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- ただきよ ありはら
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1 : BV15005
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4 (,, ). x i (i = 1,..., n), u = w 1 x w n x n., w i ( ), b.,. h. y = h(u) 1.4 ( ). n n + 1., n i n + 1 j w (n+1) ji, b (n+1) j, u (n+1) j., n + 1 i z (n+1) i, h (n+1), u (n+1) j = i w (n+1) ji z (n) i + b (n+1) j, z (n+1) j = h (n+1) (u (n+1) j ).,, u (n+1) = w (n+1) z (n) + b (n+1), z (n+1) = h (n+1) (u (n+1) ).. ( ). x i u i w ji, u j b j, u j, u 1 = w 11 x 1 + w 12 x 2 + w 13 x 3 + w 14 x 4 + b 1 u 2 = w 21 x 1 + w 22 x 2 + w 23 x 3 + w 24 x 4 + b 2 u 3 = w 31 x 1 + w 32 x 2 + w 33 x 3 + w 34 x 4 + b 3., 2 2 h, z j = h(u j ),. l, 1, l, ( ). y, x, w (2),..., w (L), b (2),..., b (L)., y = N(x, w (2),..., w (L), b (2),..., b (L) ), 1, w = (w (2),..., w (L), b (2),..., b (L) ), y = N(x; w). N(x, w), w., 1 x d., M, D := {(x 1, d 1 ),..., (x M, d M )} 2
5 2..,,.,,,., 0 ( < u 0), f(u) = 1 (0 < u < ) ( ), 1 f(u) = 1 + e u ( ), 0 ( < u 0), f(u) = x (0 < u < ) (Relu ),. 2 N(x, w) d m. E(w),, 2 0. ( ), 0,.,,.. 2 (1) (2) (3) 1: 2.1,.,., [ 1, 1],, (, )., 2 E(w) =. M (d m N(x, w)) 2 (1) m=1 2.2,., ,. 2,. 3
6 , d = 1 p(d = 1 x). x d,, 0.5 d = 1,, d = 0. p(d = 1 x),. w, {(x m, d m )}. y(x, w) p(d = 1 x) y(x, w)., w,. w, {(x n, d n ) n = 0,... M}, p(d x; w),. d = {0, 1}, p(d x) = p(d = 1 x) d p(d = 0 x} 1 d., p(d x) = y(x; w), p(d = 0 x) = 1 y(x; w)., w, w. w, M M L(w) p(d m x m ; w) = y(x m ; w) dm {1 y(x m ; w m )} 1 dm m=1 m=1.,., M E(w) = [d m log y(x m ; w) + (1 d m ) log{1 y(x m ; w)} 1 d m ] (2) m=1.,,, u p(x, d = 1) p(x, d = 0) p(d = 1 x) = p(x, d = 1) p(x, d = 0) + p(x, d = 1), p(d = 1 x),.,, , l = L C 1,..., C K,. y k C k., p(c k x) = y k = z (L) k, x.,,,,,., d n = [d n1,..., d nk ] T (d nk = {0, 1}) 4
7 3, 1, 0.,, x m 2, C 3,,.,, d m = [0, 0, 1, 0, 0, 0, 0, 0, 0] T p(d x) = K p(c k x) d k k=1., {(x m, d m )} w L(w) = M p(d m x m ; w) = m=1 M m=1 k=1 K p(c k x m ) d mk =., E(w) = M m=1 k=1.. M m=1 k=1. C k,, p(c k x) =., u k = log p(x, C k ),, p(c k x) = K (y k (x; w)) d mk K d mk log y k (x m ; w) (3) p(x, C k ) K j=1 p(x, C j) = y k exp(u k ) K j=1 exp(u j).,., 1, u (L) 1,..., u (L) K u 0. 3,., E(w)., E(w). E(w), E(w)., w E(w),., w,.,.,. 3.1, ( E), w., ε, w (t+1) = w t ε E.,. 5
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変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy,
変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy, z + dz) Q! (x + d x + u + du, y + dy + v + dv, z +
B [ 0.1 ] x > 0 x 6= 1 f(x) µ 1 1 xn 1 + sin sin x 1 x 1 f(x) := lim. n x n (1) lim inf f(x) (2) lim sup f(x) x 1 0 x 1 0 (
![B [ 0.1 ] x > 0 x 6= 1 f(x) µ 1 1 xn 1 + sin sin x 1 x 1 f(x) := lim. n x n (1) lim inf f(x) (2) lim sup f(x) x 1 0 x 1 0 (](/thumbs/97/133036028.jpg "B [ 0.1 ] x > 0 x 6= 1 f(x) µ 1 1 xn 1 + sin sin x 1 x 1 f(x) := lim. n x n (1) lim inf f(x) (2) lim sup f(x) x 1 0 x 1 0 (")
. 28 4 14 [.1 ] x > x 6= 1 f(x) µ 1 1 xn 1 + sin + 2 + sin x 1 x 1 f(x) := lim. 1 + x n (1) lim inf f(x) (2) lim sup f(x) x 1 x 1 (3) lim inf x 1+ f(x) (4) lim sup f(x) x 1+ [.2 ] [, 1] Ω æ x (1) (2) nx(1
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3 () 3,,C = a, C = a, C = b, C = θ(0 < θ < π) cos θ = a + (a) b (a) = 5a b 4a b = 5a 4a cos θ b = a 5 4 cos θ a ( b > 0) C C l = a + a + a 5 4 cos θ = a(3 + 5 4 cos θ) C a l = 3 + 5 4 cos θ < cos θ < 4
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II. () 7 F 7 = { 0,, 2, 3, 4, 5, 6 }., F 7 a, b F 7, a b, F 7,. (a) a, b,,. (b) 7., 4 5 = 20 = 2 7 + 6, 4 5 = 6 F 7., F 7,., 0 a F 7, ab = F 7 b F 7. (2) 7, 6 F 6 = { 0,, 2, 3, 4, 5 },,., F 6., 0 0 a F
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