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At least 91 records · Page 5

Acceleration of Graph Neural Network-Based Prediction Models in Chemistry via Co-Design Optimization on Intelligence Processing Units

Atomic structure prediction and associated property calculations are the bedrock of chemical physics. Since high-fidelity ab initio modeling techniques for computing the structure and properties can be prohibitively expensive, this motivates the development of machine-learning (ML) models that make these predictions more efficiently. Training graph neural networks over large atomistic databases introduces unique computational challenges such as the need to process millions of small graphs with variable size and support communication patterns that are distinct from learning over large graphs such as social networks. We demonstrate a novel hardware-software co-design approach to scale up the training of atomistic graph neural networks (GNN) for structure and property prediction. First, to eliminate redundant computation and memory associated with alternative padding techniques and to improve throughput via minimizing communication, we formulate the effective coalescing of the batches of variable-size atomistic graphs as the bin packing problem and introduce a hardware-agnostic algorithm to pack these batches. In addition, we propose hardware-specific optimizations including a planner and vectorization for the gather-scatter operations targeted for Graphcore’s Intelligence Processing Unit (IPU), as well as model-specific optimizations such as merged communication collectives and optimized softplus. Putting these all together, we demonstrate the effectiveness of the proposed co-design approach by providing an implementation of a well-established atomistic GNN on the Graphcore IPUs. We evaluate the training performance on multiple atomistic graph databases with varying degrees of graph counts, sizes and sparsity. Here, we demonstrate that such a co-design approach can reduce the training time of atomistic GNNs and can improve the performance by up to 1.5× compared to the baseline implementation of the model on the IPUs. Additionally, we compare our IPU implementation with a Nvidia GPU-based implementation and show that our atomistic GNN implementation on the IPUs can run 1.8× faster on average compared to the execution time on the GPUs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Network-Level Traffic Signal Cooperation: A Higher-Order Conflict Graph Approach

Traffic signal control and cooperation are extremely important to alleviate traffic congestion in a large traffic network. This study develops a higher-order conflict graph approach for network-wide traffic signal control and cooperation. A conflict graph is applied to model the traffic signal configurations, which identifies the conflict and unconflicted movements for each intersection. In conflict graph, the node represents each movement. The weight of each node can be defined as traffic volume, queue length, fuel consumption, or any weighted combinations of these measurements. The calculation of the optimal green light duration and green light sequence (for different movements) is equivalent to sequentially finding the maximum weight independent set (MWIS) in the conflict graph. The conflict graph also provides a uniform and efficient way to connect traffic signal operations among nearby intersections spatially. Then, we introduced the concept of the k -th order neighborhood to model the degree of connectivity between each movement to the movements at upstream or downstream intersections. The weight of each node in the higher-order conflict graph not only represents its own congestion level, but also relates to the traffic conditions of nearby intersections. Through this approach, the cooperation of multiple intersections can be realized by incorporating their spatial connectivity into conflict graph and solving the MWIS problem. A simulation network is built in SUMO to test the effectiveness of the proposed method. Results suggested that the proposed model outperformed other state-of-the-art signal control methods. Also, the scheme maintains good performance under varying traffic demands.

42 ENGINEERING↗

Harnessing graph convolutional neural networks for identification of glassy states in metallic glasses

Graph Convolutional Neural Networks (GCNNs) have emerged as powerful tools for analyzing materials. In this study, we employ GCNNs to examine structural characteristics of CuZr metallic glasses (MGs) and identify their states. We use molecular dynamics to simulate the quenching process of CuZr, using cooling rates ranging from 10 9 to 10 15 K/s, to produce six unique glassy states. For each state, we create a dataset comprising 1,800 distinct samples. We evaluate the effectiveness of various GCNNs, including Graph Attention Neural Network (GANN), Graph Sample and AggreGatE (GraphSAGE), Graph Isomorphism Network (GIN), and Relational Graph Convolutional Neural Network (RGCN). GANN and GraphSAGE demonstrate comparable performance, achieving an overall accuracy of 81% in classifying the MG states. Furthermore, these results underscore the potential of GCNNs to detect subtle structural variances in disordered materials and point to broader application of deep learning in the analysis of MGs and other amorphous substances.

36 MATERIALS SCIENCE↗

GraphTango: A Hybrid Representation Format for Efficient Streaming Graph Updates and Analysis

Abstract Streaming graph processing performs batched updates and analytics on a time-evolving graph. The underlying representation format of the graph largely determines the throughputs of these updates and analytics phases. Existing representation formats usually employ variations of hash tables or adjacency lists. However, a recent study showed that the adjacency-list-based approaches perform poorly on heavy-tailed graphs, and the hash table-based approaches suffer on short-tailed graphs. We propose GraphTango, a hybrid representation format that provides excellent update and analytics throughput regardless of the graph’s degree distribution. GraphTango dynamically switches among three different formats based on a vertex’s degree: (i) Low-degree vertices store the edges directly with the neighborhood metadata, confining accesses to a single cache line, (2) Medium-degree vertices use adjacency lists, and (3) High-degree vertices use hash tables as well as adjacency lists. In this case, the adjacency list provides fast traversal during the analytics phase, while the hash table provides constant-time lookups during the update phase. We further optimized the performance by designing an open-addressing-based hash table that fully utilizes every fetched cache line. In addition, we developed a thread-local lock-free memory pool that allows fast growing/shrinking of the adjacency lists and hash tables in a multi-threaded environment. We evaluated GraphTango with the help of the SAGA-Bench framework and compared it with four other representation formats: Stinger, Degree-aware Robin Hood Hashing, and two adjacency list-based formats with different workload balancing scheme. On average, GraphTango provides 4.5x higher insertion throughput, 3.2x higher deletion throughput, and 1.1x higher analytics throughput over the next best format. Furthermore, we integrated GraphTango with the state-of-the-art graph processing frameworks DZiG and RisGraph. Compared to the vanilla DZiG and vanilla RisGraph , [ GraphTango + DZiG ] and [ GraphTango + RisGraph ] reduces the average batch processing time by 2.3x and 1.5x, respectively.

Ahmed, Alif↗

Impact of graph structures for QAOA on MaxCut

The quantum approximate optimization algorithm (QAOA) is a promising method of solving combinatorial optimization problems using quantum computing. QAOA on the MaxCut problem has been studied extensively on graphs with specific structure; however, little is known about the general performance of the algorithm on arbitrary graphs. Here, we investigate how different graph characteristics correlate with QAOA performance at depths at most three on the MaxCut problem for all connected non-isomorphic graphs with at most eight vertices. Some good predictors of QAOA success relate to graph symmetries, odd cycles, and density. For example, on eight vertex graphs, the average probability for selecting an optimal solution for graphs that contain no odd cycles after three iterations of QAOA is 60.6% compared to 48.2% for those that do. The data generated from these studies are shared in a publicly accessible database to serve as a benchmark for QAOA calculations and experiments. Knowing the relationship between structure and performance can be used to identify classes of combinatorial problems that are likely to exhibit a quantum advantage.

97 MATHEMATICS AND COMPUTING↗

Spatiotemporal Graph Convolutional Networks for Earthquake Source Characterization

Abstract Accurate earthquake location and magnitude estimation play critical roles in seismology. Recent deep learning frameworks have produced encouraging results on various seismological tasks (e.g., earthquake detection, phase picking, seismic classification, and earthquake early warning). Many existing machine learning earthquake location methods utilize waveform information from a single station. However, multiple stations contain more complete information for earthquake source characterization. Inspired by recent successes in applying graph neural networks (GNNs) in graph‐structured data, we develop a Spatiotemporal Graph Neural Network (STGNN) for estimating earthquake locations and magnitudes. Our graph neural network leverages geographical and waveform information from multiple stations to construct graphs automatically and dynamically by adaptive message passing based on graphs' edges. Using a recent graph neural network and a fully convolutional neural network as baselines, we apply STGNN to earthquakes recorded by the Southern California Seismic Network from 2000 to 2019 and earthquakes collected in Oklahoma from 2014 to 2015. STGNN yields more accurate earthquake locations than those obtained by the baseline models and performs comparably in terms of depth and magnitude prediction, though the ability to predict depth and magnitude remains weak for all tested models. Our work demonstrates the potential of using GNNs and multiple stations for better automatic estimation of earthquake epicenters.

58 GEOSCIENCES↗

Graph states of atomic ensembles engineered by photon-mediated entanglement

Abstract Graph states are a broad family of entangled quantum states, each defined by a graph composed of edges representing the correlations between subsystems. Such states constitute versatile resources for quantum computation and quantum-enhanced measurement. Their generation and engineering require a high level of control over entanglement. Here we report on the generation of continuous-variable graph states of atomic spin ensembles, which form the nodes of the graph. We program the entanglement structure encoded in the graph edges by combining global photon-mediated interactions in an optical cavity with local spin rotations. By tuning the entanglement between two subsystems, we either localize correlations within each subsystem or enable Einstein–Podolsky–Rosen steering—a strong form of entanglement that enables the extraction of precise information from one subsystem through measurements on the other. We further engineer a four-mode square graph state, highlighting the flexibility of our approach. Our method is scalable to larger and more complex graphs, laying groundwork for measurement-based quantum computation and advanced protocols in quantum metrology.

74 ATOMIC AND MOLECULAR PHYSICS↗

On the degeneracy of spin ice graphs, and its estimate via the Bethe permanent

The concept of spin ice can be extended to a general graph. We study the degeneracy of spin ice graph on arbitrary interaction structures via graph theory. We map spin ice graphs to the Ising model on a graph and clarify whether the inverse mapping is possible via a modified Krausz construction. From the gauge freedom of frustrated Ising systems, we derive exact, general results about frustration and degeneracy. We demonstrate for the first time that every spin ice graph, with the exception of the one-dimensional Ising model, is degenerate. We then study how degeneracy scales in size, using the mapping between Eulerian trails and spin ice manifolds, and a permanental identity for the number of Eulerian orientations. Furthermore, we show that the Bethe permanent technique provides both an estimate and a lower bound to the frustration of spin ices on arbitrary graphs of even degree. While such a technique can also be used to obtain an upper bound, we find that in all finite degree examples we studied, another upper bound based on Schrijver inequality is tighter.

97 MATHEMATICS AND COMPUTING↗

Coherent manipulation of graph states composed of finite-energy Gottesman-Kitaev-Preskill-encoded qubits

Graph states are a central resource in measurement-based quantum information processing. In the photonic qubit architecture based on Gottesman-Kitaev-Preskill (GKP) encoding, the generation of high-fidelity graph states composed of realistic, finite-energy approximate GKP-encoded qubits thus constitutes a key task. We consider the finite-energy approximation of GKP-qubit states given by a coherent superposition of shifted finite-squeezed vacuum states, where the displacements are Gaussian distributed. We present an exact description of graph states composed of such approximate GKP qubits as a coherent superposition of a Gaussian ensemble of randomly displaced ideal GKP-qubit graph states. Using standard Gaussian dynamics, we track the transformation of the covariance matrix and the mean-displacement vector elements of the Gaussian distribution of the ensemble under tools such as GKP-Steane error-correction and fusion operations that can be used to grow large high-fidelity GKP-qubit graph states. The covariance matrix elements capture the noise in the graph state due to the finite-energy approximation of GKP qubits, while the mean displacements relate to the possible absolute shift errors on the individual qubits arising conditionally from the homodyne measurements that are a part of these tools. Our work thus pins down an exact coherent error model for graph states generated from truly finite-energy GKP qubits, which can shed light on their error-correction properties.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Augmenting Graph Convolution with Distance Preserving Embedding for Improved Learning

Graph convolution incorporates topological information of a graph into learning. Message passing corresponds to traversal of a local neighborhood in classical graph algorithms. We show that incorporating additional global structures, such as shortest paths, through distance preserving embedding can improve performance. Our approach, Gavotte, significantly improves the performance of a range of popular graph neu-ral networks such as GCN, GA T,Graph SAGE, and GCNII for transductive learning. Gavotte also improves the performance of graph neural networks for full-supervised tasks, albeit to a smaller degree. As high-quality embeddings are generated by Gavotte as a by-product, we leverage clustering algorithms on these embed dings to augment the training set and introduce Gavotte+. Our results of Gavotte+ on datasets with very few labels demonstrate the advantage of augmenting graph convolution with distance preserving embedding.

Cong, Guojing↗

Revisit the Scalability of Deep Auto-Regressive Models for Graph Generation

As a new promising approach to graph generations, deep auto-regressive graph generation has drawn increasing attention. It however has been commonly deemed as hard to scale up to work with large graphs. In existing studies, it is perceived that the consideration of the full non-local graph dependences is indispensable for this approach to work, which entails the needs for keeping the entire graph’s info in memory and hence the perceived “inherent” scalability limitation of the approach. This paper revisits the common perception. It proposes three ways to relax the dependences and conducts a series of empirical measurements. It concludes that the perceived “inherent” scalability limitation is a misperception; with the right design and implementation, deep auto-regressive graph generation can be applied to graphs much larger than the device memory. The rectified perception removes a fundamental barrier for this approach to meet practical needs.

Yang, Shuai↗

Scalable Comparative Visualization of Ensembles of Call Graphs

Optimizing the performance of large-scale parallel codes is critical for efficient utilization of computing resources. Code developers often explore various execution parameters, such as hardware configurations, system software choices, and application parameters, and are interested in detecting and understanding bottlenecks in different executions. They often collect hierarchical performance profiles represented as call graphs, which combine performance metrics with their execution contexts. The crucial task of exploring multiple call graphs together is tedious and challenging because of the many structural differences in the execution contexts and significant variability in the collected performance metrics (e.g., execution runtime). In this paper, we present Ensemble CallFlow to support the exploration of ensembles of call graphs using new types of visualizations, analysis, graph operations, and features. We introduce ensemble-Sankey , a new visual design that combines the strengths of resource-flow (Sankey) and box-plot visualization techniques. Whereas the resource-flow visualization can easily and intuitively describe the graphical nature of the call graph, the box plots overlaid on the nodes of Sankey convey the performance variability within the ensemble. Our interactive visual interface provides linked views to help explore ensembles of call graphs, e.g., by facilitating the analysis of structural differences, and identifying similar or distinct call graphs. Finally, we demonstrate the effectiveness and usefulness of our design through case studies on large-scale parallel codes.

97 MATHEMATICS AND COMPUTING↗

Topological Analysis of The SPOKE Graph

The SPOKE graph [2, 6] is a sparse decorated semantic graph representing a collection of knowledge collected in many scientific databases from the fields of healthcare, biochemistry, chemistry, biology, et cetera. This knowledge graph is stored as a relational dataset decorated with metadata on each constituent vertex and edge. Formally, the graph is G(V, E, D), where V is a set of n vertices V := {1, ..., n} and edges of the form (i, j) ϵ E for i, j ϵ V, and table D that for any item in V υ E stores unstructured data such as vertex/edge type, nature of a relationship, et cetera. D(i) = {data involving vertex i ϵ V}, and D(i, j) = {data involving edge (i, j) ϵ E}. Here, we treat the graph as undirected in the sense that a direct relationship for (i, j) causes a (possibly opposite) reverse direct relationship for (j, i). The SPOKE graph G(V, E, D) is formed by processing a collection of relational datasets from medicine, chemistry, and biology, connecting many entities. Here, we analyze an instance from 2019, Spoke-20190707, where a graph file contains 6.16M edges and associated metadata and a vertex file contains 2.15M vertices and the associated metadata. There are 12 different types of vertex entities; all edge types used are implicit (see §2). There is other metadata in D on edges and vertices, but we just use the topology and the vertex labels in this report. SPOKE is growing as more knowledge is gained and more datasets are added. SPOKE is likely to grow 10x during the next phase of this project, and we therefore would like to consider topoligical analysis techniques that are scalable to several orders of magnitude larger than the current dataset (say >1B edges).

59 BASIC BIOLOGICAL SCIENCES↗

Track Seeding and Labelling with Embedded-space Graph Neural Networks

To address the unprecedented scale of HL-LHC data, the Exa.TrkX project is investigating a variety of machine learning approaches to particle track reconstruction. The most promising of these solutions, graph neural networks (GNN), process the event as a graph that connects track measurements (detector hits corresponding to nodes) with candidate line segments between the hits (corresponding to edges). Detector information can be associated with nodes and edges, enabling a GNN to propagate the embedded parameters around the graph and predict node-, edge- and graph-level observables. Previously, message-passing GNNs have shown success in predicting doublet likelihood, and we here report updates on the state-of-the-art architectures for this task. In addition, the Exa.TrkX project has investigated innovations in both graph construction, and embedded representations, in an effort to achieve fully learned end-to-end track finding. Hence, we present a suite of extensions to the original model, with encouraging results for hitgraph classification. In addition, we explore increased performance by constructing graphs from learned representations which contain non-linear metric structure, allowing for efficient clustering and neighborhood queries of data points. We demonstrate how this framework fits in with both traditional clustering pipelines, and GNN approaches. The embedded graphs feed into high-accuracy doublet and triplet classifiers, or can be used as an end-to-end track classifier by clustering in an embedded space. A set of post-processing methods improve performance with knowledge of the detector physics. Finally, we present numerical results on the TrackML particle tracking challenge dataset, where our framework shows favorable results in both seeding and track finding.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Improved Bounds for Burning Fence Graphs

Graph burning studies how fast a contagion, modeled as a set of fires, spreads in a graph. The burning process takes place in synchronous, discrete rounds. In each round, a fire breaks out at a vertex, and the fire spreads to all vertices that are adjacent to a burning vertex. Additionally, the burning number of a graph G is the minimum number of rounds necessary for each vertex of G to burn. We consider the burning number of the \(m \times n\) Cartesian grid graphs, written \(G_{m,n}\) . For \(m = \omega (\sqrt{n})\) , the asymptotic value of the burning number of \(G_{m,n}\) was determined, but only the growth rate of the burning number was investigated in the case \(m = O(\sqrt{n})\) , which we refer to as fence graphs. We provide new explicit bounds on the burning number of fence graphs \(G_{c\sqrt{n},n}\) , where \(c > 0\) .

79 ASTRONOMY AND ASTROPHYSICS↗

Quantum graph learning and algorithms applied in quantum computer sciences and image classification

Graph and network theory play a fundamental role in quantum computer sciences, including quantum information and computation. Random graphs and complex network theory are pivotal in predicting novel quantum phenomena, where entangled links are represented by edges. Quantum algorithms have been developed to enhance solutions for various network problems, giving rise to quantum graph computing and quantum graph learning (QGL). Here, in this review, we explore graph theory and graph learning methods as powerful tools for quantum computers to generate efficient solutions to problems beyond the reach of classical systems. We delve into the development of quantum complex network theory and its applications in quantum computation, materials discovery, and research. We also discuss quantum machine learning (QML) methodologies for effective image classification using qubits, quantum gates, and quantum circuits. Additionally, the paper addresses the challenges of QGL and algorithms, emphasizing the steps needed to develop flexible QGL solvers. This review presents a comprehensive overview of the fields of QGL and QML, highlights recent advancements, and identifies opportunities for future research.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Local structure graph models with higher-order dependence

Local structure graph models (LSGMs) describe random graphs and networks as a Markov random field (MRF)—each graph edge has a specified conditional distribution dependent on explicit neighbourhoods of other graph edges. Centered parameterizations of LSGMs allow for direct control and interpretation of parameters for large- and small-scale structures (e.g., marginal means vs. dependence). Here, we extend this parameterization to account for triples of dependent edges and illustrate the importance of centered parameterizations for incorporating covariates and interpreting parameters. Using a MRF framework, common exponential random graph models are also shown to induce conditional distributions without centered parameterizations and thereby have undesirable features. This work attempts to advance graph models through conditional model specifications with modern parameterizations, covariates and higher-order dependencies.

97 MATHEMATICS AND COMPUTING↗

Hybrid Quantum–Classical Graph Transformers for Efficient Sentiment Analysis

Quantum Machine Learning (QML) offers a promising paradigm that leverages quantum computing principles to develop efficient and expressive models for learning from complex and structured data. Recent advances in natural language processing (NLP) and artificial intelligence (AI) have demonstrated capabilities in understanding, generating, and reasoning over linguistic and multimodal information. In this work, we present the Quantum Graph Transformer (QGT), a hybrid quantum–classical architecture that extends graph transformer capabilities through quantum self-attention. The QGT models variable-length sentences as token graphs, where both the embedding encoding and the self-attention mechanisms are implemented using parameterized quantum circuits (PQCs), enabling efficient contextual learning with significantly fewer trainable parameters. We train QGT using both fully connected and 𝑘 -nearest-neighbor graph structures and evaluate it on five benchmark sentiment-classification datasets. Experimental results show that QGT consistently achieves higher or comparable accuracy to existing quantum NLP models and outperforms a Classical Graph Transformer (CGT) baseline with identical architecture, achieving 29.4 × fewer parameters while requiring 3–5 × fewer samples to reach comparable performance. These findings highlight the potential of graph-based quantum models as scalable and data-efficient architectures for natural language understanding.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗