[ML] Neural Net for XOR

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Neural Net

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XOR with logistic regression

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소스 코드

import tensorflow as tf
import numpy as np
 
tf.set_random_seed(777)  # for reproducibility
learning_rate = 0.1
 
x_data = [[0, 0],
          [0, 1],
          [1, 0],
          [1, 1]]
y_data = [[0],
          [1],
          [1],
          [0]]
x_data = np.array(x_data, dtype=np.float32)
y_data = np.array(y_data, dtype=np.float32)
 
X = tf.placeholder(tf.float32, [None, 2])
Y = tf.placeholder(tf.float32, [None, 1])
 
W = tf.Variable(tf.random_normal([2, 1]), name='weight')
b = tf.Variable(tf.random_normal([1]), name='bias')
 
# Hypothesis using sigmoid: tf.div(1., 1. + tf.exp(tf.matmul(X, W)))
hypothesis = tf.sigmoid(tf.matmul(X, W) + b)
 
# cost/loss function
cost = -tf.reduce_mean(Y * tf.log(hypothesis) + (1 - Y) *
                       tf.log(1 - hypothesis))
 
train = tf.train.GradientDescentOptimizer(learning_rate=learning_rate).minimize(cost)
 
# Accuracy computation
# True if hypothesis>0.5 else False
predicted = tf.cast(hypothesis > 0.5, dtype=tf.float32)
accuracy = tf.reduce_mean(tf.cast(tf.equal(predicted, Y), dtype=tf.float32))
 
# Launch graph
with tf.Session() as sess:
    # Initialize TensorFlow variables
    sess.run(tf.global_variables_initializer())
 
    for step in range(10001):
        sess.run(train, feed_dict={X: x_data, Y: y_data})
        if step % 100 == 0:
            print(step, sess.run(cost, feed_dict={
                  X: x_data, Y: y_data}), sess.run(W))
 
    # Accuracy report
    h, c, a = sess.run([hypothesis, predicted, accuracy],
                       feed_dict={X: x_data, Y: y_data})
    print("\nHypothesis: ", h, "\nCorrect: ", c, "\nAccuracy: ", a)

실행 결과

소스 코드를 보면 X, Y 데이터를 제대로 줬음에도 불구하고 Accuracy가 좋지 않다.

10000번이나 돌렸음에도 불구하고 상당히 낮은 것을 볼 수 있다.

어떻게 해야 이 문제를 해결할까?

이때 Neural Net을 사용하여 코딩하면 된다.

아래와 같이 계산을 하게 되면 XOR 연산을 풀 수 있다.

소스 코드

import tensorflow as tf
import numpy as np
 
tf.set_random_seed(777)  # for reproducibility
learning_rate = 0.1
 
x_data = [[0, 0],
          [0, 1],
          [1, 0],
          [1, 1]]
y_data = [[0],
          [1],
          [1],
          [0]]
x_data = np.array(x_data, dtype=np.float32)
y_data = np.array(y_data, dtype=np.float32)
 
X = tf.placeholder(tf.float32, [None, 2])
Y = tf.placeholder(tf.float32, [None, 1])
 
W1 = tf.Variable(tf.random_normal([2, 2]), name='weight1')
b1 = tf.Variable(tf.random_normal([2]), name='bias1')
layer1 = tf.sigmoid(tf.matmul(X, W1) + b1)
 
W2 = tf.Variable(tf.random_normal([2, 1]), name='weight2')
b2 = tf.Variable(tf.random_normal([1]), name='bias2')
hypothesis = tf.sigmoid(tf.matmul(layer1, W2) + b2)
 
# cost/loss function
cost = -tf.reduce_mean(Y * tf.log(hypothesis) + (1 - Y) *
                       tf.log(1 - hypothesis))
 
train = tf.train.GradientDescentOptimizer(learning_rate=learning_rate).minimize(cost)
 
# Accuracy computation
# True if hypothesis>0.5 else False
predicted = tf.cast(hypothesis > 0.5, dtype=tf.float32)
accuracy = tf.reduce_mean(tf.cast(tf.equal(predicted, Y), dtype=tf.float32))
 
# Launch graph
with tf.Session() as sess:
    # Initialize TensorFlow variables
    sess.run(tf.global_variables_initializer())
 
    for step in range(10001):
        sess.run(train, feed_dict={X: x_data, Y: y_data})
        if step % 100 == 0:
            print(step, sess.run(cost, feed_dict={
                  X: x_data, Y: y_data}), sess.run([W1, W2]))
 
    # Accuracy report
    h, c, a = sess.run([hypothesis, predicted, accuracy],
                       feed_dict={X: x_data, Y: y_data})
    print("\nHypothesis: ", h, "\nCorrect: ", c, "\nAccuracy: ", a)

실행 결과

Accruacy가 완벽해진것을 볼 수 있다.