DNN_1

1.深い学習の基本概念

2. XOR

3.学習深度ネットワーク連携

Back propagation(chain rule)
f=wx+b,g=wx,f=g+bの場合
wがfに及ぼす影響を理解するために,xがfに及ぼす影響,bがfに対するゼロ荷重を微分した.


の後から、一歩一歩微分していきます.
誤差を損失と呼び,逆伝搬損失微分によりネットワークを学習した.
chain rule
fはg+bなので、gを微分*w、gを微分

4. Neural Net(NN) for XOR

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
import tensorflow as tf
tf.random.set_seed(777)  # for reproducibility


x_data = [[0, 0],
          [0, 1],
          [1, 0],
          [1, 1]]
y_data = [[0],
          [1],
          [1],
          [0]]

plt.scatter(x_data[0][0],x_data[0][1], c='red' , marker='^')
plt.scatter(x_data[3][0],x_data[3][1], c='red' , marker='^')
plt.scatter(x_data[1][0],x_data[1][1], c='blue' , marker='^')
plt.scatter(x_data[2][0],x_data[2][1], c='blue' , marker='^')

dataset = tf.data.Dataset.from_tensor_slices((x_data, y_data)).batch(len(x_data))
def preprocess_data(features, labels):
  features = tf.cast(features, tf.float32)
  labels = tf.cast(labels, tf.float32)
  return features, labels

#NN를 통해 XOR 해결
W1 = tf.Variable(tf.random.normal((2,1)), name='weight1')
b1 = tf.Variable(tf.random.normal((1,)), name = 'bias1')
W2 = tf.Variable(tf.random.normal((2, 1)), name='weight2')
b2 = tf.Variable(tf.random.normal((1,)), name='bias2')
W3 = tf.Variable(tf.random.normal((2, 1)), name='weight3')
b3 = tf.Variable(tf.random.normal((1,)), name='bias3')

def neural_net(features):
  layer1 = tf.sigmoid(tf.matmul(features, W1) + b1)
  layer2 = tf.sigmoid(tf.matmul(features, W2) + b2)
  layer3 = tf.concat([layer1, layer2],-1)
  layer3 = tf.reshape(layer3, shape = [-1,2])
  hypothesis = tf.sigmoid(tf.matmul(layer3, W3) + b3)
  return hypothesis

def loss_fn(hypothesis, labels):
  cost = -tf.reduce_mean(labels * tf.math.log(hypothesis) + (1 - labels) * tf.math.log(1 - hypothesis))
  return cost

optimizer = tf.keras.optimizers.SGD(learning_rate=0.01)

def accuracy_fn(hypothesis, labels):
    predicted = tf.cast(hypothesis > 0.5, dtype=tf.float32)
    accuracy = tf.reduce_mean(tf.cast(tf.equal(predicted, labels), dtype=tf.float32))
    return accuracy

def grad(hypothesis, features, labels):
    with tf.GradientTape() as tape:
        loss_value = loss_fn(neural_net(features),labels)
    return tape.gradient(loss_value, [W1, W2, W3, b1, b2, b3])

EPOCHS = 50000

for step in range(EPOCHS):
    for features, labels  in dataset:
        features, labels = preprocess_data(features, labels)
        grads = grad(neural_net(features), features, labels)
        optimizer.apply_gradients(grads_and_vars=zip(grads,[W1, W2, W3, b1, b2, b3]))
        if step % 5000 == 0:
            print("Iter: {}, Loss: {:.4f}".format(step, loss_fn(neural_net(features),labels)))
x_data, y_data = preprocess_data(x_data, y_data)
test_acc = accuracy_fn(neural_net(x_data),y_data)
print("Testset Accuracy: {:.4f}".format(test_acc))

5. ReLU