformulated as a bilinear saddle-point problem, we develop a restart-free accelerated stochastic gradient sliding algorithm. We show that the resulting method requires only O(log(1ε)) gradient computations for the smooth component while preserving an overall iteration complexity of O(1{sqrtε}) for solving the corresponding saddle-point problems. Our work thus provides simpler, restart-f

In this work, we introduce a single parameter omega, to effectively control granularity in diffusion-based synthesis. This parameter is incorporated during the denoising steps of the diffusion model's reverse process. Our approach does not require model retraining, architectural modifications, or additional computational overhead during inference, yet enables precise control over the level of details in the generated outputs. Moreover, spatial masks or denoising schedules with varying omega values can be applied to achieve region-specific or timestep-specific granularity control. Prior knowledge of image composition from control signals or reference images further facilitates the creation of precise omega masks for granularity control on specific objects. To highlight the parameter's role in controlling subtle detail variations, the technique is named Omegance, combining "omega" and "nuance". Our method demonstrates impressive performance across various image and video synthesis tasks and is adaptable to advanced diffusion models. The code is available at https://github.com/itsmag11/Omegance.

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

LLMs are commonly trained with a learning rate (LR) warmup, followed by cosine decay to 10% of the maximum (10x decay). In a large-scale empirical study, we show that under an optimal peak LR, a simple linear decay-to-zero (D2Z) schedule consistently outperforms other schedules when training at compute-optimal dataset sizes. D2Z is superior across a range of model sizes, batch sizes, datasets, and vocabularies. Benefits increase as dataset size increases. Leveraging a novel interpretation of AdamW as an exponential moving average of weight updates, we show how linear D2Z optimally balances the demands of early training (moving away from initial conditions) and late training (averaging over more updates in order to mitigate gradient noise). In experiments, a 610M-parameter model trained for 80 tokens-per-parameter (TPP) using D2Z achieves lower loss than when trained for 200 TPP using 10x decay, corresponding to an astonishing 60% compute savings. Models such as Llama2-7B, trained for 286 TPP with 10x decay, could likely have saved a majority of compute by training with D2Z.

Pipeline parallelism is one of the key components for large-scale distributed training, yet its efficiency suffers from pipeline bubbles which were deemed inevitable. In this work, we introduce a scheduling strategy that, to our knowledge, is the first to successfully achieve zero pipeline bubbles under synchronous training semantics. The key idea behind this improvement is to split the backward computation into two parts, one that computes gradient for the input and another that computes for the parameters. Based on this idea, we handcraft novel pipeline schedules that significantly outperform the baseline methods. We further develop an algorithm that automatically finds an optimal schedule based on specific model configuration and memory limit. Additionally, to truly achieve zero bubble, we introduce a novel technique to bypass synchronizations during the optimizer step. Experimental evaluations show that our method outperforms the 1F1B schedule up to 23% in throughput under a similar memory limit. This number can be further pushed to 31% when the memory constraint is relaxed. We believe our results mark a major step forward in harnessing the true potential of pipeline parallelism. We open sourced our implementation based on the popular Megatron-LM repository on https://github.com/sail-sg/zero-bubble-pipeline-parallelism.

This paper presents an equivalence between feasible kinodynamic planning and optimal kinodynamic planning, in that any optimal planning problem can be transformed into a series of feasible planning problems in a state-cost space whose solutions approach the optimum. This transformation gives rise to a meta-algorithm that produces an asymptotically optimal planner, given any feasible kinodynamic planner as a subroutine. The meta-algorithm is proven to be asymptotically optimal, and a formula is derived relating expected running time and solution suboptimality. It is directly applicable to a wide range of optimal planning problems because it does not resort to the use of steering functions or numerical boundary-value problem solvers. On a set of benchmark problems, it is demonstrated to perform, using the EST and RRT algorithms as subroutines, at a superior or comparable level to related planners.

The rise of deep neural networks (DNNs) has driven an increased demand for computing power and memory. Modern DNNs exhibit high data volume variation (HDV) across tasks, which poses challenges for FPGA acceleration: conventional accelerators rely on fixed execution patterns (dataflow or sequential) that can lead to pipeline stalls or necessitate frequent off-chip memory accesses. To address these challenges, we introduce the Inter-Task Auto-Reconfigurable Accelerator (InTAR), a novel accelerator design methodology for HDV applications on FPGAs. InTAR combines the high computational efficiency of sequential execution with the reduced off-chip memory overhead of dataflow execution. It switches execution patterns automatically with a static schedule determined before circuit design based on resource constraints and problem sizes. Unlike previous reconfigurable accelerators, InTAR encodes reconfiguration schedules during circuit design, allowing model-specific optimizations that allocate only the necessary logic and interconnects. Thus, InTAR achieves a high clock frequency with fewer resources and low reconfiguration time. Furthermore, InTAR supports high-level tools such as HLS for fast design generation. We implement a set of multi-task HDV DNN kernels using InTAR. Compared with dataflow and sequential accelerators, InTAR exhibits 1.8times and 7.1 times speedups correspondingly. Moreover, we extend InTAR to GPT-2 medium as a more complex example, which is 3.65 sim 39.14times faster and a 1.72 sim 10.44times more DSP efficient than SoTA accelerators (Allo and DFX) on FPGAs. Additionally, this design demonstrates 1.66 sim 7.17times better power efficiency than GPUs. Code: https://github.com/OswaldHe/InTAR

Automatic Differentiation (AD) has become a dominant technique in ML. AD frameworks have first been implemented for imperative languages using tapes. Meanwhile, functional implementations of AD have been developed, often based on dual numbers, which are close to the formal specification of differentiation and hence easier to prove correct. But these papers have focussed on correctness not efficiency. Recently, it was shown how an approach using dual numbers could be made efficient through the right optimizations. Optimizations are highly dependent on order, as one optimization can enable another. It can therefore be useful to have fine-grained control over the scheduling of optimizations. One method expresses compiler optimizations as rewrite rules, whose application can be combined and controlled using strategy languages. Previous work describes the use of term rewriting and strategies to generate high-performance code in a compiler for a functional language. In this work, we implement dual numbers AD in a functional array programming language using rewrite rules and strategy combinators for optimization. We aim to combine the elegance of differentiation using dual numbers with a succinct expression of the optimization schedule using a strategy language. We give preliminary evidence suggesting the viability of the approach on a micro-benchmark.

We introduce Reprompting, an iterative sampling algorithm that searches for the Chain-of-Thought (CoT) recipes for a given task without human intervention. Through Gibbs sampling, we infer CoT recipes that work consistently well for a set of training samples. Our method iteratively samples new recipes using previously sampled solutions as parent prompts to solve other training problems. On five Big-Bench Hard tasks that require multi-step reasoning, Reprompting achieves consistently better performance than the zero-shot, few-shot, and human-written CoT baselines. Reprompting can also facilitate transfer of knowledge from a stronger model to a weaker model leading to substantially improved performance of the weaker model. Overall, Reprompting brings up to +17 point improvements over the previous state-of-the-art method that uses human-written CoT prompts.

Consistency models are a new family of generative models capable of producing high-quality samples in either a single step or multiple steps. Recently, consistency models have demonstrated impressive performance, achieving results on par with diffusion models in the pixel space. However, the success of scaling consistency training to large-scale datasets, particularly for text-to-image and video generation tasks, is determined by performance in the latent space. In this work, we analyze the statistical differences between pixel and latent spaces, discovering that latent data often contains highly impulsive outliers, which significantly degrade the performance of iCT in the latent space. To address this, we replace Pseudo-Huber losses with Cauchy losses, effectively mitigating the impact of outliers. Additionally, we introduce a diffusion loss at early timesteps and employ optimal transport (OT) coupling to further enhance performance. Lastly, we introduce the adaptive scaling-c scheduler to manage the robust training process and adopt Non-scaling LayerNorm in the architecture to better capture the statistics of the features and reduce outlier impact. With these strategies, we successfully train latent consistency models capable of high-quality sampling with one or two steps, significantly narrowing the performance gap between latent consistency and diffusion models. The implementation is released here: https://github.com/quandao10/sLCT/

Diffusion models have been widely adopted in image and video generation. However, their complex network architecture leads to high inference overhead for its generation process. Existing diffusion quantization methods primarily focus on the quantization of the model structure while ignoring the impact of time-steps variation during sampling. At the same time, most current approaches fail to account for significant activations that cannot be eliminated, resulting in substantial performance degradation after quantization. To address these issues, we propose Time-Rotation Diffusion Quantization (TR-DQ), a novel quantization method incorporating time-step and rotation-based optimization. TR-DQ first divides the sampling process based on time-steps and applies a rotation matrix to smooth activations and weights dynamically. For different time-steps, a dedicated hyperparameter is introduced for adaptive timing modeling, which enables dynamic quantization across different time steps. Additionally, we also explore the compression potential of Classifier-Free Guidance (CFG-wise) to establish a foundation for subsequent work. TR-DQ achieves state-of-the-art (SOTA) performance on image generation and video generation tasks and a 1.38-1.89x speedup and 1.97-2.58x memory reduction in inference compared to existing quantization methods.

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

In this work, we introduce MO-SeGMan, a Multi-Objective Sequential and Guided Manipulation planner for highly constrained rearrangement problems. MO-SeGMan generates object placement sequences that minimize both replanning per object and robot travel distance while preserving critical dependency structures with a lazy evaluation method. To address highly cluttered, non-monotone scenarios, we propose a Selective Guided Forward Search (SGFS) that efficiently relocates only critical obstacles and to feasible relocation points. Furthermore, we adopt a refinement method for adaptive subgoal selection to eliminate unnecessary pick-and-place actions, thereby improving overall solution quality. Extensive evaluations on nine benchmark rearrangement tasks demonstrate that MO-SeGMan generates feasible motion plans in all cases, consistently achieving faster solution times and superior solution quality compared to the baselines. These results highlight the robustness and scalability of the proposed framework for complex rearrangement planning problems.

Modern recurrent architectures, such as xLSTM and Mamba, have recently challenged the Transformer in language modeling. However, their structure constrains their applicability to sequences only or requires processing multi-dimensional data structures, such as images or molecular graphs, in a pre-defined sequential order. In contrast, Multi-Dimensional RNNs (MDRNNs) are well suited for data with a higher level structure, like 2D grids, trees, and directed acyclic graphs (DAGs). In this work, we extend the notion of multi-dimensionality to linear RNNs. We introduce parallelizable Linear Source Transition Mark networks (pLSTMs) using Source, Transition, and Mark gates that act on the line graph of a general DAG. This enables parallelization in analogy to parallel associative scans and the chunkwise-recurrent form of sequential linear RNNs, but for DAGs. For regular grids (1D and 2D), like images, this scheme can be efficiently implemented using einsum operations, concatenations, and padding in logarithmic time. pLSTMs tackle the vanishing/exploding activation/gradient problem for long distances in DAGs via two distinct modes: a directed propagation mode (P-mode) and a diffusive distribution mode (D-mode). To showcase the long-range capabilities of pLSTM, we introduce arrow-pointing extrapolation as a synthetic computer vision task that contains long-distance directional information. We demonstrate that pLSTMs generalize well to larger image sizes, whereas Transformers struggle to extrapolate. On established molecular graph and computer vision benchmarks, pLSTMs also show strong performance. Code and Datasets are available at: https://github.com/ml-jku/plstm_experiments.

Since Isaac Newton first studied the Kissing Number Problem in 1694, determining the maximal number of non-overlapping spheres around a central sphere has remained a fundamental challenge. This problem is the local analogue of Hilbert's 18th problem, bridging geometry, number theory, and information theory. Although significant progress has been made through lattices and codes, the irregularities of high-dimensional geometry, dimensional structure variability, and combinatorial explosion beyond Go limit the scalability and generality of existing methods. Here we model the problem as a two-player matrix completion game and train the reinforcement learning system, PackingStar, to play the games. The matrix entries represent pairwise cosines of sphere center vectors. One player fills entries while another corrects suboptimal ones to improve exploration quality, cooperatively maximizing the matrix size, corresponding to the kissing number. These matrices are decomposed into representative substructures, providing diverse bases and structural constraints that steer subsequent games and make extremely large spaces tractable. PackingStar surpasses records from dimensions 25 to 31 and sets new lower bounds for generalized kissing numbers under various angular constraints. It achieves the first breakthrough beyond rational structures from 1971 in 13 dimensions and discovers over 6000 new structures in other dimensions. Notably, some configurations challenge long-held antipodal paradigms, revealing algebraic correspondences with finite simple groups as well as geometric relationships across dimensions. Inspired by these patterns, humans devised further improved constructions. These results demonstrate AI's power to explore high-dimensional spaces beyond human intuition via extreme-scale reinforcement learning and open new pathways for the Kissing Number Problem and broader geometry research.

3D Gaussian Splatting (3DGS) optimization is most commonly performed using standard optimizers (Adam, SGD). While stable across diverse scenes, standard optimizers are general-purpose and not tailored to the structure of the problem. In particular, they produce independent parameter updates that do not capture the structural and spatial relationships within a scene, leading to inefficient optimization and slow convergence. Recent works introduced learned optimizers that predict correlated updates informed by inter-parameter and inter-Gaussian dependencies. However, these methods are trained for a fixed number of optimization iterations and rely on manually scheduled learning rates to avoid degradation. In this paper, we introduce a learned optimizer for 3DGS that avoids degradation over extended optimization horizons without auxiliary mechanisms. To enable this, we propose a meta-learning scheme that extends the optimization horizon via a checkpoint buffer and an optimizer rollout strategy, combined with an architecture that encodes gradient scale information in its latent states. Results show improved early novel view synthesis quality while remaining stable over long horizons, with zero-shot generalization to unseen reconstruction settings. To support our findings, we introduce the first unified framework for training and evaluating both learned and conventional optimizers across sparse and dense view settings. Code and models will be released publicly. Our project page is available at https://naamapearl.github.io/learn2splat .

We introduce WARP (Weight-space Adaptive Recurrent Prediction), a simple yet powerful model that unifies weight-space learning with linear recurrence to redefine sequence modeling. Unlike conventional recurrent neural networks (RNNs) which collapse temporal dynamics into fixed-dimensional hidden states, WARP explicitly parametrizes its hidden state as the weights and biases of a distinct auxiliary neural network, and uses input differences to drive its recurrence. This brain-inspired formulation enables efficient gradient-free adaptation of the auxiliary network at test-time, in-context learning abilities, and seamless integration of domain-specific physical priors. Empirical validation shows that WARP matches or surpasses state-of-the-art baselines on diverse classification tasks, featuring in the top three in 5 out of 6 real-world challenging datasets. Furthermore, extensive experiments across sequential image completion, multivariate time series forecasting, and dynamical system reconstruction demonstrate its expressiveness and generalisation capabilities. Remarkably, a physics-informed variant of our model outperforms the next best model by more than 10x. Ablation studies confirm the architectural necessity of key components, solidifying weight-space linear RNNs as a transformative paradigm for adaptive machine intelligence.

Scaling of deep neural networks, especially Transformers, is pivotal for their surging performance and has further led to the emergence of sophisticated reasoning capabilities in foundation models. Such scaling generally requires training large models from scratch with random initialization, failing to leverage the knowledge acquired by their smaller counterparts, which are already resource-intensive to obtain. To tackle this inefficiency, we present LosslEss MOdel ExpansioN (LEMON), a recipe to initialize scaled models using the weights of their smaller but pre-trained counterparts. This is followed by model training with an optimized learning rate scheduler tailored explicitly for the scaled models, substantially reducing the training time compared to training from scratch. Notably, LEMON is versatile, ensuring compatibility with various network structures, including models like Vision Transformers and BERT. Our empirical results demonstrate that LEMON reduces computational costs by 56.7% for Vision Transformers and 33.2% for BERT when compared to training from scratch.

In lung radiotherapy, infrared cameras can track reflective objects on the chest to estimate tumor motion due to breathing, but treatment system latencies hinder radiation beam precision. Real-time recurrent learning (RTRL) is a potential solution that can learn patterns within non-stationary respiratory data but has high complexity. This study assesses the capabilities of resource-efficient online RNN algorithms, namely unbiased online recurrent optimization (UORO), sparse-1 step approximation (SnAp-1), and decoupled neural interfaces (DNI) to forecast respiratory motion during radiotherapy treatment accurately. We use time series containing the 3D positions of external markers on the chest of healthy subjects. We propose efficient implementations for SnAp-1 and DNI that compress the influence and immediate Jacobian matrices and accurately update the linear coefficients used in credit assignment estimation, respectively. Data was originally sampled at 10Hz; we resampled it at 3.33Hz and 30Hz to analyze the effect of the sampling rate on performance. We use UORO, SnAp-1, and DNI to forecast each marker's 3D position with horizons h<=2.1s (the time interval in advance for which the prediction is made) and compare them with RTRL, least mean squares, kernel support vector regression, and linear regression. RNNs trained online achieved similar or better accuracy than most previous works using larger training databases and deep learning, even though we used only the first minute of each sequence to predict motion within that exact sequence. SnAp-1 had the lowest normalized root mean square errors (nRMSEs) averaged over the horizon values considered, equal to 0.335 and 0.157, at 3.33Hz and 10.0Hz, respectively. Similarly, UORO had the lowest nRMSE at 30Hz, equal to 0.086. DNI's inference time (6.8ms per time step at 30Hz, Intel Core i7-13700 CPU) was the lowest among the RNN methods.

Artificial neural networks are a popular and effective machine learning technique. Great progress has been made parallelizing the expensive training phase of an individual network, leading to highly specialized pieces of hardware, many based on GPU-type architectures, and more concurrent algorithms such as synthetic gradients. However, the training phase continues to be a bottleneck, where the training data must be processed serially over thousands of individual training runs. This work considers a multigrid reduction in time (MGRIT) algorithm that is able to parallelize over the thousands of training runs and converge to the exact same solution as traditional training would provide. MGRIT was originally developed to provide parallelism for time evolution problems that serially step through a finite number of time-steps. This work recasts the training of a neural network similarly, treating neural network training as an evolution equation that evolves the network weights from one step to the next. Thus, this work concerns distributed computing approaches for neural networks, but is distinct from other approaches which seek to parallelize only over individual training runs. The work concludes with supporting numerical results for two model problems.

Production scheduling is highly susceptible to dynamic disruptions, such as variations in processing times, machine availability, and unexpected task insertions. Conventional approaches typically rely on event-specific models and explicit analytical formulations, which limits their adaptability and generalization across previously unseen disturbances. To overcome these limitations, this paper proposes DScheLLM, a dynamic scheduling approach that leverages fine-tuned large language models within a dual-system (fast-slow) reasoning architecture to address disturbances of different scales. A unified large language model-based framework is constructed to handle dynamic events, where training datasets for both fast and slow reasoning modes are generated using exact schedules obtained from an operations research solver. The Huawei OpenPangu Embedded-7B model is subsequently fine-tuned under the hybrid reasoning paradigms using LoRA. Experimental evaluations on standard job shop scheduling benchmarks demonstrate that the fast-thinking mode can efficiently generate high-quality schedules and the slow-thinking mode can produce solver-compatible and well-formatted decision inputs. To the best of our knowledge, this work represents one of the earliest studies applying large language models to job shop scheduling in dynamic environments, highlighting their considerable potential for intelligent and adaptive scheduling optimization.

Accurate mathematical reasoning with Large Language Models (LLMs) is crucial in revolutionizing domains that heavily rely on such reasoning. However, LLMs often encounter difficulties in certain aspects of mathematical reasoning, leading to flawed reasoning and erroneous results. To mitigate these issues, we introduce a novel mechanism, the Chain of Self-Correction (CoSC), specifically designed to embed self-correction as an inherent ability in LLMs, enabling them to validate and rectify their own results. The CoSC mechanism operates through a sequence of self-correction stages. In each stage, the LLMs generate a program to address a given problem, execute this program using program-based tools to obtain an output, subsequently verify this output. Based on the verification, the LLMs either proceed to the next correction stage or finalize the answer. This iterative self-correction process allows the LLMs to refine their reasoning steps and improve the accuracy of their mathematical reasoning. To enable the CoSC mechanism at a low cost, we employ a two-phase finetuning approach. In the first phase, the LLMs are trained with a relatively small volume of seeding data generated from GPT-4, establishing an initial CoSC capability. In the second phase, the CoSC capability is further enhanced by training with a larger volume of self-generated data using the trained model in the first phase, without relying on the paid GPT-4. Our comprehensive experiments demonstrate that CoSC significantly improves performance on traditional mathematical datasets among existing open-source LLMs. Notably, our CoSC-Code-34B model achieved a 53.5% score on MATH, the most challenging mathematical reasoning dataset in the public domain, surpassing the performance of well-established models such as ChatGPT, GPT-4, and even multi-modal LLMs like GPT-4V, Gemini-1.0 Pro, and Gemini-1.0 Ultra.

The task of video generation requires synthesizing visually realistic and temporally coherent video frames. Existing methods primarily use asynchronous auto-regressive models or synchronous diffusion models to address this challenge. However, asynchronous auto-regressive models often suffer from inconsistencies between training and inference, leading to issues such as error accumulation, while synchronous diffusion models are limited by their reliance on rigid sequence length. To address these issues, we introduce Auto-Regressive Diffusion (AR-Diffusion), a novel model that combines the strengths of auto-regressive and diffusion models for flexible, asynchronous video generation. Specifically, our approach leverages diffusion to gradually corrupt video frames in both training and inference, reducing the discrepancy between these phases. Inspired by auto-regressive generation, we incorporate a non-decreasing constraint on the corruption timesteps of individual frames, ensuring that earlier frames remain clearer than subsequent ones. This setup, together with temporal causal attention, enables flexible generation of videos with varying lengths while preserving temporal coherence. In addition, we design two specialized timestep schedulers: the FoPP scheduler for balanced timestep sampling during training, and the AD scheduler for flexible timestep differences during inference, supporting both synchronous and asynchronous generation. Extensive experiments demonstrate the superiority of our proposed method, which achieves competitive and state-of-the-art results across four challenging benchmarks.

This paper presents a novel approach, named the Group Marching Tree (GMT*) algorithm, to planning on GPUs at rates amenable to application within control loops, allowing planning in real-world settings via repeated computation of near-optimal plans. GMT*, like the Fast Marching Tree (FMT) algorithm, explores the state space with a "lazy" dynamic programming recursion on a set of samples to grow a tree of near-optimal paths. GMT*, however, alters the approach of FMT with approximate dynamic programming by expanding, in parallel, the group of all active samples with cost below an increasing threshold, rather than only the minimum cost sample. This group approximation enables low-level parallelism over the sample set and removes the need for sequential data structures, while the "lazy" collision checking limits thread divergence---all contributing to a very efficient GPU implementation. While this approach incurs some suboptimality, we prove that GMT* remains asymptotically optimal up to a constant multiplicative factor. We show solutions for complex planning problems under differential constraints can be found in ~10 ms on a desktop GPU and ~30 ms on an embedded GPU, representing a significant speed up over the state of the art, with only small losses in performance. Finally, we present a scenario demonstrating the efficacy of planning within the control loop (~100 Hz) towards operating in dynamic, uncertain settings.

We introduce the Series-Parallel Workflow Decomposition (SP\-WD) heuristic algorithm for the Workflow Scheduling Problem (WSP) decomposition. We demonstrate that the SPWD algorithm facilitates the scheduling of large WSP instances with the hybrid D-Wave Constrained Quadratic Model solver, enabling the scheduling of instances that would otherwise exceed its capacity limitations. We also describe the accompanying execution environment used to obtain the results of the experiments with real-life workflow instances available in the WfCommons standardization initiative repository.

Differentiable architecture search (DARTS) yields highly efficient gradient-based neural architecture search (NAS) by relaxing the discrete operation selection to optimize continuous architecture parameters that maps NAS from the discrete optimization to a continuous problem. DARTS then remaps the relaxed supernet back to the discrete space by one-off post-search pruning to obtain the final architecture (finalnet). Some emerging works argue that this remap is inherently prone to mismatch the network between training and evaluation which leads to performance discrepancy and even model collapse in extreme cases. We propose to close the gap between the relaxed supernet in training and the pruned finalnet in evaluation through utilizing small temperature to sparsify the continuous distribution in the training phase. To this end, we first formulate sparse-noisy softmax to get around gradient saturation. We then propose an exponential temperature schedule to better control the outbound distribution and elaborate an entropy-based adaptive scheme to finally achieve the enhancement. We conduct extensive experiments to verify the efficiency and efficacy of our method.

Hybrid methods have been shown to outperform pure statistical and pure deep learning methods at forecasting tasks and quantifying the associated uncertainty with those forecasts (prediction intervals). One example is Exponential Smoothing Recurrent Neural Network (ES-RNN), a hybrid between a statistical forecasting model and a recurrent neural network variant. ES-RNN achieves a 9.4\% improvement in absolute error in the Makridakis-4 Forecasting Competition. This improvement and similar outperformance from other hybrid models have primarily been demonstrated only on univariate datasets. Difficulties with applying hybrid forecast methods to multivariate data include (i) the high computational cost involved in hyperparameter tuning for models that are not parsimonious, (ii) challenges associated with auto-correlation inherent in the data, as well as (iii) complex dependency (cross-correlation) between the covariates that may be hard to capture. This paper presents Multivariate Exponential Smoothing Long Short Term Memory (MES-LSTM), a generalized multivariate extension to ES-RNN, that overcomes these challenges. MES-LSTM utilizes a vectorized implementation. We test MES-LSTM on several aggregated coronavirus disease of 2019 (COVID-19) morbidity datasets and find our hybrid approach shows consistent, significant improvement over pure statistical and deep learning methods at forecast accuracy and prediction interval construction.