Bifurcation structure of equilibria of iterated softmax

Peter Tiňo

Chaos, Solitons & Fractals, 2009, vol. 41, issue 4, 1804-1816

Abstract: We present a detailed bifurcation study of iterated renormalization process driven by softmax transformation parametrized by a temperature parameter. For each emerging equilibrium we give exact characterization of stable/unstable manifolds of the linearized dynamics. As the system cools down, new equilibria emerge in a strong structure until finally a complex skeleton of saddle type equilibria surrounding an unstable maximum entropy point, with decision enforcing “one-hot” stable equilibria emerges.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:41:y:2009:i:4:p:1804-1816

DOI: 10.1016/j.chaos.2008.07.026

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