  Dataset distillation offers a potential means to enhance data efficiency in
deep learning. Recent studies have shown its ability to counteract backdoor
risks present in original training samples. In this study, we delve into the
theoretical aspects of backdoor attacks and dataset distillation based on
kernel methods. We introduce two new theory-driven trigger pattern generation
methods specialized for dataset distillation. Following a comprehensive set of
analyses and experiments, we show that our optimization-based trigger design
framework informs effective backdoor attacks on dataset distillation. Notably,
datasets poisoned by our designed trigger prove resilient against conventional
backdoor attack detection and mitigation methods. Our empirical results
validate that the triggers developed using our approaches are proficient at
executing resilient backdoor attacks.
