Stochastic Manhattan learning: Time-evolution operator for the ensemble dynamics

Todd K. Leen, John E. Moody

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Typical theoretical descriptions of the ensemble dynamics of stochastic learning algorithms rely on a truncated expansion to approximate the time-evolution operator appearing in the master equation. In this paper we give an exact expression for the time-evolution operator for Manhattan learning, a variant of stochastic gradient-descent learning in which the weights are updated in proportion to the sign of the cost function gradient. This closed form for the time evolution captures the full nonlinearity of the problem without approximation, allowing exact study of the ensemble dynamics.

Original languageEnglish (US)
Pages (from-to)1262-1265
Number of pages4
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number1
StatePublished - Jan 1 1997

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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