Neural Networks: Prediction (i.e. the forward pass) · Based on slides and material from Geoffrey...
Transcript of Neural Networks: Prediction (i.e. the forward pass) · Based on slides and material from Geoffrey...
MachineLearning
NeuralNetworks:Prediction
(i.e.theforwardpass)
1BasedonslidesandmaterialfromGeoffreyHinton,RichardSocher,DanRoth,
Yoav Goldberg,ShaiShalev-Shwartz andShaiBen-David,andothers
NeuralNetworks
• Whatisaneuralnetwork?
• Predictingwithaneuralnetwork
• Trainingneuralnetworks
• Practicalconcerns
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Thislecture
• Whatisaneuralnetwork?
• Predictingwithaneuralnetwork
• Trainingneuralnetworks
• Practicalconcerns
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Letusconsideranexamplenetwork
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Wewillusethisexamplenetwork
astointroducethegeneral
principleofhowtomake
predictionswithaneuralnetwork.
Letusconsideranexamplenetwork
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Namingconventionsforthis
example
• Inputs:x
• Hidden:z
• Output:y
Letusconsideranexamplenetwork
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Biasfeature,
always1
Namingconventionsforthis
example
• Inputs:x
• Hidden:z
• Output:y
Letusconsideranexamplenetwork
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Biasfeature,
always1
Sigmoidactivations
Linearactivation
Namingconventionsforthis
example
• Inputs:x
• Hidden:z
• Output:y
Letusconsideranexamplenetwork
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NamingConventionforWeights
!"#$%,'$'(#)*'_,(-*#
Letusconsideranexamplenetwork
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NamingConventionforWeights
!"#$%,'$'(#)*'_,(-*#
!./$Fromneuron#0
toneuron#1in
outputlayer
Howtopredictwithaneuralnetwork:The
forwardpass
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Givenaninputx,howistheoutputpredicted
Theforwardpass
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z/ = 2(!./4 + !//4 6/ + !7/4 67)
Givenaninputx,howistheoutputpredicted
Theforwardpass
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97 = 2(!.74 + !/74 6/ + !774 67)
Givenaninputx,howistheoutputpredicted
z/ = 2(!./4 + !//4 6/ + !7/4 67)
Theforwardpass
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y = !./$ + !//$ 9/ + !7/$ 97output
Givenaninputx,howistheoutputpredicted
97 = 2(!.74 + !/74 6/ + !774 67)
z/ = 2(!./4 + !//4 6/ + !7/4 67)
Theforwardpass
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y = !./$ + !//$ 9/ + !7/$ 97output
Givenaninputx,howistheoutputpredicted
97 = 2(!.74 + !/74 6/ + !774 67)
z/ = 2(!./4 + !//4 6/ + !7/4 67)
Questions?
Ingeneral,beforevisiting(i.e.computing)thevalueofanode,visitallnodesthatserveasinputstoit.