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The objective of Domain Generalization (DG) is to devise algorithms and models capable of achieving high performance on previously unseen test distributions. In the pursuit of this objective, average measure has been employed as the prevalent measure for evaluating models and comparing algorithms in the existing DG studies. Despite its significance, a comprehensive exploration of the average measure has been lacking and its suitability in approximating the true domain generalization performance has been questionable. In this study, we carefully investigate the limitations inherent in the average measure and propose worst+gap measure as a robust alternative. We establish theoretical grounds of the proposed measure by deriving two theorems starting from two different assumptions. We conduct extensive experimental investigations to compare the proposed worst+gap measure with the conventional average measure. Given the indispensable need to access the true DG performance for studying measures, we modify five existing datasets to come up with SR-CMNIST, C-Cats&Dogs, L-CIFAR10, PACS-corrupted, and VLCS-corrupted datasets. The experiment results unveil an inferior performance of the average measure in approximating the true DG performance and confirm the robustness of the theoretically supported worst+gap measure.

The ongoing artificial intelligence (AI) revolution has the potential to change almost every line of work. As AI capabilities continue to improve in accuracy, robustness, and reach, AI may outperform and even replace human experts across many valuable tasks. Despite enormous effort devoted to understanding the impact of AI on labor and the economy and AI's recent successes in accelerating scientific discovery and progress, we lack a systematic understanding of how AI advances may benefit scientific research across disciplines and fields. Here, drawing from the literature on the future of work and the science of science, we develop a measurement framework to estimate both the direct use of AI and the potential benefit of AI in scientific research, applying natural language processing techniques to 74.6 million publications and 7.1 million patents. We find that the use of AI in research is widespread throughout the sciences, growing especially rapidly since 2015, and papers that use AI exhibit a citation premium, more likely to be highly cited both within and outside their disciplines. Moreover, our analysis reveals considerable potential for AI to benefit numerous scientific fields, yet a notable disconnect exists between AI education and its research applications, highlighting a mismatch between the supply of AI expertise and its demand in research. Lastly, we examine demographic disparities in AI's benefits across scientific disciplines and find that disciplines with a higher proportion of women or Black scientists tend to be associated with less benefit, suggesting that AI's growing impact on research may further exacerbate existing inequalities in science. As the connection between AI and scientific research deepens, our findings may become increasingly important, with implications for the equity and sustainability of the research enterprise.

Algorithmic predictions are increasingly used to inform the allocations of goods and interventions in the public sphere. In these domains, predictions serve as a means to an end. They provide stakeholders with insights into likelihood of future events as a means to improve decision making quality, and enhance social welfare. However, if maximizing welfare is the ultimate goal, prediction is only a small piece of the puzzle. There are various other policy levers a social planner might pursue in order to improve bottom-line outcomes, such as expanding access to available goods, or increasing the effect sizes of interventions. Given this broad range of design decisions, a basic question to ask is: What is the relative value of prediction in algorithmic decision making? How do the improvements in welfare arising from better predictions compare to those of other policy levers? The goal of our work is to initiate the formal study of these questions. Our main results are theoretical in nature. We identify simple, sharp conditions determining the relative value of prediction vis-\`a-vis expanding access, within several statistical models that are popular amongst quantitative social scientists. Furthermore, we illustrate how these theoretical insights may be used to guide the design of algorithmic decision making systems in practice.

In the present paper, an algorithm for the numerical solution of the external Dirichlet generalized harmonic problem for a sphere by the method of probabilistic solution (MPS) is given, where generalized indicates that a boundary function has a finite number of first kind discontinuity curves. The algorithm consists of the following main stages: (1) the transition from an infinite domain to a finite domain by an inversion; (2) the consideration of a new Dirichlet generalized harmonic problem on the basis of Kelvin theorem for the obtained finite domain; (3) the numerical solution of the new problem for the finite domain by the MPS, which in turn is based on a computer simulation of the Weiner process; (4) finding the probabilistic solution of the posed generalized problem at any fixed points of the infinite domain by the solution of the new problem. For illustration, numerical examples are considered and results are presented.

The success of AI models relies on the availability of large, diverse, and high-quality datasets, which can be challenging to obtain due to data scarcity, privacy concerns, and high costs. Synthetic data has emerged as a promising solution by generating artificial data that mimics real-world patterns. This paper provides an overview of synthetic data research, discussing its applications, challenges, and future directions. We present empirical evidence from prior art to demonstrate its effectiveness and highlight the importance of ensuring its factuality, fidelity, and unbiasedness. We emphasize the need for responsible use of synthetic data to build more powerful, inclusive, and trustworthy language models.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

Graph Neural Networks (GNNs) have been studied from the lens of expressive power and generalization. However, their optimization properties are less well understood. We take the first step towards analyzing GNN training by studying the gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that despite the non-convexity of training, convergence to a global minimum at a linear rate is guaranteed under mild assumptions that we validate on real-world graphs. Second, we study what may affect the GNNs' training speed. Our results show that the training of GNNs is implicitly accelerated by skip connections, more depth, and/or a good label distribution. Empirical results confirm that our theoretical results for linearized GNNs align with the training behavior of nonlinear GNNs. Our results provide the first theoretical support for the success of GNNs with skip connections in terms of optimization, and suggest that deep GNNs with skip connections would be promising in practice.

Deep Convolutional Neural Networks have pushed the state-of-the art for semantic segmentation provided that a large amount of images together with pixel-wise annotations is available. Data collection is expensive and a solution to alleviate it is to use transfer learning. This reduces the amount of annotated data required for the network training but it does not get rid of this heavy processing step. We propose a method of transfer learning without annotations on the target task for datasets with redundant content and distinct pixel distributions. Our method takes advantage of the approximate content alignment of the images between two datasets when the approximation error prevents the reuse of annotation from one dataset to another. Given the annotations for only one dataset, we train a first network in a supervised manner. This network autonomously learns to generate deep data representations relevant to the semantic segmentation. Then the images in the new dataset, we train a new network to generate a deep data representation that matches the one from the first network on the previous dataset. The training consists in a regression between feature maps and does not require any annotations on the new dataset. We show that this method reaches performances similar to a classic transfer learning on the PASCAL VOC dataset with synthetic transformations.

While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, the most widely used perceptual metrics today, such as PSNR and SSIM, are simple, shallow functions, and fail to account for many nuances of human perception. Recently, the deep learning community has found that features of the VGG network trained on the ImageNet classification task has been remarkably useful as a training loss for image synthesis. But how perceptual are these so-called "perceptual losses"? What elements are critical for their success? To answer these questions, we introduce a new Full Reference Image Quality Assessment (FR-IQA) dataset of perceptual human judgments, orders of magnitude larger than previous datasets. We systematically evaluate deep features across different architectures and tasks and compare them with classic metrics. We find that deep features outperform all previous metrics by huge margins. More surprisingly, this result is not restricted to ImageNet-trained VGG features, but holds across different deep architectures and levels of supervision (supervised, self-supervised, or even unsupervised). Our results suggest that perceptual similarity is an emergent property shared across deep visual representations.