将卷积神经网络从欧式空间拓展到双曲空间，提升模型表达能力。
On the Universal Statistical Consistency of Expansive Hyperbolic Deep Convolutional Neural Networks
- 基于庞加莱圆盘构建双曲卷积网络，采用扩张型卷积机制
- 理论证明双曲扩张卷积具有全局一致性，实验证明性能显著优于欧式模型
- 适合处理层次结构数据，如语言、知识图谱等复杂关系建模
深度卷积神经网络（DCNN）在计算机视觉领域广泛应用。尽管其能捕捉数据中的复杂模式，但其嵌入空间仍为欧式空间，主要依赖收缩型卷积。近年来，双曲空间神经网络的发展激发了在非欧空间构建卷积网络的兴趣。本文提出基于庞加莱圆盘的双曲深度卷积神经网络（Hyperbolic DCNN），重点分析非欧空间中扩张卷积的性质。进一步提供了关于双曲空间中扩张卷积全局一致性的理论分析。通过在合成数据集和真实数据集上的大量实验，结果表明双曲卷积架构在性能上显著优于欧式模型。
原文摘要 · Abstract (English)
The emergence of Deep Convolutional Neural Networks (DCNNs) has been a pervasive tool for accomplishing widespread applications in computer vision. Despite its potential capability to capture intricate patterns inside the data, the underlying embedding space remains Euclidean and primarily pursues contractive convolution. Several instances can serve as a precedent for the exacerbating performance of DCNNs. The recent advancement of neural networks in the hyperbolic spaces gained traction, incentivizing the development of convolutional deep neural networks in the hyperbolic space. In this work, we propose Hyperbolic DCNN based on the Poincaré Disc. The work predominantly revolves around analyzing the nature of expansive convolution in the context of the non-Euclidean domain. We further offer extensive theoretical insights pertaining to the universal consistency of the expansive convolution in the hyperbolic space. Several simulations were performed not only on the synthetic datasets but also on some real-world datasets. The experimental results reveal that the hyperbolic convolutional architecture outperforms the Euclidean ones by a commendable margin.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。