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• W2913930213 abstract "We prove that for an $L$-layer fully-connected linear neural network, if the width of every hidden layer is $tildeOmega (L cdot r cdot d_{mathrm{out}} cdot kappa^3 )$, where $r$ and $kappa$ are the rank and the condition number of the input data, and $d_{mathrm{out}}$ is the output dimension, then gradient descent with Gaussian random initialization converges to a global minimum at a linear rate. The number of iterations to find an $epsilon$-suboptimal solution is $O(kappa log(frac{1}{epsilon}))$. Our polynomial upper bound on the total running time for wide deep linear networks and the $expleft(Omegaleft(Lright)right)$ lower bound for narrow deep linear neural networks [Shamir, 2018] together demonstrate that wide layers are necessary for optimizing deep models." @default.
• W2913930213 created "2019-02-21" @default.
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• W2913930213 date "2019-01-24" @default.
• W2913930213 modified "2023-09-27" @default.
• W2913930213 title "Width Provably Matters in Optimization for Deep Linear Neural Networks" @default.
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