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arXiv 2303.15919cs.CVcs.LG

全双曲卷积神经网络用于计算机视觉

Fully Hyperbolic Convolutional Neural Networks for Computer Vision

University of Hildesheim(希尔德斯海姆大学)

Ahmad Bdeir, Kristian Schwethelm, Niels Landwehr

AI总结:

本文提出全双曲卷积神经网络HCNN,基于Lorentz模型推广CNN核心组件,在混合和全双曲设置下于标准视觉任务中展现良好性能,为更强大的双曲神经网络奠定基础。

摘要:

真实世界的视觉数据展现出内在的层级结构,这些结构可以在双曲空间中有效地表示。双曲神经网络(HNNs)是在此类空间中学习特征表示的一种有前景的方法。然而,当前计算机视觉中的双曲神经网络依赖于欧几里得骨干网络,仅在任务头中将特征投影到双曲空间,限制了其充分利用双曲几何优势的能力。为解决此问题,我们提出了HCNN,一种专为计算机视觉任务设计的全双曲卷积神经网络(CNN)。基于Lorentz模型,我们推广了CNN的基本组件,并提出了卷积层、批归一化以及多项逻辑回归的新公式。在标准视觉任务上的实验表明,我们的HCNN框架在混合和全双曲设置下均展现出有前景的性能。总体而言,我们相信我们的贡献为开发更强大的HNNs奠定了基础,这些HNNs能够更好地表示图像数据中发现的复杂结构。我们的代码公开于https://github.com/kschwethelm/HyperbolicCV。

英文摘要:

Real-world visual data exhibit intrinsic hierarchical structures that can be represented effectively in hyperbolic spaces. Hyperbolic neural networks (HNNs) are a promising approach for learning feature representations in such spaces. However, current HNNs in computer vision rely on Euclidean backbones and only project features to the hyperbolic space in the task heads, limiting their ability to fully leverage the benefits of hyperbolic geometry. To address this, we present HCNN, a fully hyperbolic convolutional neural network (CNN) designed for computer vision tasks. Based on the Lorentz model, we generalize fundamental components of CNNs and propose novel formulations of the convolutional layer, batch normalization, and multinomial logistic regression. {Experiments on standard vision tasks demonstrate the promising performance of our HCNN framework in both hybrid and fully hyperbolic settings.} Overall, we believe our contributions provide a foundation for developing more powerful HNNs that can better represent complex structures found in image data. Our code is publicly available at https://github.com/kschwethelm/HyperbolicCV.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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