The paper introduces a degree‑resolved framework for nonlinear interactions between irreducible representations in graph neural networks, enabling mixing of non‑isomorphic representations that linear equivariant maps cannot achieve. Using this framework, the authors build Specht Triple, a residual module for unordered graph triples, and demonstrate that it reduces aggregate standardised test MSE by 11.05% on a synthetic structural benchmark compared to a parameter‑matched linear baseline. The results highlight irreducible decomposition as a useful inductive bias for nonlinear higher‑order equivariant processing.
arXiv:2609.25776v1 Announce Type: cross Abstract: Nonlinear activations can create equivariant interactions between irreducible representations that linear maps cannot. We use the Gaussian degree dec...
arXiv:2412. 19419v2 Announce Type: replace-cross Abstract: Graph neural networks are deep neural networks designed for graphs with attributes attached to nodes or edges.
arXiv:2510. 15814v2 Announce Type: replace-cross Abstract: Universality results for equivariant neural networks remain rare.
arXiv:2410. 06665v4 Announce Type: replace-cross Abstract: This paper explores the characterization of equivariant linear layers for representations of permutations and related groups.
HyPE-GT introduces a framework that generates learnable hyperbolic positional encodings for Graph Transformers, enabling the capture of complex hierarchical relationships in graph-structured data. Unlike traditional Euclidean encodings, HyPE’s hyperbolic encodings can be selected to suit specific downstream tasks and help mitigate oversmoothing in deep Graph Neural Networks. Experiments on molecular benchmarks and large-scale Open Graph Benchmark datasets demonstrate improved performance, while additional tests on Coauthor and Copurchase networks confirm HyPE’s effectiveness in controlling oversmoothing.
arXiv:2607. 19042v1 Announce Type: cross Abstract: Neural hypergraphs are a natural generalization of neural networks, the reference models in modern machine learning.
arXiv:2608. 12010v1 Announce Type: new Abstract: Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields.
arXiv:2605.06462v2 Announce Type: replace Abstract: Progress in graph learning is hindered by benchmark practices that conflate the contributions of node features and graph structure, making it hard...
arXiv:2607. 02166v1 Announce Type: cross Abstract: The rapid advancements in using neural networks as implicit data representations have attracted significant interest in developing machine learning methods that analyze and process the weight spaces of other neural networks.
arXiv:2406. 08966v3 Announce Type: replace Abstract: The separation power of a machine learning model refers to its ability to distinguish between different inputs and is often used as a proxy for its expressivity.
arXiv:2509.21624v4 Announce Type: replace Abstract: Molecular Hessians, the second derivatives of the potential energy, are fundamental to many workflows in computational chemistry. Usually, accurate...
arXiv:2505.11298v2 Announce Type: replace Abstract: Graph Neural Networks (GNNs) are powerful tools for learning on structured data, yet the relationship between their expressivity and predictive per...