Arman Mielke

Timo Stoll, Chendi Qian, Ben Finkelshtein et al.

Machine learning on graphs has recently achieved impressive progress in various domains, including molecular property prediction and chip design. However, benchmarking practices remain fragmented, often relying on narrow, task-specific datasets and inconsistent evaluation protocols, which hampers reproducibility and broader progress. To address this, we introduce GraphBench, a comprehensive benchmarking suite that spans diverse domains and prediction tasks, including node-level, edge-level, graph-level, and generative settings. GraphBench provides standardized evaluation protocols -- with consistent dataset splits and performance metrics that account for out-of-distribution generalization -- as well as a unified hyperparameter tuning framework. Additionally, we benchmark GraphBench using message-passing neural networks and graph transformer models, providing principled baselines and establishing a reference performance. See www.graphbench.io for further details.

Semih Cantürk, Andrei Manolache, Arman Mielke et al.

A wide range of graph learning tasks, such as structure discovery, temporal graph analysis, and combinatorial optimization, focus on inferring graph structures from data, rather than making predictions on given graphs. However, the respective methods to solve such problems are often developed in an isolated, task-specific manner and thus lack a unifying theoretical foundation. Here, we provide a stepping stone towards the formation of such a foundation and further development by introducing the Neural Graph Inverse Problem (GraIP) conceptual framework, which formalizes and reframes a broad class of graph learning tasks as inverse problems. Unlike discriminative approaches that directly predict target variables from given graph inputs, the GraIP paradigm addresses inverse problems, i.e., it relies on observational data and aims to recover the underlying graph structure by reversing the forward process, such as message passing or network dynamics, that produced the observed outputs. We demonstrate the versatility of GraIP across various graph learning tasks, including rewiring, causal discovery, and neural relational inference. We also propose benchmark datasets and metrics for each GraIP domain considered, and characterize and empirically evaluate existing baseline methods used to solve them. Overall, our unifying perspective bridges seemingly disparate applications and provides a principled approach to structural learning in constrained and combinatorial settings while encouraging cross-pollination of existing methods across graph inverse problems.

Arman Mielke, Uwe Bauknecht, Thilo Strauss et al.

Combinatorial optimization (CO) problems arise across a broad spectrum of domains, including medicine, logistics, and manufacturing. While exact solutions are often computationally infeasible, many practical applications require high-quality solutions within a given time budget. To address this, we propose a learning-based approach that enhances existing non-learned approximation algorithms for CO. Specifically, we parameterize these approximation algorithms and train graph neural networks (GNNs) to predict parameter values that yield near-optimal solutions. Our method is trained end-to-end in a self-supervised fashion, using a novel gradient estimation scheme that treats the approximation algorithm as a black box. This approach combines the strengths of learning and traditional algorithms: the GNN learns from data to guide the algorithm toward better solutions, while the approximation algorithm ensures feasibility. We validate our method on two well-known combinatorial optimization problems: the travelling salesman problem (TSP) and the minimum k-cut problem. Our results demonstrate that the proposed approach is competitive with state-of-the-art learned CO solvers.

Luca Della Libera, Vladimir Golkov, Yue Zhu et al.

Convolutional networks are successful due to their equivariance/invariance under translations. However, rotatable data such as images, volumes, shapes, or point clouds require processing with equivariance/invariance under rotations in cases where the rotational orientation of the coordinate system does not affect the meaning of the data (e.g. object classification). On the other hand, estimation/processing of rotations is necessary in cases where rotations are important (e.g. motion estimation). There has been recent progress in methods and theory in all these regards. Here we provide an overview of existing methods, both for 2D and 3D rotations (and translations), and identify commonalities and links between them.