Author name cluster

Ernst Röell

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3 papers

2 author rows

ICLR Conference 2025 Conference Paper

MANTRA: The Manifold Triangulations Assemblage

Rubén Ballester
Ernst Röell
Daniel Bin Schmid
Mathieu Alain
Sergio Escalera
Carles Casacuberta
Bastian Rieck

The rising interest in leveraging higher-order interactions present in complex systems has led to a surge in more expressive models exploiting higher-order structures in the data, especially in topological deep learning (TDL), which designs neural networks on higher-order domains such as simplicial complexes. However, progress in this field is hindered by the scarcity of datasets for benchmarking these architectures. To address this gap, we introduce MANTRA, the first large-scale, diverse, and intrinsically higher-order dataset for benchmarking higher-order models, comprising over 43,000 and 250,000 triangulations of surfaces and three-dimensional manifolds, respectively. With MANTRA, we assess several graph- and simplicial complex-based models on three topological classification tasks. We demonstrate that while simplicial complex-based neural networks generally outperform their graph-based counterparts in capturing simple topological invariants, they also struggle, suggesting a rethink of TDL. Thus, MANTRA serves as a benchmark for assessing and advancing topological methods, paving the way towards more effective higher-order models.

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NeurIPS Conference 2025 Conference Paper

Point Cloud Synthesis Using Inner Product Transforms

Ernst Röell
Bastian Rieck

Point cloud synthesis, i. e. the generation of novel point clouds from an input distribution, remains a challenging task, for which numerous complex machine learning models have been devised. We develop a novel method that encodes geometrical-topological characteristics of point clouds using inner products, leading to a highly-efficient point cloud representation with provable expressivity properties. Integrated into deep learning models, our encoding exhibits high quality in typical tasks like reconstruction, generation, and interpolation, with inference times orders of magnitude faster than existing methods.

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ICLR Conference 2024 Conference Paper

Differentiable Euler Characteristic Transforms for Shape Classification

Ernst Röell
Bastian Rieck

The _Euler Characteristic Transform_ (ECT) is a powerful invariant, combining geometrical and topological characteristics of shapes and graphs. However, the ECT was hitherto unable to learn task-specific representations. We overcome this issue and develop a novel computational layer that enables learning the ECT in an end-to-end fashion. Our method, the _Differentiable Euler Characteristic Transform_ (DECT) is fast and computationally efficient, while exhibiting performance on a par with more complex models in both graph and point cloud classification tasks. Moreover, we show that this seemingly simple statistic provides the same topological expressivity as more complex topological deep learning layers.

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