Neural Information Processing Systems http://nips.cc/

In the course of preparing the supplementary materials we identified the following two mistakes. For the convenience of the reader we provide the full, corrected table below. C is an appropriatly chosen constant. Frei et al. (2022) Xu & Gu (2023) Theorem 3.1 Theorem 3.6 Theorem 3.8n C log null 1 δ null log null m δ null 1 δ 1 log null m δ null m C 1 log null n δ null log null n δ null log null n δ null log null n δ null γ 1 C 1 n 1 n 1 n 1 nd 1 k γ C 1 nd null log( The same mistake also means that the sentence starting on line 188 "Comparing In order to provide a convenient reference for the reader, we summarize our notation as follows. As such we typically resort to using a generically large enough constant C . For the reader's convenience we recap the data model studied in this work. We assume test data are drawn mutually i.i.d. In regard to the initialization of the network weights, for convenience we assume each neuron's To this end, we introduce the following notation, where p { 1, 1}. P(( B < κT) (T > 0) | w, v > 0) 1 P( T = 0 | w, v > 0) P( B κT | w, v > 0), therefore it suffices to upper bound the two probabilities on the right-hand-side. Using a variant of Hoeffding's bound for sampling without replacement (see Proposition Based on Lemma B.2, the following lemma bounds the probability that " on the counting functions: in particular we write P (i, l) + P (i, l) = P ( i, i) = 1 /2 and hence we conclude p + q = 1 / 2. As a result Observe by the data model, described in Section B.2, that We will often make use of the following similar but more pessimistic bounds on the activations.

We study benign overfitting in two-layer ReLU networks trained using gradient descent and hinge loss on noisy data for binary classification.

The discovery likely dates back to the continent's gold rushes. Breakthroughs, discoveries, and DIY tips sent six days a week. A metal detector hobbyist discovered a centuries' old coin while scouring an abandoned sports field--and the coin is especially rare for the area. In the southern Australian province of Victoria, treasure hunting enthusiast Angus James recently spotted a well-preserved 100 Mon Tenpō Tsūhō, a 19th century Japanese coin likely deposited during Australia's decades' long gold rush. "You never know what you'll find next," James posted to social media on January 25th, along with photos of his recent haul.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

However, this can be computationally prohibitive for realistic systems.

Neural Information Processing Systems http://nips.cc/