前言

仅记录学习过程，有问题欢迎讨论

获取数据

自定义一个方程，获取一批数据X,Y

import matplotlib.pyplot as pyplot
import math
import sysX = [0.01 * x for x in range(100)]
Y = [2*x**2 + 3*x + 4 for x in X]
print(X)
print(Y)
pyplot.scatter(X, Y, color='red')
pyplot.show()
input()

利用nn模型计算w

X = [0.0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18,0.19, 0.2, 0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3, 0.31, 0.32, 0.33, 0.34, 0.35000000000000003,0.36, 0.37, 0.38, 0.39, 0.4, 0.41000000000000003, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47000000000000003, 0.48, 0.49,0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.5700000000000001, 0.58, 0.59, 0.6, 0.61, 0.62, 0.63, 0.64, 0.65, 0.66,0.67, 0.68, 0.6900000000000001, 0.7000000000000001, 0.71, 0.72, 0.73, 0.74, 0.75, 0.76, 0.77, 0.78, 0.79, 0.8,0.81, 0.8200000000000001, 0.8300000000000001, 0.84, 0.85, 0.86, 0.87, 0.88, 0.89, 0.9, 0.91, 0.92, 0.93,0.9400000000000001, 0.9500000000000001, 0.96, 0.97, 0.98, 0.99]
Y = [4.0, 4.0302, 4.0608, 4.0918, 4.1232, 4.155, 4.1872, 4.2198, 4.2528, 4.2862, 4.32, 4.3542, 4.3888, 4.4238, 4.4592,4.495, 4.5312, 4.5678, 4.6048, 4.6422, 4.68, 4.7181999999999995, 4.7568, 4.7958, 4.8352, 4.875, 4.9152000000000005,4.9558, 4.9968, 5.0382, 5.08, 5.122199999999999, 5.1648, 5.2078, 5.2512, 5.295, 5.3392, 5.3838, 5.4288, 5.4742,5.5200000000000005, 5.5662, 5.6128, 5.6598, 5.7072, 5.755, 5.8032, 5.851800000000001, 5.9008, 5.9502, 6.0, 6.0502,6.1008, 6.1518, 6.203200000000001, 6.255000000000001, 6.3072, 6.3598, 6.4128, 6.4662, 6.52, 6.5742, 6.6288, 6.6838,6.7392, 6.795, 6.8512, 6.9078, 6.9648, 7.022200000000001, 7.08, 7.138199999999999, 7.1968, 7.2558, 7.3152, 7.375,7.4352, 7.4958, 7.5568, 7.6182, 7.680000000000001, 7.7422, 7.8048, 7.867800000000001, 7.9312, 7.994999999999999,8.0592, 8.1238, 8.1888, 8.2542, 8.32, 8.3862, 8.4528, 8.5198, 8.587200000000001, 8.655000000000001, 8.7232, 8.7918,8.8608, 8.9302]# 标签
def func(x):y = w1 * x**2 + w2 * x + w3return y# 损失函数
def loss(y_pre, y_true):return (y_true - y_pre) ** 2# 随机定义 w
w1, w2, w3 = 1, 2, 3
# 学习率
lr = 0.1# 训练过程
for epoch in range(500):epoch_loss = 0for x, y_true in zip(X, Y):y_pre = func(x)# 本轮loss 总值epoch_loss += loss(y_pre, y_true)# 梯度计算grad_w1 = 2 * (y_pre - y_true) * x ** 2grad_w2 = 2 * (y_pre - y_true) * xgrad_w3 = 2 * (y_pre - y_true)# 权重更新w1 = w1 - lr * grad_w1  # sgdw2 = w2 - lr * grad_w2w3 = w3 - lr * grad_w3# 本轮结束 计算平均lossepoch_loss /= len(X)print("第%d轮， loss %f" % (epoch, epoch_loss))if epoch_loss < 0.00001:breakprint(f"训练后权重:w1:{w1} w2:{w2} w3:{w3}")
# #使用训练后模型输出预测值
Yp = [func(i) for i in X]
# 预测值与真实值比对数据分布
pyplot.scatter(X, Y, color="red")
pyplot.scatter(X, Yp)
pyplot.show()

优化梯度、权重计算

X = [0.0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18,0.19, 0.2, 0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3, 0.31, 0.32, 0.33, 0.34, 0.35000000000000003,0.36, 0.37, 0.38, 0.39, 0.4, 0.41000000000000003, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47000000000000003, 0.48, 0.49,0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.5700000000000001, 0.58, 0.59, 0.6, 0.61, 0.62, 0.63, 0.64, 0.65, 0.66,0.67, 0.68, 0.6900000000000001, 0.7000000000000001, 0.71, 0.72, 0.73, 0.74, 0.75, 0.76, 0.77, 0.78, 0.79, 0.8,0.81, 0.8200000000000001, 0.8300000000000001, 0.84, 0.85, 0.86, 0.87, 0.88, 0.89, 0.9, 0.91, 0.92, 0.93,0.9400000000000001, 0.9500000000000001, 0.96, 0.97, 0.98, 0.99]
Y = [4.0, 4.0302, 4.0608, 4.0918, 4.1232, 4.155, 4.1872, 4.2198, 4.2528, 4.2862, 4.32, 4.3542, 4.3888, 4.4238, 4.4592,4.495, 4.5312, 4.5678, 4.6048, 4.6422, 4.68, 4.7181999999999995, 4.7568, 4.7958, 4.8352, 4.875, 4.9152000000000005,4.9558, 4.9968, 5.0382, 5.08, 5.122199999999999, 5.1648, 5.2078, 5.2512, 5.295, 5.3392, 5.3838, 5.4288, 5.4742,5.5200000000000005, 5.5662, 5.6128, 5.6598, 5.7072, 5.755, 5.8032, 5.851800000000001, 5.9008, 5.9502, 6.0, 6.0502,6.1008, 6.1518, 6.203200000000001, 6.255000000000001, 6.3072, 6.3598, 6.4128, 6.4662, 6.52, 6.5742, 6.6288, 6.6838,6.7392, 6.795, 6.8512, 6.9078, 6.9648, 7.022200000000001, 7.08, 7.138199999999999, 7.1968, 7.2558, 7.3152, 7.375,7.4352, 7.4958, 7.5568, 7.6182, 7.680000000000001, 7.7422, 7.8048, 7.867800000000001, 7.9312, 7.994999999999999,8.0592, 8.1238, 8.1888, 8.2542, 8.32, 8.3862, 8.4528, 8.5198, 8.587200000000001, 8.655000000000001, 8.7232, 8.7918,8.8608, 8.9302]# 标签
def func(x):y = w1 * x**2 + w2 * x + w3return y# 损失函数
def loss(y_pre, y_true):return (y_true - y_pre) ** 2# 随机定义 w
w1, w2, w3 = 1, 2, 3
# 学习率
lr = 0.1batch_size = 20
# 训练过程
for epoch in range(500):epoch_loss = 0count = 0grad_w1 = 0grad_w2 = 0grad_w3 = 0for x, y_true in zip(X, Y):count += 1y_pre = func(x)# 本轮loss 总值epoch_loss += loss(y_pre, y_true)# 梯度计算grad_w1 += 2 * (y_pre - y_true) * x ** 2grad_w2 += 2 * (y_pre - y_true) * xgrad_w3 += 2 * (y_pre - y_true)# 更新权重if count == batch_size:count = 0# 权重更新w1 = w1 - lr * grad_w1/batch_size  # sgdw2 = w2 - lr * grad_w2/batch_sizew3 = w3 - lr * grad_w3/batch_size# 本轮结束 计算平均lossepoch_loss /= len(X)print("第%d轮， loss %f" % (epoch, epoch_loss))if epoch_loss < 0.00001:breakprint(f"训练后权重:w1:{w1} w2:{w2} w3:{w3}")
# #使用训练后模型输出预测值
Yp = [func(i) for i in X]
# 预测值与真实值比对数据分布
pyplot.scatter(X, Y, color="red")
pyplot.scatter(X, Yp)
pyplot.show()