  Large pre-trained sequence models, such as transformer-based architectures,
have been recently shown to have the capacity to carry out in-context learning
(ICL). In ICL, a decision on a new input is made via a direct mapping of the
input and of a few examples from the given task, serving as the task's context,
to the output variable. No explicit updates of the model parameters are needed
to tailor the decision to a new task. Pre-training, which amounts to a form of
meta-learning, is based on the observation of examples from several related
tasks. Prior work has shown ICL capabilities for linear regression. In this
study, we leverage ICL to address the inverse problem of multiple-input and
multiple-output (MIMO) equalization based on a context given by pilot symbols.
A task is defined by the unknown fading channel and by the signal-to-noise
ratio (SNR) level, which may be known. To highlight the practical potential of
the approach, we allow the presence of quantization of the received signals. We
demonstrate via numerical results that transformer-based ICL has a threshold
behavior, whereby, as the number of pre-training tasks grows, the performance
switches from that of a minimum mean squared error (MMSE) equalizer with a
prior determined by the pre-trained tasks to that of an MMSE equalizer with the
true data-generating prior.
