arXiv Machine Learning August 20, 2026 By Tianqi Shen, Jinji Yang, Junze He, Kunhan Gao, Zeyu Zheng, Ziye Ma

Escaping Local Minima Provably in Non-convex Matrix Sensing: A Deterministic Framework via Simulated Lifting

Read the original on arXiv Machine Learning →

The paper introduces a deterministic Simulated Oracle Direction (SOD) framework that enables escaping spurious local minima in non‑convex low‑rank matrix sensing without explicit tensor lifting. By projecting over‑parameterized escape directions back into the original parameter space, the method guarantees a strict decrease in objective value from existing local minima. Experiments show reliable escape from local minima and convergence to global optima with minimal computational overhead compared to explicit over‑parameterization.

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