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2 深層学習技術の進展 ImageNet Classification 画像認識 音声認識 自然言語処理 機械翻訳 深層学習技術は これらの分野において 特に圧倒的な強みを見せている Figure (Left) Eight ILSVRC-2010 test Deep images and the cited4: from: ``ImageNet Classification with Networks et the al. pr TheConvolutional correct labelneural is written under, Alex eachkrizhevsky image, and with a red bar (if it happens to be in the top 5). (Right) Fiv remaining columns show the six training images that prod
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11 f : R n R f : R n R
12 f Θ : R n R Θ
13 f Θ : R n R y y
14 f Θ : R n R m Θ = {W 1, b 1, W 2, b 2, } h h Wh + b g h W h b
15 ( ) h W h b
16 Θ = {W 1, b 1, W 2, b 2, } y = f Θ (x) loss(y, y) x y
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19 D = {(x 1, y 1 ), (x 2, y 2 ),, (x T, y T )} B = {(x b1, y b1 ), (x b2, y b2 ),, (x bk, y bk )} G B (Θ) = 1 K K k=1 loss(y bk f Θ (x bk )) Step 1 () Θ := Θ 0 Step 2 () B Step 3 () g := G B (Θ) Step 4 () Θ := Θ αg Step 5 () Step 2
20 loss(y, y)
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33 λ β α β α β j i = λ j + k B( j)\i α k j α i j = 2 tanh 1 1 tanh ( k A(i)\j 2 βk i )
34 λ β α β α β j i = λ j + k B( j)\i w k,j α k j α i j = 2 tanh 1 1 tanh ( k A(i)\j 2 βk i )
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37 N x M A w y
38 Input layer Hidden layer Output layer round Index of signal component Fig. 2. Sparse signal recovery for a 6-sparse vector. (top: the original sparse signal x, bottom: the output y = Φ θ (x) from the trained neural network. n =256,m=120)
39 r t = s t + βa T (y As t ) s t+1 = η(r t ; τ),
40 x = y Ax λ x 1 r t = s t + βa T (y As t ) s t+1 = η(r t ; τ),
41 r t = Bs t + Sy s t+1 = η(r t ; τ t )
42 r t = s t + γ t W (y As t ), s t+1 = η MMSE (r t ; τ 2 t ), { y vt 2 Ast 2 2 = max Mσ2 trace(a T A) }, ϵ τ 2 t = v 2 t N (N +(γ2 t 2γ t )M)+ γ2 t σ 2 N trace(ww T ),
43 r t = s t + γ t W (y As t ), s t+1 = η MMSE (r t ; τ 2 t ), { y vt 2 Ast 2 2 = max Mσ2 trace(a T A) }, ϵ τ 2 t = v 2 t N (N +(γ2 t 2γ t )M)+ γ2 t σ 2 N trace(ww T ), 3 2 output of MMSE estimator
44 y x
45 TISTA LISTA LAMP # of params T T (N 2 + MN +1) T (NM +2) [2] M. Borgerding and P. Schniter, Onsager-corrected deep learning for sparse linear inverse problems, 2016 IEEE Global Conf. Signal and Inf. Proc. (GlobalSIP), Washington, DC, Dec. 2016, pp
46 NMSE of TISTA, LISTA and AMP; N A i,j N (0, 1/M), N = 500, M = 250, SNR = 40dB. N TISTA LISTA AMP NMSE [db] iteration
47 Three sequences of learned parameters γ t ; A i,j N (0, 1/M), N = 500, M = 250, p = 0.1, SNR = 40dB. N TISTA1 TISTA2 TISTA value iteration
48 Three sequences of learned parameters γ t ; A i,j N (0, 1/M), N = 500, M = 250, p = 0.1, SNR = 40dB. N TISTA1 TISTA2 TISTA value iteration
49 N = 500, M = 250, p = 0.1, A i,j { 1, 1}, SNR = 40 db TISTA LISTA -15 NMSE [db] iteration
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51 N M H x w y
52 mulas that are based on those of ISTA: r t = s t + γ t W (y Hs t ), ( ) rt s t+1 = tanh, θ t Fig. 1. The -th layer of the TI-detector. The trainable param
53 mulas that are based on those of ISTA: r t = s t + γ t W (y Hs t ), ( ) rt s t+1 = tanh, θ t Fig. 1. The -th layer of the TI-detector. The trainable param
54 BER TI-detector(T=50) MMSE IW-SOAV(L=1,K itr =50) IW-SOAV(L=2,K itr =50) IW-SOAV(L=5,K itr =50) SNR per receive antenna(db) R. Hayakawa and K. Hayashi, Convex optimizationbased signal detection for massive overloaded MIMO systems, in IEEE Trans. Wireless Comm., vol. 16, no. 11, pp , Nov Fig. 3. BER performance for.
55 value value index t γ t θ t index t
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60 W 1 y + b 1 relu W i h i 1 + b i W T h T 1 + b T y α ỹ h h i h T 1 soft staircase functions f( ; S, σ 2 )
61 W 1 y + b 1 relu W i h i 1 + b i W T h T 1 + b T y α ỹ h 1... f(r; S, sigma 2 ) h i sigma 2 = 0.0 sigma 2 = 0.1 sigma 2 = h T 1 soft staircase functions f( ; S, σ 2 ) r
62 W 1 y + b 1 relu W i h i 1 + b i W T h T 1 + b T y α ỹ h h i h T 1 soft staircase functions f( ; S, σ 2 ) y
63 f(r; S, sigma 2 ) sigma 2 = 0.0 sigma 2 = 0.1 sigma 2 = 0.5 W 1 y + b 1 relu W i h i 1 + b i y h 1 h i W T h T 1 + b T α ỹ h T 1 soft staircase functions f( ; S, σ 2 ) r x y x
64 PEGReg252x504 PEGReg504x1008 Bit error rate y Max steps=25-3 Max steps=100 Max steps=500-4 No quantization SNR (db) x
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67 GAN VAE NADE, Wavenet NICE, Glow
68 GPU GPU CPU ()
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72 NVIDIA TESLA GPU Google Tensor Processing Unit (TPU) 出典 出典
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