构建黎曼神经网络变换层
Building Transformation Layers for Riemannian Neural Networks
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中文总结 AI 辅助
本工作提出一个在计算上可处理的黎曼空间上构建全连接和卷积层的统一框架，涵盖多种几何作为特例，并在十个代表性流形上验证其有效性与适用性。
中文摘要 AI 辅助
近年来，基于流形值表示的深度神经网络在各种机器学习应用中引起了广泛关注。近期的一个焦点是将欧几里得全连接（FC）层和卷积层推广到非欧几里得几何。然而，以往的方法通常只关注少数选定的流形，并依赖于目标流形的特定性质。相比之下，本工作提出了一个在计算上可处理的黎曼空间上构建FC层和卷积层的框架。该框架将先前不同几何上的多个FC层作为特例纳入其中，并在十个代表性流形上进行了实例化，包括三种双曲模型、五种对称正定（SPD）流形的几何以及两种格拉斯曼视角。在不同流形上的实验证明了我们方法的有效性和适用性。代码可在该https URL找到。
英文摘要
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.
发表机构
- University of Trento（特伦托大学）
- MPI for Intelligent Systems, Tübingen（马克斯·普朗克智能系统研究所（蒂宾根））
机构由 AI 辅助整理，请以论文原文为准。
