神经网络有时收敛到 0.5

问题描述

感谢您抽出宝贵时间。

我编写了一个带有随机输入的神经网络。网络试图对“图片”中的 5 个符号之一进行分类，该图片是一个 3x3 网格，我在 (0,1) 之间给出了随机值以指示“像素”的“亮度”。

有时神经网络会收敛到 0.5（误差）。当我提高学习率时，这总是发生（learning_rate > 0.5）。例如，当 learning_rate 为 0.02 时，网络收敛到 0 错误。

你们中的任何人都可以看看我是否做错了什么吗？

非常感谢！

# -*- coding: utf-8 -*-
"""
Created on Tue Jan  5 23:55:49 2021

@author: Stein
"""

import numpy as np 
import matplotlib.pyplot as plt
from tqdm import tqdm
import math as m

def derivative_c(x):
    return x

def derivative_sigmoid(x):
  
    return sigmoid(x) * (1 - sigmoid(x))
    
def sigmoid(x):

    return 1/(1+np.exp(-1*x))


sim_cons = 5000
n_of_input_neurons = 9
n_of_output_neurons = 5
training_data = np.random.rand(sim_cons,n_of_input_neurons)
brightness_matrix = np.zeros((sim_cons,n_of_input_neurons))
truth_vector = np.zeros((sim_cons,n_of_output_neurons))
rows = training_data.shape[0]
cols = training_data.shape[1]

weight_matrix = np.random.uniform(-1,1,(n_of_input_neurons+1,n_of_output_neurons))
output_layer = np.zeros((n_of_output_neurons,1))
weights_init = weight_matrix

n__o_sq = 0
n__o_cr = 0
n__o_div = 0
n__o_backsl = 0
n__o_min = 0





for i in range(rows):
    for j in range(cols):
        brightness_matrix[i][j] = m.ceil(training_data[i][j]*4)
    if brightness_matrix[i][0] <= 3 and brightness_matrix[i][1] > 3 and brightness_matrix[i][2] <= 3 and brightness_matrix[i][3] > 3 and brightness_matrix[i][4] > 3 and brightness_matrix[i][5] > 3 and brightness_matrix[i][6] <= 3 and brightness_matrix[i][7] > 3 and brightness_matrix[i][8] <= 3 or brightness_matrix[i][0] <= 2 and brightness_matrix[i][1] > 2 and brightness_matrix[i][2] <= 2 and brightness_matrix[i][3] > 2 and brightness_matrix[i][4] > 2 and brightness_matrix[i][5] > 2 and brightness_matrix[i][6] <= 2 and brightness_matrix[i][7] > 2 and brightness_matrix[i][8] <= 2 or brightness_matrix[i][0] <= 1 and brightness_matrix[i][1] > 1 and brightness_matrix[i][2] <= 1 and brightness_matrix[i][3] > 1 and brightness_matrix[i][4] > 1 and brightness_matrix[i][5] > 1 and brightness_matrix[i][6] <= 1 and brightness_matrix[i][7] > 1 and brightness_matrix[i][8] <= 1:
        n__o_sq += 1
        truth_vector[i][0] = 1
    elif brightness_matrix[i][0] > 3 and brightness_matrix[i][1] <= 3 and brightness_matrix[i][2] > 3 and brightness_matrix[i][3] <= 3 and brightness_matrix[i][4] > 3 and brightness_matrix[i][5] <= 3 and brightness_matrix[i][6] > 3 and brightness_matrix[i][7] <= 3 and brightness_matrix[i][8] > 3 or brightness_matrix[i][0] > 2 and brightness_matrix[i][1] <= 2 and brightness_matrix[i][2] > 2 and brightness_matrix[i][3] <= 2 and brightness_matrix[i][4] > 2 and brightness_matrix[i][5] <= 2 and brightness_matrix[i][6] > 2 and brightness_matrix[i][7] <= 2 and brightness_matrix[i][8] > 2 or brightness_matrix[i][0] > 1 and brightness_matrix[i][1] <= 1 and brightness_matrix[i][2] > 1 and brightness_matrix[i][3] <= 1 and brightness_matrix[i][4] > 1 and brightness_matrix[i][5] <= 1 and brightness_matrix[i][6] > 1 and brightness_matrix[i][7] <= 1 and brightness_matrix[i][8] > 1:
        n__o_cr += 1
        truth_vector[i][1] = 1
    elif brightness_matrix[i][0] <= 3 and brightness_matrix[i][1] <= 3 and brightness_matrix[i][2] > 3 and brightness_matrix[i][3] <= 3 and brightness_matrix[i][4] > 3 and brightness_matrix[i][5] <= 3 and brightness_matrix[i][6] > 3 and brightness_matrix[i][7] <= 3 and brightness_matrix[i][8] <= 3 or brightness_matrix[i][0] <= 2 and brightness_matrix[i][1] <= 2 and brightness_matrix[i][2] > 2 and brightness_matrix[i][3] <= 2 and brightness_matrix[i][4] > 2 and brightness_matrix[i][5] <= 2 and brightness_matrix[i][6] > 2 and brightness_matrix[i][7] <= 2 and brightness_matrix[i][8] <= 2 or brightness_matrix[i][0] <= 1 and brightness_matrix[i][1] <= 1 and brightness_matrix[i][2] > 1 and brightness_matrix[i][3] <= 1 and brightness_matrix[i][4] > 1 and brightness_matrix[i][5] <= 1 and brightness_matrix[i][6] > 1 and brightness_matrix[i][7] <= 1 and brightness_matrix[i][8] <= 1:
        n__o_div += 1
        truth_vector[i][2] = 1        
    elif brightness_matrix[i][0] > 3 and brightness_matrix[i][1] <= 3 and brightness_matrix[i][2] <= 3 and brightness_matrix[i][3] <= 3 and brightness_matrix[i][4] > 3 and brightness_matrix[i][5] <= 3 and brightness_matrix[i][6] <= 3 and brightness_matrix[i][7] <= 3 and brightness_matrix[i][8] > 3 or brightness_matrix[i][0] > 2 and brightness_matrix[i][1] <= 2 and brightness_matrix[i][2] <= 2 and brightness_matrix[i][3] <= 2 and brightness_matrix[i][4] > 2 and brightness_matrix[i][5] <= 2 and brightness_matrix[i][6] <= 2 and brightness_matrix[i][7] <= 2 and brightness_matrix[i][8] > 2 or brightness_matrix[i][0] > 1 and brightness_matrix[i][1] <= 1 and brightness_matrix[i][2] <= 1 and brightness_matrix[i][3] <= 1 and brightness_matrix[i][4] > 1 and brightness_matrix[i][5] <= 1 and brightness_matrix[i][6] <= 1 and brightness_matrix[i][7] <= 1 and brightness_matrix[i][8] > 1:
        n__o_backsl += 1
        truth_vector[i][3] = 1
    elif brightness_matrix[i][0] <= 3 and brightness_matrix[i][1] <= 3 and brightness_matrix[i][2] <= 3 and brightness_matrix[i][3] > 3 and brightness_matrix[i][4] > 3 and brightness_matrix[i][5] > 3 and brightness_matrix[i][6] <= 3 and brightness_matrix[i][7] <= 3 and brightness_matrix[i][8] <= 3 or brightness_matrix[i][0] <= 2 and brightness_matrix[i][1] <= 2 and brightness_matrix[i][2] <= 2 and brightness_matrix[i][3] > 2 and brightness_matrix[i][4] > 2 and brightness_matrix[i][5] > 2 and brightness_matrix[i][6] <= 2 and brightness_matrix[i][7] <= 2 and brightness_matrix[i][8] <= 2 or brightness_matrix[i][0] <= 1 and brightness_matrix[i][1] <= 1 and brightness_matrix[i][2] <= 1 and brightness_matrix[i][3] > 1 and brightness_matrix[i][4] > 1 and brightness_matrix[i][5] > 1 and brightness_matrix[i][6] <= 1 and brightness_matrix[i][7] <= 1 and brightness_matrix[i][8] <= 1:
        n__o_min += 1
        truth_vector[i][4] = 1
        
## remove noise samples
print(n__o_sq) 
print(n__o_cr) 
print(n__o_div) 
print(n__o_backsl) 
print(n__o_min) 
real_training_data = np.where(truth_vector > 0)
range_1 = len(real_training_data[0])
print(range_1)
truth_vector_new = np.zeros((range_1,5))
j=0
training_data_new = np.zeros((range_1,n_of_input_neurons))
for i in range(len(truth_vector)):
    if sum(truth_vector[i]) > 0:
        truth_vector_new[j] = truth_vector[i]        
        training_data_new[j] = training_data[i]
        j+=1
bias_array = np.ones((range_1,1))        
  
training_data_new = np.hstack([training_data_new,bias_array])



def forward_prop(weight_matrix,k):

    forward_sum = 0
    rows = weight_matrix.shape[0]
    cols = weight_matrix.shape[1]
    forward_sum_array = np.zeros((n_of_output_neurons,1))
    error_array = np.zeros((n_of_output_neurons,1))
    
    for i in range(cols):

        forward_sum = 0
        
        for j in range(rows):
    
            forward_sum += float(training_data_new[k][j] * weight_matrix[j][i])
        
        forward_sum_array[i] = forward_sum
        
        output_layer[i] = sigmoid(forward_sum)

    for i in range(n_of_output_neurons):

        error_array[i] = (0.5 * (output_layer[i] - truth_vector_new[k][i])**2)
    
    return forward_sum_array,sum(error_array),error_array







derivatives_total = np.zeros((n_of_input_neurons+1,n_of_output_neurons))



def backward_prop(weight_matrix,derivatives_total,k):
     
    truth_vector_temp = np.matrix.transpose(truth_vector_new)
    der_1_v = np.zeros((n_of_output_neurons,1))
    for i in range(len(der_1_v)):
        der_1_v[i] = output_layer[i] - truth_vector_temp[i][k]
    derivative_cost = derivative_c(der_1_v)
    derivative_2 = derivative_sigmoid(forward_sum_array)
    
    final_derivative = derivative_cost * derivative_2

    derivatives = np.zeros((n_of_input_neurons+1,n_of_output_neurons))

    rows = derivatives.shape[0]
    cols = derivatives.shape[1]

    for i in range(cols):
        for j in range(rows):
            derivatives[j][i] = final_derivative[i] * training_data_new[k][j]
    derivatives_total += derivatives

    return weight_matrix,error,derivatives_total









error = 100
counter = []
error_array  = []
i = 0



while error >= 0.00000001:
    for k in range(range_1):
        forward_sum_array,a = forward_prop(weight_matrix,k)
        
        weight_matrix,derivatives_total = backward_prop(weight_matrix,k)
    weight_matrix = weight_matrix - 0.0001 * derivatives_total
    print(error)
    error_array.append(error)
    counter.append(i)
    i+=1
    plt.plot(counter,error_array)
    plt.show()

else:
    print('done')
    print('')
    print('input was')
    print(training_data_new)
    print('truth was')
    print(truth_vector_new)
    print('weights init')
    print(weights_init)
    print('weights end')
    print(weight_matrix)
correct_counter = 0
for k in range(range_1):    

    forward_sum_array,a  = forward_prop(weight_matrix,k)

    print(output_layer)
    print(truth_vector_new[k])
    print(np.argmax(truth_vector_new[k]))
    print(np.argmax(output_layer))
    if np.argmax(truth_vector_new[k]) == np.argmax(output_layer):
                 correct_counter += 1
    print(correct_counter/range_1)

解决方法

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