Hyperbolic spaces have recently gained momentum in the context of machine
learning due to their high capacity and tree-likeliness properties. However,
the representational power of hyperbolic geometry is not yet on par with
Euclidean geometry, mostly because of the absence of corresponding hyperbolic
neural network layers. This makes it hard to use hyperbolic embeddings in
downstream tasks. Here, we bridge this gap in a principled manner by combining
the formalism of M\"obius gyrovector spaces with the Riemannian geometry of the
Poincar\'e model of hyperbolic spaces. As a result, we derive hyperbolic
versions of important deep learning tools: multinomial logistic regression,
feed-forward and recurrent neural networks such as gated recurrent units. This
allows to embed sequential data and perform classification in the hyperbolic
space. Empirically, we show that, even if hyperbolic optimization tools are
limited, hyperbolic sentence embeddings either outperform or are on par with
their Euclidean variants on textual entailment and noisy-prefix recognition
tasks.

通过将 M"obius gyrovector 空间的形式主义与 Poincarе模型的 Riemannian 几何相结合，我们提出了重要深度学习工具的超几何版本：多项式逻辑回归、前馈和循环神经网络。这样可以在超几何空间中嵌入序列数据并进行分类。实验证明，即使超几何优化工具受限，超几何句子嵌入在文本蕴含和噪声前缀识别任务中的表现要么优于，要么与欧几里得变体相当。