arXiv subjects

Nils M. Kriege

Publications and source records attributed to Nils M. Kriege.

At least 19 recordsLinked to original sources

arXiv2026

On the Complexity of Graph Edit Distance in Restricted Graph Classes

The graph edit distance generalizes several well-known NP-hard problems and is therefore NP-hard itself. However, the relationship between the considered graph class, the edit cost function, and the resulting computational complexity is not well understood. We investigate this interplay by revisiting polynomial-time reductions from the literature, which reduce subgraph isomorphism and maximum common induced subgraph to the graph edit distance. For these classical problems, a sharp distinction between NP-hard and polynomial-time solvable cases is known, and we make the implications for the complexity of the graph edit distance explicit. We establish a graph-class-preserving correspondence between the maximum common edge subgraph and graph edit distance under a specific cost function, both in labeled and unlabeled graphs. In the unlabeled setting, the maximum common edge subgraph problem is polynomial-time solvable when one graph is a path and the other is a tree. In contrast, for labeled graphs, we prove that both the maximum common edge subgraph and the graph edit distance remain NP-hard, even when both graphs are paths.

cs.CC↗

arXiv2026

XIMP: Cross Graph Inter-Message Passing for Molecular Property Prediction

Accurate molecular property prediction is central to drug discovery, yet graph neural networks often underperform in data-scarce regimes and fail to surpass traditional fingerprints. We introduce cross-graph inter-message passing (XIMP), which performs message passing both within and across multiple related graph representations. For small molecules, we combine the molecular graph with scaffold-aware junction trees and pharmacophore-encoding extended reduced graphs, integrating complementary abstractions. While prior work is either limited to a single abstraction or non-iterative communication across graphs, XIMP supports an arbitrary number of abstractions and both direct and indirect communication between them in each layer. Across ten diverse molecular property prediction tasks, XIMP outperforms state-of-the-art baselines in most cases, leveraging interpretable abstractions as an inductive bias that guides learning toward established chemical concepts, enhancing generalization in low-data settings.

cs.LG↗

arXiv2025

Visualization and Analysis of the Loss Landscape in Graph Neural Networks

Graph Neural Networks (GNNs) are powerful models for graph-structured data, with broad applications. However, the interplay between GNN parameter optimization, expressivity, and generalization remains poorly understood. We address this by introducing an efficient learnable dimensionality reduction method for visualizing GNN loss landscapes, and by analyzing the effects of over-smoothing, jumping knowledge, quantization, sparsification, and preconditioner on GNN optimization. Our learnable projection method surpasses the state-of-the-art PCA-based approach, enabling accurate reconstruction of high-dimensional parameters with lower memory usage. We further show that architecture, sparsification, and optimizer's preconditioning significantly impact the GNN optimization landscape and their training process and final prediction performance. These insights contribute to developing more efficient designs of GNN architectures and training strategies.

cs.LG↗

arXiv2025

Weisfeiler and Leman Go Gambling: Why Expressive Lottery Tickets Win

The lottery ticket hypothesis (LTH) is well-studied for convolutional neural networks but has been validated only empirically for graph neural networks (GNNs), for which theoretical findings are largely lacking. In this paper, we identify the expressivity of sparse subnetworks, i.e. their ability to distinguish non-isomorphic graphs, as crucial for finding winning tickets that preserve the predictive performance. We establish conditions under which the expressivity of a sparsely initialized GNN matches that of the full network, particularly when compared to the Weisfeiler-Leman test, and in that context put forward and prove a Strong Expressive Lottery Ticket Hypothesis. We subsequently show that an increased expressivity in the initialization potentially accelerates model convergence and improves generalization. Our findings establish novel theoretical foundations for both LTH and GNN research, highlighting the importance of maintaining expressivity in sparsely initialized GNNs. We illustrate our results using examples from drug discovery.

cs.LG↗

arXiv2025

Efficient Mixed Precision Quantization in Graph Neural Networks

Graph Neural Networks (GNNs) have become essential for handling large-scale graph applications. However, the computational demands of GNNs necessitate the development of efficient methods to accelerate inference. Mixed precision quantization emerges as a promising solution to enhance the efficiency of GNN architectures without compromising prediction performance. Compared to conventional deep learning architectures, GNN layers contain a wider set of components that can be quantized, including message passing functions, aggregation functions, update functions, the inputs, learnable parameters, and outputs of these functions. In this paper, we introduce a theorem for efficient quantized message passing to aggregate integer messages. It guarantees numerical equality of the aggregated messages using integer values with respect to those obtained with full (FP32) precision. Based on this theorem, we introduce the Mixed Precision Quantization for GNN (MixQ-GNN) framework, which flexibly selects effective integer bit-widths for all components within GNN layers. Our approach systematically navigates the wide set of possible bit-width combinations, addressing the challenge of optimizing efficiency while aiming at maintaining comparable prediction performance. MixQ-GNN integrates with existing GNN quantization methods, utilizing their graph structure advantages to achieve higher prediction performance. On average, MixQ-GNN achieved reductions in bit operations of 5.5x for node classification and 5.1x for graph classification compared to architectures represented in FP32 precision.

cs.LG↗

arXiv2025

On the Relationship Between Robustness and Expressivity of Graph Neural Networks

We investigate the vulnerability of Graph Neural Networks (GNNs) to bit-flip attacks (BFAs) by introducing an analytical framework to study the influence of architectural features, graph properties, and their interaction. The expressivity of GNNs refers to their ability to distinguish non-isomorphic graphs and depends on the encoding of node neighborhoods. We examine the vulnerability of neural multiset functions commonly used for this purpose and establish formal criteria to characterize a GNN's susceptibility to losing expressivity due to BFAs. This enables an analysis of the impact of homophily, graph structural variety, feature encoding, and activation functions on GNN robustness. We derive theoretical bounds for the number of bit flips required to degrade GNN expressivity on a dataset, identifying ReLU-activated GNNs operating on highly homophilous graphs with low-dimensional or one-hot encoded features as particularly susceptible. Empirical results using ten real-world datasets confirm the statistical significance of our key theoretical insights and offer actionable results to mitigate BFA risks in expressivity-critical applications.

cs.LG↗

arXiv2024

Preventing Representational Rank Collapse in MPNNs by Splitting the Computational Graph

The ability of message-passing neural networks (MPNNs) to fit complex functions over graphs is limited as most graph convolutions amplify the same signal across all feature channels, a phenomenon known as rank collapse, and over-smoothing as a special case. Most approaches to mitigate over-smoothing extend common message-passing schemes, e.g., the graph convolutional network, by utilizing residual connections, gating mechanisms, normalization, or regularization techniques. Our work contrarily proposes to directly tackle the cause of this issue by modifying the message-passing scheme and exchanging different types of messages using multi-relational graphs. We identify a sufficient condition to ensure linearly independent node representations. As one instantion, we show that operating on multiple directed acyclic graphs always satisfies our condition and propose to obtain these by defining a strict partial ordering of the nodes. We conduct comprehensive experiments that confirm the benefits of operating on multi-relational graphs to achieve more informative node representations.

cs.LG↗

arXiv2024

On the Two Sides of Redundancy in Graph Neural Networks

Message passing neural networks iteratively generate node embeddings by aggregating information from neighboring nodes. With increasing depth, information from more distant nodes is included. However, node embeddings may be unable to represent the growing node neighborhoods accurately and the influence of distant nodes may vanish, a problem referred to as oversquashing. Information redundancy in message passing, i.e., the repetitive exchange and encoding of identical information amplifies oversquashing. We develop a novel aggregation scheme based on neighborhood trees, which allows for controlling redundancy by pruning redundant branches of unfolding trees underlying standard message passing. While the regular structure of unfolding trees allows the reuse of intermediate results in a straightforward way, the use of neighborhood trees poses computational challenges. We propose compact representations of neighborhood trees and merge them, exploiting computational redundancy by identifying isomorphic subtrees. From this, node and graph embeddings are computed via a neural architecture inspired by tree canonization techniques. Our method is less susceptible to oversquashing than traditional message passing neural networks and can improve the accuracy on widely used benchmark datasets.

cs.LG↗

arXiv2023

Approximating the Graph Edit Distance with Compact Neighborhood Representations

The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance between local substructures. While faster ones only consider vertices and their incident edges, leading to poor accuracy, other approaches require computationally intense exact distance computations between subgraphs. Our new method abstracts local substructures to neighborhood trees and compares them using efficient tree matching techniques. This results in a ground distance for mapping vertices that yields high quality approximations of the graph edit distance. By limiting the maximum tree height, our method supports steering between more accurate results and faster execution. We thoroughly analyze the running time of the tree matching method and propose several techniques to accelerate computation in practice. We use compressed tree representations, recognize redundancies by tree canonization and exploit them via caching. Experimentally we show that our method provides a significantly improved trade-off between running time and approximation quality compared to existing state-of-the-art approaches.

cs.DS↗

arXiv2023

Weisfeiler and Leman go Machine Learning: The Story so far

In recent years, algorithms and neural architectures based on the Weisfeiler--Leman algorithm, a well-known heuristic for the graph isomorphism problem, have emerged as a powerful tool for machine learning with graphs and relational data. Here, we give a comprehensive overview of the algorithm's use in a machine-learning setting, focusing on the supervised regime. We discuss the theoretical background, show how to use it for supervised graph and node representation learning, discuss recent extensions, and outline the algorithm's connection to (permutation-)equivariant neural architectures. Moreover, we give an overview of current applications and future directions to stimulate further research.

cs.LG↗

arXiv2023

A Higher-Order Temporal H-Index for Evolving Networks

The H-index of a node in a static network is the maximum value $h$ such that at least $h$ of its neighbors have a degree of at least $h$. Recently, a generalized version, the $n$-th order H-index, was introduced, allowing to relate degree centrality, H-index, and the $k$-core of a node. We extend the $n$-th order H-index to temporal networks and define corresponding temporal centrality measures and temporal core decompositions. Our $n$-th order temporal H-index respects the reachability in temporal networks leading to node rankings, which reflect the importance of nodes in spreading processes. We derive natural decompositions of temporal networks into subgraphs with strong temporal coherence. We analyze a recursive computation scheme and develop a highly scalable streaming algorithm. Our experimental evaluation demonstrates the efficiency of our algorithms and the conceptional validity of our approach. Specifically, we show that the $n$-th order temporal H-index is a strong heuristic for identifying super-spreaders in evolving social networks and detects temporally well-connected components.

cs.SI↗

arXiv2023

Weisfeiler and Leman Go Walking: Random Walk Kernels Revisited

Random walk kernels have been introduced in seminal work on graph learning and were later largely superseded by kernels based on the Weisfeiler-Leman test for graph isomorphism. We give a unified view on both classes of graph kernels. We study walk-based node refinement methods and formally relate them to several widely-used techniques, including Morgan's algorithm for molecule canonization and the Weisfeiler-Leman test. We define corresponding walk-based kernels on nodes that allow fine-grained parameterized neighborhood comparison, reach Weisfeiler-Leman expressiveness, and are computed using the kernel trick. From this we show that classical random walk kernels with only minor modifications regarding definition and computation are as expressive as the widely-used Weisfeiler-Leman subtree kernel but support non-strict neighborhood comparison. We verify experimentally that walk-based kernels reach or even surpass the accuracy of Weisfeiler-Leman kernels in real-world classification tasks.

cs.LG↗

arXiv2022

Gradual Weisfeiler-Leman: Slow and Steady Wins the Race

The classical Weisfeiler-Leman algorithm aka color refinement is fundamental for graph learning with kernels and neural networks. Originally developed for graph isomorphism testing, the algorithm iteratively refines vertex colors. On many datasets, the stable coloring is reached after a few iterations and the optimal number of iterations for machine learning tasks is typically even lower. This suggests that the colors diverge too fast, defining a similarity that is too coarse. We generalize the concept of color refinement and propose a framework for gradual neighborhood refinement, which allows a slower convergence to the stable coloring and thus provides a more fine-grained refinement hierarchy and vertex similarity. We assign new colors by clustering vertex neighborhoods, replacing the original injective color assignment function. Our approach is used to derive new variants of existing graph kernels and to approximate the graph edit distance via optimal assignments regarding vertex similarity. We show that in both tasks, our method outperforms the original color refinement with only a moderate increase in running time advancing the state of the art.

cs.LG↗

arXiv2022

A Temporal Graphlet Kernel for Classifying Dissemination in Evolving Networks

We introduce the \emph{temporal graphlet kernel} for classifying dissemination processes in labeled temporal graphs. Such dissemination processes can be spreading (fake) news, infectious diseases, or computer viruses in dynamic networks. The networks are modeled as labeled temporal graphs, in which the edges exist at specific points in time, and node labels change over time. The classification problem asks to discriminate dissemination processes of different origins or parameters, e.g., infectious diseases with different infection probabilities. Our new kernel represents labeled temporal graphs in the feature space of temporal graphlets, i.e., small subgraphs distinguished by their structure, time-dependent node labels, and chronological order of edges. We introduce variants of our kernel based on classes of graphlets that are efficiently countable. For the case of temporal wedges, we propose a highly efficient approximative kernel with low error in expectation. We show that our kernels are faster to compute and provide better accuracy than state-of-the-art methods.

cs.SI↗

arXiv2022

EmbAssi: Embedding Assignment Costs for Similarity Search in Large Graph Databases

The graph edit distance is an intuitive measure to quantify the dissimilarity of graphs, but its computation is NP-hard and challenging in practice. We introduce methods for answering nearest neighbor and range queries regarding this distance efficiently for large databases with up to millions of graphs. We build on the filter-verification paradigm, where lower and upper bounds are used to reduce the number of exact computations of the graph edit distance. Highly effective bounds for this involve solving a linear assignment problem for each graph in the database, which is prohibitive in massive datasets. Index-based approaches typically provide only weak bounds leading to high computational costs verification. In this work, we derive novel lower bounds for efficient filtering from restricted assignment problems, where the cost function is a tree metric. This special case allows embedding the costs of optimal assignments isometrically into $\ell_1$ space, rendering efficient indexing possible. We propose several lower bounds of the graph edit distance obtained from tree metrics reflecting the edit costs, which are combined for effective filtering. Our method termed EmbAssi can be integrated into existing filter-verification pipelines as a fast and effective pre-filtering step. Empirically we show that for many real-world graphs our lower bounds are already close to the exact graph edit distance, while our index construction and search scales to very large databases.

cs.DB↗

arXiv2022

Temporal Walk Centrality: Ranking Nodes in Evolving Networks

We propose the Temporal Walk Centrality, which quantifies the importance of a node by measuring its ability to obtain and distribute information in a temporal network. In contrast to the widely-used betweenness centrality, we assume that information does not necessarily spread on shortest paths but on temporal random walks that satisfy the time constraints of the network. We show that temporal walk centrality can identify nodes playing central roles in dissemination processes that might not be detected by related betweenness concepts and other common static and temporal centrality measures. We propose exact and approximation algorithms with different running times depending on the properties of the temporal network and parameters of our new centrality measure. A technical contribution is a general approach to lift existing algebraic methods for counting walks in static networks to temporal networks. Our experiments on real-world temporal networks show the efficiency and accuracy of our algorithms. Finally, we demonstrate that the rankings by temporal walk centrality often differ significantly from those of other state-of-the-art temporal centralities.

cs.SI↗

arXiv2021

The Power of the Weisfeiler-Leman Algorithm for Machine Learning with Graphs

In recent years, algorithms and neural architectures based on the Weisfeiler-Leman algorithm, a well-known heuristic for the graph isomorphism problem, emerged as a powerful tool for (supervised) machine learning with graphs and relational data. Here, we give a comprehensive overview of the algorithm's use in a machine learning setting. We discuss the theoretical background, show how to use it for supervised graph- and node classification, discuss recent extensions, and its connection to neural architectures. Moreover, we give an overview of current applications and future directions to stimulate research.

cs.LG↗

arXiv2021

Metric Indexing for Graph Similarity Search

Finding the graphs that are most similar to a query graph in a large database is a common task with various applications. A widely-used similarity measure is the graph edit distance, which provides an intuitive notion of similarity and naturally supports graphs with vertex and edge attributes. Since its computation is NP-hard, techniques for accelerating similarity search have been studied extensively. However, index-based approaches for this are almost exclusively designed for graphs with categorical vertex and edge labels and uniform edit costs. We propose a filter-verification framework for similarity search, which supports non-uniform edit costs for graphs with arbitrary attributes. We employ an expensive lower bound obtained by solving an optimal assignment problem. This filter distance satisfies the triangle inequality, making it suitable for acceleration by metric indexing. In subsequent stages, assignment-based upper bounds are used to avoid further exact distance computations. Our extensive experimental evaluation shows that a significant runtime advantage over both a linear scan and state-of-the-art methods is achieved.

cs.DB↗