1. 代码实现
from __future__ import print_function
import theano
import theano.tensor as T
import numpy as np
import matplotlib.pyplot as plt
class Layer(object):
def __init__(self, inputs, in_size, out_size, activation_function=None):
self.W = theano.shared(np.random.normal(0, 1, (in_size, out_size)))
self.b = theano.shared(np.zeros((out_size, )) + 0.1)
self.Wx_plus_b = T.dot(inputs, self.W) + self.b
self.activation_function = activation_function
if activation_function is None:
self.outputs = self.Wx_plus_b
else:
self.outputs = self.activation_function(self.Wx_plus_b)
# Make up some fake data
x_data = np.linspace(-1, 1, 300)[:, np.newaxis]
noise = np.random.normal(0, 0.05, x_data.shape)
y_data = np.square(x_data) - 0.5 + noise # y = x^2 - 0.5
# show the fake data
plt.scatter(x_data, y_data)
plt.show()
# determine the inputs dtype
x = T.dmatrix("x")
y = T.dmatrix("y")
# add layers
l1 = Layer(x, 1, 10, T.nnet.relu)
l2 = Layer(l1.outputs, 10, 1, None)
# compute the cost
cost = T.mean(T.square(l2.outputs - y))
# compute the gradients
gW1, gb1, gW2, gb2 = T.grad(cost, [l1.W, l1.b, l2.W, l2.b])
# apply gradient descent
learning_rate = 0.05
train = theano.function(
inputs=[x, y],
outputs=cost,
updates=[(l1.W, l1.W - learning_rate * gW1),
(l1.b, l1.b - learning_rate * gb1),
(l2.W, l2.W - learning_rate * gW2),
(l2.b, l2.b - learning_rate * gb2)])
# prediction
predict = theano.function(inputs=[x], outputs=l2.outputs)
for i in range(1000):
# training
err = train(x_data, y_data)
if i % 50 == 0:
print(err)
结果：
1.77825942078 0.0307547174779 0.0145354962126 0.0111276391112 0.0098326475625 0.00913968526182 0.00870222509 0.00832267806176 0.00788557725943 0.00737921234676 0.00684759006112 0.0063416352651 0.00589114798344 0.005512661812 0.00522628405891 0.00498177806607 0.00477628310217 0.00460285349102 0.00445516762566 0.00432311158005