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Bifurcation structure of equilibria of iterated softmax

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  • Tiňo, Peter

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.

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  • Tiňo, Peter, 2009. "Bifurcation structure of equilibria of iterated softmax," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1804-1816.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:4:p:1804-1816
    DOI: 10.1016/j.chaos.2008.07.026
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    References listed on IDEAS

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    1. Bishop, S.R. & Sofroniou, A. & Shi, P., 2005. "Symmetry-breaking in the response of the parametrically excited pendulum model," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 257-264.
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