我只使用NumPy实现了我自己的回归神经网络模型，当我在m>1个样本(对于m=1，效果良好(。。模型似乎崩溃了，只预测了整个批次的特定值：
Input:
X [[ 7.62316802 -6.12433912]
[ 1.11048966 4.97509421]]
Expected Output:
Y [[16.47952332 12.50288412]]
Model Output
y_hat [[10.42446234 10.42446234]]
知道是什么原因导致了这个问题吗？
我的代码：
import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
# np.seterr(all=None, divide=None, over=None, under=None, invalid=None)
data_x = np.random.uniform(0, 10, size=(2, 1))
data_y = (2 * data_x).sum(axis=0, keepdims=True)
# data_y = data_x[0, :] ** 2 + data_x[1, :] ** 2
# data_y = data_y.reshape((1, -1))
# # fig = plt.figure()
# # ax = fig.add_subplot(111, projection='3d')
# # ax.scatter(data_x[0, :], data_x[1, :], data_y)
# # plt.show()
memory = dict()
nn_architecture = [
{"input_dim": 2, "output_dim": 6, "activation": "sigmoid", "bias": True},
{"input_dim": 6, "output_dim": 4, "activation": "sigmoid", "bias": True},
{"input_dim": 4, "output_dim": 1, "activation": "relu", "bias": True}
]
def init_network_parameters(nn_architecture):
parameters = []
for idx, layer in enumerate(nn_architecture):
layer_params = {}
input_dim, output_dim, activation, bias = layer.values()
W = np.random.uniform(0, 1, (output_dim, input_dim))
B = np.zeros((output_dim, 1))
if bias:
B = np.ones((output_dim, 1))
activation_func = identity
backward_activation_func = identity_backward
if activation is 'sigmoid':
activation_func = sigmoid
backward_activation_func = sigmoid_backward
elif activation is 'relu':
activation_func = relu
backward_activation_func = relu_backward
else:
print(f"Activation function set to identity for layer {idx}")
layer_params[f"W"] = W
layer_params[f"B"] = B
layer_params[f"activation"] = activation_func
layer_params[f"backward_activation"] = backward_activation_func
layer_params[f"bias"] = bias
parameters.append(layer_params)
return parameters
def identity(z):
return z
def sigmoid(z):
return np.clip(1 / (1 + np.exp(-z)), -100, 100)
def relu(z):
output = np.array(z, copy=True)
output[z <= 0] = 0
return output
def identity_backward(z, dA):
return dA
def sigmoid_backward(z, dA):
return np.clip(z * (1-z) * dA, -100, 100)
def relu_backward(z, dA):
output = np.ones(z.shape)
output[z <= 0] = 0
return output * dA
def forward_single_layer(prev_A, parameters, idx):
W = parameters[f"W"]
B = parameters[f"B"]
activation = parameters[f"activation"]
if parameters["bias"]:
curr_Z = W.dot(prev_A) + B
else:
curr_Z = W.dot(prev_A)
curr_A = activation(curr_Z)
memory[f"Z{idx+1}"] = curr_Z
memory[f"A{idx+1}"] = curr_A
return curr_Z, curr_A
def forward(X, parameters):
prev_A = X
memory["A0"] = prev_A
for idx, layer_params in enumerate(parameters):
curr_Z, prev_A = forward_single_layer(prev_A=prev_A, parameters=layer_params, idx=idx)
return prev_A
def criteria(y_hat, y):
assert y_hat.shape == y.shape
n = y_hat.shape[0]
m = y_hat.shape[1]
loss = np.sum(y_hat - y, axis=1) / m
dA = (y_hat - y) / m
return loss, dA
def backward_single_layer(prev_A, dA, curr_W, curr_Z, backward_activation, idx):
m = prev_A.shape[1]
dZ = backward_activation(z=curr_Z, dA=dA)
dW = np.dot(dZ, prev_A.T) / m
dB = np.sum(dZ, axis=1, keepdims=True) / m
dA = np.dot(curr_W.T, dZ)
return dA, dW, dB
def backpropagation(parameters, dA):
grads = {}
for idx in reversed(range(len(parameters))):
layer = parameters[idx]
prev_A = memory[f"A{idx}"]
curr_Z = memory[f"Z{idx+1}"]
curr_W = layer["W"]
backward_activation = layer["backward_activation"]
dA, dW, dB = backward_single_layer(prev_A, dA, curr_W, curr_Z, backward_activation, idx)
grads[f"W{idx}"] = dW
grads[f"B{idx}"] = dB
return grads
def update_params(parameters, grads, lr=0.001):
new_params = []
for idx, layer in enumerate(parameters):
layer["W"] -= lr*grads[f"W{idx}"]
layer["B"] -= lr*grads[f"B{idx}"]
new_params.append(layer)
return new_params
X = np.random.uniform(-10, 10, (2, 2))
Y = 2*X[0, :] + X[1, :] ** 2
Y = Y.reshape((1, X.shape[1]))
parameters = init_network_parameters(nn_architecture)
n_epochs = 1000
lr = 0.01
loss_history = []
for i in range(n_epochs):
y_hat = forward(X, parameters)
loss, dA = criteria(y_hat, Y)
loss_history.append(loss)
grads = backpropagation(parameters, dA)
parameters = update_params(parameters, grads, lr)
if not i % 10:
print(f"Epoch {i}/{n_epochs} loss={loss}")
print("X", X)
print("Y", Y)
print("y_hat", y_hat)
我的实现没有问题，只是过拟合。更多信息可以在这里找到。