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The least-squares ReLU neural network (LSNN) method was introduced and studied for solving linear advection-reaction equation with discontinuous solution in \cite{Cai2021linear,cai2023least}. The method is based on an equivalent least-squares formulation and employs ReLU neural network (NN) functions with $\lceil \log_2(d+1)\rceil+1$-layer representations for approximating solutions. In this paper, we show theoretically that the method is also capable of approximating non-constant jumps along discontinuous interfaces that are not necessarily straight lines. Numerical results for test problems with various non-constant jumps and interfaces show that the LSNN method with $\lceil \log_2(d+1)\rceil+1$ layers approximates solutions accurately with degrees of freedom less than that of mesh-based methods and without the common Gibbs phenomena along discontinuous interfaces.

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神(shen)經(jing)(jing)(jing)網(wang)絡(luo)(luo)(Neural Networks)是世界(jie)上(shang)三個(ge)最古老的(de)(de)(de)(de)(de)神(shen)經(jing)(jing)(jing)建模學(xue)(xue)(xue)(xue)會(hui)的(de)(de)(de)(de)(de)檔案(an)期刊(kan):國(guo)際神(shen)經(jing)(jing)(jing)網(wang)絡(luo)(luo)學(xue)(xue)(xue)(xue)會(hui)(INNS)、歐洲神(shen)經(jing)(jing)(jing)網(wang)絡(luo)(luo)學(xue)(xue)(xue)(xue)會(hui)(ENNS)和(he)(he)(he)(he)日本(ben)神(shen)經(jing)(jing)(jing)網(wang)絡(luo)(luo)學(xue)(xue)(xue)(xue)會(hui)(JNNS)。神(shen)經(jing)(jing)(jing)網(wang)絡(luo)(luo)提(ti)供(gong)了一(yi)個(ge)論(lun)(lun)壇,以(yi)發(fa)展和(he)(he)(he)(he)培育(yu)一(yi)個(ge)國(guo)際社(she)會(hui)的(de)(de)(de)(de)(de)學(xue)(xue)(xue)(xue)者和(he)(he)(he)(he)實(shi)踐者感興(xing)(xing)趣(qu)的(de)(de)(de)(de)(de)所(suo)有方面(mian)的(de)(de)(de)(de)(de)神(shen)經(jing)(jing)(jing)網(wang)絡(luo)(luo)和(he)(he)(he)(he)相關方法(fa)的(de)(de)(de)(de)(de)計(ji)算(suan)(suan)智能(neng)。神(shen)經(jing)(jing)(jing)網(wang)絡(luo)(luo)歡迎高質量論(lun)(lun)文的(de)(de)(de)(de)(de)提(ti)交,有助(zhu)于全(quan)面(mian)的(de)(de)(de)(de)(de)神(shen)經(jing)(jing)(jing)網(wang)絡(luo)(luo)研究(jiu),從行為和(he)(he)(he)(he)大腦建模,學(xue)(xue)(xue)(xue)習算(suan)(suan)法(fa),通過(guo)數學(xue)(xue)(xue)(xue)和(he)(he)(he)(he)計(ji)算(suan)(suan)分(fen)析,系統的(de)(de)(de)(de)(de)工程(cheng)和(he)(he)(he)(he)技(ji)術(shu)應用,大量使(shi)用神(shen)經(jing)(jing)(jing)網(wang)絡(luo)(luo)的(de)(de)(de)(de)(de)概念和(he)(he)(he)(he)技(ji)術(shu)。這一(yi)獨特而廣(guang)泛(fan)的(de)(de)(de)(de)(de)范圍促進了生物和(he)(he)(he)(he)技(ji)術(shu)研究(jiu)之(zhi)間的(de)(de)(de)(de)(de)思想(xiang)交流,并有助(zhu)于促進對(dui)生物啟發(fa)的(de)(de)(de)(de)(de)計(ji)算(suan)(suan)智能(neng)感興(xing)(xing)趣(qu)的(de)(de)(de)(de)(de)跨學(xue)(xue)(xue)(xue)科(ke)社(she)區的(de)(de)(de)(de)(de)發(fa)展。因此,神(shen)經(jing)(jing)(jing)網(wang)絡(luo)(luo)編委會(hui)代表(biao)(biao)的(de)(de)(de)(de)(de)專(zhuan)家領域包括心(xin)理學(xue)(xue)(xue)(xue),神(shen)經(jing)(jing)(jing)生物學(xue)(xue)(xue)(xue),計(ji)算(suan)(suan)機科(ke)學(xue)(xue)(xue)(xue),工程(cheng),數學(xue)(xue)(xue)(xue),物理。該(gai)雜志發(fa)表(biao)(biao)文章(zhang)、信件和(he)(he)(he)(he)評論(lun)(lun)以(yi)及給(gei)編輯的(de)(de)(de)(de)(de)信件、社(she)論(lun)(lun)、時事、軟件調查和(he)(he)(he)(he)專(zhuan)利信息(xi)。文章(zhang)發(fa)表(biao)(biao)在五(wu)個(ge)部分(fen)之(zhi)一(yi):認知科(ke)學(xue)(xue)(xue)(xue),神(shen)經(jing)(jing)(jing)科(ke)學(xue)(xue)(xue)(xue),學(xue)(xue)(xue)(xue)習系統,數學(xue)(xue)(xue)(xue)和(he)(he)(he)(he)計(ji)算(suan)(suan)分(fen)析、工程(cheng)和(he)(he)(he)(he)應用。 官網(wang)地(di)址:

At present, large multimodal models (LMMs) have exhibited impressive generalization capabilities in understanding and generating visual signals. However, they currently still lack sufficient capability to perceive low-level visual quality akin to human perception. Can LMMs achieve this and show the same degree of generalization in this regard? If so, not only could the versatility of LMMs be further enhanced, but also the challenge of poor cross-dataset performance in the field of visual quality assessment could be addressed. In this paper, we explore this question and provide the answer "Yes!". As the result of this initial exploration, we present VisualCritic, the first LMM for broad-spectrum image subjective quality assessment. VisualCritic can be used across diverse data right out of box, without any requirements of dataset-specific adaptation operations like conventional specialist models. As an instruction-following LMM, VisualCritic enables new capabilities of (1) quantitatively measuring the perceptual quality of given images in terms of their Mean Opinion Score (MOS), noisiness, colorfulness, sharpness, and other numerical indicators, (2) qualitatively evaluating visual quality and providing explainable descriptions, (3) discerning whether a given image is AI-generated or photographic. Extensive experiments demonstrate the efficacy of VisualCritic by comparing it with other open-source LMMs and conventional specialist models over both AI-generated and photographic images.

Decentralized Gradient Descent (DGD) is a popular algorithm used to solve decentralized optimization problems in diverse domains such as remote sensing, distributed inference, multi-agent coordination, and federated learning. Yet, executing DGD over wireless systems affected by noise, fading and limited bandwidth presents challenges, requiring scheduling of transmissions to mitigate interference and the acquisition of topology and channel state information -- complex tasks in wireless decentralized systems. This paper proposes a DGD algorithm tailored to wireless systems. Unlike existing approaches, it operates without inter-agent coordination, topology information, or channel state information. Its core is a Non-Coherent Over-The-Air (NCOTA) consensus scheme, exploiting a noisy energy superposition property of wireless channels. With a randomized transmission strategy to accommodate half-duplex operation, transmitters map local optimization signals to energy levels across subcarriers in an OFDM frame, and transmit concurrently without coordination. It is shown that received energies form a noisy consensus signal, whose fluctuations are mitigated via a consensus stepsize. NCOTA-DGD leverages the channel pathloss for consensus formation, without explicit knowledge of the mixing weights. It is shown that, for the class of strongly-convex problems, the expected squared distance between the local and globally optimum models vanishes with rate $\mathcal O(1/\sqrt{k})$ after $k$ iterations, with a proper design of decreasing stepsizes. Extensions address a broad class of fading models and frequency-selective channels. Numerical results on an image classification task depict faster convergence vis-\`a-vis running time than state-of-the-art schemes, especially in densely deployed networks.

Electromagnetic information theory (EIT) is one of the important topics for 6G communication due to its potential to reveal the performance limit of wireless communication systems. For EIT, the research foundation is reasonable and accurate channel modeling. Existing channel modeling works for EIT in non-line-of-sight (NLoS) scenario focus on far-field modeling, which can not accurately capture the characteristics of the channel in near-field. In this paper, we propose the near-field channel model for EIT based on electromagnetic scattering theory. We model the channel by using non-stationary Gaussian random fields and derive the analytical expression of the correlation function of the fields. Furthermore, we analyze the characteristics of the proposed channel model, e.g., the sparsity of the model in wavenumber domain. Based on the sparsity of the model, we design a channel estimation scheme for near-field scenario. Numerical analysis verifies the correctness of the proposed scheme and shows that it can outperform existing schemes like least square (LS) and orthogonal matching pursuit (OMP).

The emergence of diffusion models has revolutionized the field of image generation, providing new methods for creating high-quality, high-resolution images across various applications. However, the potential of these models for generating domain-specific images, particularly remote sensing (RS) images, remains largely untapped. RS images that are notable for their high resolution, extensive coverage, and rich information content, bring new challenges that general diffusion models may not adequately address. This paper proposes CRS-Diff, a pioneering diffusion modeling framework specifically tailored for generating remote sensing imagery, leveraging the inherent advantages of diffusion models while integrating advanced control mechanisms to ensure that the imagery is not only visually clear but also enriched with geographic and temporal information. The model integrates global and local control inputs, enabling precise combinations of generation conditions to refine the generation process. A comprehensive evaluation of CRS-Diff has demonstrated its superior capability to generate RS imagery both in a single condition and multiple conditions compared with previous methods in terms of image quality and diversity.

We consider the penalized distributionally robust optimization (DRO) problem with a closed, convex uncertainty set, a setting that encompasses the $f$-DRO, Wasserstein-DRO, and spectral/$L$-risk formulations used in practice. We present Drago, a stochastic primal-dual algorithm that achieves a state-of-the-art linear convergence rate on strongly convex-strongly concave DRO problems. The method combines both randomized and cyclic components with mini-batching, which effectively handles the unique asymmetric nature of the primal and dual problems in DRO. We support our theoretical results with numerical benchmarks in classification and regression.

In turbulence modeling, we are concerned with finding closure models that represent the effect of the subgrid scales on the resolved scales. Recent approaches gravitate towards machine learning techniques to construct such models. However, the stability of machine-learned closure models and their abidance by physical structure (e.g. symmetries, conservation laws) are still open problems. To tackle both issues, we take the `discretize first, filter next' approach. In this approach we apply a spatial averaging filter to existing fine-grid discretizations. The main novelty is that we introduce an additional set of equations which dynamically model the energy of the subgrid scales. Having an estimate of the energy of the subgrid scales, we can use the concept of energy conservation to derive stability. The subgrid energy containing variables are determined via a data-driven technique. The closure model is used to model the interaction between the filtered quantities and the subgrid energy. Therefore the total energy should be conserved. Abiding by this conservation law yields guaranteed stability of the system. In this work, we propose a novel skew-symmetric convolutional neural network architecture that satisfies this law. The result is that stability is guaranteed, independent of the weights and biases of the network. Importantly, as our framework allows for energy exchange between resolved and subgrid scales it can model backscatter. To model dissipative systems (e.g. viscous flows), the framework is extended with a diffusive component. The introduced neural network architecture is constructed such that it also satisfies momentum conservation. We apply the new methodology to both the viscous Burgers' equation and the Korteweg-De Vries equation in 1D. The novel architecture displays superior stability properties when compared to a vanilla convolutional neural network.

Robust optimization provides a mathematical framework for modeling and solving decision-making problems under worst-case uncertainty. This work addresses two-stage robust optimization (2RO) problems (also called adjustable robust optimization), wherein first-stage and second-stage decisions are made before and after uncertainty is realized, respectively. This results in a nested min-max-min optimization problem which is extremely challenging computationally, especially when the decisions are discrete. We propose Neur2RO, an efficient machine learning-driven instantiation of column-and-constraint generation (CCG), a classical iterative algorithm for 2RO. Specifically, we learn to estimate the value function of the second-stage problem via a novel neural network architecture that is easy to optimize over by design. Embedding our neural network into CCG yields high-quality solutions quickly as evidenced by experiments on two 2RO benchmarks, knapsack and capital budgeting. For knapsack, Neur2RO finds solutions that are within roughly $2\%$ of the best-known values in a few seconds compared to the three hours of the state-of-the-art exact branch-and-price algorithm; for larger and more complex instances, Neur2RO finds even better solutions. For capital budgeting, Neur2RO outperforms three variants of the $k$-adaptability algorithm, particularly on the largest instances, with a 10 to 100-fold reduction in solution time. Our code and data are available at //github.com/khalil-research/Neur2RO.

We present variational inference with sequential sample-average approximation (VISA), a method for approximate inference in computationally intensive models, such as those based on numerical simulations. VISA extends importance-weighted forward-KL variational inference by employing a sequence of sample-average approximations, which are considered valid inside a trust region. This makes it possible to reuse model evaluations across multiple gradient steps, thereby reducing computational cost. We perform experiments on high-dimensional Gaussians, Lotka-Volterra dynamics, and a Pickover attractor, which demonstrate that VISA can achieve comparable approximation accuracy to standard importance-weighted forward-KL variational inference with computational savings of a factor two or more for conservatively chosen learning rates.

In stochastic simulation, input uncertainty refers to the propagation of the statistical noise in calibrating input models to impact output accuracy, in addition to the Monte Carlo simulation noise. The vast majority of the input uncertainty literature focuses on estimating target output quantities that are real-valued. However, outputs of simulation models are random and real-valued targets essentially serve only as summary statistics. To provide a more holistic assessment, we study the input uncertainty problem from a distributional view, namely we construct confidence bands for the entire output distribution function. Our approach utilizes a novel test statistic whose asymptotic consists of the supremum of the sum of a Brownian bridge and a suitable mean-zero Gaussian process, which generalizes the Kolmogorov-Smirnov statistic to account for input uncertainty. Regarding implementation, we also demonstrate how to use subsampling to efficiently estimate the covariance function of the Gaussian process, thereby leading to an implementable estimation of the quantile of the test statistic and a statistically valid confidence band. Numerical results demonstrate how our new confidence bands provide valid coverage for output distributions under input uncertainty that is not achievable by conventional approaches.

Conventionally, spatiotemporal modeling network and its complexity are the two most concentrated research topics in video action recognition. Existing state-of-the-art methods have achieved excellent accuracy regardless of the complexity meanwhile efficient spatiotemporal modeling solutions are slightly inferior in performance. In this paper, we attempt to acquire both efficiency and effectiveness simultaneously. First of all, besides traditionally treating H x W x T video frames as space-time signal (viewing from the Height-Width spatial plane), we propose to also model video from the other two Height-Time and Width-Time planes, to capture the dynamics of video thoroughly. Secondly, our model is designed based on 2D CNN backbones and model complexity is well kept in mind by design. Specifically, we introduce a novel multi-view fusion (MVF) module to exploit video dynamics using separable convolution for efficiency. It is a plug-and-play module and can be inserted into off-the-shelf 2D CNNs to form a simple yet effective model called MVFNet. Moreover, MVFNet can be thought of as a generalized video modeling framework and it can specialize to be existing methods such as C2D, SlowOnly, and TSM under different settings. Extensive experiments are conducted on popular benchmarks (i.e., Something-Something V1 & V2, Kinetics, UCF-101, and HMDB-51) to show its superiority. The proposed MVFNet can achieve state-of-the-art performance with 2D CNN's complexity.

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