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.

翻译：图神经网络通常依赖于图拓扑结构对网络可用且对下游任务最优的假设。潜在图推断允许模型动态学习数据连接模式可能无法直接获取的问题的固有图结构。在本工作中，我们推广了用于潜在图学习的离散可微图模块（dDGM）。原始dDGM架构使用欧几里得平面编码潜在特征，并基于这些特征生成潜在图。通过将黎曼几何融入模型并生成更复杂的嵌入空间，我们可以提升潜在图推断系统的性能。特别地，我们提出了一种计算上可行的方法，用于生成常曲率模型空间的乘积流形，该流形可编码不同结构的潜在特征。映射到推断所得乘积流形上的潜在表示被用于计算更丰富的相似性度量，这些度量由潜在图学习模型利用以获取优化后的潜在图。此外，乘积流形的曲率在训练过程中与网络其他参数一起基于下游任务进行学习，而非作为静态嵌入空间。我们的新方法在广泛的数据集上进行了测试，并优于原始dDGM模型。