Study error bounds in evaluating distributional computational graphs.
problem Error analysis in evaluating graphs with inputs as probability distributions.
method Establish non-asymptotic error bounds using Wasserstein-1 distance.
result Non-asymptotic error bounds for discretization errors in distributional computational graphs.
Parallelizes graph embedding for large graphs.
problem Large graphs make existing graph embedding techniques inefficient.
method Distributed parallel computation framework using a cluster of compute nodes.
result Parallel computation scales well and maintains embedding quality.
CoSimGNN improves graph similarity computation for large graphs.
problem Efficiently computing graph similarity scores for large graphs.
method Embedding-coarsening-matching framework with adaptive pooling and fine-grained interactions.
result CoSimGNN achieves best performance in graph similarity computation.
Graph similarity computation is one of the core operations in many graph-based applications, such as graph similarity search, graph database analysis, graph clustering, etc. Since computing the exact distance/similarity between two graphs is typically NP-hard, a series of approximate methods have been proposed with a t…
We introduce GSimCNN (Graph Similarity Computation via Convolutional Neural Networks) for predicting the similarity score between two graphs. As the core operation of graph similarity search, pairwise graph similarity computation is a challenging problem due to the NP-hard nature of computing many graph distance/simila…
PSimGNN partitions graphs into subgraphs for efficient graph similarity computation.
problem Efficiently compute graph similarity scores for large graphs.
method Graph partitioning followed by subgraph-level and node-level comparisons using a graph neural network.
result PSimGNN outperforms state-of-the-art methods in graph similarity computation tasks.
Efficiently computes embeddings for large graphs using coarsening.
problem Inefficient computation of graph embeddings for large-scale graphs.
method Graph coarsening based on Schur complements and Gaussian elimination.
result Efficiently computed embeddings on coarsened graph match Schur complement embeddings in expectation.
This paper examines properties of feedforward graphs to improve neural network performance.
problem The choice of computational graph can significantly impact neural network performance.
method The paper introduces two measures: fidelity and mixing time, and evaluates popular graphs using these measures.
result Popular graphs are evaluated based on fidelity and mixing time, revealing their performance implications.
HAGs eliminate redundant computations in GNNs, improving training efficiency.
problem Redundant computations in GNNs leading to inefficiencies.
method Hierarchically Aggregated computation Graphs (HAGs) to manage and eliminate redundant computations.
result Significant improvement in training efficiency (up to 2.8x) with HAGs.
Graph similarity search is among the most important graph-based applications, e.g. finding the chemical compounds that are most similar to a query compound. Graph similarity computation, such as Graph Edit Distance (GED) and Maximum Common Subgraph (MCS), is the core operation of graph similarity search and many other …
New graph attention operators improve performance and reduce computational costs.
problem Excessive computational resources in graph attention operators.
method Proposed hGAO and cGAO using hard and channel-wise attention mechanisms.
result Improved performance and computational savings with new operators.
Quantum computing improves graph neural network aggregation.
problem Limitations of classical GNNs in processing global graph features.
method Quantum computer-generated aggregation weights for graph neural networks.
result Quantum-enhanced GNN performs similarly to classical models on standard datasets.
Empirical error estimates improve graph sparsification reliability.
problem Uncertainty in sparsification error limits downstream computations reliability.
method Data-driven approach to compute empirical error estimates.
result Empirical error estimates provide theoretical guarantees and are computationally feasible.
The von Neumann graph entropy (VNGE) facilitates measurement of information divergence and distance between graphs in a graph sequence. It has been successfully applied to various learning tasks driven by network-based data. While effective, VNGE is computationally demanding as it requires the full eigenspectrum of the…
FastGAT reduces GNN computation time by 10x using graph sparsification.
problem High computational burden in attention-based GNNs.
method Spectral sparsification to generate optimal graph pruning.
result Per-epoch time is almost linear in graph nodes, reducing computational time by up to 10x.
Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different shape and size for every input, such networks do not directly support batched t…
Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph kernels, based on return probabilities of random walks. The advantages of our proposed…
Graph potentials link to topological QFTs, with computational methods.
problem Defining a topological quantum field theory using graph potentials.
method Using colored trivalent graphs and birational type to define a topological QFT.
result Graph potentials' birational type depends on the graph's homotopy type.
The article uses PageRank and persistent homology for scalable graph comparison.
problem Comparing the similarities between complex networks.
method Combines PageRank and persistent homology to compute a scalable graph descriptor.
result Shows the effectiveness of the method on shape mesh datasets.
Statistical-computational gap found in aligning multiple Gaussian graphs.
problem Aligning multiple Gaussian graphs with unknown signals.
method Generalized informational threshold and computational barrier analysis.
result Existence of a statistical-computational gap in multiple Gaussian graph alignment.
Quantum computing techniques improve graph analysis and community detection.
problem Analyzing large graphs efficiently and accurately.
method Used quantum annealing and quantum gate computers for community detection and regularity checking.
result Demonstrated the effectiveness of quantum computing in solving complex graph problems.
PASCO speeds up graph clustering for large graphs.
problem Efficiently clustering large graphs with many communities.
method Overlay method combining coarsening and parallel clustering.
result PASCO accelerates clustering with improved efficiency and quality.
Linear time algorithm for random walk kernels on sparse graphs.
problem Efficient computation of general random walk kernels for large graphs.
method Sample dependent random walks to compute graph embeddings without direct graph product.
result Up to 27x faster and scalable to 128x larger graphs than previous methods.
Paper improves GNN inference speed and memory usage.
problem Scalability issues in GNNs during inference.
method Graph coarsening techniques for faster inference.
result Significant reduction in inference time and memory usage.
Pyramidal GNN combines RC and pooling for efficient graph embeddings.
problem Efficiently embedding graphs while maintaining accuracy.
method Alternates RC layers with pooling to reduce complexity.
result Formally shows how pooling reduces complexity and speeds convergence.
WEGL embeds graphs in a vector space for faster machine learning.
problem Efficiently embedding graphs for machine learning tasks.
method Wasserstein distance for node embedding similarity, Monge maps for graph representation.
result State-of-the-art classification performance with superior computational efficiency.
A fast graph embedding method for large graphs.
problem Efficiently embedding large graphs for various applications.
method One-hot graph encoder embedding with linear complexity.
result Graph encoder embedding is approximately normally distributed and converges to its mean.
Graph normalizing flows use neural networks for graph prediction and generation.
problem Efficiently processing and generating graph data with reduced memory usage.
method Reversible graph neural network model combining auto-encoder and normalizing flows.
result Graph normalizing flows achieve competitive results in graph generation and prediction.
DGL simplifies graph neural network computations for faster, more efficient tensor operations.
problem Lack of efficient tools for graph neural network computations.
method Design principles and implementation of DGL, a graph-centric library for GNNs, using sparse tensor operations and parallelization.
result DGL significantly outperforms other GNN frameworks in speed and memory consumption.
We construct maps on hat Heegaard Floer homology for cobordisms decorated with graphs. The graph TQFT allows for cobordisms with disconnected ends. Our construction uses Juhász's sutured Floer TQFT. We compute the maps for several elementary graph cobordisms. As an application, we compute the action of the fundamental …
Explicit computation of Kontsevich weights for symplectic Poisson structures.
problem Computing weights of Kontsevich graphs in symplectic Poisson structures.
method Detailed explicit computation using hypergeometric functions and simpler formulas.
result Explicit expressions for curvature weights and their simplification in cotangent bundles.
We present a deep reinforcement learning approach to minimizing the execution cost of neural network computation graphs in an optimizing compiler. Unlike earlier learning-based works that require training the optimizer on the same graph to be optimized, we propose a learning approach that trains an optimizer offline an…
Surveying machine learning for solving graph optimization problems.
problem Solving combinatorial optimization problems on graphs requires algorithmic engineering.
method Surveying machine learning approaches for graph optimization.
result Machine learning offers new ways to solve graph optimization problems.
The paper computes an approximation to the sample Frechet mean of graph sets using spectral information.
problem Characterizing the location of a set of graphs in a metric space.
method The Frechet mean is computed for sets of large graphs using the pseudometric defined by the norm between eigenvalues of adjacency matrices.
result An algorithm to approximate the sample Frechet mean of undirected unweighted graphs is described.
We compute the average Tristram---Levine signature of any graph link with positive weights in a three sphere, generalizing the results of Kirby and Melvin. The main tools are the Neumann's algorithm for computing the equivariant signatures of graph links and the Reciprocity Law for Dedekind sums.
PES method reduces bias in gradient estimation for unrolled graphs.
problem High variance and bias in gradient estimation for unrolled computation graphs.
method Divide graph into unrolls, apply ES update, accumulate correction terms.
result PES provides unbiased, low-variance gradient estimates.
The graph complexity of a compact 3-manifold is defined as the minimum order among all 4-colored graphs representing it. Exact calculations of graph complexity have been already performed, through tabulations, for closed orientable manifolds (up to graph complexity 32) and for compact orientable 3-manifolds with toric …
Graph learning method improves brain state classification.
problem Classifying brain states from iEEG signals.
method Representation learning on graphs for time-varying brain networks.
result 9.13% improvement in AUC for seizure vs. non-seizure classification.
The study provides a criterion to compute the total Thurston-Bennequin invariant of Legendrian graphs.
problem Computing the total Thurston-Bennequin invariant for Legendrian graphs.
method Generalized criterion for computing the total Thurston-Bennequin invariant from the tb of smaller cycles.
result The criterion holds for graphs with up to 9 vertices and for infinite families of examples.
Two graph homologies help compute embedding space.
problem Computing the rational homotopy group of long embeddings.
method Invented two graph homologies and constructed a map between them.
result A monomorphism from top hairy graph homology to top BCR graph homology.
NDP improves GNN efficiency by coarsening graphs without losing structure.
problem Efficiently summarize graph data for deep learning models.
method Node Decimation Pooling (NDP) reduces graph density while preserving topology.
result NDP achieves comparable performance to state-of-the-art pooling methods but with improved efficiency.
We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this end, we leverage persistent homology computed via a real-valued, learnable, filte…
A new GCN variant tackles large eigengaps in dense graphs and hypergraphs.
problem Large eigengaps in dense graphs and hypergraphs hinder popular GCN architectures.
method Uses pseudoinverse of the Laplacian and low-rank approximation for efficient computation.
result Improves runtime and accuracy in various experiments with real-world datasets.
Using different methods for laying out a graph can lead to very different visual appearances, with which the viewer perceives different information. Selecting a "good" layout method is thus important for visualizing a graph. The selection can be highly subjective and dependent on the given task. A common approach to se…
Recently, graph neural networks have been adopted in a wide variety of applications ranging from relational representations to modeling irregular data domains such as point clouds and social graphs. However, the space of graph neural network architectures remains highly fragmented impeding the development of optimized …
A neural architecture learns and refines graph correspondences.
problem Learning structural correspondences between graphs.
method Two-stage neural architecture: node embeddings followed by message passing networks.
result Message passing scheme computes well-founded consensus for corresponding neighborhoods.
Improved prediction accuracy in matrix factorization using graph-based priors.
problem Graph side-information may not align with latent-feature relations in matrix completion.
method Identify and remove 'contested' edges using graphical lasso approximation, maintaining linear scalability.
result Improved prediction accuracy with fewer graph edges, demonstrating the often inaccurate nature of graph side-information.
A new method solves graph coloring problems using gradient descent.
problem Graph coloring problems, computationally difficult.
method Population-based weight learning framework, gradient descent on GPUs.
result Improved best-known results for several large graphs.