The paper formalizes a version of parallel online directed acyclic graph (DAG) exploration, general enough to be readily mapped to many computational scenarios. In both the offline and online versions, vertices are weighted with the work units required for their processing, at least one parent must be completely processed before a child is processed, and at any given time only one processor can work on any given vertex. The online version has the following additional natural restriction: only after a vertex is processed, are its required work units or its children known. Using the Actor Model of parallel computation, it is shown that a natural class of parallel online algorithms meets a simple competitive ratio bound. We demonstrate and focus on the problem's occurrence in the scenario of energy landscape roadmapping or atlasing under pair-potentials, a highly compute-and-storage intensive modeling component integral to diverse applications involving soft-matter assembly. The method is experimentally validated using a C++ Actor Framework (CAF) software implementation built atop EASAL (Efficient Atlasing and Search of Assembly Landscapes), a substantial opensource software suite, running on multiple CPU cores of the HiperGator supercomputer, demonstrating linear speedup results.
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This paper presents a simplified weak Galerkin (WG) finite element method for solving biharmonic equations avoiding the use of traditional stabilizers. The proposed WG method supports both convex and non-convex polytopal elements in finite element partitions, utilizing bubble functions as a critical analytical tool. The simplified WG method is symmetric and positive definite. Optimal-order error estimates are established for WG approximations in both the discrete $H^2$ norm and the $L^2$ norm.
The rapid development of image generation models has facilitated the widespread dissemination of generated images on social networks, creating favorable conditions for provably secure image steganography. However, existing methods face issues such as low quality of generated images and lack of semantic control in the generation process. To leverage provably secure steganography with more effective and high-performance image generation models, and to ensure that stego images can accurately extract secret messages even after being uploaded to social networks and subjected to lossy processing such as JPEG compression, we propose a high-quality, provably secure, and robust image steganography method based on state-of-the-art autoregressive (AR) image generation models using Vector-Quantized (VQ) tokenizers. Additionally, we employ a cross-modal error-correction framework that generates stego text from stego images to aid in restoring lossy images, ultimately enabling the extraction of secret messages embedded within the images. Extensive experiments have demonstrated that the proposed method provides advantages in stego quality, embedding capacity, and robustness, while ensuring provable undetectability.
Graph propagation (GP) computation plays a crucial role in graph data analysis, supporting various applications such as graph node similarity queries, graph node ranking, graph clustering, and graph neural networks. Existing methods, mainly relying on power iteration or push computation frameworks, often face challenges with slow convergence rates when applied to large-scale graphs. To address this issue, we propose a novel and powerful approach that accelerates power iteration and push methods using Chebyshev polynomials. Specifically, we first present a novel Chebyshev expansion formula for general GP functions, offering a new perspective on GP computation and achieving accelerated convergence. Building on these theoretical insights, we develop a novel Chebyshev power iteration method (\ltwocheb) and a novel Chebyshev push method (\chebpush). Our \ltwocheb method demonstrates an approximate acceleration of $O(\sqrt{N})$ compared to existing power iteration techniques for both personalized PageRank and heat kernel PageRank computations, which are well-studied GP problems. For \chebpush, we propose an innovative subset Chebyshev recurrence technique, enabling the design of a push-style local algorithm with provable error guarantee and reduced time complexity compared to existing push methods. We conduct extensive experiments using 5 large real-world datasets to evaluate our proposed algorithms, demonstrating their superior efficiency compared to state-of-the-art approaches.
We propose a novel formalism for describing Structural Causal Models (SCMs) as fixed-point problems on causally ordered variables, eliminating the need for Directed Acyclic Graphs (DAGs), and establish the weakest known conditions for their unique recovery given the topological ordering (TO). Based on this, we design a two-stage causal generative model that first infers in a zero-shot manner a valid TO from observations, and then learns the generative SCM on the ordered variables. To infer TOs, we propose to amortize the learning of TOs on synthetically generated datasets by sequentially predicting the leaves of graphs seen during training. To learn SCMs, we design a transformer-based architecture that exploits a new attention mechanism enabling the modeling of causal structures, and show that this parameterization is consistent with our formalism. Finally, we conduct an extensive evaluation of each method individually, and show that when combined, our model outperforms various baselines on generated out-of-distribution problems. The code is available on \href{//github.com/microsoft/causica/tree/main/research_experiments/fip}{Github}.
In this paper, we present an information-theoretic method for clustering mixed-type data, that is, data consisting of both continuous and categorical variables. The proposed approach is built on the deterministic variant of the Information Bottleneck algorithm, designed to optimally compress data while preserving its relevant structural information. We evaluate the performance of our method against four well-established clustering techniques for mixed-type data -- KAMILA, K-Prototypes, Factor Analysis for Mixed Data with K-Means, and Partitioning Around Medoids using Gower's dissimilarity -- using both simulated and real-world datasets. The results highlight that the proposed approach offers a competitive alternative to traditional clustering techniques, particularly under specific conditions where heterogeneity in data poses significant challenges.
This paper introduces a novel approach to quantify the uncertainties in fault diagnosis of motor drives using Bayesian neural networks (BNN). Conventional data-driven approaches used for fault diagnosis often rely on point-estimate neural networks, which merely provide deterministic outputs and fail to capture the uncertainty associated with the inference process. In contrast, BNNs offer a principled framework to model uncertainty by treating network weights as probability distributions rather than fixed values. It offers several advantages: (a) improved robustness to noisy data, (b) enhanced interpretability of model predictions, and (c) the ability to quantify uncertainty in the decision-making processes. To test the robustness of the proposed BNN, it has been tested under a conservative dataset of gear fault data from an experimental prototype of three fault types at first, and is then incrementally trained on new fault classes and datasets to explore its uncertainty quantification features and model interpretability under noisy data and unseen fault scenarios.
This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. With the framelet system, we can decompose the graph feature into low-pass and high-pass frequencies as extracted features for network training, which then defines a framelet-based graph convolution. The framelet decomposition naturally induces a graph pooling strategy by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. The graph neural networks with the proposed framelet convolution and pooling achieve state-of-the-art performance in many types of node and graph prediction tasks. Moreover, we propose shrinkage as a new activation for the framelet convolution, which thresholds the high-frequency information at different scales. Compared to ReLU, shrinkage in framelet convolution improves the graph neural network model in terms of denoising and signal compression: noises in both node and structure can be significantly reduced by accurately cutting off the high-pass coefficients from framelet decomposition, and the signal can be compressed to less than half its original size with the prediction performance well preserved.
Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.
Recent advancements in deep neural networks for graph-structured data have led to state-of-the-art performance on recommender system benchmarks. However, making these methods practical and scalable to web-scale recommendation tasks with billions of items and hundreds of millions of users remains a challenge. Here we describe a large-scale deep recommendation engine that we developed and deployed at Pinterest. We develop a data-efficient Graph Convolutional Network (GCN) algorithm PinSage, which combines efficient random walks and graph convolutions to generate embeddings of nodes (i.e., items) that incorporate both graph structure as well as node feature information. Compared to prior GCN approaches, we develop a novel method based on highly efficient random walks to structure the convolutions and design a novel training strategy that relies on harder-and-harder training examples to improve robustness and convergence of the model. We also develop an efficient MapReduce model inference algorithm to generate embeddings using a trained model. We deploy PinSage at Pinterest and train it on 7.5 billion examples on a graph with 3 billion nodes representing pins and boards, and 18 billion edges. According to offline metrics, user studies and A/B tests, PinSage generates higher-quality recommendations than comparable deep learning and graph-based alternatives. To our knowledge, this is the largest application of deep graph embeddings to date and paves the way for a new generation of web-scale recommender systems based on graph convolutional architectures.
High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.
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