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 (18) 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

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... xed 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, vol. 25, no. 10, pp. 3955–3966, 2021.