Machine Learning 1

Complex social phenomena, such as polarization, often emerge from the dynamics of social networks. However,studying these phenomena is challenging due to the lack of representative network data. Recently, population-leveladministrative networks from Statistics Netherlands have become available. These networks capture connectionsbetween all 17 million individuals in the Netherlands through five key social contexts: schools, families, workplaces,households, and close neighbors. Moreover, population-level networks can be linked to representative surveys, containingindividual information about values and behavior. While these networks have been shown to correlate with simplecontagion phenomena such as epidemics, their value for understanding complex phenomena remains unclear.In this work, we apply recent advances in graph machine learning to address two key questions: (i) To what extentdoes network structure predict populist voting behavior, and (ii) which network substructures correlate with this behavior?Although the structural position of nodes (Fig. 1A) can be compressed into low-dimensional embeddings (Fig. 1B),these are not directly interpretable. To fill this gap, we use the DINE framework to identify interpretable substructures(Fig. 1C–D) that are associated with populist voting behavior.The substructures uncovered can provide intuitive explanations for the spread of complex phenomena, for example,hubs which are connected through ”wide” bridges (Fig. 1D). This allows domain experts to interpret and validate thelearned embeddings in the specific social context. We make these substructures available to all researchers using datafrom Statistics Netherlands. Our work contributes to network science by expanding the understanding of how networkstructure shapes the diffusion of behaviors and ideas and to social science by bridging computational approaches withsociological theory to better understand the drivers of political behavior.

Open Source Software (OSS) communities are key to innovation but often face challenges retaining developers. High developer churn disrupts projects, limits knowledge sharing, and undermines community stability. Predicting and understanding churn is critical to fostering long-term engagement. This study explores the use of Graph Neural Networks (GNNs) to analyze developers' social environments and improve retention strategies.We examined collaboration networks from 50 OSS projects, covering diverse team sizes, topics, and programming languages. For each project, we built co-editing networks where nodes represent developers and edges denote changes in code ownership through shared edits. These dynamic, time-stamped, directed, weighted, multi-edge graphs capture the evolution of interactions and collaborative dynamics. Prior research shows these networks effectively reflect social structures and knowledge transfer. Using network data from the first half of each project's timeline, we predicted developer churn in the second half.Our approach applies GNNs to these networks without relying on external developer attributes. We evaluated four models: a static GNN (GCN), a time-aware higher-order static GNN (DBGNN), a time-aware node embedding (EVO), and a temporal GNN (TGN). By leveraging temporal interaction patterns, we identified signals that indicate developers' likelihood to disengage.This work demonstrates the synergy between temporal network analysis, higher-order models, and GNNs to address developer churn. It highlights how network-based insights can tackle practical challenges in OSS communities. We would be excited to present our insights in a talk.

Lying at the interface between Network Science and Machine Learning, node embedding algorithms take a graph as input and encode its structure onto output vectors that represent nodes in an abstract geometric space, enabling various vector-based downstream tasks such as network modelling, data compression, link prediction, and community detection. Two apparently unrelated limitations affect these algorithms. On one hand, it is not clear what the basic operation defining vector spaces, i.e. the vector sum, corresponds to in terms of the original nodes in the network (see Figure (a)). On the other hand, while the same input network can be represented at multiple levels of resolution by coarse-graining the constituent nodes into arbitrary block-nodes, the relationship between node embeddings obtained at different hierarchical levels is not understood. In Fig. (b), one can visualize these drawbacks for LPCA [1], a representative of this class of model.Here [2], building on recent results in network renormalization theory, we address these two limitations at once and define a multiscale node embedding method that, upon arbitrary coarse-grainings, ensures statistical consistency of the embedding vector of a block-node with the sum of the embedding vectors of its constituent nodes. We illustrate the power of this approach on two economic networks that can be naturally represented at multiple resolution levels: namely, international trade between (sets of) countries and input-output flows among (sets of) industries in the Netherlands. We confirm the statistical consistency between networks retrieved from coarse-grained node vectors and networks retrieved from sums of fine-grained node vectors, a result that cannot be achieved by alternative methods.Several key network properties, including a large number of triangles, are successfully replicated already from embeddings of very low dimensionality, allowing for the generation of faithful replicas of the original net. [...]

Topological signals are variables or features associated with both nodes and edges of a network. Recently, in the context of Topological Machine Learning, great attention has been devoted to signal processing of such topological signals. Most of the previous topological signal processing algorithms treat node and edge signals separately and work under the hypothesis that the true signal is smooth and/or well approximated by a harmonic eigenvector of the Hodge-Laplacian, which may be violated in practice. Here we propose the Dirac-equation signal processing (DESP) that can efficiently reconstruct true signals on nodes and edges, also if they are not smooth or harmonic, by processing them jointly. The proposed physics-inspired algorithm is based on the spectral properties of the topological Dirac operator. It leverages the mathematical structure of the topological Dirac equation to boost the performance of the signal processing algorithm. We discuss how the relativistic dispersion relation obeyed by the topological Dirac equation can be used to assess the quality of the signal reconstruction. Finally, we demonstrate the improved performance of the algorithm with respect to previous algorithms and show that processing jointly nodes and edges allows to exploit all relevant information present in the data across the different dimensions of the topological signal. Specifically, we show that by considering the Iterated Dirac-equation signal processing (IDESP) can also be used efficiently if the true signal is a non-trivial linear combination of more than one eigenstate of the Dirac equation, as it generally occurs for real signals.This work opens new perspectives in Artificial Intelligence as this approach can be generalized to investigate signal processing on multiplex networks. Moreover, the principles on which the DESP reside might allows to tackle in the future the outstanding problem of oversmothing in topological deep learning.

The barycenter graph (or sample Fréchet mean) of a set of networks is an essential location parameter at the core of almost every machine learning algorithm working on networks. In this paper, we introduce a new algorithm to estimate the graph barycenter which is computationally efficient, has reduced dimensionality, and captures topological information of the training set on various scales. We use the eigenvalues of the adjacency matrix to measure the proximity between graphs, and parameterize the definition of the graph barycenter by approximating complex networks using a stochastic block model (SBM). We provide theoretical justifications for the algorithm's design using analysis from spectral graph theory of the eigenvalues of the SBM. Extensive validation is performed on synthetic networks sampled from true SBMs of various geometries, and our algorithm successfully recovers a Fréchet mean converging to the population Fréchet mean associated with the generative model. Additionally, we test the algorithm's robustness with non-SBM graphs exhibiting community structure, and our results show that the algorithm converges in few iterations, is computationally efficient, and that the parameters describing the output sample Fréchet mean graph can quantify significant topological changes in the real networks.

Link prediction---a task of distinguishing actual hidden edges from random unconnected node pairs---is one of the quintessential tasks in graph machine learning. Despite being widely accepted as a universal benchmark and a downstream task for representation learning, the link prediction benchmark's validity has rarely been questioned. Here, we show that the common edge sampling procedure in the link prediction task has an implicit bias toward high-degree nodes. This produces a highly skewed evaluation that favors methods overly dependent on node degree. In fact a ``null'' link prediction method based solely on node degree can yield nearly optimal performance in this setting. We propose a degree-corrected link prediction benchmark that offers a more reasonable assessment and better aligns with the performance on the recommendation task. Finally, we demonstrate that the degree-corrected benchmark can more effectively train graph machine-learning models by reducing overfitting to node degrees and facilitating the learning of relevant structures in graphs.