The paper introduces sample-independent and sample-dependent critical lifting between networks of different widths, shows known embeddings do not capture all sample-independent liftings, and proves sample-dependent lifted critical points and saddles exist for sufficiently large sample sizes.
Cooper , title Global minima of overparameterized neural networks , journal SIAM Journal on Mathematics of Data Science volume 3 ( year 2021 ) pages 676--691
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Uncovering Critical Sets of Deep Neural Networks via Sample-Independent Critical Lifting
The paper introduces sample-independent and sample-dependent critical lifting between networks of different widths, shows known embeddings do not capture all sample-independent liftings, and proves sample-dependent lifted critical points and saddles exist for sufficiently large sample sizes.