We investigate implications of the (extended) low-degree conjecture (recently formalized in [moitra et al2023]) in the context of the symmetric stochastic block model. Assuming the conjecture holds, we establish that no polynomial-time algorithm can weakly recover community labels below the Kesten-Stigum (KS) threshold. In particular, we rule out polynomial-time estimators that, with constant probability, achieve $n^{-0.49}$

We develop a technique to design efficiently computable estimators for sparse linear regression in the simultaneous presence of two adversaries: oblivious and adaptive.Consider the model $y^*=X^*\beta^*+ \eta$ where $X^*$ is an $n\times d$ random design matrix, $\beta^*\in \mathbb{R}^d$ is a $k$-sparse vector, and the noise $\eta$ is independent of $X^*$ and chosen by the \emph{oblivious adversary}. Apart from the independence of $X^*$, we only require a small fraction entries of $\eta$ to have magnitude at most $1$.

We consider the problem of learning function classes computed by neural networks with various activations (e.g. ReLU or Sigmoid), a task believed to be computationally intractable in the worst-case. A major open problem is to understand the minimal assumptions under which these classes admit provably efficient algorithms. In this work we show that a natural distributional assumption corresponding to {\em eigenvalue decay} of the Gram matrix yields polynomial-time algorithms in the non-realizable setting for expressive classes of networks (e.g.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

We consider adaptive control of the Linear Quadratic Regulator (LQR), where an unknown linear system is controlled subject to quadratic costs.