Revisiting the Landscape of Matrix Factorization

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4 Scopus citations


Prior work has shown that low-rank matrix factorization has infinitely many critical points, each of which is either a global minimum or a (strict) saddle point. We revisit this problem and provide simple, intuitive proofs of a set of extended results for low-rank and general-rank problems. We couple our investigation with a known invariant manifold M0 of gradient flow. This restriction admits a uniform negative upper bound on the least eigenvalue of the Hessian map at all strict saddles in M0. The bound depends on the size of the nonzero singular values and the separation between distinct singular values of the matrix to be factorized.

Original languageEnglish (US)
Pages (from-to)1629-1638
Number of pages10
JournalProceedings of Machine Learning Research
StatePublished - 2020
Externally publishedYes
Event23rd International Conference on Artificial Intelligence and Statistics, AISTATS 2020 - Virtual, Online
Duration: Aug 26 2020Aug 28 2020

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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