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Date
2024-05-06Type
- Journal Article
ETH Bibliography
yes
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Abstract
This paper studies the infinite-width limit of deep linear neural networks (NNs) initialized with random parameters. We obtain that, when the number of parameters diverges, the training dynamics converge (in a precise sense) to the dynamics obtained from a gradient descent on an infinitely wide deterministic linear NN. Moreover, even if the weights remain random, we get their precise law along the training dynamics, and prove a quantitative convergence result of the linear predictor in terms of the number of parameters. We finally study the continuous-time limit obtained for infinitely wide linear NNs and show that the linear predictors of the NN converge at an exponential rate to the minimal & ell;2$\ell _2$-norm minimizer of the risk. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000673033Publication status
publishedExternal links
Journal / series
Communications on Pure and Applied MathematicsPublisher
WileyMore
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ETH Bibliography
yes
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