train_xを減らしてmnistでval_accを0.02%伸ばす方法

TL;DR

trainデータで間違えるところだけを学習するとちょっと0.02%伸びたよ

やったこと

mnistでモデルを作っていると、

学習率を落としても、数値が上がりそうで上がらず振幅して悲しいことが多いと思いますが、

train_xを工夫すると若干(0.02%)val_accを向上させられたので、ご紹介。

まず普通にモデル作成

こんなモデルを作りました。

# 乱数固定おまじない
import os
import numpy as np
import random as rn
import tensorflow as tf

os.environ['PYTHONHASHSEED'] = '0'
np.random.seed(0)
rn.seed(0)

session_conf = tf.ConfigProto(
    intra_op_parallelism_threads=1,
    inter_op_parallelism_threads=1
)

from keras import backend as K

tf.set_random_seed(0)
sess = tf.Session(graph=tf.get_default_graph(), config=session_conf)
K.set_session(sess)

from keras import datasets
import numpy as np
((train_x,train_y_org),(test_x,test_y)) = datasets.mnist.load_data()
train_x = (train_x/255).astype("float32").reshape(-1,28,28,1)
test_x  = (test_x /255).astype("float32").reshape(-1,28,28,1)
train_y = np.eye(10)[train_y_org]
test_y = np.eye(10)[test_y]

from tensorflow.keras.layers import *
from tensorflow.keras.models import *
from tensorflow.keras.optimizers import Adam
from tensorflow.keras.callbacks import ModelCheckpoint
from tensorflow.keras.losses import categorical_crossentropy

cp_cb = ModelCheckpoint(filepath = "model_{epoch:02d}.model")

model = Sequential()
model.add(Conv2D(filters=32,kernel_size=(3,3),input_shape=(28,28,1),padding="same"))
model.add(PReLU())
model.add(Dropout(0.15))
model.add(BatchNormalization())
model.add(Conv2D(filters=32,kernel_size=(3,3),padding="same"))
model.add(PReLU())
model.add(Dropout(0.15))
model.add(BatchNormalization())
model.add(MaxPool2D(pool_size=(2,2),padding="same")) # 28,28 -> 14,14
model.add(Conv2D(filters=64,kernel_size=(3,3),padding="same"))
model.add(PReLU())
model.add(Dropout(0.15))
model.add(BatchNormalization())
model.add(Conv2D(filters=64,kernel_size=(3,3),padding="same"))
model.add(PReLU())
model.add(Dropout(0.15))
model.add(BatchNormalization())
model.add(MaxPool2D(pool_size=(2,2),padding="same")) # 14,14 -> 7,7
model.add(Conv2D(filters=64,kernel_size=(3,3),padding="same"))
model.add(PReLU())
model.add(Dropout(0.15))
model.add(BatchNormalization())
model.add(Conv2D(filters=64,kernel_size=(3,3),padding="same"))
model.add(PReLU())
model.add(Dropout(0.15))
model.add(BatchNormalization())
model.add(MaxPool2D(pool_size=(2,2),padding="same")) # 7,7 -> 4,4
model.add(Conv2D(filters=64,kernel_size=(3,3),padding="same"))
model.add(PReLU())
model.add(Dropout(0.15))
model.add(BatchNormalization())
model.add(Conv2D(filters=64,kernel_size=(3,3),padding="same"))
model.add(PReLU())
model.add(Dropout(0.15))
model.add(BatchNormalization())
model.add(MaxPool2D(pool_size=(2,2),padding="same")) # 4,4 -> 2,2
model.add(Conv2D(filters=128,kernel_size=(2,2),padding="same"))
model.add(PReLU())
model.add(Dropout(0.15))
model.add(BatchNormalization())
model.add(MaxPool2D(pool_size=(2,2),padding="same")) # 2,2 -> 1,1
model.add(Flatten())
model.add(Dense(10,activation="softmax"))
model.summary()

model.compile(optimizer=Adam(lr=0.0001),metrics=['accuracy'],loss="categorical_crossentropy")

model_history = model.fit(train_x,train_y,batch_size=16,epochs=64,validation_data=(test_x,test_y),callbacks=[cp_cb])

結果は下記の通り

Train on 60000 samples, validate on 10000 samples
Epoch 1/64
60000/60000 [==============================] - 82s 1ms/step - loss: 0.8120 - acc: 0.7451 - val_loss: 0.4310 - val_acc: 0.8647
Epoch 2/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.1514 - acc: 0.9529 - val_loss: 0.0841 - val_acc: 0.9783
Epoch 3/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0911 - acc: 0.9720 - val_loss: 0.0681 - val_acc: 0.9835
Epoch 4/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0661 - acc: 0.9793 - val_loss: 0.0346 - val_acc: 0.9899
Epoch 5/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0537 - acc: 0.9841 - val_loss: 0.0359 - val_acc: 0.9898
Epoch 6/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0438 - acc: 0.9867 - val_loss: 0.0265 - val_acc: 0.9925
Epoch 7/64
60000/60000 [==============================] - 77s 1ms/step - loss: 0.0396 - acc: 0.9879 - val_loss: 0.0329 - val_acc: 0.9901
Epoch 8/64
60000/60000 [==============================] - 77s 1ms/step - loss: 0.0336 - acc: 0.9894 - val_loss: 0.0227 - val_acc: 0.9934
Epoch 9/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0305 - acc: 0.9900 - val_loss: 0.0257 - val_acc: 0.9929
Epoch 10/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0268 - acc: 0.9917 - val_loss: 0.0291 - val_acc: 0.9909
Epoch 11/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0250 - acc: 0.9920 - val_loss: 0.0221 - val_acc: 0.9934
Epoch 12/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0236 - acc: 0.9927 - val_loss: 0.0297 - val_acc: 0.9915
Epoch 13/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0215 - acc: 0.9933 - val_loss: 0.0189 - val_acc: 0.9940
Epoch 14/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0191 - acc: 0.9939 - val_loss: 0.0210 - val_acc: 0.9940
Epoch 15/64
60000/60000 [==============================] - 79s 1ms/step - loss: 0.0180 - acc: 0.9944 - val_loss: 0.0188 - val_acc: 0.9948
Epoch 16/64
60000/60000 [==============================] - 79s 1ms/step - loss: 0.0165 - acc: 0.9950 - val_loss: 0.0161 - val_acc: 0.9953
Epoch 17/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0159 - acc: 0.9949 - val_loss: 0.0202 - val_acc: 0.9936
Epoch 18/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0141 - acc: 0.9956 - val_loss: 0.0233 - val_acc: 0.9925
Epoch 19/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0143 - acc: 0.9954 - val_loss: 0.0187 - val_acc: 0.9945
Epoch 20/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0133 - acc: 0.9957 - val_loss: 0.0221 - val_acc: 0.9938
Epoch 21/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0131 - acc: 0.9958 - val_loss: 0.0178 - val_acc: 0.9950
Epoch 22/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0124 - acc: 0.9961 - val_loss: 0.0171 - val_acc: 0.9950
Epoch 23/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0121 - acc: 0.9961 - val_loss: 0.0169 - val_acc: 0.9950
Epoch 24/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0099 - acc: 0.9967 - val_loss: 0.0207 - val_acc: 0.9942
Epoch 25/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0103 - acc: 0.9967 - val_loss: 0.0172 - val_acc: 0.9953
Epoch 26/64
60000/60000 [==============================] - 77s 1ms/step - loss: 0.0097 - acc: 0.9970 - val_loss: 0.0189 - val_acc: 0.9946
Epoch 27/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0095 - acc: 0.9970 - val_loss: 0.0182 - val_acc: 0.9944
Epoch 28/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0084 - acc: 0.9972 - val_loss: 0.0214 - val_acc: 0.9942
Epoch 29/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0087 - acc: 0.9972 - val_loss: 0.0193 - val_acc: 0.9945
Epoch 30/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0077 - acc: 0.9976 - val_loss: 0.0173 - val_acc: 0.9960
Epoch 31/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0089 - acc: 0.9973 - val_loss: 0.0187 - val_acc: 0.9948
Epoch 32/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0064 - acc: 0.9979 - val_loss: 0.0204 - val_acc: 0.9948
Epoch 33/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0077 - acc: 0.9975 - val_loss: 0.0205 - val_acc: 0.9949
Epoch 34/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0064 - acc: 0.9979 - val_loss: 0.0173 - val_acc: 0.9953
Epoch 35/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0068 - acc: 0.9976 - val_loss: 0.0204 - val_acc: 0.9952
Epoch 36/64
60000/60000 [==============================] - 79s 1ms/step - loss: 0.0074 - acc: 0.9976 - val_loss: 0.0183 - val_acc: 0.9952
Epoch 37/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0053 - acc: 0.9983 - val_loss: 0.0240 - val_acc: 0.9947
Epoch 38/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0064 - acc: 0.9979 - val_loss: 0.0190 - val_acc: 0.9951
Epoch 39/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0064 - acc: 0.9979 - val_loss: 0.0232 - val_acc: 0.9943
Epoch 40/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0056 - acc: 0.9981 - val_loss: 0.0177 - val_acc: 0.9956
Epoch 41/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0059 - acc: 0.9981 - val_loss: 0.0197 - val_acc: 0.9956
Epoch 42/64
60000/60000 [==============================] - 77s 1ms/step - loss: 0.0062 - acc: 0.9980 - val_loss: 0.0210 - val_acc: 0.9951
Epoch 43/64
60000/60000 [==============================] - 77s 1ms/step - loss: 0.0050 - acc: 0.9982 - val_loss: 0.0210 - val_acc: 0.9951
Epoch 44/64
60000/60000 [==============================] - 77s 1ms/step - loss: 0.0047 - acc: 0.9984 - val_loss: 0.0196 - val_acc: 0.9953
Epoch 45/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0051 - acc: 0.9982 - val_loss: 0.0230 - val_acc: 0.9945
Epoch 46/64
60000/60000 [==============================] - 77s 1ms/step - loss: 0.0056 - acc: 0.9983 - val_loss: 0.0208 - val_acc: 0.9950
Epoch 47/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0050 - acc: 0.9983 - val_loss: 0.0234 - val_acc: 0.9948
Epoch 48/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0050 - acc: 0.9983 - val_loss: 0.0221 - val_acc: 0.9947
Epoch 49/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0045 - acc: 0.9986 - val_loss: 0.0223 - val_acc: 0.9949
Epoch 50/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0040 - acc: 0.9987 - val_loss: 0.0243 - val_acc: 0.9944
Epoch 51/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0038 - acc: 0.9989 - val_loss: 0.0189 - val_acc: 0.9954
Epoch 52/64
60000/60000 [==============================] - 79s 1ms/step - loss: 0.0047 - acc: 0.9986 - val_loss: 0.0204 - val_acc: 0.9953
Epoch 53/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0042 - acc: 0.9985 - val_loss: 0.0171 - val_acc: 0.9961
Epoch 54/64
60000/60000 [==============================] - 77s 1ms/step - loss: 0.0044 - acc: 0.9986 - val_loss: 0.0223 - val_acc: 0.9951
Epoch 55/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0043 - acc: 0.9986 - val_loss: 0.0194 - val_acc: 0.9951
Epoch 56/64
60000/60000 [==============================] - 77s 1ms/step - loss: 0.0041 - acc: 0.9986 - val_loss: 0.0200 - val_acc: 0.9947
Epoch 57/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0037 - acc: 0.9988 - val_loss: 0.0203 - val_acc: 0.9953
Epoch 58/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0036 - acc: 0.9989 - val_loss: 0.0182 - val_acc: 0.9955
Epoch 59/64
60000/60000 [==============================] - 77s 1ms/step - loss: 0.0041 - acc: 0.9988 - val_loss: 0.0188 - val_acc: 0.9957
Epoch 60/64
60000/60000 [==============================] - 77s 1ms/step - loss: 0.0041 - acc: 0.9985 - val_loss: 0.0240 - val_acc: 0.9941
Epoch 61/64
60000/60000 [==============================] - 79s 1ms/step - loss: 0.0037 - acc: 0.9989 - val_loss: 0.0214 - val_acc: 0.9947
Epoch 62/64
60000/60000 [==============================] - 79s 1ms/step - loss: 0.0030 - acc: 0.9990 - val_loss: 0.0236 - val_acc: 0.9948
Epoch 63/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0037 - acc: 0.9989 - val_loss: 0.0239 - val_acc: 0.9948
Epoch 64/64
60000/60000 [==============================] - 78s 1ms/step - loss: 0.0034 - acc: 0.9990 - val_loss: 0.0204 - val_acc: 0.9952

epoch53でval_accが99.61%を記録しました。

本当にこのモデルで99.61%を記録するか確認しておきましょう。

callbackにモデルを保存する関数を入れておいたので、 各epoch毎にその時の重みとバイアスを保存してくれています。

load_modelで呼び出して確認です。

model = load_model("./model_53.model")
model.evaluate(test_x,test_y)

10000/10000 [==============================] - 2s 187us/step
[0.017076379576059116, 0.9961]

ちゃんとval_accが0.9961出してくれますね。

た だ し 今 回 は こ の モ デ ル は 使 い ま せ ん 。

理由としては、trainデータのaccがもうすでに100%だったからです。

なので恣意的にepoch30のval_acc99.6%のモデルを使います。

model = load_model("./model_30.model")

データの取捨選択

さて、このモデル、現状trainとtestに対してどれくらいの能力を持っているのか、 今一度確認します。

# 訓練データ
print(np.sum(np.argmax(model.predict(train_x),axis=1) == train_y_org))
# テストデータ
print(np.sum(np.argmax(model.predict(train_x),axis=1) == np.argmax(test_y,axis=1)))

結果は以下の通り

59976
9960

trainが60000,testが10000なので、 trainは24個間違い、testは40個間違えてますね。

さて、ここでtrainの24個に注目します。

もう合ってるものを学習してあまり意味はないし、むしろ過学習するだけで悪影響を及ぼすと考えられます。

なので間違えているものだけを、学習率を1/10に下げてちょろちょろと重みとバイアスを更新すると少なくとも学習データに対しては適合します。

それがテストデータに対してどうなるのか、が今回のお話。

なのでこんなコードをこの後に実行しました。

model.compile(optimizer=Adam(lr=0.00001),metrics=['accuracy'],loss="categorical_crossentropy")
model_history_2 = []
for i in range(32):
    choice = np.invert((np.argmax(model.predict(train_x),axis=1) == train_y_org))
    model_history_2.append(model.fit(train_x[choice],train_y[choice],batch_size=16,epochs=1,validation_data=(test_x,test_y)))

肝は4行目でtrainデータの中で間違えたものだけを取り出して、 それを5行目で学習するときに突っ込むところですね。

さて、その結果はこんな感じです。

Train on 24 samples, validate on 10000 samples
Epoch 1/1
24/24 [==============================] - 7s 280ms/step - loss: 2.9693 - acc: 0.3750 - val_loss: 0.0173 - val_acc: 0.9960
Train on 23 samples, validate on 10000 samples
Epoch 1/1
23/23 [==============================] - 2s 104ms/step - loss: 2.1650 - acc: 0.3913 - val_loss: 0.0173 - val_acc: 0.9960
Train on 21 samples, validate on 10000 samples
Epoch 1/1
21/21 [==============================] - 2s 113ms/step - loss: 2.7324 - acc: 0.3333 - val_loss: 0.0173 - val_acc: 0.9960
Train on 21 samples, validate on 10000 samples
Epoch 1/1
21/21 [==============================] - 2s 112ms/step - loss: 2.9146 - acc: 0.2381 - val_loss: 0.0173 - val_acc: 0.9960
Train on 20 samples, validate on 10000 samples
Epoch 1/1
20/20 [==============================] - 2s 119ms/step - loss: 3.5161 - acc: 0.2500 - val_loss: 0.0174 - val_acc: 0.9962
Train on 17 samples, validate on 10000 samples
Epoch 1/1
17/17 [==============================] - 2s 139ms/step - loss: 3.3470 - acc: 0.2941 - val_loss: 0.0174 - val_acc: 0.9961
Train on 17 samples, validate on 10000 samples
Epoch 1/1
17/17 [==============================] - 2s 139ms/step - loss: 2.3149 - acc: 0.4706 - val_loss: 0.0175 - val_acc: 0.9958
Train on 16 samples, validate on 10000 samples
Epoch 1/1
16/16 [==============================] - 2s 147ms/step - loss: 2.7394 - acc: 0.3750 - val_loss: 0.0175 - val_acc: 0.9959
Train on 16 samples, validate on 10000 samples
Epoch 1/1
16/16 [==============================] - 2s 146ms/step - loss: 2.2038 - acc: 0.3125 - val_loss: 0.0175 - val_acc: 0.9960
Train on 16 samples, validate on 10000 samples
Epoch 1/1
16/16 [==============================] - 2s 146ms/step - loss: 1.8772 - acc: 0.3750 - val_loss: 0.0175 - val_acc: 0.9960
Train on 15 samples, validate on 10000 samples
Epoch 1/1
15/15 [==============================] - 2s 158ms/step - loss: 2.2117 - acc: 0.3333 - val_loss: 0.0175 - val_acc: 0.9959
Train on 15 samples, validate on 10000 samples
Epoch 1/1
15/15 [==============================] - 2s 158ms/step - loss: 1.7083 - acc: 0.4000 - val_loss: 0.0175 - val_acc: 0.9959
Train on 15 samples, validate on 10000 samples
Epoch 1/1
15/15 [==============================] - 2s 157ms/step - loss: 2.1227 - acc: 0.4000 - val_loss: 0.0175 - val_acc: 0.9959
Train on 14 samples, validate on 10000 samples
Epoch 1/1
14/14 [==============================] - 2s 171ms/step - loss: 2.7587 - acc: 0.4286 - val_loss: 0.0175 - val_acc: 0.9960
Train on 14 samples, validate on 10000 samples
Epoch 1/1
14/14 [==============================] - 2s 169ms/step - loss: 3.1257 - acc: 0.2857 - val_loss: 0.0175 - val_acc: 0.9959
Train on 14 samples, validate on 10000 samples
Epoch 1/1
14/14 [==============================] - 2s 166ms/step - loss: 2.8811 - acc: 0.2857 - val_loss: 0.0176 - val_acc: 0.9959
Train on 14 samples, validate on 10000 samples
Epoch 1/1
14/14 [==============================] - 2s 166ms/step - loss: 2.2550 - acc: 0.3571 - val_loss: 0.0176 - val_acc: 0.9960
Train on 13 samples, validate on 10000 samples
Epoch 1/1
13/13 [==============================] - 2s 181ms/step - loss: 2.1959 - acc: 0.4615 - val_loss: 0.0176 - val_acc: 0.9960
Train on 12 samples, validate on 10000 samples
Epoch 1/1
12/12 [==============================] - 2s 195ms/step - loss: 3.4894 - acc: 0.0833 - val_loss: 0.0176 - val_acc: 0.9960
Train on 12 samples, validate on 10000 samples
Epoch 1/1
12/12 [==============================] - 2s 198ms/step - loss: 3.0016 - acc: 0.3333 - val_loss: 0.0176 - val_acc: 0.9960
Train on 12 samples, validate on 10000 samples
Epoch 1/1
12/12 [==============================] - 2s 199ms/step - loss: 4.0224 - acc: 0.1667 - val_loss: 0.0176 - val_acc: 0.9960
Train on 12 samples, validate on 10000 samples
Epoch 1/1
12/12 [==============================] - 2s 197ms/step - loss: 3.4493 - acc: 0.3333 - val_loss: 0.0176 - val_acc: 0.9960
Train on 11 samples, validate on 10000 samples
Epoch 1/1
11/11 [==============================] - 2s 218ms/step - loss: 3.6480 - acc: 0.2727 - val_loss: 0.0176 - val_acc: 0.9960
Train on 9 samples, validate on 10000 samples
Epoch 1/1
9/9 [==============================] - 2s 266ms/step - loss: 2.7602 - acc: 0.3333 - val_loss: 0.0176 - val_acc: 0.9960
Train on 9 samples, validate on 10000 samples
Epoch 1/1
9/9 [==============================] - 2s 264ms/step - loss: 3.2277 - acc: 0.3333 - val_loss: 0.0176 - val_acc: 0.9960
Train on 9 samples, validate on 10000 samples
Epoch 1/1
9/9 [==============================] - 2s 258ms/step - loss: 1.9044 - acc: 0.4444 - val_loss: 0.0177 - val_acc: 0.9960
Train on 9 samples, validate on 10000 samples
Epoch 1/1
9/9 [==============================] - 2s 257ms/step - loss: 3.7250 - acc: 0.1111 - val_loss: 0.0177 - val_acc: 0.9960
Train on 9 samples, validate on 10000 samples
Epoch 1/1
9/9 [==============================] - 2s 256ms/step - loss: 3.6916 - acc: 0.2222 - val_loss: 0.0177 - val_acc: 0.9959
Train on 10 samples, validate on 10000 samples
Epoch 1/1
10/10 [==============================] - 2s 234ms/step - loss: 3.0128 - acc: 0.4000 - val_loss: 0.0177 - val_acc: 0.9959
Train on 10 samples, validate on 10000 samples
Epoch 1/1
10/10 [==============================] - 2s 231ms/step - loss: 2.5596 - acc: 0.2000 - val_loss: 0.0177 - val_acc: 0.9959
Train on 10 samples, validate on 10000 samples
Epoch 1/1
10/10 [==============================] - 2s 233ms/step - loss: 3.6156 - acc: 0.2000 - val_loss: 0.0177 - val_acc: 0.9959

5ループ目に99.62%を達成してくれてます。その後は過学習したのかどんどんval_lossもval_accも落ちていきます。

ここで言いたいのは53epoch全量回し切ったのに対し、

30epoch程度のモデルに対して20個程度のデータで5回回すだけでval_accが超えたことですね。

これは計算量の効率がだいぶよいのではないでしょうか。

そんなお話。

現場で使える! TensorFlow開発入門 Kerasによる深層学習モデル構築手法 (AI & TECHNOLOGY)