Garbage Collection (GC) in the Java Virtual Machine (JVM) serves as an automatic memory management mechanism, efficiently reclaiming unused memory space in different production scenarios. To optimize JVM performance, developers typically fine-tune the garbage collector by identifying an optimal set of GC configurations for specific scenarios. Despite the sophisticated design of garbage collectors, they still have the potential for bugs in different settings, and these bugs can result in more severe consequences. Hence, comprehensive testing of these garbage collectors is imperative before their release. Code coverage criteria are typically employed to assess the comprehensiveness of a test suite. However, traditional code coverage metrics, such as branch coverage, are hardly applicable for GC testing due to their inherent concurrency. Additionally, existing JVM testing techniques do not adequately consider the characteristics of garbage collectors, making it difficult to test these garbage collectors sufficiently. In this article, we make the first effort to design coverage criteria against garbage collectors based on the events of GC called Event-Coverage . Its key insight is to measure the diversity of GC executions for testing purposes by assessing the range of GC events these executions cover. Furthermore, we design a new testing method for maximizing Event-Coverage called GCFuzz . GCFuzz conducts an exhaustive investigation of the memory state space of GC and thoroughly explores the memory state under various GC configurations. To enhance GCFuzz’s efficiency in achieving higher Event-Coverage, we have further designed a coverage-driven strategy for preserving candidate seed programs and selecting GC configurations. Extensive evaluations demonstrate a positive correlation between Event-Coverage and the bug-revealing efficiency. Moreover, GCFuzz outperforms state-of-the-art techniques in detecting unique GC-related inconsistencies and achieving higher Event-Coverage. Remarkably, GCFuzz has identified 20 previously undetected GC bugs, with 15 of them already confirmed or fixed by developers.

Graph spectra are an important class of structural features on graphs that have shown promising results in enhancing Graph Neural Networks (GNNs). Despite their widespread practical use, the theoretical understanding of the power of spectral invariants --- particularly their contribution to GNNs --- remains incomplete. In this paper, we address this fundamental question through the lens of homomorphism expressivity, providing a comprehensive and quantitative analysis of the expressive power of spectral invariants. Specifically, we prove that spectral invariant GNNs can homomorphism-count exactly a class of specific tree-like graphs which we refer to as \emph{parallel trees}. We highlight the significance of this result in various contexts, including establishing a quantitative expressiveness hierarchy across different architectural variants, offering insights into the impact of GNN depth, and understanding the subgraph counting capabilities of spectral invariant GNNs. In particular, our results significantly extend \citet{arvind2024hierarchy} and settle their open questions. Finally, we generalize our analysis to higher-order GNNs and answer an open question raised by \citet{zhang2024expressive}.

Computationally resolving turbulence remains a central challenge in fluid dynamics due to its multi-scale interactions. Fully resolving large-scale turbulence through direct numerical simulation (DNS) is computationally prohibitive, motivating data-driven machine learning alternatives. In this work, we propose EddyFormer, a Transformer-based spectral-element (SEM) architecture for large-scale turbulence simulation that combines the accuracy of spectral methods with the scalability of the attention mechanism. We introduce an SEM tokenization that decomposes the flow into grid-scale and subgrid-scale components, enabling capture of both local and global features. We create a new three-dimensional isotropic turbulence dataset and train EddyFormer to achieves DNS-level accuracy at 256^3 resolution, providing a 30x speedup over DNS. When applied to unseen domains up to 4x larger than in training, EddyFormer preserves accuracy on physics-invariant metrics-energy spectra, correlation functions, and structure functions-showing domain generalization. On The Well benchmark suite of diverse turbulent flows, EddyFormer resolves cases where prior ML models fail to converge, accurately reproducing complex dynamics across a wide range of physical conditions.

Diffusion-based generative models struggle to maintain high style consistency across generated images via text description. Although several style-aligned image generation methods have been proposed to address this issue, they exhibit suboptimal performance and are primarily built upon the U-Net architecture, limiting their compatibility with DiT diffusion models like Flux that has emerged as a predominant model in the field of image generation. To address these limitations, we propose AlignedGen, a novel training-free style-aligned image generation method for DiT models to significantly enhance style consistency across generated images. Specifically, AlignedGen incorporates two key components to achieve this: Shifted Position Embedding (ShiftPE) and Advanced Attention Sharing (AAS). ShiftPE alleviates the text controllability degradation observed in prior methods when applied to DiT models through its non-overlapping position indices design, while AAS comprises three specialized techniques to unleash the full potential of DiT for style-aligned generation. Furthermore, to broaden the applicability of our method, we present an efficient query, key, and value feature extraction algorithm, enabling our method to seamlessly incorporate external images as style references. Extensive experimental results validate that our method effectively enhances style consistency across generated images while maintaining favorable text controllability. Code: https://github.com/Jiexuanz/AlignedGen.

With the CMOS technology advancing and the complexity of circuits growing, the demand for analog/mixed-signal design automation tools is increasing quickly. Although some tools have been developed to tackle this challenge, the performance degradation caused by process, voltage, and temperature (PVT) variations has been less considered. This paper presents PVTSizing, an optimization framework for PVT-robust analog circuit synthesis. PVTSizing adopts trust region Bayesian optimization (TuRBO) for high-quality initial datasets and reference points. Multi-task reinforcement learning (RL) is utilized for PVT optimization. Both TuRBO and RL are batch-friendly, allowing parallel sampling of design solutions. Meanwhile, critic-assisted pruning and zoom target metrics are proposed to improve sample efficiency and reduce runtime. In addition, this framework naturally supports sizing over random mismatch. On 4 real-world circuits with TSMC 28/180nm process, PVTSizing achieves 1.9X --8.8X sample efficiency and 1.6X --9.8X time efficiency improvements compared to prior sizing tools from both industry and academia.

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

We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral coefficients, instantiating a spectral-based neural operator. In contrast to current machine learning approaches which enforce PDE constraints by minimizing the numerical quadrature of the residuals in the spatiotemporal domain, we leverage Parseval's identity and introduce a new training strategy through a spectral loss. Our spectral loss enables more efficient differentiation through the neural network, and substantially reduces training complexity. At inference time, the computational cost of our method remains constant, regardless of the spatiotemporal resolution of the domain. Our experimental results demonstrate that our method significantly outperforms previous machine learning approaches in terms of speed and accuracy by one to two orders of magnitude on multiple different problems, including reaction-diffusion, and forced and unforced Navier-Stokes equations. When compared to numerical solvers of the same accuracy, our method demonstrates a $10\times$ increase in performance speed. Our source code is publicly available at https://github.com/ASK-Berkeley/Neural-Spectral-Methods.

Designing expressive Graph Neural Networks (GNNs) is a fundamental topic in the graph learning community. So far, GNN expressiveness has been primarily assessed via the Weisfeiler-Lehman (WL) hierarchy. However, such an expressivity measure has notable limitations: it is inherently coarse, qualitative, and may not well reflect practical requirements (e.g., the ability to encode substructures). In this paper, we introduce a novel framework for quantitatively studying the expressiveness of GNN architectures, addressing all the above limitations. Specifically, we identify a fundamental expressivity measure termed homomorphism expressivity, which quantifies the ability of GNN models to count graphs under homomorphism. Homomorphism expressivity offers a complete and practical assessment tool: the completeness enables direct expressivity comparisons between GNN models, while the practicality allows for understanding concrete GNN abilities such as subgraph counting. By examining four classes of prominent GNNs as case studies, we derive simple, unified, and elegant descriptions of their homomorphism expressivity for both invariant and equivariant settings. Our results provide novel insights into a series of previous work, unify the landscape of different subareas in the community, and settle several open questions. Empirically, extensive experiments on both synthetic and real-world tasks verify our theory, showing that the practical performance of GNN models aligns well with the proposed metric.

Deep learning recommendation models (DLRM) rely on large embedding tables to manage categorical sparse features. Expanding such embedding tables can significantly enhance model performance, but at the cost of increased GPU/CPU/memory usage. Meanwhile, tech companies have built extensive cloud-based services to accelerate training DLRM models at scale. In this paper, we conduct a deep investigation of the DLRM training platforms at AntGroup and reveal two critical challenges: low resource utilization due to suboptimal configurations by users and the tendency to encounter abnormalities due to an unstable cloud environment. To overcome them, we introduce DLRover, an elastic training framework for DLRMs designed to increase resource utilization and handle the instability of a cloud environment. DLRover develops a resource-performance model by considering the unique characteristics of DLRMs and a three-stage heuristic strategy to automatically allocate and dynamically adjust resources for DLRM training jobs for higher resource utilization. Further, DLRover develops multiple mechanisms to ensure efficient and reliable execution of DLRM training jobs. Our extensive evaluation shows that DLRover reduces job completion times by 31%, increases the job completion rate by 6%, enhances CPU usage by 15%, and improves memory utilization by 20%, compared to state-of-the-art resource scheduling frameworks. DLRover has been widely deployed at AntGroup and processes thousands of DLRM training jobs on a daily basis. DLRover is open-sourced and has been adopted by 10+ companies.

Recently, subgraph GNNs have emerged as an important direction for developing expressive graph neural networks (GNNs). While numerous architectures have been proposed, so far there is still a limited understanding of how various design paradigms differ in terms of expressive power, nor is it clear what design principle achieves maximal expressiveness with minimal architectural complexity. To address these fundamental questions, this paper conducts a systematic study of general node-based subgraph GNNs through the lens of Subgraph Weisfeiler-Lehman Tests (SWL). Our central result is to build a complete hierarchy of SWL with strictly growing expressivity. Concretely, we prove that any node-based subgraph GNN falls into one of the six SWL equivalence classes, among which $\mathsf{SSWL}$ achieves the maximal expressive power. We also study how these equivalence classes differ in terms of their practical expressiveness such as encoding graph distance and biconnectivity. In addition, we give a tight expressivity upper bound of all SWL algorithms by establishing a close relation with localized versions of WL and Folklore WL (FWL) tests. Overall, our results provide insights into the power of existing subgraph GNNs, guide the design of new architectures, and point out their limitations by revealing an inherent gap with the 2-FWL test. Finally, experiments demonstrate that $\mathsf{SSWL}$-inspired subgraph GNNs can significantly outperform prior architectures on multiple benchmarks despite great simplicity.