Search

To analyse how diffusion models learn correlations beyond Gaussian ones, we study the behaviour of higher-order cumulants, or connected n-point functions, under both the forward and backward process. We derive explicit expressions for the moment- and cumulant-generating functionals, in terms of the distribution of the initial data and properties of forward process. It is shown analytically that during the forward process higher-order cumulants are conserved in models without a drift, such as the variance-expanding scheme, and that therefore the endpoint of the forward process maintains nontrivial correlations. We demonstrate that since these correlations are encoded in the score function, higher-order cumulants are learnt in the backward process, also when starting from a normal prior. We confirm our analytical results in an exactly solvable toy model with nonzero cumulants and in scalar lattice field theory., Comment: 21 pages, many figures. Extended version of contribution accepted in the NeurIPS 2024 workshop "Machine Learning and the Physical Sciences"

With the trend of large graph learning models, business owners tend to employ a model provided by a third party to deliver business services to users. However, these models might be backdoored, and malicious users can submit trigger-embedded inputs to manipulate the model predictions. Current graph backdoor defenses have several limitations: 1) depending on model-related details, 2) requiring additional model fine-tuning, and 3) relying upon extra explainability tools, all of which are infeasible under stringent privacy policies. To address those limitations, we propose GraphProt, which allows resource-constrained business owners to rely on third parties to avoid backdoor attacks on GNN-based graph classifiers. Our GraphProt is model-agnostic and only relies on the input graph. The key insight is to leverage subgraph information for prediction, thereby mitigating backdoor effects induced by triggers. GraphProt comprises two components: clustering-based trigger elimination and robust subgraph ensemble. Specifically, we first propose feature-topology clustering that aims to remove most of the anomalous subgraphs (triggers). Moreover, we design subgraph sampling strategies based on feature-topology clustering to build a robust classifier via majority vote. Experimental results across three backdoor attacks and six benchmark datasets demonstrate that GraphProt significantly reduces the backdoor attack success rate while preserving the model accuracy on regular graph classification tasks.

Graph Neural Networks (GNNs) have demonstrated commendable performance for graph-structured data. Yet, GNNs are often vulnerable to adversarial structural attacks as embedding generation relies on graph topology. Existing efforts are dedicated to purifying the maliciously modified structure or applying adaptive aggregation, thereby enhancing the robustness against adversarial structural attacks. It is inevitable for a defender to consume heavy computational costs due to lacking prior knowledge about modified structures. To this end, we propose an efficient defense method, called Simple and Fast Robust Graph Neural Network (SFR-GNN), supported by mutual information theory. The SFR-GNN first pre-trains a GNN model using node attributes and then fine-tunes it over the modified graph in the manner of contrastive learning, which is free of purifying modified structures and adaptive aggregation, thus achieving great efficiency gains. Consequently, SFR-GNN exhibits a 24%--162% speedup compared to advanced robust models, demonstrating superior robustness for node classification tasks.

We investigate certified robustness for GNNs under graph injection attacks. Existing research only provides sample-wise certificates by verifying each node independently, leading to very limited certifying performance. In this paper, we present the first collective certificate, which certifies a set of target nodes simultaneously. To achieve it, we formulate the problem as a binary integer quadratic constrained linear programming (BQCLP). We further develop a customized linearization technique that allows us to relax the BQCLP into linear programming (LP) that can be efficiently solved. Through comprehensive experiments, we demonstrate that our collective certification scheme significantly improves certification performance with minimal computational overhead. For instance, by solving the LP within 1 minute on the Citeseer dataset, we achieve a significant increase in the certified ratio from 0.0% to 81.2% when the injected node number is 5% of the graph size. Our step marks a crucial step towards making provable defense more practical.

Signed graphs consist of edges and signs, which can be separated into structural information and balance-related information, respectively. Existing signed graph neural networks (SGNNs) typically rely on balance-related information to generate embeddings. Nevertheless, the emergence of recent adversarial attacks has had a detrimental impact on the balance-related information. Similar to how structure learning can restore unsigned graphs, balance learning can be applied to signed graphs by improving the balance degree of the poisoned graph. However, this approach encounters the challenge "Irreversibility of Balance-related Information" - while the balance degree improves, the restored edges may not be the ones originally affected by attacks, resulting in poor defense effectiveness. To address this challenge, we propose a robust SGNN framework called Balance Augmented-Signed Graph Contrastive Learning (BA-SGCL), which combines Graph Contrastive Learning principles with balance augmentation techniques. Experimental results demonstrate that BA-SGCL not only enhances robustness against existing adversarial attacks but also achieves superior performance on link sign prediction task across various datasets.

Deep Graph Learning (DGL) has emerged as a crucial technique across various domains. However, recent studies have exposed vulnerabilities in DGL models, such as susceptibility to evasion and poisoning attacks. While empirical and provable robustness techniques have been developed to defend against graph modification attacks (GMAs), the problem of certified robustness against graph injection attacks (GIAs) remains largely unexplored. To bridge this gap, we introduce the node-aware bi-smoothing framework, which is the first certifiably robust approach for general node classification tasks against GIAs. Notably, the proposed node-aware bi-smoothing scheme is model-agnostic and is applicable for both evasion and poisoning attacks. Through rigorous theoretical analysis, we establish the certifiable conditions of our smoothing scheme. We also explore the practical implications of our node-aware bi-smoothing schemes in two contexts: as an empirical defense approach against real-world GIAs and in the context of recommendation systems. Furthermore, we extend two state-of-the-art certified robustness frameworks to address node injection attacks and compare our approach against them. Extensive evaluations demonstrate the effectiveness of our proposed certificates.

The Optimal Power Flow (OPF) problem is pivotal for power system operations, guiding generator output and power distribution to meet demand at minimized costs, while adhering to physical and engineering constraints. The integration of renewable energy sources, like wind and solar, however, poses challenges due to their inherent variability. This variability, driven largely by changing weather conditions, demands frequent recalibrations of power settings, thus necessitating recurrent OPF resolutions. This task is daunting using traditional numerical methods, particularly for extensive power systems. In this work, we present a cutting-edge, physics-informed machine learning methodology, trained using imitation learning and historical European weather datasets. Our approach directly correlates electricity demand and weather patterns with power dispatch and generation, circumventing the iterative requirements of traditional OPF solvers. This offers a more expedient solution apt for real-time applications. Rigorous evaluations on aggregated European power systems validate our method's superiority over existing data-driven techniques in OPF solving. By presenting a quick, robust, and efficient solution, this research sets a new standard in real-time OPF resolution, paving the way for more resilient power systems in the era of renewable energy., Comment: Submitted to Elsevier

This study delves into the connection between machine learning and lattice field theory by linking generative diffusion models (DMs) with stochastic quantization, from a stochastic differential equation perspective. We show that DMs can be conceptualized by reversing a stochastic process driven by the Langevin equation, which then produces samples from an initial distribution to approximate the target distribution. In a toy model, we highlight the capability of DMs to learn effective actions. Furthermore, we demonstrate its feasibility to act as a global sampler for generating configurations in the two-dimensional $\phi^4$ quantum lattice field theory., Comment: 6 pages, 3 figures, accepted at the NeurIPS 2023 workshop "Machine Learning and the Physical Sciences". Some contents overlap with arXiv:2309.17082

In this work, we establish a direct connection between generative diffusion models (DMs) and stochastic quantization (SQ). The DM is realized by approximating the reversal of a stochastic process dictated by the Langevin equation, generating samples from a prior distribution to effectively mimic the target distribution. Using numerical simulations, we demonstrate that the DM can serve as a global sampler for generating quantum lattice field configurations in two-dimensional $\phi^4$ theory. We demonstrate that DMs can notably reduce autocorrelation times in the Markov chain, especially in the critical region where standard Markov Chain Monte-Carlo (MCMC) algorithms experience critical slowing down. The findings can potentially inspire further advancements in lattice field theory simulations, in particular in cases where it is expensive to generate large ensembles., Comment: 30 pages, 15 figures. The open code can be found at https://github.com/Anguswlx/DMasSQ

Graph anomaly detection (GAD) has achieved success and has been widely applied in various domains, such as fraud detection, cybersecurity, finance security, and biochemistry. However, existing graph anomaly detection algorithms focus on distinguishing individual entities (nodes or graphs) and overlook the possibility of anomalous groups within the graph. To address this limitation, this paper introduces a novel unsupervised framework for a new task called Group-level Graph Anomaly Detection (Gr-GAD). The proposed framework first employs a variant of Graph AutoEncoder (GAE) to locate anchor nodes that belong to potential anomaly groups by capturing long-range inconsistencies. Subsequently, group sampling is employed to sample candidate groups, which are then fed into the proposed Topology Pattern-based Graph Contrastive Learning (TPGCL) method. TPGCL utilizes the topology patterns of groups as clues to generate embeddings for each candidate group and thus distinct anomaly groups. The experimental results on both real-world and synthetic datasets demonstrate that the proposed framework shows superior performance in identifying and localizing anomaly groups, highlighting it as a promising solution for Gr-GAD. Datasets and codes of the proposed framework are at the github repository https://anonymous.4open.science/r/Topology-Pattern-Enhanced-Unsupervised-Group-level-Graph-Anomaly-Detection.

We investigate adversarial robustness of unsupervised Graph Contrastive Learning (GCL) against structural attacks. First, we provide a comprehensive empirical and theoretical analysis of existing attacks, revealing how and why they downgrade the performance of GCL. Inspired by our analytic results, we present a robust GCL framework that integrates a homophily-driven sanitation view, which can be learned jointly with contrastive learning. A key challenge this poses, however, is the non-differentiable nature of the sanitation objective. To address this challenge, we propose a series of techniques to enable gradient-based end-to-end robust GCL. Moreover, we develop a fully unsupervised hyperparameter tuning method which, unlike prior approaches, does not require knowledge of node labels. We conduct extensive experiments to evaluate the performance of our proposed model, GCHS (Graph Contrastive Learning with Homophily-driven Sanitation View), against two state of the art structural attacks on GCL. Our results demonstrate that GCHS consistently outperforms all state of the art baselines in terms of the quality of generated node embeddings as well as performance on two important downstream tasks.

A physics-informed neural network (PINN) embedded with the susceptible-infected-removed (SIR) model is devised to understand the temporal evolution dynamics of infectious diseases. Firstly, the effectiveness of this approach is demonstrated on synthetic data as generated from the numerical solution of the susceptible-asymptomatic-infected-recovered-dead (SAIRD) model. Then, the method is applied to COVID-19 data reported for Germany and shows that it can accurately identify and predict virus spread trends. The results indicate that an incomplete physics-informed model can approach more complicated dynamics efficiently. Thus, the present work demonstrates the high potential of using machine learning methods, e.g., PINNs, to study and predict epidemic dynamics in combination with compartmental models., Comment: 23 pages, 14 figures

Linearized Graph Neural Networks (GNNs) have attracted great attention in recent years for graph representation learning. Compared with nonlinear Graph Neural Network (GNN) models, linearized GNNs are much more time-efficient and can achieve comparable performances on typical downstream tasks such as node classification. Although some linearized GNN variants are purposely crafted to mitigate ``over-smoothing", empirical studies demonstrate that they still somehow suffer from this issue. In this paper, we instead relate over-smoothing with the vanishing gradient phenomenon and craft a gradient-free training framework to achieve more efficient and effective linearized GNNs which can significantly overcome over-smoothing and enhance the generalization of the model. The experimental results demonstrate that our methods achieve better and more stable performances on node classification tasks with varying depths and cost much less training time.

The robustness of recommender systems under node injection attacks has garnered significant attention. Recently, GraphRfi, a GNN-based recommender system, was proposed and shown to effectively mitigate the impact of injected fake users. However, we demonstrate that GraphRfi remains vulnerable to attacks due to the supervised nature of its fraudster detection component, where obtaining clean labels is challenging in practice. In particular, we propose a powerful poisoning attack, MetaC, against both GNN-based and MF-based recommender systems. Furthermore, we analyze why GraphRfi fails under such an attack. Then, based on our insights obtained from vulnerability analysis, we design an adaptive fraudster detection module that explicitly considers label uncertainty. This module can serve as a plug-in for different recommender systems, resulting in a robust framework named PDR. Comprehensive experiments show that our defense approach outperforms other benchmark methods under attacks. Overall, our research presents an effective framework for integrating fraudster detection into recommendation systems to achieve adversarial robustness.

Graph Neural Networks (GNNs) are vulnerable to data poisoning attacks, which will generate a poisoned graph as the input to the GNN models. We present FocusedCleaner as a poisoned graph sanitizer to effectively identify the poison injected by attackers. Specifically, FocusedCleaner provides a sanitation framework consisting of two modules: bi-level structural learning and victim node detection. In particular, the structural learning module will reverse the attack process to steadily sanitize the graph while the detection module provides ``the focus" -- a narrowed and more accurate search region -- to structural learning. These two modules will operate in iterations and reinforce each other to sanitize a poisoned graph step by step. As an important application, we show that the adversarial robustness of GNNs trained over the sanitized graph for the node classification task is significantly improved. Extensive experiments demonstrate that FocusedCleaner outperforms the state-of-the-art baselines both on poisoned graph sanitation and improving robustness.

Reconstructing spectral functions from Euclidean Green's functions is an important inverse problem in physics. The prior knowledge for specific physical systems routinely offers essential regularization schemes for solving the ill-posed problem approximately. Aiming at this point, we propose an automatic differentiation framework as a generic tool for the reconstruction from observable data. We represent the spectra by neural networks and set chi-square as loss function to optimize the parameters with backward automatic differentiation unsupervisedly. In the training process, there is no explicit physical prior embedding into neural networks except the positive-definite form. The reconstruction accuracy is assessed through Kullback-Leibler(KL) divergence and mean square error(MSE) at multiple noise levels. It should be noted that the automatic differential framework and the freedom of introducing regularization are inherent advantages of the present approach and may lead to improvements of solving inverse problem in the future., Comment: 7 pages, 4 figures, accepted at the NeurIPS 2021 workshop "Machine Learning and the Physical Sciences". arXiv admin note: text overlap with arXiv:2111.14760

Reconstructing spectral functions from Euclidean Green's functions is an important inverse problem in many-body physics. However, the inversion is proved to be ill-posed in the realistic systems with noisy Green's functions. In this Letter, we propose an automatic differentiation(AD) framework as a generic tool for the spectral reconstruction from propagator observable. Exploiting the neural networks' regularization as a non-local smoothness regulator of the spectral function, we represent spectral functions by neural networks and use the propagator's reconstruction error to optimize the network parameters unsupervisedly. In the training process, except for the positive-definite form for the spectral function, there are no other explicit physical priors embedded into the neural networks. The reconstruction performance is assessed through relative entropy and mean square error for two different network representations. Compared to the maximum entropy method, the AD framework achieves better performance in the large-noise situation. It is noted that the freedom of introducing non-local regularization is an inherent advantage of the present framework and may lead to substantial improvements in solving inverse problems., Comment: 9 pages, 10 figures. Updated to the published version

Rolling bearings are subject to various faults due to its long-time operation under harsh environment, which will lead to unexpected breakdown of machinery system and cause severe accidents. Deep learning methods recently have gained growing interests and extensively applied in the data-driven bearing fault diagnosis. However, current deep learning methods perform the bearing fault diagnosis in the form of deterministic classification, which overlook the uncertainties that inevitably exist in actual practice. To tackle this issue, in this research we develop a probabilistic fault diagnosis framework that can account for the uncertainty effect in prediction, which bears practical significance. This framework fully leverages the probabilistic feature of Gaussian process classifier (GPC). To facilitate the establishment of high-fidelity GPC, the tailored feature extraction with dimensionality reduction method can be optimally determined through the cross validation-based grid search upon a prespecified method pool consisting of various kernel principal component analysis (KPCA) methods and stacked autoencoder. This strategy can ensure the complex nonlinear relations between the features and faults to be adequately characterized. Furthermore, the sensor fusion concept is adopted to enhance the diagnosis performance. As compared with the traditional deep learning methods, this proposed framework usually requires less labeled data and less effort for parameter tuning. Systematic case studies using the publicly accessible experimental rolling bearing dataset are carried out to validate this new framework. Various influencing factors on fault diagnosis performance also are thoroughly investigated.

We introduce a Python package that provides simply and unified access to a collection of datasets from fundamental physics research - including particle physics, astroparticle physics, and hadron- and nuclear physics - for supervised machine learning studies. The datasets contain hadronic top quarks, cosmic-ray induced air showers, phase transitions in hadronic matter, and generator-level histories. While public datasets from multiple fundamental physics disciplines already exist, the common interface and provided reference models simplify future work on cross-disciplinary machine learning and transfer learning in fundamental physics. We discuss the design and structure and line out how additional datasets can be submitted for inclusion. As showcase application, we present a simple yet flexible graph-based neural network architecture that can easily be applied to a wide range of supervised learning tasks. We show that our approach reaches performance close to dedicated methods on all datasets. To simplify adaptation for various problems, we provide easy-to-follow instructions on how graph-based representations of data structures, relevant for fundamental physics, can be constructed and provide code implementations for several of them. Implementations are also provided for our proposed method and all reference algorithms., Comment: 14 pages, 3 figures, 5 tables - Version accepted by Computing and Software for Big Science

Graph-based Anomaly Detection (GAD) is becoming prevalent due to the powerful representation abilities of graphs as well as recent advances in graph mining techniques. These GAD tools, however, expose a new attacking surface, ironically due to their unique advantage of being able to exploit the relations among data. That is, attackers now can manipulate those relations (i.e., the structure of the graph) to allow some target nodes to evade detection. In this paper, we exploit this vulnerability by designing a new type of targeted structural poisoning attacks to a representative regression-based GAD system termed OddBall. Specially, we formulate the attack against OddBall as a bi-level optimization problem, where the key technical challenge is to efficiently solve the problem in a discrete domain. We propose a novel attack method termed BinarizedAttack based on gradient descent. Comparing to prior arts, BinarizedAttack can better use the gradient information, making it particularly suitable for solving combinatorial optimization problems. Furthermore, we investigate the attack transferability of BinarizedAttack by employing it to attack other representation-learning-based GAD systems. Our comprehensive experiments demonstrate that BinarizedAttack is very effective in enabling target nodes to evade graph-based anomaly detection tools with limited attackers' budget, and in the black-box transfer attack setting, BinarizedAttack is also tested effective and in particular, can significantly change the node embeddings learned by the GAD systems. Our research thus opens the door to studying a new type of attack against security analytic tools that rely on graph data., Comment: Accepted to ICDE 2022

As the COVID-19 pandemic continues to ravage the world, it is of critical significance to provide a timely risk prediction of the COVID-19 in multi-level. To implement it and evaluate the public health policies, we develop a framework with machine learning assisted to extract epidemic dynamics from the infection data, in which contains a county-level spatiotemporal epidemiological model that combines a spatial Cellular Automaton (CA) with a temporal Susceptible-Undiagnosed-Infected-Removed (SUIR) model. Compared with the existing time risk prediction models, the proposed CA-SUIR model shows the multi-level risk of the county to the government and coronavirus transmission patterns under different policies. This new toolbox is first utilized to the projection of the multi-level COVID-19 prevalence over 412 Landkreis (counties) in Germany, including t-day-ahead risk forecast and the risk assessment to the travel restriction policy. As a practical illustration, we predict the situation at Christmas where the worst fatalities are 34.5 thousand, effective policies could contain it to below 21 thousand. Such intervenable evaluation system could help decide on economic restarting and public health policies making in pandemic., Comment: 17 pages, 13 figures, comments welcome!

Collective learning methods exploit relations among data points to enhance classification performance. However, such relations, represented as edges in the underlying graphical model, expose an extra attack surface to the adversaries. We study adversarial robustness of an important class of such graphical models, Associative Markov Networks (AMN), to structural attacks, where an attacker can modify the graph structure at test time. We formulate the task of learning a robust AMN classifier as a bi-level program, where the inner problem is a challenging non-linear integer program that computes optimal structural changes to the AMN. To address this technical challenge, we first relax the attacker problem, and then use duality to obtain a convex quadratic upper bound for the robust AMN problem. We then prove a bound on the quality of the resulting approximately optimal solutions, and experimentally demonstrate the efficacy of our approach. Finally, we apply our approach in a transductive learning setting, and show that robust AMN is much more robust than state-of-the-art deep learning methods, while sacrificing little in accuracy on non-adversarial data., Comment: UAI 2020

Uncertainties in a structure is inevitable, which generally lead to variation in dynamic response predictions. For a complex structure, brute force Monte Carlo simulation for response variation analysis is infeasible since one single run may already be computationally costly. Data driven meta-modeling approaches have thus been explored to facilitate efficient emulation and statistical inference. The performance of a meta-model hinges upon both the quality and quantity of training dataset. In actual practice, however, high-fidelity data acquired from high-dimensional finite element simulation or experiment are generally scarce, which poses significant challenge to meta-model establishment. In this research, we take advantage of the multi-level response prediction opportunity in structural dynamic analysis, i.e., acquiring rapidly a large amount of low-fidelity data from reduced-order modeling, and acquiring accurately a small amount of high-fidelity data from full-scale finite element analysis. Specifically, we formulate a composite neural network fusion approach that can fully utilize the multi-level, heterogeneous datasets obtained. It implicitly identifies the correlation of the low- and high-fidelity datasets, which yields improved accuracy when compared with the state-of-the-art. Comprehensive investigations using frequency response variation characterization as case example are carried out to demonstrate the performance.

As an important part of speech recognition technology, automatic speech keyword recognition has been intensively studied in recent years. Such technology becomes especially pivotal under situations with limited infrastructures and computational resources, such as voice command recognition in vehicles and robot interaction. At present, the mainstream methods in automatic speech keyword recognition are based on long short-term memory (LSTM) networks with attention mechanism. However, due to inevitable information losses for the LSTM layer caused during feature extraction, the calculated attention weights are biased. In this paper, a novel approach, namely Multi-layer Attention Mechanism, is proposed to handle the inaccurate attention weights problem. The key idea is that, in addition to the conventional attention mechanism, information of layers prior to feature extraction and LSTM are introduced into attention weights calculations. Therefore, the attention weights are more accurate because the overall model can have more precise and focused areas. We conduct a comprehensive comparison and analysis on the keyword spotting performances on convolution neural network, bi-directional LSTM cyclic neural network, and cyclic neural network with the proposed attention mechanism on Google Speech Command datasets V2 datasets. Experimental results indicate favorable results for the proposed method and demonstrate the validity of the proposed method. The proposed multi-layer attention methods can be useful for other researches related to object spotting.

Quantization can be used to form new vectors/matrices with shared values close to the original. In recent years, the popularity of scalar quantization for value-sharing applications has been soaring as it has been found huge utilities in reducing the complexity of neural networks. Existing clustering-based quantization techniques, while being well-developed, have multiple drawbacks including the dependency of the random seed, empty or out-of-the-range clusters, and high time complexity for a large number of clusters. To overcome these problems, in this paper, the problem of scalar quantization is examined from a new perspective, namely sparse least square optimization. Specifically, inspired by the property of sparse least square regression, several quantization algorithms based on $l_1$ least square are proposed. In addition, similar schemes with $l_1 + l_2$ and $l_0$ regularization are proposed. Furthermore, to compute quantization results with a given amount of values/clusters, this paper designed an iterative method and a clustering-based method, and both of them are built on sparse least square. The paper shows that the latter method is mathematically equivalent to an improved version of k-means clustering-based quantization algorithm, although the two algorithms originated from different intuitions. The algorithms proposed were tested with three types of data and their computational performances, including information loss, time consumption, and the distribution of the values of the sparse vectors, were compared and analyzed. The paper offers a new perspective to probe the area of quantization, and the algorithms proposed can outperform existing methods especially under some bit-width reduction scenarios, when the required post-quantization resolution (number of values) is not significantly lower than the original number.