  Federated learning enables training high-utility models across several
clients without directly sharing their private data. As a downside, the
federated setting makes the model vulnerable to various adversarial attacks in
the presence of malicious clients. Despite the theoretical and empirical
success in defending against attacks that aim to degrade models' utility,
defense against backdoor attacks that increase model accuracy on backdoor
samples exclusively without hurting the utility on other samples remains
challenging. To this end, we first analyze the failure modes of existing
defenses over a flat loss landscape, which is common for well-designed neural
networks such as Resnet (He et al., 2015) but is often overlooked by previous
works. Then, we propose an invariant aggregator that redirects the aggregated
update to invariant directions that are generally useful via selectively
masking out the update elements that favor few and possibly malicious clients.
Theoretical results suggest that our approach provably mitigates backdoor
attacks and remains effective over flat loss landscapes. Empirical results on
three datasets with different modalities and varying numbers of clients further
demonstrate that our approach mitigates a broad class of backdoor attacks with
a negligible cost on the model utility.
