Scaling model capacity has been vital in the success of deep learning.

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Furthermore, we obtain exactp-values, which are easily computed in terms of the Tulap random variable. We show that our results also apply to distribution-free hypothesis testsforcontinuous data.

Time series with non-uniform intervals occur in many applications, and are difficulttomodel usingstandard recurrent neural networks(RNNs).

Let = argm 2 CF ( )denote (2). T ( )+ log ( 1/ )+( 1) log ( 1/ ) log ( ) 1 , (5) where ( )isthe RDPof 2. Convergence:IfwerunAcldpwith t = DGpt, whereG2 = max{d1 Substitutingtheboundon4 into Lemma 2 together manipulationgivesproves Theorem 1; see Appendix E.2 fordetails.

Alternatively,theyrequire large-scale training data and longer training schedules to learn the IB implicitly.

This would be particularly useful for large datasets like imagenet. Table 2 shows the area under accuracydrop curve(AUC) on MNIST Figure 4for gradient when training traditionally,training using saliencyguided procedure andfine-tuning (smaller AUCindicates better performance).

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