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Found 9 papers, 2 papers with code
Absence of spurious solutions far from ground truth: A low-rank analysis with high-order losses
Matrix sensing problems exhibit pervasive non-convexity, plaguing optimization with a proliferation of suboptimal spurious solutions.
Over-parametrization via Lifting for Low-rank Matrix Sensing: Conversion of Spurious Solutions to Strict Saddle Points
This paper studies the role of over-parametrization in solving non-convex optimization problems.
Semidefinite Programming versus Burer-Monteiro Factorization for Matrix Sensing
In this paper, we shed light on some major differences between these two methods.
Noisy Low-rank Matrix Optimization: Geometry of Local Minima and Convergence Rate
We prove that as long as the RIP constant of the noiseless objective is less than $1/3$, any spurious local solution of the noisy optimization problem must be close to the ground truth solution.
Sharp Restricted Isometry Property Bounds for Low-rank Matrix Recovery Problems with Corrupted Measurements
By analyzing the landscape of the non-convex problem, we first propose a global guarantee on the maximum distance between an arbitrary local minimizer and the ground truth under the assumption that the RIP constant is smaller than $1/2$.
Towards Optimal Branching of Linear and Semidefinite Relaxations for Neural Network Robustness Certification
We extend the analysis to the SDP, where the feasible set geometry is exploited to design a branching scheme that minimizes the worst-case SDP relaxation error.
A Sequential Framework Towards an Exact SDP Verification of Neural Networks
We analyze the performance of this sequential SDP method both theoretically and empirically, and show that it bridges the gap as the number of cuts increases.
Tightened Convex Relaxations for Neural Network Robustness Certification
In this paper, we consider the problem of certifying the robustness of neural networks to perturbed and adversarial input data.
Certifiably Globally Optimal Extrinsic Calibration from Per-Sensor Egomotion
We present a certifiably globally optimal algorithm for determining the extrinsic calibration between two sensors that are capable of producing independent egomotion estimates.
Robotics
