【发布时间】：2020-05-30 23:04:10
【问题描述】：
你好，我尝试使用一个以向量为中心的神经网络，它有一个输入节点、一个输出节点和两个隐藏层，每个隐藏层有 3 个节点来拟合一个非常简单的 x**2 函数。 - 只是为了验证它的功能。因此我使用下面的代码。结果我得到橙色线，蓝色线是真正的线。
如您所见，有些东西不起作用。我试图改变迭代次数和学习率的值，但没有成功。如果我在迭代中绘制损失，我会得到以下 100 次迭代的图片：
我还没有添加偏差，但我认为这个简单的函数应该可以在没有额外偏差节点的情况下适用。此外，我假设代码中的失败最有可能出现在代码的“计算相对于权重的梯度”部分......
所以原则上我有两个问题：
- 我的代码中是否存在任何基本故障，导致代码无法正常工作
- 如果不是，为什么我的模型无法拟合简单数据
提前感谢您的帮助！
代码来了 - 可以玩了：
class Neural_Net:
"""
"""
def __init__(self, activation_function, learning_rate, runs):
self.activation_function = activation_function
self.X_train = np.linspace(0,1,1000)
self.y_train = self.X_train**2
plt.plot(self.X_train, self.y_train)
self.y_pred = None
self.W_input = np.random.randn(1, 3)
self.Partials_W_input = np.random.randn(1, 3)
self.W_hidden = np.random.randn(3,3)
self.Partials_W_hidden = np.random.randn(3,3)
self.W_output = np.random.randn(3,1)
self.Partials_W_output = np.random.randn(3,1)
self.Activations = np.ones((3,2))
self.Partials = np.ones((3,2))
self.Output_Gradient = None
self.Loss = 0
self.learning_rate = learning_rate
self.runs = runs
self.Losses = []
self.i = 0
def apply_activation_function(self, activation_vector):
return 1/(1+np.exp(-activation_vector))
def forward_pass(self, training_instance):
for layer in range(len(self.Activations[0])):
# For the first layer between X and the first hidden layer
pre_activation_first = self.W_input.T @ training_instance.reshape(1,1)
# print('pre activation: ', pre_activation)
# Apply the activation function
self.Activations[:,0] = self.apply_activation_function(pre_activation_first).ravel()
else:
pre_activation_hidden = self.W_hidden.T @ self.Activations[:, layer-1]
self.Activations[:, layer] = self.apply_activation_function(pre_activation_hidden)
# print('Activations: ', self.Activations)
output = self.W_output.T @ self.Activations[:, -1]
# print('output: ', output)
return output
def backpropagation(self, y_true, training_instance):
if self.activation_function == 'linear':
# Calculate the ouput gradient
self.Output_Gradient = -(y_true-self.y_pred)
# print('Output Gradient: ', self.Output_Gradient)
# Calculate the partial gradients of the Error with respect to the pre acitvation values in the nodes
self.Partials[:, 1] = self.Activations[:, 1]*(1-self.Activations[:, 1])*(self.W_output @ self.Output_Gradient)
self.Partials[:, 0] = self.Activations[:, 0]*(1-self.Activations[:, 0])*(self.W_hidden @ self.Partials[:, 1])
# print('Partials: ', self.Partials)
# Calculate the Gradients with respect to the weights
self.Partials_W_output = self.Output_Gradient * self.Activations[:, -1]
# print('Partials_W_output: ', self.Partials_W_output)
self.Partials_W_hidden = self.Partials[:, -1].reshape(3,1) * self.Activations[:, 0].reshape(1,3)
# print('Partials_W_hidden: ',self.Partials_W_hidden)
self.Partials_W_input = (self.Partials[:, 0].reshape(3,1) * training_instance.T).T
# print('Partials_W_input: ', self.Partials_W_input)
def weight_update(self, training_instance, learning_rate):
# Output Layer weights
w_output_old = self.W_output.copy()
self.W_output = w_output_old - learning_rate*self.Output_Gradient
# Hidden Layer weights
w_hidden_old = self.W_hidden.copy()
self.W_hidden = w_hidden_old - learning_rate * self.W_hidden
# print('W_hidden new: ', self.W_hidden)
# Input Layer weights
w_input_old = self.W_input.copy()
self.W_input = w_input_old - learning_rate * self.W_input
# print('W_input new: ', self.W_input)
def train_model(self):
for _ in range(self.runs):
for instance in range(len(self.X_train)):
# forward pass
self.y_pred = self.forward_pass(self.X_train[instance])
# Calculate loss
self.Loss = self.calc_loss(self.y_pred, self.y_train[instance])
# print('Loss: ', self.Loss)
# Calculate backpropagation
self.backpropagation(self.y_train[instance], self.X_train[instance])
# Update weights
self.weight_update(self.X_train[instance], self.learning_rate)
# print(self.Losses)
# plt.plot(range(len(self.Losses)), self.Losses)
# plt.show()
# Make predictions on training data to check if the model is basically able to fit the training data
predictions = []
for i in np.linspace(0,1,1000):
predictions.append(self.make_prediction(i))
plt.plot(np.linspace(0,1,1000), predictions)
def make_prediction(self, X_new):
return self.forward_pass(X_new)
def calc_loss(self, y_pred, y_true):
loss = (1/2)*(y_true-y_pred)**2
self.Losses.append(loss[0])
return (1/2)*(y_true-y_pred)**2
def accuracy(self):
pass
Neural_Net('linear', 0.0001, 10).train_model()
【问题讨论】：
标签： python machine-learning neural-network gradient-descent backpropagation