下面是一段用于实现numpy中拟合问题的2层神经元网络的代码。活化功能是ReLU。亚当是训练算法。损失函数是均方误差的一半。然而，当批量大（例如10000）时，在一些迭代之后损失将变为纳米。对于小批量生产，问题不会发生。任何人都可以帮我解释为什么会发生这种情况吗？（数据来自matlab工作区：6_final_mapping_pos.mat）
＃import scipy.io as sio
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
data = sio.loadmat('6_final_mapping_pos.mat')
class NeuralNetwork():
def __init__(self):
self.batch_size = 256
self.input_size = 5 # input dimension is 5
self.hidden_layer1_size = 50
self.output_size = 1 # output dimension is 5
self.train_data = data['training_data_pos']
self.df_traindata = pd.DataFrame(data=self.train_data)
self.validation_data_num = 17142
self.valid_data = data['validation_data_pos']
self.df_validdata = pd.DataFrame(data=self.valid_data)
# weight initialization for ReLu
self.W1 = np.random.randn(self.input_size, self.hidden_layer1_size)/ np.sqrt(self.input_size/2)
self.W2 = np.random.randn(self.hidden_layer1_size, self.output_size)/ np.sqrt(self.hidden_layer1_size/2)
#bias initialization
self.b1 = np.zeros((1,self.hidden_layer1_size))
self.b2 = np.zeros((1,self.output_size))
self.lr = 5e-3 # learning rate
self.reg = 1e-3 # regularization strength
self.p = 0.5 # dropout probability = 1-p
self.first_moment_W3=0
self.second_moment_W3=0
self.first_moment_W2=0
self.second_moment_W2=0
self.first_moment_W1=0
self.second_moment_W1=0
self.first_moment_b3=0
self.second_moment_b3=0
self.first_moment_b2=0
self.second_moment_b2=0
self.first_moment_b1=0
self.second_moment_b1=0
def feedforward(self):
### randomly selected mini-batch as inputs
self.df_sample_t = self.df_traindata.sample(n = self.batch_size)
self.train_input = self.df_sample_t.as_matrix(columns=[0,1,2,3,4])
self.train_output = self.df_sample_t.as_matrix(columns=[5])
#hidden layer with dropput technique
self.hidden_layer1 = np.maximum(0, (np.dot(self.train_input, self.W1) + self.b1))
U1= np.random.rand(*self.hidden_layer1.shape) < self.p # drop mask
self.hidden_layer1 *= U1 # drop!
self.output_layer = np.dot(self.hidden_layer1, self.W2) + self.b2
self.data_loss = np.sum(0.5*(self.output_layer-self.train_output)**2) / self.batch_size
self.reg_loss = 0.5*self.reg*np.sum(self.W1*self.W1) + 0.5*self.reg*np.sum(self.W2*self.W2)
self.total_loss = self.data_loss + self.reg_loss
def backpropagation(self):
self.d_output = (self.output_layer-self.train_output)/ self.batch_size
#data part
self.dW2 = np.dot(self.hidden_layer1.T, self.d_output)
self.db2 = np.sum(self.d_output, axis=0, keepdims=True)
self.dhidden1 = np.dot(self.d_output, self.W2.T)
self.dhidden1[self.hidden_layer1<= 0] = 0
self.dW1 = np.dot(self.train_input.T, self.dhidden1)
self.db1 = np.sum(self.dhidden1, axis=0, keepdims=True)
#regularization part
self.dW2 = self.dW2 + self.reg * self.W2
self.dW1 = self.dW1 + self.reg * self.W1
def Adam(self, epoch, dW2, dW1, db2, db1):
beta1 = 0.9
beta2 = 0.99
self.first_moment_W2 = beta1*self.first_moment_W2 + (1-beta1)*dW2
self.second_moment_W2 = beta2*self.second_moment_W2 + (1-beta2)*dW2*dW2
first_unbias_W2 = self.first_moment_W2 /(1-beta1 ** epoch)
second_unbias_W2 = self.second_moment_W2 /(1-beta2 ** epoch)
self.W2 -= self.lr * first_unbias_W2 / (np.sqrt(second_unbias_W2) +1e-7)
self.first_moment_W1 = beta1*self.first_moment_W1 + (1-beta1)*dW1
self.second_moment_W1 = beta2*self.second_moment_W1 + (1-beta2)*dW1*dW1
first_unbias_W1 = self.first_moment_W1 /(1-beta1 ** epoch)
second_unbias_W1 = self.second_moment_W1 /(1-beta2 ** epoch)
self.W1 -= self.lr * first_unbias_W1 / (np.sqrt(second_unbias_W1) +1e-7)
self.first_moment_b2 = beta1*self.first_moment_b2 + (1-beta1)*db2
self.second_moment_b2 = beta2*self.second_moment_b2 + (1-beta2)*db2*db2
first_unbias_b2 = self.first_moment_b2 /(1-beta1 ** epoch)
second_unbias_b2 = self.second_moment_b2 /(1-beta2 ** epoch)
self.b2 -= self.lr * first_unbias_b2 / (np.sqrt(second_unbias_b2) +1e-7)
self.first_moment_b1 = beta1*self.first_moment_b1 + (1-beta1)*db1
self.second_moment_b1 = beta2*self.second_moment_b1 + (1-beta2)*db1*db1
first_unbias_b1 = self.first_moment_b1 /(1-beta1 ** epoch)
second_unbias_b1 = self.second_moment_b1 /(1-beta2 ** epoch)
self.b1 -= self.lr * first_unbias_b1 / (np.sqrt(second_unbias_b1) +1e-7)
def validation(self):
self.df_sample_v = self.df_validdata.sample(n = self.validation_data_num)
self.valid_input = self.df_sample_v.as_matrix(columns=[0,1,2,3,4])
self.valid_output = self.df_sample_v.as_matrix(columns=[5])
self.hidden_layer1 = np.maximum(0, np.dot(self.valid_input, self.W1) + self.b1) *self.p
self.output_layer = np.dot(self.hidden_layer1, self.W2) + self.b2
self.data_loss = np.sum(0.5*(self.output_layer-self.valid_output)**2) / self.validation_data_num
self.reg_loss = 0.5*self.reg*np.sum(self.W1*self.W1) + 0.5*self.reg*np.sum(self.W2*self.W2)
self.total_loss = self.data_loss + self.reg_loss
NN = NeuralNetwork()
num_iterations = 120
training_loss = np.array([])
validation_loss = np.array([])
validation_dataloss = np.array([])
t=1
T=np.array([range(1,num_iterations)]).T
# Training and validation
while(t < num_iterations):
NN.feedforward()
NN.backpropagation()
NN.Adam(t, NN.dW2, NN.dW1, NN.db2, NN.db1)
training_loss = np.append(training_loss, NN.total_loss)
if t % 10 == 0:
print ("training:" + "total loss = %f, data loss = %f, regularization loss = %f" % (NN.total_loss,NN.data_loss,NN.reg_loss))
NN.validation()
validation_loss = np.append(validation_loss, NN.total_loss)
validation_dataloss = np.append(validation_dataloss, NN.data_loss)
if t % 10 == 0:
print ("validation:" + "total loss = %f, data loss = %f, regularization loss = %f" % (NN.total_loss,NN.data_loss,NN.reg_loss))
t+=1