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A noise-robust communication primitive is introduced, Exam Mostly Set Disjointness, and an $\Omega\left(\frac{m}{t}\log\frac{1}{\delta}\right)$ one-way lower bound is proved, which yields the correct $\log(1/\delta)$ dependence.
This monograph surveys recent advances in adversarial robustness, including techniques for insertion-only streams, connections to differential privacy, and cryptographic methods that achieve adversarial robustness.
It is proved that for any sub-multiplicative norm, the existence of an efficient classical linear sketch is equivalent to the existence of an efficient robust turnstile algorithm, up to polynomial factors, formalizing $L_1$ embeddability as the fundamental mechanism governing both models.
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