  Power allocation is one of the fundamental problems in wireless networks and
a wide variety of algorithms address this problem from different perspectives.
A common element among these algorithms is that they rely on an estimation of
the channel state, which may be inaccurate on account of hardware defects,
noisy feedback systems, and environmental and adversarial disturbances.
Therefore, it is essential that the output power allocation of these algorithms
is stable with respect to input perturbations, to the extent that the
variations in the output are bounded for bounded variations in the input. In
this paper, we focus on UWMMSE -- a modern algorithm leveraging graph neural
networks --, and illustrate its stability to additive input perturbations of
bounded energy through both theoretical analysis and empirical validation.
