Over-parameterization Is Neither Robust nor Fragile in Matrix Sensing: A Geometric Theory of Solution Robustness
Over-parameterization is ubiquitous in modern machine learning, yet its effect on robustness remains poorly understood. We study this question in matrix sensing, a canonical non-convex problem that can also be viewed, under an appropriate parameterization, as training a two-layer quadratic neural network. We develop a rank-aware robustness theory for the Burer-Monteiro factorization when the search rank k may exceed the target rank r_star, thereby capturing over-parameterization. Our analysis shows that robustness depends jointly on the degree of over-parameterization and the local geometry of the attained second-order stationary point: increasing k generally worsens sensitivity, but stat...
| Authors | Runze Shi, Ziye Ma |
|---|---|
| Primary category | cs.LG |
| Published | 13 October 2026 |
| Last updated at source | 13 October 2026 |
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