PPt3 - Derivation of Delta Rules

Tài liệu tham khảo về thuật toán tính Derivation of Delta Rules
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PPt3 - Derivation of Delta Rules DerivationofDeltaRule NguồngốccủaDeltarulechomạngsau 1 w0 w1 y = ϕ ( net ) = ϕ ( w0 + w1 x1 + w2 x2 ) x1 w2 x2 1 1E ( w0 , w1 , w2 ) = ( y − d ) = (( w0 + w1 x1 + w2 x2 ) − d ) 2 2 2 2 ∂E ∆wi = −η cho i ∈{0,1,2} ∂wi ∂E ∂E ∂E Cầntìm , , ∂w0 ∂w1 ∂w2 NNFacultyofElectronicsandTelecommunications,HUT 1 1Bangkok,Jun.14–23,2006 DerivationofDeltaRule∂E ( w0 , w1 , w2 ) 1 ∂(ϕ ( w0 + w1 x1 + w2 x2 ) − d ) 2 = ∂w1 2 ∂w1 1 ∂(ϕ ( w0 + w1 x1 + w2 x2 ) − d )= 2(ϕ ( w0 + w1 x1 + w2 x2 ) − d ) 2 ∂w1 ∂( w0 + w1 x1 + w2 x2 − d )= (ϕ ( net ) − d )ϕ ( net ) ∂w1= (ϕ ( net ) − d )ϕ ( net ) x1  Tươngtựtanhậnđược: ∂E ( w0 , w1 , w2 ) = (ϕ ( net ) − d )ϕ ( net ) x2 ∂w2 ∂E ( w0 , w1 , w2 ) và = (ϕ ( net ) − d )ϕ ( net ) ∂w0FacultyofElectronicsandTelecommunications,HUT 2Bangkok,Jun.14–23,2006 DerivationofDeltaRule Dođóluậtupdatechoweightlà: ∆w0 = η( d − ϕ ( net ))ϕ ( net ) ∆w1 = η( d − ϕ ( net ))ϕ ( net ) x1 ∆w2 = η( d − ϕ ( net ))ϕ ( net ) x2 NNFacultyofElectronicsandTelecommunications,HUT 3 3Bangkok,Jun.14–23,2006 DerivationofDeltaRule • Vi phân delta rule cho mạng sau: w1 x1 u1 w2 y = ϕ ( net ) = ϕ ( y1u1 + y2u2 ) v1 x2 u2 v2 Let net1 = w1 x1 + w2 x2 , y1 = ϕ (net1 ) net 2 = v1 x1 + v2 x2 , y 2 = ϕ (net2 ) net = y1u1 + y2u2 , y = ϕ (net ) NN FacultyofElectronicsandTelecommunications,HUT 4 4 Bangkok,Jun.14–23,2006 DerivationofDeltaRule ∂E 1 ∂ (ϕ ( y1u1 + y2u2 ) − d ) 2 1 ∂ (ϕ ( y1u1 + y2u2 ) − d ) = = 2(ϕ ( y1u1 + y2u2 ) − d ) ∂u1 2 ∂u1 2 ∂u1 ∂ ( y1u1 + y2u2 − d ) = ( y − d )ϕ ( net ) = ( y − d )ϕ ( net ) y1 ∂u1 Tương tự ta có: ∂E = ( y − d )ϕ ( net ) y2 ∂u2 ∂E 1 ∂ (ϕ ( y1u1 + y2u2 ) − d )2 1 ∂ (ϕ ( y1u1 + y2u2 ) − d ) = = 2(ϕ ( y1u1 + y2u2 ) − d ) ∂w1 2 ∂w1 2 ∂w1 ∂ ( y1u1 + y2u2 − d ) = ( y − d )ϕ ( net ) ∂w1 FacultyofElectronicsandTelecommunications,HUT 5 Bangkok,Jun.14–23,2006 DerivationofDeltaRule ∂( y1u1 + y2u2 − d ) ∂( y1u1 ) ∂y ∂(ϕ( w1 x1 + w2 x2 )) = = u1 1 = u1 ∂w1 ∂w1 ∂w1 ∂w1 ∂( w1 x1 ) = u1ϕ ( net1 ) = u1ϕ ( net1 ) x1 ∂w1 Do vậy nhận được:: ∂E ∂( y1u1 + y2u2 −d ) = ( y −d )ϕ ( net ) ∂ 1 w ∂ 1 w = ( y −d )ϕ ( net )u1ϕ ( net1 ) x1 Tương tự: ∂E = ( y − d )ϕ ( net )u1ϕ ( net1 ) x2 ∂w2 ∂E ∂E = ( y − d )ϕ ( net )u2ϕ ( net2 ) x1 , = ( y − d )ϕ ( net )u2ϕ ( net2 ) x2 ∂v1 ∂v2 NN FacultyofElectronicsandTelecommunications,HUT 6 6 Bangkok,Jun.14–23,2006