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Deep Learning A-Z™: Recurrent Neural Networks (RNN) - The Vanishing Gradient Problem

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Kirill Eremenko

Deep Learning A-Z™: Recurrent Neural Networks (RNN) - The Vanishing Gradient Problem

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© SuperDataScienceDeep Learning A-Z
© SuperDataScienceDeep Learning A-Z Image Source: people.idsia.ch
© SuperDataScienceDeep Learning A-Z Image Source: Université Montréal
© SuperDataScienceDeep Learning A-Z Image Source: recode.net
© SuperDataScienceDeep Learning A-Z C ŷ C = ½(ŷ- y)2
© SuperDataScienceDeep Learning A-Z y X2 X1 W11,1 W11,2 W11,3 W12,1 W12,2 W12,3 W21,1 W22,1 W23,1
© SuperDataScienceDeep Learning A-Z 517 Time 517 517 517 517 Win Wout Wrec Win Wout Wrec Win Wout Wrec Win Wout Wrec Win Wout yt εt xtxt-1xt-2xt-3 Formula Source: Razvan Pascanu et al. (2013) εt+1εt-1εt-2εt-3 Wrec ~ small Wrec ~ large Vanishing Exploding Wrec Wrec Wrec
© SuperDataScienceDeep Learning A-Z Solutions: 1. Exploding Gradient • Weight Initialization • Echo State Networks • Long Short-Term Memory Networks (LSTMs) • Truncated Backpropagation • Penalties • Gradient Clipping 2. Vanishing Gradient
© SuperDataScienceDeep Learning A-Z Untersuchungen zu dynamischen neuronalen Netzen By Sepp (Josef) Hochreiter (1991) Link: http://people.idsia.ch/~juergen/SeppHochreiter1991ThesisAdvisorSchmidh uber.pdf Additional Reading:
© SuperDataScienceDeep Learning A-Z Learning Long-Term Dependencies with Gradient Descent is Difficult By Yoshua Bengio et al. (1994) Link: http://www-dsi.ing.unifi.it/~paolo/ps/tnn-94-gradient.pdf Additional Reading:
© SuperDataScienceDeep Learning A-Z On the difficulty of training recurrent neural networks By Razvan Pascanu et al. (2013) Link: http://www.jmlr.org/proceedings/papers/v28/pascanu13.pdf Additional Reading:

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