8 accepted papers
This paper studies the gradient flow dynamics that arise when training deep homogeneous neural networks assumed to have locally Lipschitz gradients and an order of homogeneity strictly greater than two. It is shown here that for sufficiently small initializations, during the early stages of training…
We consider the problem of factorizing a structured 3-way tensor into its constituent Canonical Polyadic (CP) factors. This decomposition, which can be viewed as a generalization of singular value decomposition (SVD) for tensors, reveals how the tensor dimensions (features) interact with each other.…
We consider the dictionary learning problem, where the aim is to model the given data as a linear combination of a few columns of a matrix known as a dictionary, where the sparse weights forming the linear combination are known as coefficients. Since the dictionary and coefficients, parameterizing t…
We study constrained nonconvex optimization problems in machine learning and signal processing. It is well-known that these problems can be rewritten to a min-max problem in a Lagrangian form. However, due to the lack of convexity, their landscape is not well understood and how to find the stable eq…
Many machine learning techniques sacrifice convenient computational structures to gain estimation robustness and modeling flexibility. However, by exploring the modeling structures, we find these “sacrifices” do not always require more computational efforts. To shed light on such a “free-lunch” phen…
We study the least squares regression problem $\min_{\Theta \in \RR^{p_1 \times \cdots \times p_D}} \| \cA(\Theta) - b \|_2^2$, where $\Theta$ is a low-rank tensor, defined as $\Theta = \sum_{r=1}^{R} \theta_1^{(r)} \circ \cdots \circ \theta_D^{(r)}$, for vectors $\theta_d^{(r)} \in \mathbb{R}^{p_d…
We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal newton algorithm with multi-stage convex relaxation based on the difference of convex (DC) programming, and enjoys both strong comp…
We propose a stochastic variance reduced optimization algorithm for solving a class of large-scale nonconvex optimization problems with cardinality constraints, and provide sufficient conditions under which the proposed algorithm enjoys strong linear convergence guarantees and optimal estimation acc…