Original ICLR2015 paper; inspected arXiv version9, dated30January2017. First-page bylines are Diederik P. Kingma and Jimmy Lei Ba; middle initial P. retained without expansion. Algorithm1 and section2, printed p2, define moment histories, corrections and epsilon placement; section3, printed p3, derives initialization correction under moment assumptions. Used for mathematical mechanisms rather than universal performance or convergence claims.

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