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Different phases and phase transition points in hidden Markov models

Ruben Poghosyan1, Vardan Bardakhchyan2,*, and David B. Saakian2,†

  • *Contact author: vardanbardakchyan@gmail.com
  • †Contact author: saakian@yerphi.am
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Phys. Rev. E 114, 014123 – Published 14 July, 2026

DOI: https://doi.org/10.1103/vjy9-4r1f

Abstract

We are looking for different phases in hidden Markov models (HMMs). By analyzing the stationary solution of the master equation, we discover different situations with localized or delocalized distributions for the stationary distributions of the master equation. We hypothesize that these phases are related to the relaxation dynamics of the HMM ensemble. We have derived precise phase transition points. We test whether the behavior of the HMMs and their associated numerical algorithms change near the transition points. We find that the accuracy of the Viterbi and Baum-Welch algorithms sometimes is worse near the phase transition, which contradicts the edge of chaos hypothesis.

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Phys. Rev. E 114, 014123– Published 14 July, 2026
  • Received 14 November 2025
  • Accepted 7 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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