In 2014, Kingma and Ba published their Adam optimizer algorithm, together with a mathematical argument that was meant to help justify it. In 2018, Bock and colleagues reported that a key piece was missing from that argument $-$ an unproven lemma which we will call Bock's conjecture. Here we show that this conjecture is false, but we prove a modified version of it which can take its place in analyses of Adam.

翻译：在2014年,Kingma和Ba发表了他们的亚当优化算法,并发表了一个旨在为其辩护的数学论点。 2018年,Bock和同事报告说,从这一论点中缺少了一个关键部分 — — 一个我们称之为Bock猜想的未经证实的列姆马美元。 这里我们证明这一猜想是虚假的,但我们证明了一个经过修改的版本,可以取代对Adam的分析。