arXiv:2607. 22381v1 Announce Type: new Abstract: Curvature notions on graphs, particularly Ollivier-Ricci and Forman, have emerged as powerful tools for addressing fundamental issues in Graph Neural Networks (GNNs) such as oversmoothing and oversquashing, but rely almost exclusively on local edge-level comparisons and therefore fail to certify how information actually propagates over long distances.
By Rachid Caich, Yassine Abbahaddou
arXiv:2401. 14381v3 Announce Type: replace Abstract: We propose two graph neural network layers for graphs with features in a Riemannian manifold.
By Martin Hanik, Gabriele Steidl, Christoph von Tycowicz
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.
By Kushal Bose, Swagatam Das
arXiv:2607. 19305v2 Announce Type: replace-cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.
By Chen Ziheng
arXiv:2607. 19305v1 Announce Type: cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.
By Chen Ziheng
arXiv:2606. 07598v1 Announce Type: cross Abstract: We propose a topological framework for comparing trained Graph Neural Networks (GNNs) by mapping the Stochastic Block Models (SBMs) induced on the graphon-signal space of a Message Passing Neural Network (MPNN) onto the unit $n$-sphere $\sphere^{n-1}\subset\R^n$.
By Gopal Anantharaman
arXiv:2606. 03270v1 Announce Type: cross Abstract: Foundation models have sparked a revolution via a pretraining-adaptation paradigm, with recent efforts extending this success to graphs.
By Li Sun, Zhenhao Huang, Yiding Wang, Qin Chen, Pietro Lio, Philip S. Yu
arXiv:2609.35436v2 Announce Type: replace
Abstract: Recently, deep neural networks on manifold-valued representations have garnered significant attention across various machine learning applications....
By Ziheng Chen
arXiv:2606. 25456v1 Announce Type: new Abstract: Brain-Computer Interface (BCI) based on electroencephalography (EEG) enables direct interaction between the brain and external environments and has significant applications in assistive technologies, medical rehabilitation, and entertainment.
By Shaocheng Jin, Tao Zhou, Rui Wang, Ziheng Chen, Xiaoqing Luo, Xiaojun Wu, Josef Kittler
The paper introduces flow charts, a conditional invertible neural network designed to approximate normal coordinates on Riemannian manifolds, enabling fast Euclidean approximations of exponential and logarithmic maps. It presents a novel nonnegative loss function that is zero exactly when the chart is normal, and demonstrates that flow charts match or surpass specialized neural geodesic interpolators across sixteen synthetic and data‑derived geometries. When pretrained, flow charts achieve a median 60–70× speedup over numerical baselines while maintaining comparable logarithmic map estimation error and improving numerical geodesic solver accuracy.
By Edmond Cunningham
The paper introduces SPD-MetaFormer, an attention‑free architecture for decoding brain signals from small datasets. It shows that existing attention‑based models on the SPD manifold (MAtt and GBWAtt) learn nearly uniform weights, and that replacing learned weights with uniform ones does not degrade performance. SPD-MetaFormer uses uniformly weighted Fréchet aggregation with a geodesic residual and a shared spectral feedforward map, achieving competitive results on three EEG benchmarks while maintaining SPD‑valued token states until classification.
By Zhida Wang, Wei Lyu, Guo Yu, Sui Tang
arXiv:2606. 20547v1 Announce Type: new Abstract: We place the attention token on the group: a token is an element $g_i$ of a matrix Lie group $G$ -- a bare transformation, with no feature payload and no external action $\rho(g)$ carrying it.
By Przemyslaw Musialski