Please refer to the Appendix 5 for details. Besides, in order to balance the classification loss and the transformation loss we set the scalar factor to beλ = 5 throughoutthetrainingphase. Here the first rows are the untransformed and the transformed images, while the second rows are the corresponding interpretations. This is a supplement toFigure 1 in the main body of the paper. And also there are perturbation methods such as randomized input sampling (RISE) [8] and extremal perturbation (EP) [2].

Sharpness-Aware Minimization (SAM) has attracted significant attention for its effectiveness in improving generalization across various tasks. However, its underlying principles remain poorly understood.

Our experiments show that Genfer is often faster than the existing exact inference tools PSI, Dice, and Prodigy.

Afterpre-processing methodsin [are 16,087 samples, and 1, 668, 738 featuresinthedataset.

Let B be the maximum difference betweenU1t and U2t, and let (π,θ1,θ2) be a Nash Equilibrium forG. Let π1 be the best response to the first teacher (with utilityU1t) and let π1+2 be the best response policy to the joint teacher. This result shows that as we reduce the number of random episodes, the approximation to aminimax regret strategy improves. Let G be the dual curriculum game in which the first teacher maximizes regret, so U1t = URt, and the second teacher plays randomly, soU2t = UUt . Finally,we need to show thatπ2+3 isoptimal for the student.

We investigate neural network representations from a probabilistic perspective.