Gradient descent (GD) is crucial for generalization in machine learning models, as it induces
implicit regularization, promoting compact representations. In this work, we examine the role …

Most existing methodologies of estimating low-rank matrices rely on Burer-Monteiro
factorization, but these approaches can suffer from slow convergence, especially when …

Matrix sensing problems exhibit pervasive non-convexity, plaguing optimization with a
proliferation of suboptimal spurious solutions. Avoiding convergence to these critical points …

Matrix sensing represents a critical, non-convex challenge within the domain of
mathematical optimization, distinguished by its wide-ranging practical applications—such as …

The training of all modern machine learning models including deep neural networks and
large languages models can be considered as solving nonconvex optimization problems …

Matrix completion, a crucial sub-problem of non-convex matrix sensing, is integral to
numerous machine learning applications such as recommender systems. Traditionally …

Modern machine learning problems are predominantly non-convex, often containing a
potentially infinite number of local minima that can hinder gradient-based algorithms from …