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A Missing lemmas for the proof of Theorem 3.1

Neural Information Processing Systems

The following proof is from Daniely and V ardi [15], and we give it here for completeness. By Lemma A.1, there exists a DNF formula We construct such an affine layer in Lemma A.2. At least one of the k size-n slices in z contains 0 more than once. We define the outputs of our affine layer as follows. Pr [z represents a hyperedge ] = n (n 1) ... (n k + 1) null 1 n null Pr null z Z null 1 2 log(n) .




Appendix 420 A Missing Proofs of Section 4 421

Neural Information Processing Systems

We start by proving statement (ii). We now prove statement (iii). The last constraint is trivially satisfied. This can be easily shown by induction. 's constraint remains equal when Let's pick such a branching Moreover, observe that every edge in B is tight.




The Small English Town Swept Up in the Global AI Arms Race

WIRED

The residents of Potters Bar are working to protect the "green belt" of farms, forests, and meadows that surround London from the endless demand for AI infrastructure. A short drive from London, the town of Potters Bar is separated from the village of South Mimms by 85 acres of rolling farmland segmented by a scribble of hedgerows. In one of the fields, a lone oak serves as a rest stop along a public footpath. Lately, the tree has become a site of protest, too. A poster tied to its trunk reads: "NO TO DATA CENTRE."