Recently there has been significant theoretical progress on understanding the convergence
and generalization of gradient-based methods on nonconvex losses with overparameterized …

We study extensions of compressive sensing and low rank matrix recovery (matrix
completion) to the recovery of low rank tensors of higher order from a small number of linear …

We establish theoretical recovery guarantees of a family of Riemannian optimization
algorithms for low rank matrix recovery, which is about recovering an m*n rank r matrix from …

Projected least squares is an intuitive and numerically cheap technique for quantum state
tomography: compute the least-squares estimator and project it onto the space of states. The …

We describe a general framework—compressive statistical learning—for resourceefficient
large-scale learning: the training collection is compressed in one pass into a …

In deep learning, it is common to use more network parameters than training points. In such
scenario of over-parameterization, there are usually multiple networks that achieve zero …

Characterizing quantum processes is a key task in the development of quantum
technologies, especially at the noisy intermediate scale of today's devices. One method for …

This paper considers the problem of compressively sampling wide sense stationary random
vectors with a low rank Toeplitz covariance matrix. Certain families of structured …

We investigate recovery of nonnegative vectors from non-adaptive compressive
measurements in the presence of noise of unknown power. In the absence of noise, existing …

Random quantum processes play a central role both in the study of fundamental mixing
processes in quantum mechanics related to equilibration, thermalisation and fast scrambling …