Christopher Blöcker

Christopher Blöcker, Chester Tan, Ingo Scholtes

Community detection is an essential tool for unsupervised data exploration and revealing the organisational structure of networked systems. With a long history in network science, community detection typically relies on objective functions, optimised with custom-tailored search algorithms, but often without leveraging recent advances in deep learning. Recently, first works have started incorporating such objectives into loss functions for deep graph clustering and pooling. We consider the map equation, a popular information-theoretic objective function for unsupervised community detection, and express it in differentiable tensor form for optimisation through gradient descent. Our formulation turns the map equation compatible with any neural network architecture, enables end-to-end learning, incorporates node features, and chooses the optimal number of clusters automatically, all without requiring explicit regularisation. Applied to unsupervised graph clustering tasks, we achieve competitive performance against state-of-the-art deep graph clustering baselines in synthetic and real-world datasets.

Jan von Pichowski, Alžbeta Hrabošová, Ingo Scholtes et al.

Graph pooling is commonly applied in graph classification, yet its empirical gains over standard WL-1 expressive GNNs are often marginal or inconsistent. We study this gap by analysing the interaction between node features and graph topology and their effect on pooling objectives. Our analysis reveals that pooling operators require node features that are well-aligned with the graph's topology -- a condition often overlooked and not guaranteed in empirical networks. We formalise fundamental requirements for node features to enable effective pooling, and introduce a quantitative measure of feature quality. Our empirical evaluation shows that, when these requirements are satisfied, pooling can be beneficial and improve performance on appropriate datasets.

Jan von Pichowski, Christopher Blöcker, Ingo Scholtes

Graph pooling compresses graphs and summarises their topological properties and features in a vectorial representation. It is an essential part of deep graph representation learning and is indispensable in graph-level tasks like classification or regression. Current approaches pool hierarchical structures in graphs by iteratively applying shallow pooling operators up to a fixed depth. However, they disregard the interdependencies between structures at different hierarchical levels and do not adapt to datasets that contain graphs with different sizes that may require pooling with various depths. To address these issues, we propose MDL-Pool, a pooling operator based on the minimum description length (MDL) principle, whose loss formulation explicitly models the interdependencies between different hierarchical levels and facilitates a direct comparison between multiple pooling alternatives with different depths. MDP-Pool builds on the map equation, an information-theoretic objective function for community detection, which naturally implements Occam's razor and balances between model complexity and goodness-of-fit via the MDL. We demonstrate MDL-Pool's competitive performance in an empirical evaluation against various baselines across standard graph classification datasets.

Christopher Blöcker, Martin Rosvall, Ingo Scholtes et al.

Deep graph learning and network science both analyze graphs but approach similar problems from different perspectives. Whereas network science focuses on models and measures that reveal the organizational principles of complex systems with explicit assumptions, deep graph learning focuses on flexible and generalizable models that learn patterns in graph data in an automated fashion. Despite these differences, both fields share the same goal: to better model and understand patterns in graph-structured data. Early efforts to integrate methods, models, and measures from network science and deep graph learning indicate significant untapped potential. In this position, we explore opportunities at their intersection. We discuss open challenges in deep graph learning, including data augmentation, improved evaluation practices, higher-order models, and pooling methods. Likewise, we highlight challenges in network science, including scaling to massive graphs, integrating continuous gradient-based optimization, and developing standardized benchmarks.

Moritz Lampert, Christopher Blöcker, Ingo Scholtes

Dynamic link prediction is an important problem considered in many recent works that propose approaches for learning temporal edge patterns. To assess their efficacy, models are evaluated on continuous-time and discrete-time temporal graph datasets, typically using a traditional batch-oriented evaluation setup. However, as we show in this work, a batch-oriented evaluation is often unsuitable and can cause several issues. Grouping edges into fixed-sized batches regardless of their occurrence time leads to information loss or leakage, depending on the temporal granularity of the data. Furthermore, fixed-size batches create time windows with different durations, resulting in an inconsistent dynamic link prediction task. In this work, we empirically show how traditional batch-based evaluation leads to skewed model performance and hinders the fair comparison of methods. We mitigate this problem by reformulating dynamic link prediction as a link forecasting task that better accounts for temporal information present in the data.