We make progress on understanding a lower bound technique that was recently used by the authors to prove the first superpolynomial constant-depth circuit lower bounds against algebraic circuits.

More specifically, our previous work applied the well-known partial derivative method in a new setting, that of 'lopsided' set-multilinear polynomials. A ... more >>>

Recently it was shown that PLS is not contained in PPADS (ECCC report TR22-058). We show that this separation already implies that PLS is not contained in PPP. These separations are shown for the decision tree model of TFNP and imply similar separations in the type-2, relativized model.

Important note. ... more >>>

We introduce and analyse an efficient decoder for the quantum Tanner codes that can correct adversarial errors of linear weight. Previous decoders for quantum low-density parity-check codes could only handle adversarial errors of weight $O(\sqrt{n \log n})$. We also work on the link between quantum Tanner codes and the Lifted ... more >>>