E.2 Training details

We use the Chamfer loss function [457–459] for the LGAE-Min-Max and GNNAE-JL models, and MSE for LGAE-Mix and GNNAE-PL. We tested the Hungarian loss [303, 460] and differentiable energy mover’s distance (EMD) [325], calculated using the JetNet library [461], as well but found the Chamfer and MSE losses more performant.

The graph-based models are optimized using the Adam optimizer [462] implemented in PyTorch [424] with a learning rate $\gamma =10^{-3}$, coefficients $({\beta }_1,{\beta }_2)=(0.9,0.999)$, and weight decay $\lambda =0$. The CNNAE is optimized using the same optimizer implemented in TensorFlow [463]. They are all trained on single NVIDIA RTX 2080 Ti GPUs each for a maximum of 20000 epochs using early stopping with the patience of 200 epochs. The total training time for LGAE models is typically 35 hours, and at most 100 hours, while GNNAE-PL and GNNAE-JL train for 50 and 120 hours on average, respectively. By contrast, the CNNAE model, due to its simplicity, can typically converge within 3 hours.