In real-world scenarios, although data entities may possess inherent relationships, the specific graph illustrating their connections might not be directly accessible. Latent graph inference addresses this issue by enabling Graph Neural Networks (GNNs) to operate on point cloud data, dynamically learning the necessary graph structure. These graphs are often derived from a latent embedding space, which can be modeled using Euclidean, hyperbolic, spherical, or product spaces. However, currently, there is no principled differentiable method for determining the optimal embedding space. In this work, we introduce the Attentional Multi-Embedding Selection (AMES) framework, a differentiable method for selecting the best embedding space for latent graph inference through backpropagation, considering a downstream task. Our framework consistently achieves comparable or superior results compared to previous methods for latent graph inference across five benchmark datasets. Importantly, our approach eliminates the need for conducting multiple experiments to identify the optimal embedding space. Furthermore, we explore interpretability techniques that track the gradient contributions of different latent graphs, shedding light on how our attention-based, fully differentiable approach learns to choose the appropriate latent space. In line with previous works, our experiments emphasize the advantages of hyperbolic spaces in enhancing performance. More importantly, our interpretability framework provides a general approach for quantitatively comparing embedding spaces across different tasks based on their contributions, a dimension that has been overlooked in previous literature on latent graph inference.

本研究提出了一种不同iable方法，通过反向传播，根据下游任务选择最佳嵌入空间来进行潜在图推理，从而消除了进行多个实验以确定最佳嵌入空间的需要。此外，我们还探索了一种可解释性技术，通过跟踪不同潜在图的梯度贡献，揭示了我们的基于注意力的完全不同iable方法如何学习选择适当的潜在空间。与以前的研究相一致，我们的实验证明了超球面空间在提高性能方面的优势。更重要的是，我们的可解释性框架提供了一种通用方法，根据它们的贡献，量化比较不同任务中的嵌入空间，这一维度在以前的潜在图推理文献中被忽视。

AMES：一种用于潜在图推断的可微嵌入空间选择框架