  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.
