1
Faculty of Electronics and Telecommunications, HUT
Bangkok, Jun. 14 – 23, 2006
Derivation of Delta Rule
Nguồn gốc của Delta rule cho mạng sau
Cần tìm
NN 1
}2,1,0{ cho
∈
∂
∂
−=∆
i
w
E
w
i
i
η
2
22110
2
210
))((
2
1
)(
2
1
),,( dxwxwwdywwwE
−++=−=
1
x2
x1
w2
w1
w0
)()(
22110
xwxwwnety ++==
ϕϕ
, ,
210
w
E
w
E
w
E
∂
∂
∂
∂
∂
∂
2
Faculty of Electronics and Telecommunications, HUT
Bangkok, Jun. 14 – 23, 2006
Derivation of Delta Rule
Tương tự ta nhận được:
và
1
1
22110
1
22110
22110
1
2
22110
1
210
)('))((
)(
)('))((
))((
))((2
2
1
))((
2
1),,(
xnetdnet
w
dxwxww
netdnet
w
dxwxww
dxwxww
w
dxwxww
w
wwwE
ϕϕ
ϕϕ
ϕ
ϕ
ϕ
−=
∂
−++∂
−=
∂
−++∂
−++=
∂
−++∂
=
∂
∂
2
2
210
)('))((
),,( xnetdnet
w
wwwE
ϕϕ
−=
∂
∂
)('))((
),,(
0
210
netdnet
w
wwwE
ϕϕ
−=
∂
∂
3
Faculty of Electronics and Telecommunications, HUT
Bangkok, Jun. 14 – 23, 2006
Derivation of Delta Rule
Do đó luật update cho weight là:
NN 3
4
Faculty of Electronics and Telecommunications, HUT
Bangkok, Jun. 14 – 23, 2006
Derivation of Delta Rule
NN 4
)(y ,
)(y ,
)(y ,
Let
2211
2222112
1122111
netuyuynet
netxvxvnet
netxwxwnet
ϕ
ϕ
ϕ
=+=
=+=
=+=
x2
x1 w2
w1
v2
v1
u1
u2
)()(y
2211
uyuynet
+==
ϕϕ
•Vi phân delta rule cho m ng sau:ạ
5
Faculty of Electronics and Telecommunications, HUT
Bangkok, Jun. 14 – 23, 2006
Derivation of Delta Rule
1
1
2211
1
2211
2211
1
2
2211
1
)(')(
)(
)(')(
))((
))((2
2
1))((
2
1
ynetdy
u
duyuy
netdy
u
duyuy
duyuy
u
duyuy
u
E
ϕϕ
ϕ
ϕ
ϕ
−=
∂
−+∂
−=
∂
−+∂
−+=
∂
−+∂
=
∂
∂
T ng t ta có:ươ ự
2
2
)(')( ynetdy
u
E
ϕ
−=
∂
∂
1
2211
1
2211
2211
1
2
2211
1
)(
)(')(
))((
))((2
2
1))((
2
1
w
duyuy
netdy
w
duyuy
duyuy
w
duyuy
w
E
∂
−+∂
−=
∂
−+∂
−+=
∂
−+∂
=
∂
∂
ϕ
ϕ
ϕ
ϕ