24 citations · 28 across the 9 of their papers we have counts for
10 papers
Absence of spurious solutions far from ground truth: A low-rank analysis with high-order losses
Ziye Ma, Ying Chen, Javad Lavaei +1
Matrix sensing problems exhibit pervasive non-convexity, plaguing optimization with a proliferation of suboptimal spurious solutions. Avoiding convergence to these critical points…
Algorithmic Regularization in Tensor Optimization: Towards a Lifted Approach in Matrix Sensing
Ziye Ma, Javad Lavaei, Somayeh Sojoudi
Gradient descent (GD) is crucial for generalization in machine learning models, as it induces implicit regularization, promoting compact representations. In this work, we examine t…
Over-parametrization via Lifting for Low-rank Matrix Sensing: Conversion of Spurious Solutions to Strict Saddle Points
Ziye Ma, Igor Molybog, Javad Lavaei +1
This paper studies the role of over-parametrization in solving non-convex optimization problems. The focus is on the important class of low-rank matrix sensing, where we propose an…
Semidefinite Programming versus Burer-Monteiro Factorization for Matrix Sensing
Baturalp Yalcin, Ziye Ma, Javad Lavaei +1
Many fundamental low-rank optimization problems, such as matrix completion, phase synchronization/retrieval, power system state estimation, and robust PCA, can be formulated as the…
Noisy Low-rank Matrix Optimization: Geometry of Local Minima and Convergence Rate
Ziye Ma, Somayeh Sojoudi
This paper is concerned with low-rank matrix optimization, which has found a wide range of applications in machine learning. This problem in the special case of matrix sensing has…
Sharp Restricted Isometry Property Bounds for Low-rank Matrix Recovery Problems with Corrupted Measurements
Ziye Ma, Yingjie Bi, Javad Lavaei +1
In this paper, we study a general low-rank matrix recovery problem with linear measurements corrupted by some noise. The objective is to understand under what conditions on the res…
Towards Optimal Branching of Linear and Semidefinite Relaxations for Neural Network Robustness Certification
Brendon G. Anderson, Ziye Ma, Jingqi Li +1
In this paper, we study certifying the robustness of ReLU neural networks against adversarial input perturbations. To diminish the relaxation error suffered by the popular linear p…
A Sequential Framework Towards an Exact SDP Verification of Neural Networks
Ziye Ma, Somayeh Sojoudi
Although neural networks have been applied to several systems in recent years, they still cannot be used in safety-critical systems due to the lack of efficient techniques to certi…
Tightened Convex Relaxations for Neural Network Robustness Certification
Brendon G. Anderson, Ziye Ma, Jingqi Li +1
In this paper, we consider the problem of certifying the robustness of neural networks to perturbed and adversarial input data. Such certification is imperative for the application…
Certifiably Globally Optimal Extrinsic Calibration from Per-Sensor Egomotion
Matthew Giamou, Ziye Ma, Valentin Peretroukhin +1
We present a certifiably globally optimal algorithm for determining the extrinsic calibration between two sensors that are capable of producing independent egomotion estimates. Thi…