Supplementary Materials Roadmap

In this supplementary material, we provide "full versions" of Sections 2-4 from the main submission, Fact 2.5 (Uniform bound on entries of Gaussian vector) . For g N (0, Id), g/ nullg null is identical in distribution to v . We can expand the expectation and apply Fact B.2 to get We will also need the following stability result for affine linear thresholds. Putting all of these ingredients together, we can now complete the proof of the main Lemma B.1 of By Lemma B.6 applied to the projection of f to the two-dimensional This notion is motivated by Lemma 4.4 in Section C.1 where we study the critical points We first collect some elementary consequences of closeness. Suppose < 2/ 2. If ( v In the rest of the paper we will take to be small, so Lemma 3.3 will always apply.