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We present an extension of the summation-by-parts (SBP) framework to tensor-product spectral-element operators in collapsed coordinates. The proposed approach enables the construction of provably stable discretizations of arbitrary order which combine the geometric flexibility of unstructured triangular and tetrahedral meshes with the efficiency of sum-factorization algorithms. Specifically, a methodology is developed for constructing triangular and tetrahedral spectral-element operators of any order which possess the SBP property (i.e. satisfying a discrete analogue of integration by parts) as well as a tensor-product decomposition. Such operators are then employed within the context of discontinuous spectral-element methods based on nodal expansions collocated at the tensor-product quadrature nodes as well as modal expansions employing Proriol-Koornwinder-Dubiner polynomials, the latter approach resolving the time step limitation associated with the singularity of the collapsed coordinate transformation. Energy-stable formulations for curvilinear meshes are obtained using a skew-symmetric splitting of the metric terms, and a weight-adjusted approximation is used to efficiently invert the curvilinear modal mass matrix. The proposed schemes are compared to those using non-tensorial multidimensional SBP operators, and are found to offer comparable accuracy to such schemes in the context of smooth linear advection problems on curved meshes, but at a reduced computational cost for higher polynomial degrees.

An individualised head-related transfer function (HRTF) is essential for creating realistic virtual reality (VR) and augmented reality (AR) environments. However, acoustically measuring high-quality HRTFs requires expensive equipment and an acoustic lab setting. To overcome these limitations and to make this measurement more efficient HRTF upsampling has been exploited in the past where a high-resolution HRTF is created from a low-resolution one. This paper demonstrates how generative adversarial networks (GANs) can be applied to HRTF upsampling. We propose a novel approach that transforms the HRTF data for convenient use with a convolutional super-resolution generative adversarial network (SRGAN). This new approach is benchmarked against two baselines: barycentric upsampling and a HRTF selection approach. Experimental results show that the proposed method outperforms both baselines in terms of log-spectral distortion (LSD) and localisation performance using perceptual models when the input HRTF is sparse.

Uncertainty quantification (UQ) is important for reliability assessment and enhancement of machine learning models. In deep learning, uncertainties arise not only from data, but also from the training procedure that often injects substantial noises and biases. These hinder the attainment of statistical guarantees and, moreover, impose computational challenges on UQ due to the need for repeated network retraining. Building upon the recent neural tangent kernel theory, we create statistically guaranteed schemes to principally \emph{quantify}, and \emph{remove}, the procedural uncertainty of over-parameterized neural networks with very low computation effort. In particular, our approach, based on what we call a procedural-noise-correcting (PNC) predictor, removes the procedural uncertainty by using only \emph{one} auxiliary network that is trained on a suitably labeled data set, instead of many retrained networks employed in deep ensembles. Moreover, by combining our PNC predictor with suitable light-computation resampling methods, we build several approaches to construct asymptotically exact-coverage confidence intervals using as low as four trained networks without additional overheads.

Parameter inference for ordinary differential equations (ODEs) is of fundamental importance in many scientific applications. While ODE solutions are typically approximated by deterministic algorithms, new research on probabilistic solvers indicates that they produce more reliable parameter estimates by better accounting for numerical errors. However, many ODE systems are highly sensitive to their parameter values. This produces deep local minima in the likelihood function -- a problem which existing probabilistic solvers have yet to resolve. Here, we show that a Bayesian filtering paradigm for probabilistic ODE solution can dramatically reduce sensitivity to parameters by learning from the noisy ODE observations in a data-adaptive manner. Our method is applicable to ODEs with partially unobserved components and with arbitrary non-Gaussian noise. Several examples demonstrate that it is more accurate than existing probabilistic ODE solvers, and even in some cases than the exact ODE likelihood.

This paper formulates, analyzes, and demonstrates numerically a method for the partitioned solution of coupled interface problems involving combinations of projection-based reduced order models (ROM) and/or full order methods (FOMs). The method builds on the partitioned scheme developed in [1], which starts from a well-posed formulation of the coupled interface problem and uses its dual Schur complement to obtain an approximation of the interface flux. Explicit time integration of this problem decouples its subdomain equations and enables their independent solution on each subdomain. Extension of this partitioned scheme to coupled ROM-ROM or ROM-FOM problems required formulations with non-singular Schur complements. To obtain these problems, we project a well-posed coupled FOM-FOM problem onto a composite reduced basis comprising separate sets of basis vectors for the interface and interior variables, and use the interface reduced basis as a Lagrange multiplier. Our analysis confirms that the resulting coupled ROM-ROM and ROM-FOM problems have provably non-singular Schur complements, independent of the mesh size and the reduced basis size. In the ROM-FOM case, analysis shows that one can also use the interface FOM space as a Lagrange multiplier. We illustrate the theoretical and computational properties of the partitioned scheme through reproductive and predictive tests for a model advection-diffusion transmission problem.

Diffusion models are powerful generative models but suffer from slow sampling, often taking 1000 sequential denoising steps for one sample. As a result, considerable efforts have been directed toward reducing the number of denoising steps, but these methods hurt sample quality. Instead of reducing the number of denoising steps (trading quality for speed), in this paper we explore an orthogonal approach: can we run the denoising steps in parallel (trading compute for speed)? In spite of the sequential nature of the denoising steps, we show that surprisingly it is possible to parallelize sampling via Picard iterations, by guessing the solution of future denoising steps and iteratively refining until convergence. With this insight, we present ParaDiGMS, a novel method to accelerate the sampling of pretrained diffusion models by denoising multiple steps in parallel. ParaDiGMS is the first diffusion sampling method that enables trading compute for speed and is even compatible with existing fast sampling techniques such as DDIM and DPMSolver. Using ParaDiGMS, we improve sampling speed by 2-4x across a range of robotics and image generation models, giving state-of-the-art sampling speeds of 0.2s on 100-step DiffusionPolicy and 16s on 1000-step StableDiffusion-v2 with no measurable degradation of task reward, FID score, or CLIP score.

Diffusion models have been remarkably successful in data synthesis. Such successes have also driven diffusion models to apply to sensitive data, such as human face data, but this might bring about severe privacy concerns. In this work, we systematically present the first privacy study about property inference attacks against diffusion models, in which adversaries aim to extract sensitive global properties of the training set from a diffusion model, such as the proportion of the training data for certain sensitive properties. Specifically, we consider the most practical attack scenario: adversaries are only allowed to obtain synthetic data. Under this realistic scenario, we evaluate the property inference attacks on different types of samplers and diffusion models. A broad range of evaluations shows that various diffusion models and their samplers are all vulnerable to property inference attacks. Furthermore, one case study on off-the-shelf pre-trained diffusion models also demonstrates the effectiveness of the attack in practice. Finally, we propose a new model-agnostic plug-in method PriSampler to mitigate the property inference of diffusion models. PriSampler can be directly applied to well-trained diffusion models and support both stochastic and deterministic sampling. Extensive experiments illustrate the effectiveness of our defense and it makes adversaries infer the proportion of properties as close as random guesses. PriSampler also shows its significantly superior performance to diffusion models trained with differential privacy on both model utility and defense performance.

Data is a precious resource in today's society, and is generated at an unprecedented and constantly growing pace. The need to store, analyze, and make data promptly available to a multitude of users introduces formidable challenges in modern software platforms. These challenges radically transformed all research fields that gravitate around data management and processing, with the introduction of distributed data-intensive systems that offer new programming models and implementation strategies to handle data characteristics such as its volume, the rate at which it is produced, its heterogeneity, and its distribution. Each data-intensive system brings its specific choices in terms of data model, usage assumptions, synchronization, processing strategy, deployment, guarantees in terms of consistency, fault tolerance, ordering. Yet, the problems data-intensive systems face and the solutions they propose are frequently overlapping. This paper proposes a unifying model that dissects the core functionalities of data-intensive systems, and precisely discusses alternative design and implementation strategies, pointing out their assumptions and implications. The model offers a common ground to understand and compare highly heterogeneous solutions, with the potential of fostering cross-fertilization across research communities and advancing the field. We apply our model by classifying tens of systems: an exercise that brings to interesting observations on the current trends in the domain of data-intensive systems and suggests open research directions.

Computer Architecture, broadly, involves optimizing hardware and software for current and future processing systems. Although there are several other top venues to publish Computer Architecture research, including ASPLOS, HPCA, and MICRO, ISCA (the International Symposium on Computer Architecture) is one of the oldest, longest running, and most prestigious venues for publishing Computer Architecture research. Since 1973, except for 1975, ISCA has been organized annually. Accordingly, this year will be the 50th year of ISCA. Thus, we set out to analyze the past 50 years of ISCA to understand who and what has been driving and innovating computing systems in that timeframe. This analysis is intended to be a celebration of the first 50 years of ISCA. Thus, the scope should be viewed accordingly. Although we took care to practice good data collection and sanitation in our analysis (Section 2), given the long time frame and issues with digital records for early years of the conference, there may be some errors and rounding-off artifacts. Please reach out if you have any corrections and we can update our Arxiv draft to reflect this errata. Finally, while the collected data and analysis highlight several interesting trends, akin to the cautionary comment from the ISCA Hall of Fame website ("A real Hall of Fame should be determined by impact, not paper count."), we want to acknowledge that some of our numbers may only reflect a partial narrative. That said, our exercise still highlights several interesting trends that we think will be insightful to the broader community.

Learning on big data brings success for artificial intelligence (AI), but the annotation and training costs are expensive. In future, learning on small data is one of the ultimate purposes of AI, which requires machines to recognize objectives and scenarios relying on small data as humans. A series of machine learning models is going on this way such as active learning, few-shot learning, deep clustering. However, there are few theoretical guarantees for their generalization performance. Moreover, most of their settings are passive, that is, the label distribution is explicitly controlled by one specified sampling scenario. This survey follows the agnostic active sampling under a PAC (Probably Approximately Correct) framework to analyze the generalization error and label complexity of learning on small data using a supervised and unsupervised fashion. With these theoretical analyses, we categorize the small data learning models from two geometric perspectives: the Euclidean and non-Euclidean (hyperbolic) mean representation, where their optimization solutions are also presented and discussed. Later, some potential learning scenarios that may benefit from small data learning are then summarized, and their potential learning scenarios are also analyzed. Finally, some challenging applications such as computer vision, natural language processing that may benefit from learning on small data are also surveyed.