Graph Neural Networks usually rely on the assumption that the graph topology
is available to the network as well as optimal for the downstream task. Latent
graph inference allows models to dynamically learn the intrinsic graph
structure of problems where the connectivity patterns of data may not be
directly accessible. In this work, we generalize the discrete Differentiable
Graph Module (dDGM) for latent graph learning. The original dDGM architecture
used the Euclidean plane to encode latent features based on which the latent
graphs were generated. By incorporating Riemannian geometry into the model and
generating more complex embedding spaces, we can improve the performance of the
latent graph inference system. In particular, we propose a computationally
tractable approach to produce product manifolds of constant curvature model
spaces that can encode latent features of varying structure. The latent
representations mapped onto the inferred product manifold are used to compute
richer similarity measures that are leveraged by the latent graph learning
model to obtain optimized latent graphs. Moreover, the curvature of the product
manifold is learned during training alongside the rest of the network
parameters and based on the downstream task, rather than it being a static
embedding space. Our novel approach is tested on a wide range of datasets, and
outperforms the original dDGM model.

本文提出一种基于 Riemannian geometry 和 product manifolds 的可微分图模块，用于推断连接数据的复杂潜在图结构。该方法不仅可以动态地学习数据的内在结构，还可以在性能上对现有方法进行改进并成功地在各种数据集上进行了测试。

利用积流形进行潜在图推断

Latent Graph Inference using Product Manifolds

Graph deep learning has recently emerged as a powerful ML concept allowing to
generalize successful deep neural architectures to non-Euclidean structured
data. Such methods have shown promising results on a broad spectrum of
applications ranging from social science, biomedicine, and particle physics to
computer vision, graphics, and chemistry. One of the limitations of the
majority of current graph neural network architectures is that they are often
restricted to the transductive setting and rely on the assumption that the
underlying graph is {\em known} and {\em fixed}. Often, this assumption is not
true since the graph may be noisy, or partially and even completely unknown. In
such cases, it would be helpful to infer the graph directly from the data,
especially in inductive settings where some nodes were not present in the graph
at training time. Furthermore, learning a graph may become an end in itself, as
the inferred structure may provide complementary insights next to the
downstream task. In this paper, we introduce Differentiable Graph Module (DGM),
a learnable function that predicts edge probabilities in the graph which are
optimal for the downstream task. DGM can be combined with convolutional graph
neural network layers and trained in an end-to-end fashion. We provide an
extensive evaluation of applications from the domains of healthcare (disease
prediction), brain imaging (age prediction), computer graphics (3D point cloud
segmentation), and computer vision (zero-shot learning). We show that our model
provides a significant improvement over baselines both in transductive and
inductive settings and achieves state-of-the-art results.

本文提出可微分图模块 (DGM) 用于预测边缘概率，与卷积图神经网络层结合，可以在具有噪声和不完整的图形数据中进行端到端的图形学习，并在疾病预测、年龄预测、点云分割、零样本学习等领域获得了先进的结果。