我实现了具有梯度下降的神经网络的偏置单元。但我并非100％确定如果我以正确的方式实施它。如果你能快速查看我的代码，那将是林间空地。只有
的部分如果偏见：
非常重要。
我的第二个问题： 不应该将softmax函数的导数设为1-x，因为x是softmax函数的输出？ 我用1-x尝试了我的网，但性能更差。
感谢每一位帮助。 提前谢谢。
import numpy as np
import pickle
import time
import math
class FeedForwardNetwork():
def __init__(self, input_dim, hidden_dim, output_dim, dropout=False, dropout_prop=0.5, bias=False):
np.random.seed(1)
self.input_layer = np.array([])
self.hidden_layer = np.array([])
self.output_layer = np.array([])
self.hidden_dim = hidden_dim
self.dropout = dropout
self.dropout_prop = dropout_prop
self.bias = bias
r_input_hidden = math.sqrt(6 / (input_dim + hidden_dim))
r_hidden_output = math.sqrt(6 / (hidden_dim + output_dim))
#self.weights_input_hidden = np.random.uniform(low=-r_input_hidden, high=r_input_hidden, size=(input_dim, hidden_dim))
#self.weights_hidden_output = np.random.uniform(low=-r_hidden_output, high=r_hidden_output, size=(hidden_dim, output_dim))
self.weights_input_hidden = np.random.uniform(low=-0.01, high=0.01, size=(input_dim, hidden_dim))
self.weights_hidden_output = np.random.uniform(low=-0.01, high=0.01, size=(hidden_dim, output_dim))
self.validation_data = np.array([])
self.validation_data_solution = np.array([])
self.velocities_input_hidden = np.zeros(self.weights_input_hidden.shape)
self.velocities_hidden_output = np.zeros(self.weights_hidden_output.shape)
if bias:
self.weights_bias_hidden = np.random.uniform(low=-0.01, high=0.01, size=((1, hidden_dim)))
self.weights_bias_output = np.random.uniform(low=-0.01, high=0.01, size=((1, output_dim)))
self.velocities_bias_hidden = np.zeros(self.weights_bias_hidden.shape)
self.velocities_bias_output = np.zeros(self.weights_bias_output.shape)
def _tanh(self, x, deriv=False):
#The derivate is: 1-np.tanh(x)**2; Because x is already the output of tanh(x) 1-x*x is the correct derivate.
if not deriv:
return np.tanh(x)
return 1-x*x
def _softmax(self, x, deriv=False):
if not deriv:
return np.exp(x) / np.sum(np.exp(x), axis=0)
return 1 - np.exp(x) / np.sum(np.exp(x), axis=0)
def set_training_data(self, training_data_input, training_data_target, validation_data_input=None, validation_data_target=None):
"""Splits the data up into training and validation data with a ratio of 0.85/0.15 if no validation data is given.
Sets the data for training."""
if len(training_data_input) != len(training_data_target):
raise ValueError(
'Number of training examples and'
' training targets does not match!'
)
if (validation_data_input is None) and (validation_data_target is None):
len_training_data = int((len(training_data_input)/100*85//1))
self.input_layer = training_data_input[:len_training_data]
self.output_layer = training_data_target[:len_training_data]
self.validation_data = training_data_input[len_training_data:]
self.validation_data_solution = training_data_target[len_training_data:]
else:
self.input_layer = training_data_input
self.output_layer = training_data_target
self.validation_data = validation_data_input
self.validation_data_solution = validation_data_target
def save(self, filename):
"""Saves the weights into a pickle file."""
with open(filename, "wb") as network_file:
pickle.dump(self.weights_input_hidden, network_file)
pickle.dump(self.weights_hidden_output, network_file)
def load(self, filename):
"""Loads network weights from a pickle file."""
with open(filename, "rb") as network_file:
weights_input_hidden = pickle.load(network_file)
weights_hidden_output = pickle.load(network_file)
if (
len(weights_input_hidden) != len(self.weights_input_hidden)
or len(weights_hidden_output) != len(self.weights_hidden_output)
):
raise ValueError(
'File contains weights that does not'
' match the current networks size!'
)
self.weights_input_hidden = weights_input_hidden
self.weights_hidden_output = weights_hidden_output
def measure_error(self, input_data, output_data):
return 1/2 * np.sum((output_data - self.forward_propagate(input_data))**2)
#return np.sum(np.nan_to_num(-output_data*np.log(self.forward_propagate(input_data))-(1-output_data)*np.log(1-self.forward_propagate(input_data))))
def forward_propagate(self, input_data, dropout=False):
"""Proceds the input data from input neurons up to output neurons and returns the output layer.
If dropout is True some of the neurons are randomly turned off."""
input_layer = input_data
self.hidden_layer = self._tanh(np.dot(input_layer, self.weights_input_hidden))
if self.bias:
self.hidden_layer += self.weights_bias_hidden
if dropout:
self.hidden_layer *= np.random.binomial([np.ones((len(input_data),self.hidden_dim))],1-self.dropout_prop)[0] * (1.0/(1-self.dropout_prop))
if self.bias:
return self._softmax((np.dot(self.hidden_layer, self.weights_hidden_output) + self.weights_bias_output).T).T
else:
return self._softmax(np.dot(self.hidden_layer, self.weights_hidden_output).T).T
#return self._softmax(output_layer.T).T
def back_propagate(self, input_data, output_data, alpha, beta, momentum):
"""Calculates the difference between target output and output and adjusts the weights to fit the target output better.
The parameter alpha is the learning rate.
Beta is the parameter for weight decay which penaltizes large weights."""
sample_count = len(input_data)
output_layer = self.forward_propagate(input_data, dropout=self.dropout)
output_layer_error = output_layer - output_data
output_layer_delta = output_layer_error * self._softmax(output_layer, deriv=True)
print("Error: ", np.mean(np.abs(output_layer_error)))
#How much did each hidden neuron contribute to the output error?
#Multiplys delta term with weights
hidden_layer_error = output_layer_delta.dot(self.weights_hidden_output.T)
#If the prediction is good, the second term will be small and the change will be small
#Ex: target: 1 -> Slope will be 1 so the second term will be big
hidden_layer_delta = hidden_layer_error * self._tanh(self.hidden_layer, deriv=True)
#The both lines return a matrix. A row stands for all weights connected to one neuron.
#E.g. [1, 2, 3] -> Weights to Neuron A
# [4, 5, 6] -> Weights to Neuron B
hidden_weights_gradient = input_data.T.dot(hidden_layer_delta)/sample_count
output_weights_gradient = self.hidden_layer.T.dot(output_layer_delta)/sample_count
velocities_input_hidden = self.velocities_input_hidden
velocities_hidden_output = self.velocities_hidden_output
self.velocities_input_hidden = velocities_input_hidden * momentum - alpha * hidden_weights_gradient
self.velocities_hidden_output = velocities_hidden_output * momentum - alpha * output_weights_gradient
#Includes momentum term and weight decay; The weight decay parameter is beta
#Weight decay penalizes large weights to prevent overfitting
self.weights_input_hidden += -velocities_input_hidden * momentum + (1 + momentum) * self.velocities_input_hidden
- alpha * beta * self.weights_input_hidden / sample_count
self.weights_hidden_output += -velocities_hidden_output * momentum + (1 + momentum) * self.velocities_hidden_output
- alpha * beta * self.weights_hidden_output / sample_count
if self.bias:
velocities_bias_hidden = self.velocities_bias_hidden
velocities_bias_output = self.velocities_bias_output
hidden_layer_delta = np.sum(hidden_layer_delta, axis=0)
output_layer_delta = np.sum(output_layer_delta, axis=0)
self.velocities_bias_hidden = velocities_bias_hidden * momentum - alpha * hidden_layer_delta
self.velocities_bias_output = velocities_bias_output * momentum - alpha * output_layer_delta
self.weights_bias_hidden += -velocities_bias_hidden * momentum + (1 + momentum) * self.velocities_bias_hidden
- alpha * beta * self.weights_bias_hidden / sample_count
self.weights_bias_output += -velocities_bias_output * momentum + (1 + momentum) * self.velocities_bias_output
- alpha * beta * self.weights_bias_output / sample_count
def batch_train(self, epochs, alpha, beta, momentum, patience=10):
"""Trains the network in batch mode that means the weights are updated after showing all training examples.
alpha is the learning rate and patience is the number of epochs that the validation error is allowed to increase before aborting.
Beta is the parameter for weight decay which penaltizes large weights."""
#The weight decay parameter is beta
validation_error = self.measure_error(self.validation_data, self.validation_data_solution)
for epoch in range(epochs):
self.back_propagate(self.input_layer, self.output_layer, alpha, beta, momentum)
validation_error_new = self.measure_error(self.validation_data, self.validation_data_solution)
if validation_error_new < validation_error:
validation_error = validation_error_new
else:
patience -= 1
if patience == 0:
print("Abort Training. Overfitting has started! Epoch: {0}. Error: {1}".format(epoch, validation_error_new))
return
print("Epoch: {0}, Validation Error: {1}".format(epoch, validation_error))
self.save("Network_Mnist.net")
def mini_batch_train(self, batch_size, epochs, alpha, beta, momentum, patience=10):
"""Trains the network in mini batch mode, that means the weights are updated after showing only a bunch of training examples.
alpha is the learning rate and patience is the number of epochs that the validation error is allowed to increase before aborting."""
validation_error = self.measure_error(self.validation_data, self.validation_data_solution)
sample_count = len(self.input_layer)
epoch_counter = 0
for epoch in range(0, epochs*batch_size, batch_size):
epoch_counter += 1
self.back_propagate(self.input_layer[epoch%sample_count:(epoch%sample_count)+batch_size],
self.output_layer[epoch%sample_count:(epoch%sample_count)+batch_size], alpha, beta, momentum)
validation_error_new = self.measure_error(self.validation_data, self.validation_data_solution)
if validation_error_new < validation_error:
validation_error = validation_error_new
patience = 20
else:
patience -= 1
if patience == 0:
print("Abort Training. Overfitting has started! Epoch: {0}. Error: {1}".format(epoch_counter, validation_error_new))
return
print("Epoch: {0}, Validation Error: {1}".format(epoch_counter, validation_error))
self.save("Network_Mnist.net")
if __name__ == "__main__":
#If the first row is a one the first output neuron should be on the second off
x = np.array([ [0, 0, 1, 1, 0],
[0, 1, 1, 1, 1],
[1, 0, 1, 1, 1],
[1, 1, 1, 1, 0],
[0, 1, 1, 1, 0],
[1, 1, 0, 0, 0],
[1, 1, 0, 0, 0],
[1, 0, 1, 0, 0] ])
y = np.array([ [0, 1],
[0, 1],
[1, 0],
[1, 0],
[0, 1],
[1, 0],
[1, 0],
[1, 0] ])
#x = np.array([ [0, 0, 1, 1] ])
#y = np.array([[0]]).T
a = FeedForwardNetwork(input_dim=5, hidden_dim=200, output_dim=2, bias=False)
a.set_training_data(x, y)
start = time.time()
a.batch_train(epochs=2000, alpha=0.05, beta=0.0001, momentum=0.99, patience=20)
print(time.time()-start)
答案 0 :(得分：0)
与衍生物有关......
如果您使用tanh激活功能，即the derivative is: y' = 1 - y^2。 tanh是常用的，因为它以零为中心。
如果您使用的是逻辑公式，则the derivative is: y' = y(1+y)。 softmax有一个similar derivative。
好处是所有这些都可以表示为自己的函数，因此您需要查看def _softmax(self, x, deriv=False)函数，以与def _tanh(self, x, deriv=False)类似的方式定义它。