神经网络在 mnist 上失败

Question

我用 python 编写了一个神经网络来解决 mnist 任务。 但是错误率在一个时期后变化很小（逗号后的第 6 位），并且网络在 10000 个时期后并没有学到太多东西...... 你能帮我做错什么以及如何改进我的代码来解决 mnist 吗？ 我将学习率 eta 设置为 0.05。

import numpy as np
import pickle
import time

class FeedForwardNetwork():

    def __init__(self, input_dim, hidden_dim, output_dim):
        self.input_dim = input_dim
        self.hidden_dim = hidden_dim
        self.output_dim = output_dim
        self.input_layer = np.array([])
        self.hidden_layer = np.array([])
        self.output_layer = np.array([])
        self.weights_input_hidden = (2 * np.random.random((input_dim, hidden_dim)) - 1)/1000
        self.weights_hidden_output = (2* np.random.random((hidden_dim, output_dim)) - 1)/1000

        self.validation_data = np.array([])
        self.validation_data_solution = np.array([])

    def _tanh(self, x, deriv=False):
        if not deriv:
            return np.tanh(x)
        return 1-np.tanh(x)**2

    def _softmax(self, x):
        return np.exp(x) / np.sum(np.exp(x), axis=0)

    def set_training_data(self, training_data_input, training_data_target):
        """Splits the data up into training and validation data with a ratio of 0.75/0.25 and sets the data for training."""
        if len(training_data_input) != len(training_data_target):
            raise Exception("Number of training examples and training targets does not match!")
        len_training_data = int((len(training_data_input)/100*75)//1)
        self.input_layer = training_data_input[:len_training_data]
        self.output_layer = training_data_target[:len_training_data]
        self.validation_data = np.array([training_data_input[len_training_data:]])
        self.validation_data_solution = np.array([training_data_target[len_training_data:]])

    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):
            raise Exception("File contains weights that does not match the current networks size!")
        if len(weights_hidden_output) != len(self.weights_hidden_output):
            raise Exception("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.activate(input_data))**2)

    def forward_propagate(self, input_data):
        """Proceds the input data from input neurons up to output neurons and returns the output layer"""
        input_layer = input_data
        self.hidden_layer = self.__tanh(np.dot(input_layer, self.weights_input_hidden))
        output_layer = self.__tanh(np.dot(self.hidden_layer, self.weights_hidden_output))
        return output_layer

    def activate(self, input_data):
        """Sends the given input through the net and returns the net's prediction."""
        return self.forward_propagate(input_data)

    def back_propagate(self, input_data, output_data, eta):
        """Calculates the difference between target output and output and adjust the weights to fit the target output better.
           The parameter eta is the learning rate."""
        num_of_samples = len(input_data)
        output_layer = self.forward_propagate(input_data)
        output_layer_error = output_data - output_layer
        output_layer_delta = output_layer_error * self.__tanh(output_layer, deriv=True)
        #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_change = self.input_layer.T.dot(hidden_layer_delta)/num_of_samples
        output_weights_change = self.hidden_layer.T.dot(output_layer_delta)/num_of_samples

        self.weights_hidden_output += (output_weights_change * eta) / num_of_samples
        self.weights_input_hidden += (hidden_weights_change * eta) / num_of_samples

    def batch_train(self, epochs, eta, patience=10):
        """Trains the network in batch mode that means the weigts are updated after showing all training examples.
           Eta 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)
        for epoch in range(epochs):
            self.back_propagate(self.input_layer, self.output_layer, eta)
            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}, Error: {1}".format(epoch, validation_error))
            self.save("Network_Mnist.net")

谢谢！

纪元：1813，错误：7499.944371111551 纪元：1814，错误：7499.944368765047

Answer 1

我猜你可能想添加一个带有交叉熵误差的 softmax 层。 当输入为负时，Tanh 将输出负值，这显然不是您想要的输出层，因为概率应该在 [0, 1] 范围内。

This 是我实现的玩具前馈神经网络，可能对您有所帮助。