aiqbench analysis
This research advances machine learning by proposing a unified framework for constructing fully connected and convolutional layers over diverse Riemannian manifolds, addressing the limitations of previous methods that were restricted to specific geometries. By demonstrating effectiveness across hyperbolic models, SPD manifolds, and Grassmannian perspectives, the work provides a computationally tractable solution for deep neural networks operating on non-Euclidean data representations.
Building Transformation Layers for Riemannian Neural Networks
arXiv:2609.35436v1 Announce Type: cross Abstract: Recently, deep neural networks on manifold-valued representations have garnered significant attention across various machine learning applications. One recent focus is the generalization of Euclidean fully connected (FC) and convolutional layers to non-Euclidean geometries. However, previous approaches typically focus on a few selected manifolds and rely on specific properties of the target manifold. In contrast, this work proposes a framework for constructing FC and convolutional layers over computationally tractable Riemannian spaces. This framework incorporates several previous FC layers across different geometries as special cases and is instantiated on ten representative manifolds, including three hyperbolic models, five geometries of the symmetric positive definite (SPD) manifold, and two Grassmannian perspectives. Experiments on different manifolds demonstrate the effectiveness and applicability of our approach. Code can be found at https://github.com/GitZH-Chen/RieTrans.
Abstract:Recently, deep neural networks on manifold-valued representations have garnered significant attention across various machine learning applications. One recent focus is the generalization of Euclidean fully connected (FC) and convolutional layers to non-Euclidean geometries. However, previous approaches typically focus on a few selected manifolds and rely on specific properties of the target manifold. In contrast, this work proposes a framework for constructing FC and convolutional layers over computationally tractable Riemannian spaces. This framework incorporates several previous FC layers across different geometries as special cases and is instantiated on ten representative manifolds, including three hyperbolic models, five geometries of the symmetric positive definite (SPD) manifold, and two Grassmannian perspectives. Experiments on different manifolds demonstrate the effectiveness and applicability of our approach. Code can be found at this https URL.
Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
arXiv:2609.35436 [cs.AI]
(or arXiv:2609.35436v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2609.35436 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 224 words
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