This section illustrates that (7) holds.

We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point reformulation of the dynamic version of EOT which is known as the Schrödinger Bridge problem. In contrast to the prior methods for large-scale EOT, our algorithm is end-to-end and consists of a single learning step, has fast inference procedure, and allows handling small values of the entropy regularization coefficient which is of particular importance in some applied problems. Empirically, we show the performance of the method on several large-scale EOT tasks.

We study the consistency of surrogate risks for robust binary classification.

In fact, without such assumptions, this problem is NP-hard [Sim02; MR18].

Still, they suffer from the time-consuming inference which requires modeling thousands of diffusion steps.

Results are shown in Table 6. T able 6: Defense performance (multi-class classification accuracy) against influence targeted attacks. Results are shown in Table 7. To evaluate how harmful non-targeted attacks can be for GNNs, we first give results without attack and under attack (without defense), i.e., "Attack" vs. "No Attack" columns The accuracy of even the strongest GNN is reduced by 18.7% on GNN if the defender is used on clean, non-attacked graphs. GNNs when they are attacked.