Appendix for " Stability and Generalization Analysis of Gradient Methods for Shallow Neural Networks " A Lemmas

In this section, we collect several lemmas useful for our analysis. The proof is completed.Lemma A.2. Let W, W According to Taylor's theorem, there exists α [0, 1] such that ℓ(W; z) ℓ(W The proof is completed.The following lemma shows the self-bounding property of smooth and nonnegative functions. Let Assumptions 1, 2 hold. Let Assumptions 1, 2 hold. The remaining arguments in proving Lemma A.6 is the same as proving Lemma 5 in [ Let Assumptions 1, 2 hold.