Most state-of-the-art graph kernels only take local graph properties into account, i.e., the kernel is computed with regard to properties of the neighborhood of vertices or other small substructures. On the other hand, kernels that do take global graph propertiesinto account may not scale well to large graph databases.…
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48 results for “Weisfeiler-Lehman algorithm”
Graph Neural Networks outperform the Weisfeiler-Lehman algorithm in representation power.
problem Limited representation power of Graph Neural Networks compared to the Weisfeiler-Lehman algorithm.
method Algebraic analysis using eigenvalue decomposition of graph operators.
result Graph Neural Networks produce more discriminative representations than the Weisfeiler-Lehman algorithm.
Explains differences between WL and folklore-WL formulations in graph neural networks.
problem Understanding the differences between WL and folklore-WL formulations in graph neural networks.
method Visual explanation of differences between WL and folklore-WL formulations.
result Clarifies the differences between WL and folklore-WL formulations.
Improves hypergraph link prediction by breaking symmetry.
problem Limited expressivity of GWL-1 algorithm in hypergraph link prediction.
method Preprocessing algorithm to identify and replace symmetry-inducing subhypergraphs with covering hyperedges.
result Improves expressivity of GWL-1, leading to better link prediction.
Proposes a 2-WL-based graph convolution for improved graph classification.
problem Limitations of current GNN architectures in discriminative power.
method Introduces a novel 2-dimensional Weisfeiler-Lehman graph convolution.
result 2-WL-GNN architecture is more discriminative than existing GNN approaches.
Improved molecular property prediction using WL embedding in GNNs.
problem Limited performance of GNNs in predicting molecular properties.
method Explored Weisfeiler-Lehman (WL) embedding to replace GNN layers, enhancing representability and performance.
result WL embedding consistently improves GNN performance across multiple datasets.
Improved GNN simulation of WL test with exponentially lower complexity.
problem Improving the complexity of simulating the Weisfeiler-Lehman test with GNNs.
method Exponentially lower complexity simulation of WL test using GNNs with polylogarithmic parameters and O(log n) bits feature vectors.
result Near-optimal construction with logarithmic lower bounds for feature vector length and neural network size.
Interpretable Neural Architecture Search via Bayesian Optimisation with Weisfeiler-Lehman Kernelscs.LG
Bayesian optimisation with graph kernels improves neural architecture search and provides interpretability.
problem Lack of insight into why architectures perform well and how to improve them.
method Combines Bayesian optimisation with Weisfeiler-Lehman graph kernels for highly data-efficient and interpretable architecture search.
result Demonstrates state-of-the-art performance on closed- and open-domain search spaces.
Paper compares GCNs and MPNNs, finding GCNs are one step ahead of WL algorithm.
problem Comparing graph convolutional networks (GCNs) and message-passing neural networks (MPNNs).
method Casts GCNs and MPNNs as MPNNs, studies distinguishing power of different architectures.
result GCNs are one step ahead of the Weisfeiler-Lehman (WL) algorithm in distinguishing power.
This paper improves GNNs' generalization by adding a Low-Rank Global Attention module.
problem Improving the generalization power of Graph Neural Networks (GNNs).
method Incorporating a Low-Rank Global Attention (LRGA) module into GNNs.
result Augmenting GNNs with LRGA aligns them with a powerful graph isomorphism test, 2-Folklore Weisfeiler-Lehman (2-FWL).
Kernels for structured data are commonly obtained by decomposing objects into their parts and adding up the similarities between all pairs of parts measured by a base kernel. Assignment kernels are based on an optimal bijection between the parts and have proven to be an effective alternative to the established convolut…
Deep Graphscs.LG
We propose an algorithm for deep learning on networks and graphs. It relies on the notion that many graph algorithms, such as PageRank, Weisfeiler-Lehman, or Message Passing can be expressed as iterative vertex updates. Unlike previous methods which rely on the ingenuity of the designer, Deep Graphs are adaptive to the…
The ability of a graph neural network (GNN) to leverage both the graph topology and graph labels is fundamental to building discriminative node and graph embeddings. Building on previous work, we theoretically show that edGNN, our model for directed labeled graphs, is as powerful as the Weisfeiler-Lehman algorithm for …
Most graph kernels are an instance of the class of -Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of the final set of substructures, usually a sum or average, thereby potentially dis…
The success of kernel methods has initiated the design of novel positive semidefinite functions, in particular for structured data. A leading design paradigm for this is the convolution kernel, which decomposes structured objects into their parts and sums over all pairs of parts. Assignment kernels, in contrast, are ob…
The prediction of organic reaction outcomes is a fundamental problem in computational chemistry. Since a reaction may involve hundreds of atoms, fully exploring the space of possible transformations is intractable. The current solution utilizes reaction templates to limit the space, but it suffers from coverage and eff…
Applying machine learning to molecules is challenging because of their natural representation as graphs rather than vectors.Several architectures have been recently proposed for deep learning from molecular graphs, but they suffer from informationbottlenecks because they only pass information from a graph node to its d…
This work generalizes graph neural networks (GNNs) beyond those based on the Weisfeiler-Lehman (WL) algorithm, graph Laplacians, and diffusions. Our approach, denoted Relational Pooling (RP), draws from the theory of finite partial exchangeability to provide a framework with maximal representation power for graphs. RP …
Paper explores how GNNs can learn graph biconnectivity, finding ESAN is the only known expressive framework.
problem Understanding the expressive power of GNNs beyond the WL test.
method Introduces a novel class of expressivity metrics via graph biconnectivity and develops the GD-WL approach.
result GD-WL consistently outperforms prior GNN architectures in learning biconnectivity metrics.
New framework extends graph neural networks by improving expressiveness and space efficiency.
problem Limitations of existing graph neural networks, particularly in expressive power and space complexity.
method Proposed -FWL+, a flexible and powerful framework that combines -FWL and -FWL+.
result Demonstrated N-FWL, a practical and theoretically sound instance of -FWL+, achieving record-breaking results on ZINC-Subset.
New kernel speeds up graph regression in physics.
problem Handling large, sparse graphs with continuous node attributes in physics.
method Introduced Sliced Wasserstein Weisfeiler-Lehman (SWWL) graph kernel for Gaussian process regression.
result The SWWL kernel is efficient and positive definite, reducing complexity.
We study the effect of structural variation in graph data on the predictive performance of graph kernels. To this end, we introduce a novel, noise-robust adaptation of the GraphHopper kernel and validate it on benchmark data, obtaining modestly improved predictive performance on a range of datasets. Next, we investigat…
A new GNN model SPIN achieves state-of-the-art performance on diverse real-world datasets.
problem Graph classification efficiency and accuracy.
method Parallel neighborhood aggregations (PA-GNNs) and SPIN model.
result SPIN model achieves state-of-the-art performance on diverse real-world datasets.
In this paper, we develop a novel Backtrackless Aligned-Spatial Graph Convolutional Network (BASGCN) model to learn effective features for graph classification. Our idea is to transform arbitrary-sized graphs into fixed-sized backtrackless aligned grid structures and define a new spatial graph convolution operation ass…
Enhanced GNN with expanded attention window and partially random embeddings.
problem Limited expressivity of traditional GNNs in distinguishing non-isomorphic graphs.
method Graph attention network with expanding attention window and partially random initial embeddings. Head dropout for regularization.
result Improved ability to differentiate between non-isomorphic graphs.
Graph neural networks fail to distinguish certain 3D atom configurations.
problem Graph neural networks (GNN) fail to distinguish certain 3D atom configurations.
method Construction of degenerate 3D atom configurations that are indistinguishable by first-order GNNs.
result First-order GNNs are incomplete for 3D atom configurations.
TOGL adds topological info to GNNs, improving graph and node classification.
problem Graph neural networks lack substructure awareness, especially cycles.
method Integrates global topological information using persistent homology.
result Improves predictive performance for graph and node classification.
While state-of-the-art kernels for graphs with discrete labels scale well to graphs with thousands of nodes, the few existing kernels for graphs with continuous attributes, unfortunately, do not scale well. To overcome this limitation, we present hash graph kernels, a general framework to derive kernels for graphs with…
Graph neural networks (GNNs) are a powerful tool to learn representations on graphs by iteratively aggregating features from node neighbourhoods. Many variant models have been proposed, but there is limited understanding on both how to compare different architectures and how to construct GNNs systematically. Here, we p…
Enhances GNNs by capturing node relationships, outperforming 2-WL test.
problem Inability of conventional GNNs to fully capture node relationships due to permutation invariance.
method Develops permutation-sensitive aggregation mechanism using permutation groups.
result Proves superior expressivity compared to 2-WL test and not less than 3-WL test.
New walk extraction strategies improve node embeddings in KGs.
problem Improving node embeddings in knowledge graphs.
method Proposed five different walk extraction strategies to complement basic random walks.
result The n-gram strategy performs best on average for node classification tasks.
Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes. Many GNN variants have been pro…
Study extends GNN VC dimension bounds to Pfaffian activation functions.
problem Bounding GNN VC dimension for new activation functions.
method Pfaffian function theory applied to GNNs with sigmoid and hyperbolic tangent activations.
result Bounds on GNN VC dimension for various architectures and graph properties.
Graph Neural Networks struggle on random graphs without node identifiers.
problem Graph Neural Networks' limitations on random graphs without node identifiers.
method Study of Graph Neural Networks and Structural Graph Neural Networks convergence on large random graphs.
result Structural Graph Neural Networks are more powerful and universal than Graph Neural Networks on random graphs.
The ability to detect and count certain substructures in graphs is important for solving many tasks on graph-structured data, especially in the contexts of computational chemistry and biology as well as social network analysis. Inspired by this, we propose to study the expressive power of graph neural networks (GNNs) v…
Can neural networks learn to compare graphs without feature engineering? In this paper, we show that it is possible to learn representations for graph similarity with neither domain knowledge nor supervision (i.e.\ feature engineering or labeled graphs). We propose Deep Divergence Graph Kernels, an unsupervised method …
Recently, the Weisfeiler-Lehman (WL) graph isomorphism test was used to measure the expressive power of graph neural networks (GNN). It was shown that the popular message passing GNN cannot distinguish between graphs that are indistinguishable by the 1-WL test (Morris et al. 2018; Xu et al. 2019). Unfortunately, many s…
Graph data widely exist in many high-impact applications. Inspired by the success of deep learning in grid-structured data, graph neural network models have been proposed to learn powerful node-level or graph-level representation. However, most of the existing graph neural networks suffer from the following limitations…
Given a graph where every node has certain attributes associated with it and some nodes have labels associated with them, Collective Classification (CC) is the task of assigning labels to every unlabeled node using information from the node as well as its neighbors. It is often the case that a node is not only influenc…
Enhances GNNs to better capture local graph structures.
problem Limited expressiveness of GNNs due to star-shaped message passing.
method Extends local aggregation to subgraph patterns using GNN encoders.
result Significantly improved performance on graph ML tasks.
Distance Encoding: Design Provably More Powerful Neural Networks for Graph Representation Learningcs.LG
DE improves GNNs by distinguishing graph substructures, enhancing accuracy.
problem Limited expressive power of GNNs in representing graph substructures.
method Introduces Distance Encoding (DE) to assist GNNs in distinguishing graph substructures.
result DE distinguishes graph substructures that traditional GNNs cannot, improving accuracy.
Examines algorithmic modeling across three cultures.
problem Tackles algorithmic modeling in different cultural contexts.
method Uses parametric regressions, interpretable algorithms, and complex algorithms.
result Extension of Leo Breiman's thesis to include cultural differences.
Playing repeated matrix games (RMG) while maximizing the cumulative returns is a basic method to evaluate multi-agent learning (MAL) algorithms. Previous work has shown that , , or algorithms have good behaviours on average in RMG. Besides, hedging algorithms have been shown to be effective on predi…
Meta-algorithm selection aims to choose the best algorithm selector for a given problem instance.
problem Selecting the best algorithm selector for a specific problem instance.
method Apply algorithm selection to the selection of other algorithms (meta-algorithm selection).
result Meta-algorithm selection can be beneficial in some cases but faces challenges in solving the meta-level problem.
Proposes CLRS benchmark to evaluate algorithmic reasoning.
problem Difficulty in transferring results across publications due to targeted algorithmic data.
method Develops a comprehensive benchmark covering various algorithmic tasks.
result Demonstrates performance of algorithmic reasoning baselines on the CLRS benchmark.
Combines multiple bandit algorithms to create a nearly optimal single algorithm.
problem Designing a single bandit algorithm that performs nearly as well as the best individual algorithm in a stochastic environment.
method Develops two general corralling algorithms that achieve favorable regret guarantees.
result The regret of the corralling algorithms is no worse than the best individual algorithm's performance.
Accelerated Randomized Coordinate Descent Algorithms for Stochastic Optimization and Online Learningcs.LG
We propose accelerated randomized coordinate descent algorithms for stochastic optimization and online learning. Our algorithms have significantly less per-iteration complexity than the known accelerated gradient algorithms. The proposed algorithms for online learning have better regret performance than the known rando…
The exchange algorithm is studied for its convergence and asymptotic variance.
problem Theoretical limitations of the exchange algorithm in sampling from doubly-intractable distributions.
method Theoretical analysis of the exchange algorithm's convergence speed and asymptotic variance.
result The exchange algorithm converges at a geometric rate and satisfies a Central Limit Theorem.