Building a non linear model with ReLUs in TensorFlow - machine-learning

Question

I'm trying to build a simple non-linear model in TensorFlow. I have created this sample data:
x_data = np.arange(-100, 100).astype(np.float32)
y_data = np.abs(x_data + 20.)
I guess this shape should be easily reconstructed using a couple of ReLUs, but I can't figure out how.
So far, my approach is to wrap linear components with ReLUs, but this doesn't run:
W1 = tf.Variable(tf.random_uniform([1], -1.0, 1.0))
W2 = tf.Variable(tf.random_uniform([1], -1.0, 1.0))
b1 = tf.Variable(tf.zeros([1]))
b2 = tf.Variable(tf.zeros([1]))
y = tf.nn.relu(W1 * x_data + b1) + tf.nn.relu(W2 * x_data + b2)
Any ideas about how to express this model using ReLUs in TensorFlow?

Answer 1

I think you're asking how to combine ReLUs in a working model? Two options are shown below:
Option 1) Input of ReLU1 into ReLU2
This is probably the preferred method. Note that r1 is the input to r2.
x = tf.placeholder('float', shape=[None, 1])
y_ = tf.placeholder('float', shape=[None, 1])
W1 = weight_variable([1, hidden_units])
b1 = bias_variable([hidden_units])
r1 = tf.nn.relu(tf.matmul(x, W1) + b1)
# Input of r1 into r2 (which is just y)
W2 = weight_variable([hidden_units, 1])
b2 = bias_variable([1])
y = tf.nn.relu(tf.matmul(r1,W2)+b2) # ReLU2
Option 2) Add ReLU1 and ReLU2
Option 2 was listed in the original question, but I don't know if this is what you really want...read below for a full working example and try it. I think you'll find it doesn't model well.
x = tf.placeholder('float', shape=[None, 1])
y_ = tf.placeholder('float', shape=[None, 1])
W1 = weight_variable([1, hidden_units])
b1 = bias_variable([hidden_units])
r1 = tf.nn.relu(tf.matmul(x, W1) + b1)
# Add r1 to r2 -- won't be able to reduce the error.
W2 = weight_variable([1, hidden_units])
b2 = bias_variable([hidden_units])
r2 = tf.nn.relu(tf.matmul(x, W2) + b2)
y = tf.add(r1,r2) # Again, ReLU2 is just y
Full Working Example
Below is a full working example. By default it uses option 1, however, option 2 is also included in the comments.
from __future__ import print_function
import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
# Config the matlotlib backend as plotting inline in IPython
%matplotlib inline
episodes = 55
batch_size = 5
hidden_units = 10
learning_rate = 1e-3
def weight_variable(shape):
initial = tf.truncated_normal(shape, stddev=0.1)
return tf.Variable(initial)
def bias_variable(shape):
initial = tf.constant(0.1, shape=shape)
return tf.Variable(initial)
# Produce the data
x_data = np.arange(-100, 100).astype(np.float32)
y_data = np.abs(x_data + 20.)
# Plot it.
plt.plot(y_data)
plt.ylabel('y_data')
plt.show()
# Might want to randomize the data
# np.random.shuffle(x_data)
# y_data = np.abs(x_data + 20.)
# reshape data ...
x_data = x_data.reshape(200, 1)
y_data = y_data.reshape(200, 1)
# create placeholders to pass the data to the model
x = tf.placeholder('float', shape=[None, 1])
y_ = tf.placeholder('float', shape=[None, 1])
W1 = weight_variable([1, hidden_units])
b1 = bias_variable([hidden_units])
r1 = tf.nn.relu(tf.matmul(x, W1) + b1)
# Input of r1 into r2 (which is just y)
W2 = weight_variable([hidden_units, 1])
b2 = bias_variable([1])
y = tf.nn.relu(tf.matmul(r1,W2)+b2)
# OPTION 2
# Add r1 to r2 -- won't be able to reduce the error.
#W2 = weight_variable([1, hidden_units])
#b2 = bias_variable([hidden_units])
#r2 = tf.nn.relu(tf.matmul(x, W2) + b2)
#y = tf.add(r1,r2)
mean_square_error = tf.reduce_sum(tf.square(y-y_))
training = tf.train.AdamOptimizer(learning_rate).minimize(mean_square_error)
sess = tf.InteractiveSession()
sess.run(tf.initialize_all_variables())
min_error = np.inf
for _ in range(episodes):
# iterrate trough every row (with batch size of 1)
for i in range(x_data.shape[0]-batch_size+1):
_, error = sess.run([training, mean_square_error], feed_dict={x: x_data[i:i+batch_size], y_:y_data[i:i+batch_size]})
if error < min_error :
min_error = error
if min_error < 3:
print(error)
#print(error)
#print(error, x_data[i:i+batch_size], y_data[i:i+batch_size])
# error = sess.run([training, mean_square_error], feed_dict={x: x_data[i:i+batch_size], y_:y_data[i:i+batch_size]})
# if error != None:
# print(error)
sess.close()
print("\n\nmin_error:",min_error)
It might be easier to see in a jupiter notebook here

Answer 2

Here is a simple feedforward network with one hidden layer.
import numpy as np
import tensorflow as tf
episodes = 55
batch_size = 5
hidden_units = 10
learning_rate = 1e-3
def weight_variable(shape):
initial = tf.truncated_normal(shape, stddev=0.1)
return tf.Variable(initial)
def bias_variable(shape):
initial = tf.constant(0.1, shape=shape)
return tf.Variable(initial)
# normalize the data and shuffle them
x_data = np.arange(0, 1, 0.005).astype(float)
np.random.shuffle(x_data)
y_data = np.abs(x_data + .1)
# reshape data ...
x_data = x_data.reshape(200, 1)
y_data = y_data.reshape(200, 1)
# create placeholders to pass the data to the model
x = tf.placeholder('float', shape=[None, 1])
y_ = tf.placeholder('float', shape=[None, 1])
W1 = weight_variable([1, hidden_units])
b1 = bias_variable([hidden_units])
h1 = tf.nn.relu(tf.matmul(x, W1) + b1)
W2 = weight_variable([hidden_units, 1])
b2 = bias_variable([1])
y = tf.matmul(h1, W2) + b2
mean_square_error = tf.reduce_sum(tf.square(y-y_))
training = tf.train.AdamOptimizer(learning_rate).minimize(mean_square_error)
sess = tf.InteractiveSession()
sess.run(tf.initialize_all_variables())
for _ in xrange(episodes):
# iterrate trough every row (with batch size of 1)
for i in xrange(x_data.shape[0]-batch_size+1):
_, error = sess.run([training, mean_square_error], feed_dict={x: x_data[i:i+batch_size], y_:y_data[i:i+batch_size]})
#print error
print error, x_data[i:i+batch_size], y_data[i:i+batch_size]
error = sess.run([training, mean_square_error], feed_dict={x: x_data[i:i+batch_size], y_:y_data[i:i+batch_size]})
print error

Answer 3

Inspired by all responses I managed to train this model by using the proposed model in the accepted answer. Here is the code:
import tensorflow as tf
import numpy as np
# Create 200 x, y data points in NumPy to represent the function
x_data = np.arange(-100, 100).astype(np.float32)
y_data = np.abs(x_data + 20.)
W1 = tf.Variable(tf.random_uniform([1], -1.0, 1.0))
b1 = tf.Variable(tf.zeros([1]))
W2 = tf.Variable(tf.random_uniform([1], -1.0, 1.0))
b2 = tf.Variable(tf.zeros([1]))
y = tf.nn.relu(W1 * x_data + b1) + tf.nn.relu(W2 * x_data + b2)
# Minimize the mean squared errors.
mean_square_error = tf.reduce_sum(tf.square(y-y_data))
train = tf.train.AdamOptimizer(learning_rate).minimize(mean_square_error)
sess = tf.Session()
init = tf.initialize_all_variables()
sess.run(init)
# Fit the non-linear function.
for step in xrange(50000):
sess.run(train)
if step % 10000 == 0:
#Expected values: W1 = 1., W2 = -1., b1 = 20., b2 = -20.
print(step, sess.run(W1), sess.run(b1), sess.run(W2), sess.run(b2))