In [1]:
import tensorflow as tf
import numpy as np
import datetime, os
import matplotlib.pyplot as plt
plt.style.use('fivethirtyeight')
import warnings
warnings.filterwarnings('ignore')
Gradient Calculation
Example 1: Gradient of y = x^3 for x = 5¶
In [2]:
# Initialize a variable
x = tf.Variable(5.0)
# Initiate the gradient tape
with tf.GradientTape() as tape:
y = x ** 3
# Access the gradient -- derivative of y with respect to x
dy_dx = tape.gradient(y, x)
In [3]:
print(f'{dy_dx} is the gradient of y=x^3 with x={x.numpy()}')
75.0 is the gradient of y=x^3 with x=5.0
Example 2: Estimating y = 4 using SGD¶
True y value¶
In [4]:
y = 4
Initialize a random estimate (yhat) for y¶
In [5]:
yhat = tf.Variable([tf.random.normal([1])])
print(f'Initializing yhat={yhat.numpy()}')
Initializing yhat=[[-0.3535073]]
Updating yhat using gradient descent¶
Loss function, L = (yhat - y)^2
In [6]:
learning_rate = 1e-2 # learning rate for SGD
result = []
# Compute the derivative of the loss with respect to x, and perform the SGD update.
for i in range(500):
with tf.GradientTape() as tape:
loss = (yhat - y)**2
# loss minimization using gradient tape
grad = tape.gradient(loss, yhat)
new_yhat = yhat - learning_rate*grad # sgd update
yhat.assign(new_yhat) # update the value of f(x)
result.append(yhat.numpy()[0])
# Plot the evolution of yhat as we optimize towards y
plt.figure(figsize=(20,10))
plt.plot(result)
plt.plot([0, 500],[y,y])
plt.legend(('Predicted', 'True'))
plt.xlabel('Iteration')
plt.ylabel('y value')
plt.title('Evoluation of yhat as we optimize towards y');
TensorBoard for Visualization
In [7]:
# Load the TensorBoard notebook extension
%load_ext tensorboard
In [8]:
fashion_mnist = tf.keras.datasets.fashion_mnist
(x_train, y_train),(x_test, y_test) = fashion_mnist.load_data()
x_train, x_test = x_train / 255.0, x_test / 255.0 # normalizing the data
In [9]:
def create_model():
return tf.keras.models.Sequential([
tf.keras.layers.Flatten(input_shape=(28, 28)),
tf.keras.layers.Dense(512, activation='relu'),
tf.keras.layers.Dropout(0.2),
tf.keras.layers.Dense(10, activation='softmax')
])
In [10]:
def train_model():
model = create_model()
model.compile(optimizer='adam',
loss='sparse_categorical_crossentropy',
metrics=['accuracy'])
# two extra line of code
logdir = os.path.join("logs", datetime.datetime.now().strftime("%Y%m%d-%H%M%S"))
tb_callbacks = [tf.keras.callbacks.TensorBoard(log_dir=logdir, histogram_freq=1)]
model.fit(x=x_train, y=y_train, epochs=5, validation_data=(x_test, y_test), callbacks=tb_callbacks)
train_model()
Epoch 1/5 1875/1875 [==============================] - 9s 4ms/step - loss: 0.4987 - accuracy: 0.8219 - val_loss: 0.4254 - val_accuracy: 0.8460 Epoch 2/5 1875/1875 [==============================] - 8s 4ms/step - loss: 0.3828 - accuracy: 0.8591 - val_loss: 0.3848 - val_accuracy: 0.8603 Epoch 3/5 1875/1875 [==============================] - 8s 4ms/step - loss: 0.3515 - accuracy: 0.8710 - val_loss: 0.3703 - val_accuracy: 0.8667 Epoch 4/5 1875/1875 [==============================] - 8s 4ms/step - loss: 0.3294 - accuracy: 0.8771 - val_loss: 0.3700 - val_accuracy: 0.8642 Epoch 5/5 1875/1875 [==============================] - 8s 4ms/step - loss: 0.3137 - accuracy: 0.8837 - val_loss: 0.3448 - val_accuracy: 0.8708
In [11]:
%tensorboard --logdir logs
Keras
Keras is a deep learning API for Python and is one of the most powerful and easy to use library which runs on top of popular libraries like TensorFlow and Theano for creating deep learning models.
In [12]:
import keras
Example 1: Using keras to fit y = 2x - 1 for six input features and labels¶
In [13]:
from keras.models import Sequential
from tensorflow.keras.utils import to_categorical
from tensorflow.keras.layers import Dense, MaxPooling2D, Conv2D, Flatten
In [14]:
model = Sequential()
model.add(Dense(1, input_shape=(1,)))
model.compile(optimizer='sgd', loss='mean_squared_error')
X = np.array([-1.0,0.0,1.0,2.0,3.0,4.0])
y = np.array([-3.,-1.,1.,3.,5.,7.])
model.fit(X, y, epochs=500)
print(model.predict([10.0]))
Epoch 1/500 1/1 [==============================] - 0s 194ms/step - loss: 30.2472 Epoch 2/500 1/1 [==============================] - 0s 4ms/step - loss: 24.1110 Epoch 3/500 1/1 [==============================] - 0s 3ms/step - loss: 19.2769 Epoch 4/500 1/1 [==============================] - 0s 4ms/step - loss: 15.4674 Epoch 5/500 1/1 [==============================] - 0s 4ms/step - loss: 12.4640 Epoch 6/500 1/1 [==============================] - 0s 4ms/step - loss: 10.0950 Epoch 7/500 1/1 [==============================] - 0s 4ms/step - loss: 8.2253 Epoch 8/500 1/1 [==============================] - 0s 3ms/step - loss: 6.7485 Epoch 9/500 1/1 [==============================] - 0s 2ms/step - loss: 5.5809 Epoch 10/500 1/1 [==============================] - 0s 2ms/step - loss: 4.6567 Epoch 11/500 1/1 [==============================] - 0s 877us/step - loss: 3.9242 Epoch 12/500 1/1 [==============================] - 0s 4ms/step - loss: 3.3425 Epoch 13/500 1/1 [==============================] - 0s 2ms/step - loss: 2.8796 Epoch 14/500 1/1 [==============================] - 0s 2ms/step - loss: 2.5103 Epoch 15/500 1/1 [==============================] - 0s 4ms/step - loss: 2.2147 Epoch 16/500 1/1 [==============================] - 0s 2ms/step - loss: 1.9772 Epoch 17/500 1/1 [==============================] - 0s 3ms/step - loss: 1.7855 Epoch 18/500 1/1 [==============================] - 0s 3ms/step - loss: 1.6300 Epoch 19/500 1/1 [==============================] - 0s 3ms/step - loss: 1.5031 Epoch 20/500 1/1 [==============================] - 0s 3ms/step - loss: 1.3986 Epoch 21/500 1/1 [==============================] - 0s 2ms/step - loss: 1.3120 Epoch 22/500 1/1 [==============================] - 0s 3ms/step - loss: 1.2395 Epoch 23/500 1/1 [==============================] - 0s 5ms/step - loss: 1.1783 Epoch 24/500 1/1 [==============================] - 0s 4ms/step - loss: 1.1259 Epoch 25/500 1/1 [==============================] - 0s 3ms/step - loss: 1.0806 Epoch 26/500 1/1 [==============================] - 0s 5ms/step - loss: 1.0409 Epoch 27/500 1/1 [==============================] - 0s 3ms/step - loss: 1.0058 Epoch 28/500 1/1 [==============================] - 0s 3ms/step - loss: 0.9744 Epoch 29/500 1/1 [==============================] - 0s 5ms/step - loss: 0.9459 Epoch 30/500 1/1 [==============================] - 0s 4ms/step - loss: 0.9198 Epoch 31/500 1/1 [==============================] - 0s 3ms/step - loss: 0.8956 Epoch 32/500 1/1 [==============================] - 0s 5ms/step - loss: 0.8731 Epoch 33/500 1/1 [==============================] - 0s 4ms/step - loss: 0.8519 Epoch 34/500 1/1 [==============================] - 0s 3ms/step - loss: 0.8318 Epoch 35/500 1/1 [==============================] - 0s 4ms/step - loss: 0.8127 Epoch 36/500 1/1 [==============================] - 0s 2ms/step - loss: 0.7944 Epoch 37/500 1/1 [==============================] - 0s 3ms/step - loss: 0.7769 Epoch 38/500 1/1 [==============================] - 0s 4ms/step - loss: 0.7599 Epoch 39/500 1/1 [==============================] - 0s 3ms/step - loss: 0.7436 Epoch 40/500 1/1 [==============================] - 0s 2ms/step - loss: 0.7277 Epoch 41/500 1/1 [==============================] - 0s 4ms/step - loss: 0.7123 Epoch 42/500 1/1 [==============================] - 0s 4ms/step - loss: 0.6973 Epoch 43/500 1/1 [==============================] - 0s 3ms/step - loss: 0.6826 Epoch 44/500 1/1 [==============================] - 0s 4ms/step - loss: 0.6684 Epoch 45/500 1/1 [==============================] - 0s 4ms/step - loss: 0.6545 Epoch 46/500 1/1 [==============================] - 0s 2ms/step - loss: 0.6409 Epoch 47/500 1/1 [==============================] - 0s 2ms/step - loss: 0.6276 Epoch 48/500 1/1 [==============================] - 0s 3ms/step - loss: 0.6146 Epoch 49/500 1/1 [==============================] - 0s 5ms/step - loss: 0.6019 Epoch 50/500 1/1 [==============================] - 0s 2ms/step - loss: 0.5895 Epoch 51/500 1/1 [==============================] - 0s 3ms/step - loss: 0.5774 Epoch 52/500 1/1 [==============================] - 0s 3ms/step - loss: 0.5655 Epoch 53/500 1/1 [==============================] - 0s 4ms/step - loss: 0.5538 Epoch 54/500 1/1 [==============================] - 0s 3ms/step - loss: 0.5424 Epoch 55/500 1/1 [==============================] - 0s 3ms/step - loss: 0.5313 Epoch 56/500 1/1 [==============================] - 0s 3ms/step - loss: 0.5203 Epoch 57/500 1/1 [==============================] - 0s 3ms/step - loss: 0.5096 Epoch 58/500 1/1 [==============================] - 0s 2ms/step - loss: 0.4992 Epoch 59/500 1/1 [==============================] - 0s 3ms/step - loss: 0.4889 Epoch 60/500 1/1 [==============================] - 0s 3ms/step - loss: 0.4789 Epoch 61/500 1/1 [==============================] - 0s 2ms/step - loss: 0.4690 Epoch 62/500 1/1 [==============================] - 0s 4ms/step - loss: 0.4594 Epoch 63/500 1/1 [==============================] - 0s 2ms/step - loss: 0.4499 Epoch 64/500 1/1 [==============================] - 0s 4ms/step - loss: 0.4407 Epoch 65/500 1/1 [==============================] - 0s 3ms/step - loss: 0.4316 Epoch 66/500 1/1 [==============================] - 0s 3ms/step - loss: 0.4228 Epoch 67/500 1/1 [==============================] - 0s 3ms/step - loss: 0.4141 Epoch 68/500 1/1 [==============================] - 0s 5ms/step - loss: 0.4056 Epoch 69/500 1/1 [==============================] - 0s 2ms/step - loss: 0.3973 Epoch 70/500 1/1 [==============================] - 0s 1ms/step - loss: 0.3891 Epoch 71/500 1/1 [==============================] - 0s 4ms/step - loss: 0.3811 Epoch 72/500 1/1 [==============================] - 0s 3ms/step - loss: 0.3733 Epoch 73/500 1/1 [==============================] - 0s 2ms/step - loss: 0.3656 Epoch 74/500 1/1 [==============================] - 0s 2ms/step - loss: 0.3581 Epoch 75/500 1/1 [==============================] - 0s 6ms/step - loss: 0.3507 Epoch 76/500 1/1 [==============================] - 0s 2ms/step - loss: 0.3435 Epoch 77/500 1/1 [==============================] - 0s 2ms/step - loss: 0.3365 Epoch 78/500 1/1 [==============================] - 0s 3ms/step - loss: 0.3296 Epoch 79/500 1/1 [==============================] - 0s 4ms/step - loss: 0.3228 Epoch 80/500 1/1 [==============================] - 0s 4ms/step - loss: 0.3162 Epoch 81/500 1/1 [==============================] - 0s 3ms/step - loss: 0.3097 Epoch 82/500 1/1 [==============================] - 0s 3ms/step - loss: 0.3033 Epoch 83/500 1/1 [==============================] - 0s 3ms/step - loss: 0.2971 Epoch 84/500 1/1 [==============================] - 0s 2ms/step - loss: 0.2910 Epoch 85/500 1/1 [==============================] - 0s 2ms/step - loss: 0.2850 Epoch 86/500 1/1 [==============================] - 0s 4ms/step - loss: 0.2791 Epoch 87/500 1/1 [==============================] - 0s 2ms/step - loss: 0.2734 Epoch 88/500 1/1 [==============================] - 0s 2ms/step - loss: 0.2678 Epoch 89/500 1/1 [==============================] - 0s 2ms/step - loss: 0.2623 Epoch 90/500 1/1 [==============================] - 0s 3ms/step - loss: 0.2569 Epoch 91/500 1/1 [==============================] - 0s 3ms/step - loss: 0.2516 Epoch 92/500 1/1 [==============================] - 0s 1ms/step - loss: 0.2465 Epoch 93/500 1/1 [==============================] - 0s 3ms/step - loss: 0.2414 Epoch 94/500 1/1 [==============================] - 0s 3ms/step - loss: 0.2364 Epoch 95/500 1/1 [==============================] - 0s 3ms/step - loss: 0.2316 Epoch 96/500 1/1 [==============================] - 0s 3ms/step - loss: 0.2268 Epoch 97/500 1/1 [==============================] - 0s 2ms/step - loss: 0.2222 Epoch 98/500 1/1 [==============================] - 0s 5ms/step - loss: 0.2176 Epoch 99/500 1/1 [==============================] - 0s 3ms/step - loss: 0.2131 Epoch 100/500 1/1 [==============================] - 0s 4ms/step - loss: 0.2088 Epoch 101/500 1/1 [==============================] - 0s 3ms/step - loss: 0.2045 Epoch 102/500 1/1 [==============================] - 0s 3ms/step - loss: 0.2003 Epoch 103/500 1/1 [==============================] - 0s 2ms/step - loss: 0.1962 Epoch 104/500 1/1 [==============================] - 0s 3ms/step - loss: 0.1921 Epoch 105/500 1/1 [==============================] - 0s 4ms/step - loss: 0.1882 Epoch 106/500 1/1 [==============================] - 0s 3ms/step - loss: 0.1843 Epoch 107/500 1/1 [==============================] - 0s 3ms/step - loss: 0.1805 Epoch 108/500 1/1 [==============================] - 0s 3ms/step - loss: 0.1768 Epoch 109/500 1/1 [==============================] - 0s 4ms/step - loss: 0.1732 Epoch 110/500 1/1 [==============================] - 0s 3ms/step - loss: 0.1696 Epoch 111/500 1/1 [==============================] - 0s 3ms/step - loss: 0.1661 Epoch 112/500 1/1 [==============================] - 0s 5ms/step - loss: 0.1627 Epoch 113/500 1/1 [==============================] - 0s 3ms/step - loss: 0.1594 Epoch 114/500 1/1 [==============================] - 0s 2ms/step - loss: 0.1561 Epoch 115/500 1/1 [==============================] - 0s 2ms/step - loss: 0.1529 Epoch 116/500 1/1 [==============================] - 0s 3ms/step - loss: 0.1498 Epoch 117/500 1/1 [==============================] - 0s 2ms/step - loss: 0.1467 Epoch 118/500 1/1 [==============================] - 0s 2ms/step - loss: 0.1437 Epoch 119/500 1/1 [==============================] - 0s 3ms/step - loss: 0.1407 Epoch 120/500 1/1 [==============================] - 0s 4ms/step - loss: 0.1378 Epoch 121/500 1/1 [==============================] - 0s 2ms/step - loss: 0.1350 Epoch 122/500 1/1 [==============================] - 0s 3ms/step - loss: 0.1322 Epoch 123/500 1/1 [==============================] - 0s 2ms/step - loss: 0.1295 Epoch 124/500 1/1 [==============================] - 0s 3ms/step - loss: 0.1269 Epoch 125/500 1/1 [==============================] - 0s 3ms/step - loss: 0.1243 Epoch 126/500 1/1 [==============================] - 0s 2ms/step - loss: 0.1217 Epoch 127/500 1/1 [==============================] - 0s 2ms/step - loss: 0.1192 Epoch 128/500 1/1 [==============================] - 0s 2ms/step - loss: 0.1168 Epoch 129/500 1/1 [==============================] - 0s 3ms/step - loss: 0.1144 Epoch 130/500 1/1 [==============================] - 0s 2ms/step - loss: 0.1120 Epoch 131/500 1/1 [==============================] - 0s 2ms/step - loss: 0.1097 Epoch 132/500 1/1 [==============================] - 0s 2ms/step - loss: 0.1075 Epoch 133/500 1/1 [==============================] - 0s 4ms/step - loss: 0.1052 Epoch 134/500 1/1 [==============================] - 0s 3ms/step - loss: 0.1031 Epoch 135/500 1/1 [==============================] - 0s 3ms/step - loss: 0.1010 Epoch 136/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0989 Epoch 137/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0969 Epoch 138/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0949 Epoch 139/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0929 Epoch 140/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0910 Epoch 141/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0891 Epoch 142/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0873 Epoch 143/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0855 Epoch 144/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0838 Epoch 145/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0820 Epoch 146/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0804 Epoch 147/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0787 Epoch 148/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0771 Epoch 149/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0755 Epoch 150/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0740 Epoch 151/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0724 Epoch 152/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0709 Epoch 153/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0695 Epoch 154/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0681 Epoch 155/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0667 Epoch 156/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0653 Epoch 157/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0640 Epoch 158/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0626 Epoch 159/500 1/1 [==============================] - 0s 4ms/step - loss: 0.0614 Epoch 160/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0601 Epoch 161/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0589 Epoch 162/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0577 Epoch 163/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0565 Epoch 164/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0553 Epoch 165/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0542 Epoch 166/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0531 Epoch 167/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0520 Epoch 168/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0509 Epoch 169/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0499 Epoch 170/500 1/1 [==============================] - 0s 4ms/step - loss: 0.0488 Epoch 171/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0478 Epoch 172/500 1/1 [==============================] - 0s 4ms/step - loss: 0.0468 Epoch 173/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0459 Epoch 174/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0449 Epoch 175/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0440 Epoch 176/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0431 Epoch 177/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0422 Epoch 178/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0414 Epoch 179/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0405 Epoch 180/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0397 Epoch 181/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0389 Epoch 182/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0381 Epoch 183/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0373 Epoch 184/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0365 Epoch 185/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0358 Epoch 186/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0350 Epoch 187/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0343 Epoch 188/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0336 Epoch 189/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0329 Epoch 190/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0322 Epoch 191/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0316 Epoch 192/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0309 Epoch 193/500 1/1 [==============================] - 0s 5ms/step - loss: 0.0303 Epoch 194/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0297 Epoch 195/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0291 Epoch 196/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0285 Epoch 197/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0279 Epoch 198/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0273 Epoch 199/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0267 Epoch 200/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0262 Epoch 201/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0257 Epoch 202/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0251 Epoch 203/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0246 Epoch 204/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0241 Epoch 205/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0236 Epoch 206/500 1/1 [==============================] - 0s 1ms/step - loss: 0.0231 Epoch 207/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0227 Epoch 208/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0222 Epoch 209/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0217 Epoch 210/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0213 Epoch 211/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0209 Epoch 212/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0204 Epoch 213/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0200 Epoch 214/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0196 Epoch 215/500 1/1 [==============================] - 0s 4ms/step - loss: 0.0192 Epoch 216/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0188 Epoch 217/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0184 Epoch 218/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0180 Epoch 219/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0177 Epoch 220/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0173 Epoch 221/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0169 Epoch 222/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0166 Epoch 223/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0163 Epoch 224/500 1/1 [==============================] - 0s 4ms/step - loss: 0.0159 Epoch 225/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0156 Epoch 226/500 1/1 [==============================] - 0s 5ms/step - loss: 0.0153 Epoch 227/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0150 Epoch 228/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0147 Epoch 229/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0144 Epoch 230/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0141 Epoch 231/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0138 Epoch 232/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0135 Epoch 233/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0132 Epoch 234/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0129 Epoch 235/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0127 Epoch 236/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0124 Epoch 237/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0122 Epoch 238/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0119 Epoch 239/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0117 Epoch 240/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0114 Epoch 241/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0112 Epoch 242/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0110 Epoch 243/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0107 Epoch 244/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0105 Epoch 245/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0103 Epoch 246/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0101 Epoch 247/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0099 Epoch 248/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0097 Epoch 249/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0095 Epoch 250/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0093 Epoch 251/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0091 Epoch 252/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0089 Epoch 253/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0087 Epoch 254/500 1/1 [==============================] - 0s 4ms/step - loss: 0.0085 Epoch 255/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0084 Epoch 256/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0082 Epoch 257/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0080 Epoch 258/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0079 Epoch 259/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0077 Epoch 260/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0075 Epoch 261/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0074 Epoch 262/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0072 Epoch 263/500 1/1 [==============================] - 0s 5ms/step - loss: 0.0071 Epoch 264/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0069 Epoch 265/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0068 Epoch 266/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0067 Epoch 267/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0065 Epoch 268/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0064 Epoch 269/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0063 Epoch 270/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0061 Epoch 271/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0060 Epoch 272/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0059 Epoch 273/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0058 Epoch 274/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0056 Epoch 275/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0055 Epoch 276/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0054 Epoch 277/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0053 Epoch 278/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0052 Epoch 279/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0051 Epoch 280/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0050 Epoch 281/500 1/1 [==============================] - 0s 4ms/step - loss: 0.0049 Epoch 282/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0048 Epoch 283/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0047 Epoch 284/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0046 Epoch 285/500 1/1 [==============================] - 0s 4ms/step - loss: 0.0045 Epoch 286/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0044 Epoch 287/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0043 Epoch 288/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0042 Epoch 289/500 1/1 [==============================] - 0s 5ms/step - loss: 0.0041 Epoch 290/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0040 Epoch 291/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0040 Epoch 292/500 1/1 [==============================] - 0s 4ms/step - loss: 0.0039 Epoch 293/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0038 Epoch 294/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0037 Epoch 295/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0036 Epoch 296/500 1/1 [==============================] - 0s 4ms/step - loss: 0.0036 Epoch 297/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0035 Epoch 298/500 1/1 [==============================] - 0s 4ms/step - loss: 0.0034 Epoch 299/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0034 Epoch 300/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0033 Epoch 301/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0032 Epoch 302/500 1/1 [==============================] - 0s 4ms/step - loss: 0.0032 Epoch 303/500 1/1 [==============================] - 0s 4ms/step - loss: 0.0031 Epoch 304/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0030 Epoch 305/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0030 Epoch 306/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0029 Epoch 307/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0028 Epoch 308/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0028 Epoch 309/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0027 Epoch 310/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0027 Epoch 311/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0026 Epoch 312/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0026 Epoch 313/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0025 Epoch 314/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0025 Epoch 315/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0024 Epoch 316/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0024 Epoch 317/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0023 Epoch 318/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0023 Epoch 319/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0022 Epoch 320/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0022 Epoch 321/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0021 Epoch 322/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0021 Epoch 323/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0020 Epoch 324/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0020 Epoch 325/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0020 Epoch 326/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0019 Epoch 327/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0019 Epoch 328/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0018 Epoch 329/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0018 Epoch 330/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0018 Epoch 331/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0017 Epoch 332/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0017 Epoch 333/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0017 Epoch 334/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0016 Epoch 335/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0016 Epoch 336/500 1/1 [==============================] - 0s 4ms/step - loss: 0.0016 Epoch 337/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0015 Epoch 338/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0015 Epoch 339/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0015 Epoch 340/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0014 Epoch 341/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0014 Epoch 342/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0014 Epoch 343/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0013 Epoch 344/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0013 Epoch 345/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0013 Epoch 346/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0013 Epoch 347/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0012 Epoch 348/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0012 Epoch 349/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0012 Epoch 350/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0012 Epoch 351/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0011 Epoch 352/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0011 Epoch 353/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0011 Epoch 354/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0011 Epoch 355/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0010 Epoch 356/500 1/1 [==============================] - 0s 3ms/step - loss: 0.0010 Epoch 357/500 1/1 [==============================] - 0s 2ms/step - loss: 0.0010 Epoch 358/500 1/1 [==============================] - 0s 3ms/step - loss: 9.8661e-04 Epoch 359/500 1/1 [==============================] - 0s 3ms/step - loss: 9.6634e-04 Epoch 360/500 1/1 [==============================] - 0s 2ms/step - loss: 9.4649e-04 Epoch 361/500 1/1 [==============================] - 0s 2ms/step - loss: 9.2705e-04 Epoch 362/500 1/1 [==============================] - 0s 2ms/step - loss: 9.0800e-04 Epoch 363/500 1/1 [==============================] - 0s 3ms/step - loss: 8.8935e-04 Epoch 364/500 1/1 [==============================] - 0s 2ms/step - loss: 8.7109e-04 Epoch 365/500 1/1 [==============================] - 0s 2ms/step - loss: 8.5319e-04 Epoch 366/500 1/1 [==============================] - 0s 3ms/step - loss: 8.3567e-04 Epoch 367/500 1/1 [==============================] - 0s 3ms/step - loss: 8.1851e-04 Epoch 368/500 1/1 [==============================] - 0s 3ms/step - loss: 8.0169e-04 Epoch 369/500 1/1 [==============================] - 0s 2ms/step - loss: 7.8522e-04 Epoch 370/500 1/1 [==============================] - 0s 2ms/step - loss: 7.6909e-04 Epoch 371/500 1/1 [==============================] - 0s 2ms/step - loss: 7.5330e-04 Epoch 372/500 1/1 [==============================] - 0s 2ms/step - loss: 7.3783e-04 Epoch 373/500 1/1 [==============================] - 0s 2ms/step - loss: 7.2267e-04 Epoch 374/500 1/1 [==============================] - 0s 2ms/step - loss: 7.0783e-04 Epoch 375/500 1/1 [==============================] - 0s 3ms/step - loss: 6.9329e-04 Epoch 376/500 1/1 [==============================] - 0s 4ms/step - loss: 6.7905e-04 Epoch 377/500 1/1 [==============================] - 0s 2ms/step - loss: 6.6510e-04 Epoch 378/500 1/1 [==============================] - 0s 2ms/step - loss: 6.5144e-04 Epoch 379/500 1/1 [==============================] - 0s 2ms/step - loss: 6.3806e-04 Epoch 380/500 1/1 [==============================] - 0s 3ms/step - loss: 6.2495e-04 Epoch 381/500 1/1 [==============================] - 0s 3ms/step - loss: 6.1212e-04 Epoch 382/500 1/1 [==============================] - 0s 2ms/step - loss: 5.9954e-04 Epoch 383/500 1/1 [==============================] - 0s 3ms/step - loss: 5.8723e-04 Epoch 384/500 1/1 [==============================] - 0s 2ms/step - loss: 5.7516e-04 Epoch 385/500 1/1 [==============================] - 0s 3ms/step - loss: 5.6335e-04 Epoch 386/500 1/1 [==============================] - 0s 2ms/step - loss: 5.5178e-04 Epoch 387/500 1/1 [==============================] - 0s 2ms/step - loss: 5.4044e-04 Epoch 388/500 1/1 [==============================] - 0s 2ms/step - loss: 5.2934e-04 Epoch 389/500 1/1 [==============================] - 0s 2ms/step - loss: 5.1847e-04 Epoch 390/500 1/1 [==============================] - 0s 3ms/step - loss: 5.0782e-04 Epoch 391/500 1/1 [==============================] - 0s 2ms/step - loss: 4.9739e-04 Epoch 392/500 1/1 [==============================] - 0s 2ms/step - loss: 4.8717e-04 Epoch 393/500 1/1 [==============================] - 0s 2ms/step - loss: 4.7717e-04 Epoch 394/500 1/1 [==============================] - 0s 3ms/step - loss: 4.6737e-04 Epoch 395/500 1/1 [==============================] - 0s 3ms/step - loss: 4.5777e-04 Epoch 396/500 1/1 [==============================] - 0s 3ms/step - loss: 4.4836e-04 Epoch 397/500 1/1 [==============================] - 0s 2ms/step - loss: 4.3915e-04 Epoch 398/500 1/1 [==============================] - 0s 2ms/step - loss: 4.3013e-04 Epoch 399/500 1/1 [==============================] - 0s 2ms/step - loss: 4.2130e-04 Epoch 400/500 1/1 [==============================] - 0s 2ms/step - loss: 4.1264e-04 Epoch 401/500 1/1 [==============================] - 0s 2ms/step - loss: 4.0417e-04 Epoch 402/500 1/1 [==============================] - 0s 2ms/step - loss: 3.9587e-04 Epoch 403/500 1/1 [==============================] - 0s 3ms/step - loss: 3.8773e-04 Epoch 404/500 1/1 [==============================] - 0s 2ms/step - loss: 3.7977e-04 Epoch 405/500 1/1 [==============================] - 0s 2ms/step - loss: 3.7197e-04 Epoch 406/500 1/1 [==============================] - 0s 3ms/step - loss: 3.6433e-04 Epoch 407/500 1/1 [==============================] - 0s 2ms/step - loss: 3.5684e-04 Epoch 408/500 1/1 [==============================] - 0s 2ms/step - loss: 3.4952e-04 Epoch 409/500 1/1 [==============================] - 0s 2ms/step - loss: 3.4234e-04 Epoch 410/500 1/1 [==============================] - 0s 2ms/step - loss: 3.3530e-04 Epoch 411/500 1/1 [==============================] - 0s 2ms/step - loss: 3.2842e-04 Epoch 412/500 1/1 [==============================] - 0s 3ms/step - loss: 3.2167e-04 Epoch 413/500 1/1 [==============================] - 0s 2ms/step - loss: 3.1506e-04 Epoch 414/500 1/1 [==============================] - 0s 2ms/step - loss: 3.0859e-04 Epoch 415/500 1/1 [==============================] - 0s 2ms/step - loss: 3.0225e-04 Epoch 416/500 1/1 [==============================] - 0s 2ms/step - loss: 2.9604e-04 Epoch 417/500 1/1 [==============================] - 0s 4ms/step - loss: 2.8996e-04 Epoch 418/500 1/1 [==============================] - 0s 2ms/step - loss: 2.8400e-04 Epoch 419/500 1/1 [==============================] - 0s 2ms/step - loss: 2.7817e-04 Epoch 420/500 1/1 [==============================] - 0s 2ms/step - loss: 2.7246e-04 Epoch 421/500 1/1 [==============================] - 0s 3ms/step - loss: 2.6686e-04 Epoch 422/500 1/1 [==============================] - 0s 3ms/step - loss: 2.6138e-04 Epoch 423/500 1/1 [==============================] - 0s 2ms/step - loss: 2.5601e-04 Epoch 424/500 1/1 [==============================] - 0s 2ms/step - loss: 2.5075e-04 Epoch 425/500 1/1 [==============================] - 0s 3ms/step - loss: 2.4560e-04 Epoch 426/500 1/1 [==============================] - 0s 2ms/step - loss: 2.4056e-04 Epoch 427/500 1/1 [==============================] - 0s 3ms/step - loss: 2.3561e-04 Epoch 428/500 1/1 [==============================] - 0s 2ms/step - loss: 2.3078e-04 Epoch 429/500 1/1 [==============================] - 0s 2ms/step - loss: 2.2604e-04 Epoch 430/500 1/1 [==============================] - 0s 4ms/step - loss: 2.2139e-04 Epoch 431/500 1/1 [==============================] - 0s 2ms/step - loss: 2.1684e-04 Epoch 432/500 1/1 [==============================] - 0s 2ms/step - loss: 2.1239e-04 Epoch 433/500 1/1 [==============================] - 0s 3ms/step - loss: 2.0803e-04 Epoch 434/500 1/1 [==============================] - 0s 2ms/step - loss: 2.0375e-04 Epoch 435/500 1/1 [==============================] - 0s 3ms/step - loss: 1.9957e-04 Epoch 436/500 1/1 [==============================] - 0s 2ms/step - loss: 1.9547e-04 Epoch 437/500 1/1 [==============================] - 0s 3ms/step - loss: 1.9145e-04 Epoch 438/500 1/1 [==============================] - 0s 2ms/step - loss: 1.8752e-04 Epoch 439/500 1/1 [==============================] - 0s 4ms/step - loss: 1.8367e-04 Epoch 440/500 1/1 [==============================] - 0s 2ms/step - loss: 1.7990e-04 Epoch 441/500 1/1 [==============================] - 0s 3ms/step - loss: 1.7620e-04 Epoch 442/500 1/1 [==============================] - 0s 2ms/step - loss: 1.7258e-04 Epoch 443/500 1/1 [==============================] - 0s 3ms/step - loss: 1.6904e-04 Epoch 444/500 1/1 [==============================] - 0s 3ms/step - loss: 1.6557e-04 Epoch 445/500 1/1 [==============================] - 0s 2ms/step - loss: 1.6217e-04 Epoch 446/500 1/1 [==============================] - 0s 3ms/step - loss: 1.5884e-04 Epoch 447/500 1/1 [==============================] - 0s 2ms/step - loss: 1.5557e-04 Epoch 448/500 1/1 [==============================] - 0s 3ms/step - loss: 1.5238e-04 Epoch 449/500 1/1 [==============================] - 0s 3ms/step - loss: 1.4925e-04 Epoch 450/500 1/1 [==============================] - 0s 3ms/step - loss: 1.4618e-04 Epoch 451/500 1/1 [==============================] - 0s 2ms/step - loss: 1.4318e-04 Epoch 452/500 1/1 [==============================] - 0s 3ms/step - loss: 1.4024e-04 Epoch 453/500 1/1 [==============================] - 0s 3ms/step - loss: 1.3736e-04 Epoch 454/500 1/1 [==============================] - 0s 2ms/step - loss: 1.3454e-04 Epoch 455/500 1/1 [==============================] - 0s 2ms/step - loss: 1.3177e-04 Epoch 456/500 1/1 [==============================] - 0s 3ms/step - loss: 1.2906e-04 Epoch 457/500 1/1 [==============================] - 0s 2ms/step - loss: 1.2641e-04 Epoch 458/500 1/1 [==============================] - 0s 2ms/step - loss: 1.2382e-04 Epoch 459/500 1/1 [==============================] - 0s 2ms/step - loss: 1.2127e-04 Epoch 460/500 1/1 [==============================] - 0s 2ms/step - loss: 1.1878e-04 Epoch 461/500 1/1 [==============================] - 0s 3ms/step - loss: 1.1634e-04 Epoch 462/500 1/1 [==============================] - 0s 2ms/step - loss: 1.1395e-04 Epoch 463/500 1/1 [==============================] - 0s 3ms/step - loss: 1.1161e-04 Epoch 464/500 1/1 [==============================] - 0s 3ms/step - loss: 1.0932e-04 Epoch 465/500 1/1 [==============================] - 0s 4ms/step - loss: 1.0707e-04 Epoch 466/500 1/1 [==============================] - 0s 2ms/step - loss: 1.0488e-04 Epoch 467/500 1/1 [==============================] - 0s 3ms/step - loss: 1.0272e-04 Epoch 468/500 1/1 [==============================] - 0s 2ms/step - loss: 1.0061e-04 Epoch 469/500 1/1 [==============================] - 0s 2ms/step - loss: 9.8544e-05 Epoch 470/500 1/1 [==============================] - 0s 4ms/step - loss: 9.6520e-05 Epoch 471/500 1/1 [==============================] - 0s 1ms/step - loss: 9.4538e-05 Epoch 472/500 1/1 [==============================] - 0s 3ms/step - loss: 9.2596e-05 Epoch 473/500 1/1 [==============================] - 0s 3ms/step - loss: 9.0694e-05 Epoch 474/500 1/1 [==============================] - 0s 2ms/step - loss: 8.8831e-05 Epoch 475/500 1/1 [==============================] - 0s 3ms/step - loss: 8.7006e-05 Epoch 476/500 1/1 [==============================] - 0s 2ms/step - loss: 8.5219e-05 Epoch 477/500 1/1 [==============================] - 0s 2ms/step - loss: 8.3469e-05 Epoch 478/500 1/1 [==============================] - 0s 2ms/step - loss: 8.1755e-05 Epoch 479/500 1/1 [==============================] - 0s 3ms/step - loss: 8.0076e-05 Epoch 480/500 1/1 [==============================] - 0s 2ms/step - loss: 7.8430e-05 Epoch 481/500 1/1 [==============================] - 0s 3ms/step - loss: 7.6819e-05 Epoch 482/500 1/1 [==============================] - 0s 2ms/step - loss: 7.5242e-05 Epoch 483/500 1/1 [==============================] - 0s 2ms/step - loss: 7.3697e-05 Epoch 484/500 1/1 [==============================] - 0s 5ms/step - loss: 7.2183e-05 Epoch 485/500 1/1 [==============================] - 0s 4ms/step - loss: 7.0700e-05 Epoch 486/500 1/1 [==============================] - 0s 3ms/step - loss: 6.9248e-05 Epoch 487/500 1/1 [==============================] - 0s 3ms/step - loss: 6.7826e-05 Epoch 488/500 1/1 [==============================] - 0s 2ms/step - loss: 6.6432e-05 Epoch 489/500 1/1 [==============================] - 0s 3ms/step - loss: 6.5067e-05 Epoch 490/500 1/1 [==============================] - 0s 3ms/step - loss: 6.3732e-05 Epoch 491/500 1/1 [==============================] - 0s 2ms/step - loss: 6.2422e-05 Epoch 492/500 1/1 [==============================] - 0s 3ms/step - loss: 6.1140e-05 Epoch 493/500 1/1 [==============================] - 0s 2ms/step - loss: 5.9884e-05 Epoch 494/500 1/1 [==============================] - 0s 2ms/step - loss: 5.8654e-05 Epoch 495/500 1/1 [==============================] - 0s 3ms/step - loss: 5.7449e-05 Epoch 496/500 1/1 [==============================] - 0s 2ms/step - loss: 5.6269e-05 Epoch 497/500 1/1 [==============================] - 0s 2ms/step - loss: 5.5113e-05 Epoch 498/500 1/1 [==============================] - 0s 3ms/step - loss: 5.3981e-05 Epoch 499/500 1/1 [==============================] - 0s 3ms/step - loss: 5.2872e-05 Epoch 500/500 1/1 [==============================] - 0s 3ms/step - loss: 5.1787e-05 [[18.979004]]
Example 2: Using keras for MNIST classification task¶
In [15]:
# Load Dataset
from keras.datasets import mnist
(train_images, train_labels), (test_images, test_labels) = mnist.load_data()
In [16]:
train_images.shape
Out[16]:
(60000, 28, 28)
Network Architecture¶
In [17]:
model = Sequential()
# First layer
model.add(Conv2D(32, (3,3), activation='relu', input_shape=(28,28,1)))
model.add(MaxPooling2D((2,2)))
# Second layer
model.add(Conv2D(64, (3,3), activation='relu'))
model.add(MaxPooling2D((2,2)))
# Third layer
model.add(Conv2D(64, (3,3), activation='relu'))
model.add(Flatten())
# Fourth layer
model.add(Dense(64, activation='relu'))
# Fifth layer : output
model.add(Dense(10, activation='softmax'))
Model Summary¶
In [18]:
model.summary()
Model: "sequential_2"
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
conv2d (Conv2D) (None, 26, 26, 32) 320
max_pooling2d (MaxPooling2D (None, 13, 13, 32) 0
)
conv2d_1 (Conv2D) (None, 11, 11, 64) 18496
max_pooling2d_1 (MaxPooling (None, 5, 5, 64) 0
2D)
conv2d_2 (Conv2D) (None, 3, 3, 64) 36928
flatten_1 (Flatten) (None, 576) 0
dense_3 (Dense) (None, 64) 36928
dense_4 (Dense) (None, 10) 650
=================================================================
Total params: 93,322
Trainable params: 93,322
Non-trainable params: 0
_________________________________________________________________
Train the Convnet¶
In [19]:
# reshape training data
train_images = train_images.reshape((60000, 28, 28, 1))
train_images = train_images.astype('float32')/255
# reshape test data
test_images = test_images.reshape((10000, 28, 28, 1))
test_images = test_images.astype('float32')/255
# convert class vector (int) to binary class matrix
train_labels = to_categorical(train_labels)
test_labels = to_categorical(test_labels)
# compile the model
model.compile(optimizer='rmsprop',
loss='categorical_crossentropy',
metrics=['accuracy'])
# fit or train the model
model.fit(train_images, train_labels, epochs=5, batch_size=64)
Epoch 1/5 938/938 [==============================] - 26s 27ms/step - loss: 0.1701 - accuracy: 0.9477 Epoch 2/5 938/938 [==============================] - 25s 27ms/step - loss: 0.0460 - accuracy: 0.9858 Epoch 3/5 938/938 [==============================] - 22s 24ms/step - loss: 0.0320 - accuracy: 0.9902 Epoch 4/5 938/938 [==============================] - 21s 22ms/step - loss: 0.0248 - accuracy: 0.9921 Epoch 5/5 938/938 [==============================] - 21s 23ms/step - loss: 0.0191 - accuracy: 0.9939
Out[19]:
<keras.callbacks.History at 0x197db9dd520>
Evaluate the Model¶
In [20]:
# measure loss and accuracy
test_loss, test_acc = model.evaluate(test_images, test_labels)
test_acc
313/313 [==============================] - 1s 4ms/step - loss: 0.0361 - accuracy: 0.9902
Out[20]:
0.9901999831199646
Save Model¶
In [21]:
# save model for future use
model.save('mnist_model.h5')
Making Predictions¶
In [22]:
from keras.models import load_model
from keras.preprocessing.image import load_img, img_to_array
model = load_model('mnist_model.h5')
Testing the model with the following sample image:
In [23]:
# load the image
img = load_img('sample_image.png', grayscale=True, target_size=(28,28))
# conver to array
img = img_to_array(img)
# reshape into required format
img = img.reshape(1,28,28,1)
# prepare pixel dat
img = img.astype('float32')/255
# predict the class
digit = np.argmax(model.predict(img),axis=1)
# output predicted class
print(digit[0])
8