We study the problem of algorithmically optimizing the Hamiltonian of a spherical or Ising
mean field spin glass. The maximum asymptotic value OPT of this random function is …

Recently, research in unsupervised learning has gravitated towards exploring statistical-
computational gaps induced by sparsity. A line of work initiated in Berthet and Rigollet …

Local algorithms on graphs are algorithms that run in parallel on the nodes of a graph to
compute some global structural feature of the graph. Such algorithms use only local …

Let Φ be a uniformly random k-SAT formula with n variables and m clauses. We study the
algorithmic task of finding a satisfying assignment of Φ. It is known that satisfying …

We give upper and lower bounds on the information-theoretic threshold for community
detection in the stochastic block model. Specifically, consider a symmetric stochastic block …

We consider the algorithmic problem of finding a near ground state (near optimal solution) of
a p-spin model. We show that for a class of algorithms broadly defined as Approximate …

We study the algorithmic task of finding a large independent set in a sparse Erdos–Rényi
random graph with n vertices and average degree d. The maximum independent set is …

The recent work by Schuetz et al. 1 'Combinatorial optimization with physics-inspired graph
neural networks' introduces a physics-inspired unsupervised graph neural network (GNN) to …

The binary (or Ising) perceptron is a toy model of a single-layer neural network and can be
viewed as a random constraint satisfaction problem with a high degree of connectivity. The …

The Sum-of-Squares (SoS) hierarchy of semidefinite programs is a powerful algorithmic
paradigm which captures state-of-the-art algorithmic guarantees for a wide array of …