Arbitrary Graph Structures Research Articles

SEA-GWNN: Simple and Effective Adaptive Graph Wavelet Neural Network

The utilization of wavelet-based techniques in graph neural networks (GNNs) has gained considerable attention, particularly in the context of node classification. Although existing wavelet-based approaches have shown promise, they are constrained by their reliance on pre-defined wavelet filters, rendering them incapable of effectively adapting to signals that reside on graphs based on tasks at hand. Recent research endeavors address this issue through the introduction of a wavelet lifting transform. However, this technique necessitates the use of bipartite graphs, causing a transformation of the original graph structure into a bipartite configuration. This alteration of graph topology results in the generation of undesirable wavelet filters, thereby undermining the effectiveness of the method. In response to these challenges, we propose a novel simple and effective adaptive graph wavelet neural network (SEA-GWNN) class that employs the lifting scheme on arbitrary graph structures while upholding the original graph topology by leveraging multi-hop computation trees. A noteworthy aspect of the approach is the focus on local substructures represented as acyclic trees, wherein the lifting strategy is applied in a localized manner. This locally defined lifting scheme effectively combines high-pass and low-pass frequency information to enhance node representations. Furthermore, to reduce computing costs, we propose to decouple the higher- order lifting operators and induce them from the lower-order structures. Finally, we benchmark our model on several real- world datasets spanning four distinct categories, including citation networks, webpages, the film industry, and large-scale graphs and the experimental results showcase the efficacy of the proposed SEA-GWNN.

Existence of the weak and strong core in a sharing model with arbitrary graph structures <br>

Existence of the weak and strong core in a sharing model with arbitrary graph structures <br>

Multi-node wind speed forecasting based on a novel dynamic spatial–temporal graph network

Providing reliable and accurate wind speed predictions for the power system ensures a stable power output. However, the high wind speed uncertainty and the complex spatial–temporal correlation between wind turbines still make wind speed prediction a significant challenge. This paper proposes a novel dynamic spatial–temporal graph network (DSTGN) to make wind speed predictions by accurately capturing the dynamic dependencies of multi-turbine on an arbitrary graph structure. DSTGN adopts an extensible and serialized structure consisting of stacked dynamic spatial–temporal blocks to model dependencies. In spatial dependency extraction, a graph generation module is used in the spatial block to produce static and dynamic spatial information. A parameterized adjacency matrix expands the spatial hypothesis space rather than being limited by the distance between turbines. In temporal dependency extraction, the multi-head attention mechanism models temporal associations of diverse time horizons. Based on publicly available wind datasets, extensive experimental results showed that the proposed model significantly improves performance. Compared to recent state-of-the-art models, MAE, RMSE and MAPE are improved over 4.57%, 4.25% and 8.31%, respectively. Furthermore, through ablation studies, we verified the benefits of each component of the proposed model, especially the positive role of graph sampling in improving performance.

A novel spatial–temporal generative autoencoder for wind speed uncertainty forecasting

Wind speed interval prediction is one of the most long-standing challenges because of the high uncertainty and the complex spatial–temporal correlation between wind turbines. In this paper, based on variational Bayesian inference, we propose a novel spatial–temporal generative autoencoder (STGAE) model to capture the continuous probability distribution of each wind turbine on an arbitrary graph structure. In the encoding process, a parameterization strategy is used to expand the hypothesis space of the adjacency matrix rather than being limited by the distance between nodes. The multiple graph convolution layers with kernels approximated by Chebyshev polynomials adjust the collecting scope of spatial information. The bi-directional dependency is modeled by the multi-head attention to tap correlations of different time horizons effectively. The interval prediction at each node is yielded based on the probability densities of generated samples produced by the decoder. Using publicly available wind data from the Global Energy Forecasting Competition 2014, numerical experiments are conducted to compare the prediction reliability and accuracy between the proposed model and the recent state-of-the-art models. The forecasting results suggest that the proposed model significantly improves performance, especially the strong generalization ability makes it practical under different weather conditions.

그래프 트랜스포머 기반 농가 사과 품질 이미지의 그래프 표현 학습 연구

Recently, a convolutional neural network (CNN) based system is being developed to overcome the limitations of human resources in the apple quality classification of farmhouse. However, since convolutional neural networks receive only images of the same size, preprocessing such as sampling may be required, and in the case of oversampling, information loss of the original image such as image quality degradation and blurring occurs. In this paper, in order to minimize the above problem, to generate a image patch based graph of an original image and propose a random walk-based positional encoding method to apply the graph transformer model. The above method continuously learns the position embedding information of patches which don`t have a positional information based on the random walk algorithm, and finds the optimal graph structure by aggregating useful node information through the self-attention technique of graph transformer model. Therefore, it is robust and shows good performance even in a new graph structure of random node order and an arbitrary graph structure according to the location of an object in an image. As a result, when experimented with 5 apple quality datasets, the learning accuracy was higher than other GNN models by a minimum of 1.3% to a maximum of 4.7%, and the number of parameters was 3.59M, which was about 15% less than the 23.52M of the ResNet18 model. Therefore, it shows fast reasoning speed according to the reduction of the amount of computation and proves the effect.

3DMol-Net: Learn 3D Molecular Representation Using Adaptive Graph Convolutional Network Based on Rotation Invariance.

Studying the deep learning-based molecular representation has great significance on predicting molecular property, promoted the development of drug screening and new drug discovery, and improving human well-being for avoiding illnesses. It is essential to learn the characterization of drug for various downstream tasks, such as molecular property prediction. In particular, the 3D structure features of molecules play an important role in biochemical function and activity prediction. The 3D characteristics of molecules largely determine the properties of the drug and the binding characteristics of the target. However, most current methods merely rely on 1D or 2D properties while ignoring the 3D topological structure, thereby degrading the performance of molecular inferring. In this paper, we propose 3DMol-Net to enhance the molecular representation, considering both the topology and rotation invariance (RI) of the 3D molecular structure. Specifically, we construct a molecular graph with soft relations related to the spatial arrangement of the 3D coordinates to learn 3D topology of arbitrary graph structure and employ an adaptive graph convolutional network to predict molecular properties and biochemical activities. Comparing with current graph-based methods, 3DMol-Net demonstrates superior performance in terms of both regression and classification tasks. Further verification of RI and visualization also show better robustness and representation capacity of our model.

ExaTN: Scalable GPU-Accelerated High-Performance Processing of General Tensor Networks at Exascale

We present ExaTN (Exascale Tensor Networks), a scalable GPU-accelerated C++ library which can express and process tensor networks on shared- as well as distributed-memory high-performance computing platforms, including those equipped with GPU accelerators. Specifically, ExaTN provides the ability to build, transform, and numerically evaluate tensor networks with arbitrary graph structures and complexity. It also provides algorithmic primitives for the optimization of tensor factors inside a given tensor network in order to find an extremum of a chosen tensor network functional, which is one of the key numerical procedures in quantum many-body theory and quantum-inspired machine learning. Numerical primitives exposed by ExaTN provide the foundation for composing rather complex tensor network algorithms. We enumerate multiple application domains which can benefit from the capabilities of our library, including condensed matter physics, quantum chemistry, quantum circuit simulations, as well as quantum and classical machine learning, for some of which we provide preliminary demonstrations and performance benchmarks just to emphasize a broad utility of our library.

Generalized Hamiltonian dynamics and chaos in evolutionary games on networks

We study the network replicator equation and characterize its fixed points on arbitrary graph structures for 2 × 2 symmetric games. We show a relationship between the asymptotic behavior of the network replicator and the existence of an independent vertex set in the graph and also show that complex behavior cannot emerge in 2 × 2 games. This links a property of the dynamical system with a combinatorial graph property. We contrast this by showing that ordinary rock–paper–scissors (RPS) exhibits chaos on the 3-cycle and that on general graphs with ≥3 vertices the network replicator with RPS is a generalized Hamiltonian system. This stands in stark contrast to the established fact that RPS does not exhibit chaos in the standard replicator dynamics or the bimatrix replicator dynamics, which is equivalent to the network replicator on a graph with one edge and two vertices (K2).

Modeling Speech Acts in Asynchronous Conversations: A Neural-CRF Approach

Participants in an asynchronous conversation (e.g., forum, e-mail) interact with each other at different times, performing certain communicative acts, called speech acts (e.g., question, request). In this article, we propose a hybrid approach to speech act recognition in asynchronous conversations. Our approach works in two main steps: a long short-term memory recurrent neural network (LSTM-RNN) first encodes each sentence separately into a task-specific distributed representation, and this is then used in a conditional random field (CRF) model to capture the conversational dependencies between sentences. The LSTM-RNN model uses pretrained word embeddings learned from a large conversational corpus and is trained to classify sentences into speech act types. The CRF model can consider arbitrary graph structures to model conversational dependencies in an asynchronous conversation. In addition, to mitigate the problem of limited annotated data in the asynchronous domains, we adapt the LSTM-RNN model to learn from synchronous conversations (e.g., meetings), using domain adversarial training of neural networks. Empirical evaluation shows the effectiveness of our approach over existing ones: (i) LSTM-RNNs provide better task-specific representations, (ii) conversational word embeddings benefit the LSTM-RNNs more than the off-the-shelf ones, (iii) adversarial training gives better domain-invariant representations, and (iv) the global CRF model improves over local models.

Generate tensor network state by sequential single-photon scattering in waveguide QED systems

We propose a scheme to generate photonic tensor network states by sequential scattering of photons in waveguide QED systems. We show that sequential scatterings can convert a series of unentangled photons into any type of matrix product states. We also demonstrate the possibility of generating projected entangled pair states with an arbitrary graph structure by photon re-scattering.

P systems with randomized right-hand sides of rules

P systems are a model of distributed and compartmentalized multiset rewriting, complete with various signal transmission mechanisms. We introduce a novel kind of P systems in which rules are dynamically constructed in each step by non-deterministic pairing of left-hand and right-hand sides. We define three variants of right-hand side randomization and compare each of them with the power of conventional P systems. It turns out that all three variants enable non-cooperative P systems to generate exponential (and thus non-semi-linear) number languages. We also give a binary normal form for one of the variants of P systems with randomized rule right-hand sides. Finally, we also discuss extensions of the three variants to tissue P systems, i.e., P systems on an arbitrary graph structure.

Adaptive Graph Convolutional Neural Networks

Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and connectivity. The paper proposes a generalized and flexible graph CNN taking data of arbitrary graph structure as input. In that way a task-driven adaptive graph is learned for each graph data while training. To efficiently learn the graph, a distance metric learning is proposed. Extensive experiments on nine graph-structured datasets have demonstrated the superior performance improvement on both convergence speed and predictive accuracy.

Quantum simulation of discrete-time Hamiltonians using directionally unbiased linear optical multiports

Recently, a generalization of the standard optical multiport was proposed [Phys. Rev. A 93, 043845 (2016)]. These directionally unbiased multiports allow photons to reverse direction and exit backwards from the input port, providing a realistic linear optical scattering vertex for quantum walks on arbitrary graph structures. Here, it is shown that arrays of these multiports allow the simulation of a range of discrete-time Hamiltonian systems. Examples are described, including a case where both spatial and internal degrees of freedom are simulated. Because input ports also double as output ports, there is substantial savings of resources compared to feed-forward networks carrying out the same functions. The simulation is implemented in a scalable manner using only linear optics, and can be generalized to higher dimensional systems in a straightforward fashion, thus offering a concrete experimentally achievable implementation of graphical models of discrete-time quantum systems.

Interdependent Defense Games with Applications to Internet Security at the Level of Autonomous Systems

We propose interdependent defense (IDD) games, a computational game-theoretic framework to study aspects of the interdependence of risk and security in multi-agent systems under deliberate external attacks. Our model builds upon interdependent security (IDS) games, a model by Heal and Kunreuther that considers the source of the risk to be the result of a fixed randomized-strategy. We adapt IDS games to model the attacker’s deliberate behavior. We define the attacker’s pure-strategy space and utility function and derive appropriate cost functions for the defenders. We provide a complete characterization of mixed-strategy Nash equilibria (MSNE), and design a simple polynomial-time algorithm for computing all of them for an important subclass of IDD games. We also show that an efficient algorithm to determine whether some attacker’s strategy can be a part of an MSNE in an instance of IDD games is unlikely to exist. Yet, we provide a dynamic programming (DP) algorithm to compute an approximate MSNE when the graph/network structure of the game is a directed tree with a single source. We also show that the DP algorithm is a fully polynomial-time approximation scheme. In addition, we propose a generator of random instances of IDD games based on the real-world Internet-derived graph at the level of autonomous systems (≈27 K nodes and ≈100 K edges as measured in March 2010 by the DIMES project). We call such games Internet games. We introduce and empirically evaluate two heuristics from the literature on learning-in-games, best-response gradient dynamics (BRGD) and smooth best-response dynamics (SBRD), to compute an approximate MSNE in IDD games with arbitrary graph structures, such as randomly-generated instances of Internet games. In general, preliminary experiments applying our proposed heuristics are promising. Our experiments show that, while BRGD is a useful technique for the case of Internet games up to certain approximation level, SBRD is more efficient and provides better approximations than BRGD. Finally, we discuss several extensions, future work, and open problems.

Learning Gaussian graphical models with fractional marginal pseudo-likelihood

We propose a Bayesian approximate inference method for learning the dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we derive an analytical expression to approximate the marginal likelihood for an arbitrary graph structure without invoking any assumptions about decomposability. The majority of the existing methods for learning Gaussian graphical models are either restricted to decomposable graphs or require specification of a tuning parameter that may have a substantial impact on learned structures. By combining a simple sparsity inducing prior for the graph structures with a default reference prior for the model parameters, we obtain a fast and easily applicable scoring function that works well for even high-dimensional data. We demonstrate the favourable performance of our approach by large-scale comparisons against the leading methods for learning non-decomposable Gaussian graphical models. A theoretical justification for our method is provided by showing that it yields a consistent estimator of the graph structure.

Parsing fashion image into mid‐level semantic parts based on chain‐conditional random fields

In this study, the authors address the problem of parsing fashion images into mid-level semantic parts including upper-clothing, lower-clothing, skin, hair and background. These mid-level parts provide the regional information of fashion items and have potential value in high-level parsing process. The key idea of the method is to parse the mid-level parts by region expanding. Owing to the co-occurrence of pose skeleton and the proposed parts, the region expanding process starts from the super-pixels crossed by specific segments of pose skeleton. The super-pixels are then merged with their neighbours by conditional inference based on their position and perceptual similarity. To avoid the difficulties of training on arbitrary graph structures, conditional random fields (CRFs) are constructed on super-pixel chains, which are extracted from the generated expanding trees. This is followed by a voting stage to mix up the probabilities estimated by the chain-CRFs to obtain the final result. Experiments on two datasets show that the new method outperforms related approaches in regional accuracy and has good generalisation capability. Furthermore, the method can be easily employed to improve the performance of high-level parsing. Its effectiveness has been verified by another group of experiments on two state-of-the-art high-level parsing approaches.

The duality of spatial death–birth and birth–death processes and limitations of the isothermal theorem

Evolutionary models on graphs, as an extension of the Moran process, have two major implementations: birth–death (BD) models (or the invasion process) and death–birth (DB) models (or voter models). The isothermal theorem states that the fixation probability of mutants in a large group of graph structures (known as isothermal graphs, which include regular graphs) coincides with that for the mixed population. This result has been proved by Lieberman et al. (2005 Nature 433, 312–316. (doi:10.1038/nature03204)) in the case of BD processes, where mutants differ from the wild-types by their birth rate (and not by their death rate). In this paper, we discuss to what extent the isothermal theorem can be formulated for DB processes, proving that it only holds for mutants that differ from the wild-type by their death rate (and not by their birth rate). For more general BD and DB processes with arbitrary birth and death rates of mutants, we show that the fixation probabilities of mutants are different from those obtained in the mass-action populations. We focus on spatial lattices and show that the difference between BD and DB processes on one- and two-dimensional lattices is non-small even for large population sizes. We support these results with a generating function approach that can be generalized to arbitrary graph structures. Finally, we discuss several biological applications of the results.

Computing Nash Equilibrium in Interdependent Defense Games

Roughly speaking, Interdependent Defense (IDD) games, previously proposed, model the situation where an attacker wants to cause as much damage as possible to a network by attacking one of the sites in the network. Each site must make an investment decision regarding security to protect itself against a direct or indirect attack, the latter due to potential transfer-risk from an unprotected neighboring site. The work introducing IDD games discusses potential applications to model the essence of real-world scenarios such as the 2006 transatlantic aircraft plot. In this paper, our focus is the study of the problem of computing a Nash Equilibrium (NE) in IDD games. We show that an efficient algorithm to determine whether some attacker’s strategy can be a part of a NE in an instance of IDD games is unlikely to exist. Yet, we provide a dynamic programming algorithm to compute an approximate NE when the graph/network structure of the game is a directed tree with a single source, and show that it is an FPTAS. We also introduce an improved heuristic to compute an approximate NE on arbitrary graph structures. Our experiments show that our heuristic is more efficient, and provides better approximations, than best-response-gradient dynamics for the case of Internet games, a class of games introduced and studied in the original work on IDD games.

Distributed control of linear time‐varying systems interconnected over arbitrary graphs

SUMMARYIn this paper, we focus on designing distributed controllers for interconnected systems in situations where the controller sensing and actuation topology is inherited from that of the plant. The distributed systems considered are composed of discrete‐time linear time‐varying subsystems interconnected over arbitrary graph structures. The main contribution of this paper is to provide results on general graph interconnection structures in which the graphs have potentially an infinite number of vertices. This is accomplished by first extending previous machinery developed for systems with spatial dynamics on the lattice . We derive convex analysis and synthesis conditions for design in this setting. These conditions reduce to finite sequences of LMIs in the case of eventually periodic subsystems interconnected over finite graphs. The paper also provides results on distributed systems with communication latency and gives an illustrative example on the distributed control of hovercrafts along eventually periodic trajectories. The methodology developed here provides a unifying viewpoint for our previous and related work on distributed control. Copyright © 2013 John Wiley & Sons, Ltd.

Analytically solvable processes on networks

We introduce a broad class of analytically solvable processes on networks. In the special case, they reduce to random walk and consensus process, the two most basic processes on networks. Our class differs from previous models of interactions (such as the stochastic Ising model, cellular automata, infinite particle systems, and the voter model) in several ways, the two most important being (i) the model is analytically solvable even when the dynamical equation for each node may be different and the network may have an arbitrary finite graph and influence structure and (ii) when local dynamics is described by the same evolution equation, the model is decomposable, with the equilibrium behavior of the system expressed as an explicit function of network topology and node dynamics.