Wholly communion, literary nationalism, and the sorrows of the counterculture

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The Average Sensitivity of an Intersection of Half Spaces

We prove new bounds on the average sensitivity of the indicator function of an intersection of $k$ halfspaces. In particular, we prove the optimal bound of $O(\sqrt{n\log(k)})$. This generalizes a result of Nazarov, who proved the analogous result in the Gaussian case, and improves upon a result of Harsha, Klivans and Meka. Furthermore, our result has implications for the runtime required to learn intersections of halfspaces

A Polylogarithmic PRG for Degree 22 Threshold Functions in the Gaussian Setting

We devise a new pseudorandom generator against degree 2 polynomial threshold functions in the Gaussian setting. We manage to achieve $\epsilon$ error with seed length polylogarithmic in $\epsilon$ and the dimension, and exponential improvement over previous constructions

A Pseudorandom Generator for Polynomial Threshold Functions of Gaussian with Subpolynomial Seed Length

We develop a pseudorandom generator that fools degree-$d$ polynomial threshold functions in $n$ variables with respect to the Gaussian distribution and has seed length $O_{c,d}(\log(n) \epsilon^{-c})$