For symmetric low-rank matrix factorization gradient flow, a Schur-complement cascade gives a complete characterization of equilibria and global convergence: signal variables converge exponentially, excess-parameter variables at O(1/t).
Solving random quadratic systems of equations is nearly as easy as solving linear systems,
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Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem
For symmetric low-rank matrix factorization gradient flow, a Schur-complement cascade gives a complete characterization of equilibria and global convergence: signal variables converge exponentially, excess-parameter variables at O(1/t).