https://hackerpaper.kaipfister.de/p/1509.08101/Collected HN comments and submissions linking this paper.enMon, 02 Nov 2026 11:16:22 GMThttps://news.ycombinator.com/item?id=10419265urn:hackerpapers:mention:1509.08101:10419265Tue, 20 Oct 2015 14:17:30 GMT<p>There is a recent 5 page theoretical paper on this topic that I thought was pretty interesting, and it tackles both deep nets and recurrent nets: http://arxiv.org/abs/1509.08101 Here is the abstract: This note provides a family of classification problems, indexed by a positive integer k, where all shallow networks with fewer than exponentially (in k) many nodes exhibit error at least 1/6, whereas a deep network with 2 nodes in each of 2k layers achieves zero error, as does a recurrent network with 3 distinct nodes iterated k times. The proof is elementary, and the networks are standard…</p><p><a href="https://hackerpaper.kaipfister.de/p/1509.08101/">Paper and discussion history</a>. A mention is not an endorsement.</p>cs.LGhttps://news.ycombinator.com/item?id=10419236urn:hackerpapers:submission:1509.08101:10419236Tue, 20 Oct 2015 14:14:07 GMT<p>Representation Benefits of Deep Feedforward Networks</p><p></p><p>1 point; 0 discussion replies on HN. <a href="https://hackerpaper.kaipfister.de/p/1509.08101/">Paper and source history</a>. A submission is not an endorsement.</p>cs.LG