Fig. 6: Attribute recovery in the inferred latent spaces.
From: On the design and evaluation of generative models in high energy density physics
a Shows geodesic interpolation between two points in the latent space with hyperbolic prior. We show the points generated along this geodesic are scientifically valid (top left), and the corresponding images show high visual fidelity (top right). b The schema on top shows the setup of sequential optimization to evaluate the effectiveness of this hyperbolic latent space in optimizing for an attribute of interest. Specifically, we want to find regions in the latent space that produce images with the maximum brightness, as it captures the amount of energy in the current experiment. This not only measures the effectiveness of structure in the latent space, but also the ability to sample from the Poincaré prior. The sample images in the left panel, show that Geom-WAE (Poincaré) consistently outperforms its Euclidean counterpart in achieving higher peaks for the target function and often does so more rapidly, as illustrated in the right panel. The shaded region represents variations observed across five trials.
