We study convergence lower bounds of without-replacement stochastic gradient descent
(SGD) for solving smooth (strongly-) convex finite-sum minimization problems. Unlike most …

We prove novel algorithmic guarantees for several online problems in the smoothed
analysis model. In this model, at each time step an adversary chooses an input distribution …

Random reshuffling, which randomly permutes the dataset each epoch, is widely adopted in
model training because it yields faster convergence than with-replacement sampling …

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 …

We introduce kernel thinning, a new procedure for compressing a distribution $\mathbb {P} $
more effectively than iid sampling or standard thinning. Given a suitable reproducing kernel …

We study a family of Ising perceptron models with {0, 1}-valued activation functions. This
includes the classical half-space models, as well as some of the symmetric models …

We consider the spherical perceptron with Gaussian disorder. This is the set S of points σ∈
RN on the sphere of radius N satisfying⟨ ga, σ⟩≥ κ N for all 1≤ a≤ M, where (ga) a= 1 M …

In the stochastic online vector balancing problem, vectors v 1, v 2,…, vT chosen
independently from an arbitrary distribution in ℝ n arrive one-by-one and must be …

Discrepancy theory has provided powerful tools for producing higher-quality objects which
“beat the union bound” in fundamental settings throughout combinatorics and computer …

The binary perceptron problem asks us to find a sign vector in the intersection of
independently chosen random halfspaces with intercept $-\kappa $. We analyze the …