Substantial progress has been made recently on develo** provably accurate and efficient
algorithms for low-rank matrix factorization via nonconvex optimization. While conventional …

Low-rank matrices play a fundamental role in modeling and computational methods for
signal processing and machine learning. In many applications where low-rank matrices …

Deep neural networks have shown the ability to extract universal feature representations
from data such as images and text that have been useful for a variety of learning tasks …

Efforts to understand the generalization mystery in deep learning have led to the belief that
gradient-based optimization induces a form of implicit regularization, a bias towards models …

Spectral methods have emerged as a simple yet surprisingly effective approach for
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …

Since its inception in" Attention Is All You Need", transformer architecture has led to
revolutionary advancements in NLP. The attention layer within the transformer admits a …

Matrix completion is a basic machine learning problem that has wide applications,
especially in collaborative filtering and recommender systems. Simple non-convex …

In this paper we develop a new framework that captures the common landscape underlying
the common non-convex low-rank matrix problems including matrix sensing, matrix …

Can we recover a complex signal from its Fourier magnitudes? More generally, given a set
of m measurements, y_k=\left| a _k^* x\right| yk= ak∗ x for k= 1, ..., mk= 1,…, m, is it possible …

We show that the gradient descent algorithm provides an implicit regularization effect in the
learning of over-parameterized matrix factorization models and one-hidden-layer neural …