This paper studies the properties of solutions to multi-task shallow ReLU neural network learning problems, wherein the network is trained to fit a dataset with minimal sum of squared weights. Remarkably, the solutions learned for each individual task resemble those obtained by solving a kernel method, revealing a novel connection between neural networks and kernel methods. It is known that single-task neural network training problems are equivalent to minimum norm interpolation problem in a non-Hilbertian Banach space, and that the solutions of such problems are generally non-unique. In contrast, we prove that the solutions to univariate-input, multi-task neural network interpolation problems are almost always unique, and coincide with the solution to a minimum-norm interpolation problem in a Sobolev (Reproducing Kernel) Hilbert Space. We also demonstrate a similar phenomenon in the multivariate-input case; specifically, we show that neural network learning problems with large numbers of diverse tasks are approximately equivalent to an $\ell^2$ (Hilbert space) minimization problem over a fixed kernel determined by the optimal neurons.
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Networking：IFIP International Conferences on Networking。
Explanation：國(guo)際網絡會議。
Publisher：IFIP。
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Signed graphs serve as fundamental data structures for representing positive and negative relationships in social networks, with signed graph neural networks (SGNNs) emerging as the primary tool for their analysis. Our investigation reveals that balance theory, while essential for modeling signed relationships in SGNNs, inadvertently introduces exploitable vulnerabilities to black-box attacks. To demonstrate this vulnerability, we propose balance-attack, a novel adversarial strategy specifically designed to compromise graph balance degree, and develop an efficient heuristic algorithm to solve the associated NP-hard optimization problem. While existing approaches attempt to restore attacked graphs through balance learning techniques, they face a critical challenge we term "Irreversibility of Balance-related Information," where restored edges fail to align with original attack targets. To address this limitation, we introduce Balance Augmented-Signed Graph Contrastive Learning (BA-SGCL), an innovative framework that combines contrastive learning with balance augmentation techniques to achieve robust graph representations. By maintaining high balance degree in the latent space, BA-SGCL effectively circumvents the irreversibility challenge and enhances model resilience. Extensive experiments across multiple SGNN architectures and real-world datasets demonstrate both the effectiveness of our proposed balance-attack and the superior robustness of BA-SGCL, advancing the security and reliability of signed graph analysis in social networks. Datasets and codes of the proposed framework are at the github repository //anonymous.4open.science/r/BA-SGCL-submit-DF41/.
This paper studies sample average approximation (SAA) in solving convex or strongly convex stochastic programming (SP) problems. Under some common regularity conditions, we show -- perhaps for the first time -- that SAA's sample complexity can be completely free from any quantification of metric entropy (such as the logarithm of the covering number), leading to a significantly more efficient rate with dimensionality $d$ than most existing results. From the newly established complexity bounds, an important revelation is that SAA and the canonical stochastic mirror descent (SMD) method, two mainstream solution approaches to SP, entail almost identical rates of sample efficiency, lifting a theoretical discrepancy of SAA from SMD by the order of $O(d)$. Furthermore, this paper explores non-Lipschitzian scenarios where SAA maintains provable efficacy but the corresponding results for SMD remain mostly unexplored, indicating the potential of SAA's better applicability in some irregular settings.
Online learning of deep neural networks suffers from challenges such as hysteretic non-incremental updating, increasing memory usage, past retrospective retraining, and catastrophic forgetting. To alleviate these drawbacks and achieve progressive immediate decision-making, we propose a novel Incremental Online Learning (IOL) process of Randomized Neural Networks (Randomized NN), a framework facilitating continuous improvements to Randomized NN performance in restrictive online scenarios. Within the framework, we further introduce IOL with ridge regularization (-R) and IOL with forward regularization (-F). -R generates stepwise incremental updates without retrospective retraining and avoids catastrophic forgetting. Moreover, we substituted -R with -F as it enhanced precognition learning ability using semi-supervision and realized better online regrets to offline global experts compared to -R during IOL. The algorithms of IOL for Randomized NN with -R/-F on non-stationary batch stream were derived respectively, featuring recursive weight updates and variable learning rates. Additionally, we conducted a detailed analysis and theoretically derived relative cumulative regret bounds of the Randomized NN learners with -R/-F in IOL under adversarial assumptions using a novel methodology and presented several corollaries, from which we observed the superiority on online learning acceleration and regret bounds of employing -F in IOL. Finally, our proposed methods were rigorously examined across regression and classification tasks on diverse datasets, which distinctly validated the efficacy of IOL frameworks of Randomized NN and the advantages of forward regularization.
Numerous studies have focused on learning and understanding the dynamics of physical systems from video data, such as spatial intelligence. Artificial intelligence requires quantitative assessments of the uncertainty of the model to ensure reliability. However, there is still a relative lack of systematic assessment of the uncertainties, particularly the uncertainties of the physical data. Our motivation is to introduce conformal prediction into the uncertainty assessment of dynamical systems, providing a method supported by theoretical guarantees. This paper uses the conformal prediction method to assess uncertainties with benchmark operator learning methods. We have also compared the Monte Carlo Dropout and Ensemble methods in the partial differential equations dataset, effectively evaluating uncertainty through straight roll-outs, making it ideal for time-series tasks.
We study the Out-of-Distribution (OOD) generalization in machine learning and propose a general framework that establishes information-theoretic generalization bounds. Our framework interpolates freely between Integral Probability Metric (IPM) and $f$-divergence, which naturally recovers some known results (including Wasserstein- and KL-bounds), as well as yields new generalization bounds. Additionally, we show that our framework admits an optimal transport interpretation. When evaluated in two concrete examples, the proposed bounds either strictly improve upon existing bounds in some cases or match the best existing OOD generalization bounds. Moreover, by focusing on $f$-divergence and combining it with the Conditional Mutual Information (CMI) methods, we derive a family of CMI-based generalization bounds, which include the state-of-the-art ICIMI bound as a special instance. Finally, leveraging these findings, we analyze the generalization of the Stochastic Gradient Langevin Dynamics (SGLD) algorithm, showing that our derived generalization bounds outperform existing information-theoretic generalization bounds in certain scenarios.
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.
We present a large-scale study on unsupervised spatiotemporal representation learning from videos. With a unified perspective on four recent image-based frameworks, we study a simple objective that can easily generalize all these methods to space-time. Our objective encourages temporally-persistent features in the same video, and in spite of its simplicity, it works surprisingly well across: (i) different unsupervised frameworks, (ii) pre-training datasets, (iii) downstream datasets, and (iv) backbone architectures. We draw a series of intriguing observations from this study, e.g., we discover that encouraging long-spanned persistency can be effective even if the timespan is 60 seconds. In addition to state-of-the-art results in multiple benchmarks, we report a few promising cases in which unsupervised pre-training can outperform its supervised counterpart. Code is made available at //github.com/facebookresearch/SlowFast
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.
We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.
In this paper, we propose the joint learning attention and recurrent neural network (RNN) models for multi-label classification. While approaches based on the use of either model exist (e.g., for the task of image captioning), training such existing network architectures typically require pre-defined label sequences. For multi-label classification, it would be desirable to have a robust inference process, so that the prediction error would not propagate and thus affect the performance. Our proposed model uniquely integrates attention and Long Short Term Memory (LSTM) models, which not only addresses the above problem but also allows one to identify visual objects of interests with varying sizes without the prior knowledge of particular label ordering. More importantly, label co-occurrence information can be jointly exploited by our LSTM model. Finally, by advancing the technique of beam search, prediction of multiple labels can be efficiently achieved by our proposed network model.
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