In this supplementary material corresponding to the paper `Unsupervised Self-Adaptive Auditory Attention Decoding' by Geirnaert et al. [1], which has also been peer-reviewed together with the original article in [1], we show convergence to a unique fixed point of the fixed-point iteration on the updating model (Equation (16) in the original paper [1]). We hypothesize and show that under three reasonable conditions on the accuracies of the attended and unattended decoder, there exists a unique fixed point to which the fixed-point iteration converges, starting from any (possibly random) decoder. [1] S. Geirnaert, T. Francart, and A. Bertrand, "Unsupervised Self-Adaptive Auditory Attention Decoding," IEEE Journal of Biomedical and Health Informatics, 2021.

This research is funded by an Aspirant Grant from the Research Foundation - Flanders (FWO) (for S. Geirnaert, nr. 1136219N), FWO project nr. G0A4918N, the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 802895 and grant agreement No 637424), and the Flemish Government (AI Research Program).