Notations: In this homework, we will use the notations in Lectures for neural tangent kernels. Some common conditions and notations for all problems in this homework are listed as follows: Let 0(t) = max(0,t). We denote A0 = Amin (H*) . 6 > 0 is an arbitrary constant. We assume \"xi\" = 1 and |y| g 1for'i, = 1,...,n. 2 Question 2: (Hint: Use Bernstein inequality) Let w1, W2, ..., Wm E Rd be any set of weight vectors which are in the neighborhood of the initialization, i.e., IWE - Wk(0) 1/2 (1 + ()/max) S d (1 te)le E 20. 4.2 Lemma 2: Bernstein inequality Let X1, . .., Xn be independent zero-mean random variables. Suppose we have |Xi| 0, it holds that n P [Xi> ESexp E2 /2 =1 EYE [X}] + ME/3