Tricking the Hashing Trick: A Tight Lower Bound on the Robustness of CountSketch to Adaptive Inputs. (arXiv:2207.00956v1 [cs.DS])

CountSketch and Feature Hashing (the "hashing trick") are popular randomized
dimensionality reduction methods that support recovery of $\ell_2$-heavy
hitters (keys $i$ where $v_i^2 > \epsilon \|\boldsymbol{v}\|_2^2$) and
approximate inner products. When the inputs are {\em not adaptive} (do not
depend on prior outputs), classic estimators applied to a sketch of size
$O(\ell/\epsilon)$ are accurate for a number of queries that is exponential in
$\ell$. When inputs are adaptive, however, an adversarial input can be
constructed after $O(\ell)$ queries with the …

ds hashing inputs robustness