On the Convergence of Semi Unsupervised Calibration through Prior
  Adaptation Algorithm
Lautaro Estienne Roberta Hansen Matias Vera Luciana Ferrer Pablo Piantanida
Calibration is an essential key in machine leaning. Semi Unsupervised
Calibration through Prior Adaptation (SUCPA) is a calibration algorithm used in
(but not limited to) large-scale language models defined by a {system of
first-order difference equation. The map derived by this system} has the
peculiarity of being non-hyperbolic {with a non-bounded set of non-isolated
fixed points}. In this work, we prove several convergence properties of this
algorithm from the perspective of dynamical systems. For a binary
classification problem, it can be shown that the algorithm always converges,
{more precisely, the map is globally asymptotically stable, and the orbits
converge} to a single line of fixed points. Finally, we perform numerical
experiments on real-world application to support the presented results.
Experiment codes are available online.