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Diaaeldin Taha

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3 papers

2 author rows

TMLR Journal 2026 Journal Article

Relative Geometry of Neural Forecasters: Linking Accuracy and Alignment in Learned Latent Geometry

Deniz Kucukahmetler
Maximilian Jean Hemmann
Julian Mosig von Aehrenfeld
Maximilian Amthor
Christian Deubel
Nico Scherf
Diaaeldin Taha

Neural networks can accurately forecast complex dynamical systems, yet how they internally represent underlying latent geometry remains poorly understood. We study neural forecasters through the lens of representational alignment, introducing anchor-based, geometry-agnostic relative embeddings that remove rotational and scaling ambiguities in latent spaces. Applying this framework across seven canonical dynamical systems—ranging from periodic to chaotic—we reveal reproducible family-level structure: multilayer perceptrons align with other MLPs, recurrent networks with RNNs, while transformers and echo-state networks achieve strong forecasts despite weaker alignment. Alignment generally correlates with forecasting accuracy, yet high accuracy can coexist with low alignment. Relative geometry thus provides a simple, reproducible foundation for comparing how model families internalize and represent dynamical structure.

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ICLR Conference 2025 Conference Paper

Demystifying Topological Message-Passing with Relational Structures: A Case Study on Oversquashing in Simplicial Message-Passing

Diaaeldin Taha
James Chapman 0007
Marzieh Eidi
Karel Devriendt
Guido Montúfar

Topological deep learning (TDL) has emerged as a powerful tool for modeling higher-order interactions in relational data. However, phenomena such as oversquashing in topological message-passing remain understudied and lack theoretical analysis. We propose a unifying axiomatic framework that bridges graph and topological message-passing by viewing simplicial and cellular complexes and their message-passing schemes through the lens of relational structures. This approach extends graph-theoretic results and algorithms to higher-order structures, facilitating the analysis and mitigation of oversquashing in topological message-passing networks. Through theoretical analysis and empirical studies on simplicial networks, we demonstrate the potential of this framework to advance TDL.

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TMLR Journal 2024 Journal Article

Normed Spaces for Graph Embedding

Diaaeldin Taha
Wei Zhao
J. Maxwell Riestenberg
Michael Strube

Theoretical results from discrete geometry suggest that normed spaces can abstractly embed finite metric spaces with surprisingly low theoretical bounds on distortion in low dimensions. Inspired by this theoretical insight, we highlight in this paper normed spaces as a more flexible and computationally efficient alternative to several popular Riemannian manifolds for learning graph embeddings. Normed space embeddings significantly outperform several popular manifolds on a large range of synthetic and real-world graph reconstruction benchmark datasets while requiring significantly fewer computational resources. We also empirically verify the superiority of normed space embeddings on growing families of graphs associated with negative, zero, and positive curvature, further reinforcing the flexibility of normed spaces in capturing diverse graph structures as graph sizes increase. Lastly, we demonstrate the utility of normed space embeddings on two applied graph embedding tasks, namely, link prediction and recommender systems. Our work highlights the potential of normed spaces for geometric graph representation learning, raises new research questions, and offers a valuable tool for experimental mathematics in the field of finite metric space embeddings. We make our code and data publically available \footnote{\url{https://github.com/andyweizhao/graphs-normed-spaces}}.

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