  Collaborative Machine Learning (CML) allows participants to jointly train a
machine learning model while keeping their training data private. In many
scenarios where CML is seen as the solution to privacy issues, such as
health-related applications, safety is also a primary concern. To ensure that
CML processes produce models that output correct and reliable decisions
\emph{even in the presence of potentially untrusted participants}, researchers
propose to use \textit{robust aggregators} to filter out malicious
contributions that negatively influence the training process. In this work, we
formalize the two prevalent forms of robust aggregators in the literature. We
then show that neither can provide the intended protection: either they use
distance-based metrics that cannot reliably identify malicious inputs to
training; or use metrics based on the behavior of the loss function which
create a conflict with the ability of CML participants to learn, i.e., they
cannot eliminate the risk of compromise without preventing learning.
