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python - 具有正弦功能的神经网络：误差不会减少

问题描述

我从 Tariq Rashid 那里获取了一个 Python 神经网络代码来预测手写数字，并尝试调整它来预测窦函数。它适用于书面数字。但是使用 sinus 函数，误差并没有减少。

我对 sinus 函数的设置如下：

在这里，您可以看到带有手写预测的误差函数，因为它随着时间的推移而减小，工作正常：

修正误差函数

在这里你可以看到我的窦曲线预测的误差函数。它只是没有减少。我尝试了很多不同的设置，但我不知道如何找到问题。

正弦曲线的误差函数不减小

有人知道如何定位错误吗？我花了几天时间，但我不知道可能出了什么问题。我在示例中看到，使用 sigmoid 函数原则上它应该可以工作。

代码来了。这是训练数据：https ://www.dropbox.com/s/c9xe1wq7b0i9h2y/train-sin-pi-norm_shuffle.csv?dl=0

# python notebook for Make Your Own Neural Network  
# original code for a 3-layer neural network, and code for learning the MNIST dataset
# (c) Tariq Rashid, 2016
# license is GPLv2
# code was changed by a random user for learning the sinus function


# numpy provides arrays and useful functions for working with them
import numpy
# scipy.special for the sigmoid function expit()
import scipy.special
import csv   
import matplotlib.pyplot as plt

# neural network class definition
class neuralNetwork:

# initialise the neural network
def __init__(self, inputnodes, hiddennodes, outputnodes, learningrate):
    # set number of nodes in each input, hidden, output layer
    self.inodes = inputnodes
    self.hnodes = hiddennodes
    self.onodes = outputnodes

    # link weight matrices, wih and who
    # weights inside the arrays are w_i_j, where link is from node i to node j in the next layer
    # w11 w21
    # w12 w22 etc 
    self.wih = numpy.random.normal(0.0, pow(self.hnodes, -0.5), (self.hnodes, self.inodes))
    self.who = numpy.random.normal(0.0, pow(self.onodes, -0.5), (self.onodes, self.hnodes))

    # learning rate
    self.lr = learningrate

    # activation function is the sigmoid function
    self.activation_function = lambda x: scipy.special.expit(x)

    pass

# train the neural network
def train(self, inputs_list, targets_list):
    # convert inputs list to 2d array (probably not necessary for the sinus curve model)
    inputs = numpy.array(inputs_list, ndmin=2).T
    targets = numpy.array(targets_list, ndmin=2).T
    # calculate signals into hidden layer
    hidden_inputs = numpy.dot(self.wih, inputs)
    # calculate the signals emerging from hidden layer
    hidden_outputs = self.activation_function(hidden_inputs)
    # calculate signals into final output layer
    final_inputs = numpy.dot(self.who, hidden_outputs)
    # calculate the signals emerging from final output layer
    final_outputs = self.activation_function(final_inputs)
    # output layer error is the (target - actual)
    output_errors = targets - final_outputs

    error_array.append(float(output_errors))

    # hidden layer error is the output_errors, split by weights, recombined at hidden nodes
    hidden_errors = numpy.dot(self.who.T, output_errors)

    # update the weights for the links between the hidden and output layers
    self.who += self.lr * numpy.dot((output_errors * final_outputs * (1.0 - final_outputs)), numpy.transpose(hidden_outputs))
    # update the weights for the links between the input and hidden layers
    self.wih += self.lr * numpy.dot((hidden_errors * hidden_outputs * (1.0 - hidden_outputs)), numpy.transpose(inputs))     
    pass

# query the neural network
def query(self, inputs_list):

    # convert inputs list to 2d array
    inputs = numpy.array(inputs_list, ndmin=2).T

    # calculate signals into hidden layer
    hidden_inputs = numpy.dot(self.wih, inputs)

    # calculate the signals emerging from hidden layer       
    hidden_outputs = self.activation_function(hidden_inputs)

    # calculate signals into final output layer
    final_inputs = numpy.dot(self.who, hidden_outputs)

    # calculate the signals emerging from final output layer
    final_outputs = self.activation_function(final_inputs)

    return final_outputs

# number of input, hidden and output nodes
input_nodes = 1
hidden_nodes = 10
output_nodes = 1
learning_rate = 0.1
error_array = []

# create instance of neural network
n = neuralNetwork(input_nodes,hidden_nodes,output_nodes, learning_rate)

# load the training data CSV file into a list
training_data_file = open("train-sin-pi-norm_shuffle.csv", 'r')
training_data_list = training_data_file.readlines()
training_data_file.close()


# train the neural network

# epochs is the number of times the training data set is used for training
epochs =10

for e in range(epochs):

# go through all records in the training data set
for record in training_data_list:
    # split the record by the ';' commas

    all_values = record.split(';')
    inputs = numpy.asfarray(all_values[0])
    targets = float(all_values[1])  
    n.train(inputs, targets)
    pass
pass

# normally here would be the testing of a test data set, but this is not important at the moment.    

plt.plot(error_array, label="Error")
plt.legend()
plt.show()

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