Transformers come with a high computational cost, yet their effectiveness in addressing problems in language and vision has sparked extensive research aimed at enhancing their efficiency. However, diverse experimental conditions, spanning multiple input domains, prevent a fair comparison based solely on reported results, posing challenges for model selection. To address this gap in comparability, we design a comprehensive benchmark of more than 30 models for image classification, evaluating key efficiency aspects, including accuracy, speed, and memory usage. This benchmark provides a standardized baseline across the landscape of efficiency-oriented transformers and our framework of analysis, based on Pareto optimality, reveals surprising insights. Despite claims of other models being more efficient, ViT remains Pareto optimal across multiple metrics. We observe that hybrid attention-CNN models exhibit remarkable inference memory- and parameter-efficiency. Moreover, our benchmark shows that using a larger model in general is more efficient than using higher resolution images. Thanks to our holistic evaluation, we provide a centralized resource for practitioners and researchers, facilitating informed decisions when selecting transformers or measuring progress of the development of efficient transformers.
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With the advent of supercomputers, multi-processor environments and parallel-in-time (PinT) algorithms offer ways to solve initial value problems for ordinary and partial differential equations (ODEs and PDEs) over long time intervals, a task often unfeasible with sequential solvers within realistic time frames. A recent approach, GParareal, combines Gaussian Processes with traditional PinT methodology (Parareal) to achieve faster parallel speed-ups. The method is known to outperform Parareal for low-dimensional ODEs and a limited number of computer cores. Here, we present Nearest Neighbors GParareal (nnGParareal), a novel data-enriched PinT integration algorithm. nnGParareal builds upon GParareal by improving its scalability properties for higher-dimensional systems and increased processor count. Through data reduction, the model complexity is reduced from cubic to log-linear in the sample size, yielding a fast and automated procedure to integrate initial value problems over long time intervals. First, we provide both an upper bound for the error and theoretical details on the speed-up benefits. Then, we empirically illustrate the superior performance of nnGParareal, compared to GParareal and Parareal, on nine different systems with unique features (e.g., stiff, chaotic, high-dimensional, or challenging-to-learn systems).
The curse-of-dimensionality taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional PDEs, as Richard E. Bellman first pointed out over 60 years ago. While there has been some recent success in solving numerically partial differential equations (PDEs) in high dimensions, such computations are prohibitively expensive, and true scaling of general nonlinear PDEs to high dimensions has never been achieved. We develop a new method of scaling up physics-informed neural networks (PINNs) to solve arbitrary high-dimensional PDEs. The new method, called Stochastic Dimension Gradient Descent (SDGD), decomposes a gradient of PDEs into pieces corresponding to different dimensions and randomly samples a subset of these dimensional pieces in each iteration of training PINNs. We prove theoretically the convergence and other desired properties of the proposed method. We demonstrate in various diverse tests that the proposed method can solve many notoriously hard high-dimensional PDEs, including the Hamilton-Jacobi-Bellman (HJB) and the Schr\"{o}dinger equations in tens of thousands of dimensions very fast on a single GPU using the PINNs mesh-free approach. Notably, we solve nonlinear PDEs with nontrivial, anisotropic, and inseparable solutions in 100,000 effective dimensions in 12 hours on a single GPU using SDGD with PINNs. Since SDGD is a general training methodology of PINNs, it can be applied to any current and future variants of PINNs to scale them up for arbitrary high-dimensional PDEs.
According to many researchers, conceptual model (CM) development is a hard task, and system requirements are difficult to collect, causing many miscommunication problems. CMs require more than modeling ability alone - they first require an understanding of the targeted domain that the model attempts to represent. Accordingly, a preconceptual modeling (pre-CM) stage is intended to address ontological issues before typical CM development is initiated. It involves defining a portion of reality when entities and processes are differentiated and integrated as unified wholes. This pre-CM phase forms the focus of research in this paper. The purpose is not show how to model; rather, it is to demonstrate how to establish a metaphysical basis of the involved portion of reality. To demonstrate such a venture, we employ the so-called thinging machine (TM) modeling that has been proposed as a high-level CM. A TM model integrates staticity and dynamism grounded in a fundamental construct called a thimac (things/machine). It involves two modes of reality, existence (events) and subsistence (regions - roughly, specifications of things and processes). Currently, the dominant approach in CM has evolved to limit its scope of application to develop ontological categorization (types of things). In the TM approach, pre-CM metaphysics is viewed as a part and parcel of CM itself. The general research problem is how to map TM constructs to what is out there in the targeted domain. Discussions involve the nature of thimacs (things and processes) and subsistence and existence as they are superimposed over each other in reality. Specifically, we make two claims, (a) the perceptibility of regions as a phenomenon and (b) the distinctiveness of existence as a construct for events. The results contribute to further the understanding of TM modeling in addition to introducing some metaphysical insights.
The way heuristic optimizers are designed has evolved over the decades, as computing power has increased. Initially, trajectory metaheuristics used to shape the state of the art in many problems, whereas today, population-based mechanisms tend to be more effective.Such has been the case for the Linear Ordering Problem (LOP), a field in which strategies such as Iterated Local Search and Variable Neighborhood Search led the way during the 1990s, but which have now been surpassed by evolutionary and memetic schemes. This paper focuses on understanding how the design of LOP optimizers will change in the future, as computing power continues to increase, yielding two main contributions. On the one hand, a metaheuristic was designed that is capable of effectively exploiting a large amount of computational resources, specifically, computing power equivalent to what a recent core can output during runs lasting over four months. Our analysis of this aspect relied on parallelization, and allowed us to conclude that as the power of the computational resources increases, it will be necessary to boost the capacities of the intensification methods applied in the memetic algorithms to keep the population from stagnating. And on the other, the best-known results for today's most challenging set of instances (xLOLIB2) were significantly outperformed. Instances with sizes ranging from 300 to 1000 were analyzed, and new bounds were established that provide a frame of reference for future research.
Quantization for CNN has shown significant progress with the intention of reducing the cost of computation and storage with low-bitwidth data representations. There are, however, no systematic studies on how an existing full-bitwidth processing unit, such as ALU in CPUs and DSP in FPGAs, can be better utilized to deliver significantly higher computation throughput for convolution under various quantized bitwidths. In this study, we propose HiKonv, a unified solution that maximizes the throughput of convolution on a given underlying processing unit with low-bitwidth quantized data inputs through novel bit-wise management and parallel computation. We establish theoretical framework and performance models using a full-bitwidth multiplier for highly parallelized low-bitwidth convolution, and demonstrate new breakthroughs for high-performance computing in this critical domain. For example, a single 32-bit processing unit in CPU can deliver 128 binarized convolution operations (multiplications and additions) and 13 4-bit convolution operations with a single multiplication instruction, and a single 27x18 multiplier in the FPGA DSP can deliver 60, 8 or 2 convolution operations with 1, 4 or 8-bit inputs in one clock cycle. We demonstrate the effectiveness of HiKonv on both CPU and FPGA. On CPU, HiKonv outperforms the baseline implementation with 1 to 8-bit inputs and provides up to 7.6x and 1.4x performance improvements for 1-D convolution, and performs 2.74x and 3.19x over the baseline implementation for 4-bit signed and unsigned data inputs for 2-D convolution. On FPGA, HiKonv solution enables a single DSP to process multiple convolutions with a shorter processing latency. For binarized input, each DSP with HiKonv is equivalent up to 76.6 LUTs. Compared to the DAC-SDC 2020 champion model, HiKonv achieves a 2.37x throughput improvement and 2.61x DSP efficiency improvement, respectively.
In pace with developments in the research field of artificial intelligence, knowledge graphs (KGs) have attracted a surge of interest from both academia and industry. As a representation of semantic relations between entities, KGs have proven to be particularly relevant for natural language processing (NLP), experiencing a rapid spread and wide adoption within recent years. Given the increasing amount of research work in this area, several KG-related approaches have been surveyed in the NLP research community. However, a comprehensive study that categorizes established topics and reviews the maturity of individual research streams remains absent to this day. Contributing to closing this gap, we systematically analyzed 507 papers from the literature on KGs in NLP. Our survey encompasses a multifaceted review of tasks, research types, and contributions. As a result, we present a structured overview of the research landscape, provide a taxonomy of tasks, summarize our findings, and highlight directions for future work.
Recently, Mutual Information (MI) has attracted attention in bounding the generalization error of Deep Neural Networks (DNNs). However, it is intractable to accurately estimate the MI in DNNs, thus most previous works have to relax the MI bound, which in turn weakens the information theoretic explanation for generalization. To address the limitation, this paper introduces a probabilistic representation of DNNs for accurately estimating the MI. Leveraging the proposed MI estimator, we validate the information theoretic explanation for generalization, and derive a tighter generalization bound than the state-of-the-art relaxations.
Influenced by the stunning success of deep learning in computer vision and language understanding, research in recommendation has shifted to inventing new recommender models based on neural networks. In recent years, we have witnessed significant progress in developing neural recommender models, which generalize and surpass traditional recommender models owing to the strong representation power of neural networks. In this survey paper, we conduct a systematic review on neural recommender models, aiming to summarize the field to facilitate future progress. Distinct from existing surveys that categorize existing methods based on the taxonomy of deep learning techniques, we instead summarize the field from the perspective of recommendation modeling, which could be more instructive to researchers and practitioners working on recommender systems. Specifically, we divide the work into three types based on the data they used for recommendation modeling: 1) collaborative filtering models, which leverage the key source of user-item interaction data; 2) content enriched models, which additionally utilize the side information associated with users and items, like user profile and item knowledge graph; and 3) context enriched models, which account for the contextual information associated with an interaction, such as time, location, and the past interactions. After reviewing representative works for each type, we finally discuss some promising directions in this field, including benchmarking recommender systems, graph reasoning based recommendation models, and explainable and fair recommendations for social good.
Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.
Recent years have witnessed the enormous success of low-dimensional vector space representations of knowledge graphs to predict missing facts or find erroneous ones. Currently, however, it is not yet well-understood how ontological knowledge, e.g. given as a set of (existential) rules, can be embedded in a principled way. To address this shortcoming, in this paper we introduce a framework based on convex regions, which can faithfully incorporate ontological knowledge into the vector space embedding. Our technical contribution is two-fold. First, we show that some of the most popular existing embedding approaches are not capable of modelling even very simple types of rules. Second, we show that our framework can represent ontologies that are expressed using so-called quasi-chained existential rules in an exact way, such that any set of facts which is induced using that vector space embedding is logically consistent and deductively closed with respect to the input ontology.
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