W N E(W) = N ∑ n=1 En (W) = N ∑ n=1 ( 1 2 D ∑ d=1 (yn,d − a(L) n,d )2 ) En (W) a(L) n,d = HL−1 ∑ hL−1 =1 w(L) d,hL−1 z(L−1) n,hL−1 = HL−1 ∑ hL−1 =1 w(L) d,hL−1 ϕ(a(L−1) n,hL−1 ) z(L−1) n,hL−1 = ϕ(a(L−1) n,hL−1 ) ∂En ∂w(L) d,hL−1 = ∂En ∂a(L) n,d ∂a(L) n,d ∂w(L) d,hL−1 En (W) = 1 2 D ∑ d=1 (yn,d − a(L) n,d )2 a(L−1) n,hL−1 = HL−2 ∑ hL−2 =1 w(L−1) hL−1 ,hL−2 z(L−2) n,hL−2 = (an,d − yn,d )z(L−1) n,hL−1 = δ(L) n,d z(L−1) n,hL−1 L L − 1 ∂En ∂w(L−1) hL−1,hL−2 = D ∑ d=1 ∂En ∂a(L) n,d ∂a(L) n,d ∂a(L−1) n,hL−1 ∂a(L−1) n,hL−1 ∂w(L−1) hL−1,hL−2 ∂a(L) n,d ∂a(L−1) n,hL−1 = ∂ ∂a(L−1) n,hL−1 ( HL−1 ∑ h=1 w(L) d,h ϕ(a(L−1) n,h ) ) = w(L) d,hL−1 ϕ′(a(L−1) n,hL−1 ) ∂a(L−1) n,hL−1 ∂w(L−1) hL−1,hL−2 = ∂ ∂w(L−1) hL−1,hL−2 HL−2 ∑ h=1 w(L−1) hL−1,h z(L−2) n,h = z(L−2) n,hL−2 = D ∑ d=1 δ(L) n,d (w(L) d,hL−1 ϕ′(a(L−1) n,hL−1 ))z(L−2) n,hL−2 = ϕ′(a(L−1) n,hL−1 ) ( D ∑ d=1 δ(L) n,d w(L) d,hL−1) z(L−2) n,hL−2 = δ(L−1) n,hL−1 z(L−2) n,hL−2 a(l) n,hl = Hl−1 ∑ hl−1 =1 w(l) hl ,hl−1 z(l−1) n,hl−1 z(l) n,hl = ϕ(a(l) n,hl ) l δ(l) n,hl = a(L) n,hl − yn,hl , if l = L ϕ′(a(l) n,hl )∑Hl+1 h=1 δ(l+1) n,h w(l+1) h,hl if l ≠ L ∂En ∂w(l) hl,hl−1 = δ(l) n,hl z(l−1) n,hl−1 ͷಋؔɽ ϕ′ ϕ