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Self-Averaging and On-line Learning

G. Reents·R. Urbanczik
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Abstract

Conditions are given under which one may prove that the stochastic dynamics of on-line learning can be described by the deterministic evolution of a finite set of order parameters in the thermodynamic limit. A global constraint on the average magnitude of the increments in the stochastic process is necessary to ensure self-averaging. In the absence of such a constraint, convergence may only be in probability.

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G. Reents, R. Urbanczik. 1998-05-26. Self-Averaging and On-line Learning. https://doi.org/10.1103/physrevlett.80.5445

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