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State-Dependent Lyapunov Analysis of Rank-1 Matrix Factorization
We develop a state-dependent Lyapunov framework for gradient descent on rank-1 matrix factorization. A parameterized quadratic certificate $I(δ;\,\cdot)$ generates strictly nested sublevel sets. Their ordering assigns each point a state $δ$, while a boundary-inward property makes this state monotone
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