A line of recent works showed that for a large class of learning problems, any learning algorithm requires either super-linear memory size or a super-polynomial number of samples [Raz16,KRT17,Raz17,MM18,BOGY18,GRT18]. For example, any algorithm for learning parities of size $n$ requires either a memory of size $\Omega(n^{2})$ or an exponential number ... more >>>

Non-signaling strategies are a generalization of quantum strategies that have been studied in physics for decades, and have recently found applications in theoretical computer science. These applications motivate the study of local-to-global phenomena for non-signaling functions.

We present general results about the local testability of linear codes in the non-signaling ... more >>>

We prove that there is a constant $K$ such that \emph{Tseitin} formulas for an undirected graph $G$ requires proofs of
size $2^{\mathrm{tw}(G)^{\Omega(1/d)}}$ in depth-$d$ Frege systems for $d<\frac{K \log n}{\log \log n}$, where $\tw(G)$ is the treewidth of $G$. This extends H{\aa}stad recent lower bound for the grid graph ... more >>>