【笔记】【B站课程 pytorch】梯度下降模型

训练代码

python 复制代码

import matplotlib.pyplot as plt

x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]
w = 1.0


# 定义y hat
def forward(x):
    return x * w


def cost(xs, ys):
    cost_value = 0
    for x, y in zip(xs, ys):
        y_pred = forward(x)
        cost_value += (y_pred - y) ** 2
    return cost_value / len(xs)


def gradient(xs, ys):
    grad = 0
    for x, y in zip(xs, ys):
        grad += 2 * x * (x * w - y)
    return grad / len(xs)


print('Predict (before training)', 4, forward(4))

# 轮次
epoch_list = []
# 损失值
cost_list = []
for epoch in range(100):
    cost_val = cost(x_data, y_data)
    grad_val = gradient(x_data, y_data)
    w -= 0.05 * grad_val
    print('Epoch:', epoch, 'w=', w, 'loss=', cost_val)
    epoch_list.append(epoch)
    cost_list.append(cost_val)
print('Predict (after training)', 4, forward(4))

训练日志

复制代码

Predict (before training) 4 4.0
Epoch: 0 w= 1.4666666666666668 loss= 4.666666666666667
Epoch: 1 w= 1.7155555555555557 loss= 1.3274074074074067
Epoch: 2 w= 1.8482962962962963 loss= 0.3775736625514398
Epoch: 3 w= 1.9190913580246913 loss= 0.10739873068129853
Epoch: 4 w= 1.9568487242798354 loss= 0.030548972282680543
Epoch: 5 w= 1.976985986282579 loss= 0.008689485449295776
Epoch: 6 w= 1.9877258593507088 loss= 0.0024716758611330204
Epoch: 7 w= 1.9934537916537114 loss= 0.0007030544671667267
Epoch: 8 w= 1.9965086888819794 loss= 0.0001999799373274173
Epoch: 9 w= 1.9981379674037223 loss= 5.688318217313286e-05
Epoch: 10 w= 1.9990069159486519 loss= 1.618010515146993e-05
Epoch: 11 w= 1.9994703551726143 loss= 4.602341020862254e-06
Epoch: 12 w= 1.9997175227587276 loss= 1.3091103348236213e-06
Epoch: 13 w= 1.9998493454713213 loss= 3.723691619052323e-07
Epoch: 14 w= 1.999919650918038 loss= 1.0591833938645004e-07
Epoch: 15 w= 1.999957147156287 loss= 3.0127883203364745e-08
Epoch: 16 w= 1.9999771451500197 loss= 8.569709000094413e-09
Epoch: 17 w= 1.999987810746677 loss= 2.4376061155645925e-09
Epoch: 18 w= 1.9999934990648944 loss= 6.933635173220451e-10
Epoch: 19 w= 1.9999965328346103 loss= 1.9722340048226596e-10
Epoch: 20 w= 1.9999981508451254 loss= 5.609910058542032e-11
Epoch: 21 w= 1.9999990137840669 loss= 1.5957077500436847e-11
Epoch: 22 w= 1.999999474018169 loss= 4.538902045415441e-12
Epoch: 23 w= 1.9999997194763568 loss= 1.2910654708931954e-12
Epoch: 24 w= 1.9999998503873904 loss= 3.6723640039091726e-13
Epoch: 25 w= 1.999999920206608 loss= 1.0445835388749555e-13
Epoch: 26 w= 1.9999999574435243 loss= 2.971259855722779e-14
Epoch: 27 w= 1.9999999773032129 loss= 8.451583569452665e-15
Epoch: 28 w= 1.999999987895047 loss= 2.4040060320624316e-15
Epoch: 29 w= 1.999999993544025 loss= 6.838061337110749e-16
Epoch: 30 w= 1.9999999965568134 loss= 1.9450486402996616e-16
Epoch: 31 w= 1.9999999981636338 loss= 5.532582289380589e-17
Epoch: 32 w= 1.9999999990206048 loss= 1.573712494993027e-17
Epoch: 33 w= 1.9999999994776558 loss= 4.4763367583436385e-18
Epoch: 34 w= 1.9999999997214164 loss= 1.2732695708436325e-18
Epoch: 35 w= 1.9999999998514222 loss= 3.6217462890900584e-19
Epoch: 36 w= 1.9999999999207585 loss= 1.0301831624602159e-19
Epoch: 37 w= 1.9999999999577378 loss= 2.9303006500354953e-20
Epoch: 38 w= 1.9999999999774603 loss= 8.335100760491641e-21
Epoch: 39 w= 1.9999999999879787 loss= 2.3708344012213664e-21
Epoch: 40 w= 1.9999999999935887 loss= 6.743793343241322e-22
Epoch: 41 w= 1.9999999999965807 loss= 1.9182889646896314e-22
Epoch: 42 w= 1.9999999999981763 loss= 5.455821876973161e-23
Epoch: 43 w= 1.9999999999990274 loss= 1.5520779885212614e-23
Epoch: 44 w= 1.9999999999994813 loss= 4.4140317521189105e-24
Epoch: 45 w= 1.9999999999997233 loss= 1.2555468094916013e-24
Epoch: 46 w= 1.9999999999998523 loss= 3.5696409556271286e-25
Epoch: 47 w= 1.9999999999999212 loss= 1.0181467785899592e-25
Epoch: 48 w= 1.999999999999958 loss= 2.896140110957243e-26
Epoch: 49 w= 1.9999999999999776 loss= 8.237499222146303e-27
Epoch: 50 w= 1.999999999999988 loss= 2.357067080993807e-27
Epoch: 51 w= 1.9999999999999936 loss= 6.603423160787553e-28
Epoch: 52 w= 1.9999999999999967 loss= 1.9637706159345563e-28
Epoch: 53 w= 1.9999999999999982 loss= 5.030631731003161e-29
Epoch: 54 w= 1.9999999999999991 loss= 1.4725403564125555e-29
Epoch: 55 w= 1.9999999999999996 loss= 3.681350891031389e-30
Epoch: 56 w= 1.9999999999999998 loss= 1.3805065841367707e-30
Epoch: 57 w= 2.0 loss= 3.4512664603419266e-31
Epoch: 58 w= 2.0 loss= 0.0
Epoch: 59 w= 2.0 loss= 0.0
Epoch: 60 w= 2.0 loss= 0.0
Epoch: 61 w= 2.0 loss= 0.0
Epoch: 62 w= 2.0 loss= 0.0
Epoch: 63 w= 2.0 loss= 0.0
Epoch: 64 w= 2.0 loss= 0.0
Epoch: 65 w= 2.0 loss= 0.0
Epoch: 66 w= 2.0 loss= 0.0
Epoch: 67 w= 2.0 loss= 0.0
Epoch: 68 w= 2.0 loss= 0.0
Epoch: 69 w= 2.0 loss= 0.0
Epoch: 70 w= 2.0 loss= 0.0
Epoch: 71 w= 2.0 loss= 0.0
Epoch: 72 w= 2.0 loss= 0.0
Epoch: 73 w= 2.0 loss= 0.0
Epoch: 74 w= 2.0 loss= 0.0
Epoch: 75 w= 2.0 loss= 0.0
Epoch: 76 w= 2.0 loss= 0.0
Epoch: 77 w= 2.0 loss= 0.0
Epoch: 78 w= 2.0 loss= 0.0
Epoch: 79 w= 2.0 loss= 0.0
Epoch: 80 w= 2.0 loss= 0.0
Epoch: 81 w= 2.0 loss= 0.0
Epoch: 82 w= 2.0 loss= 0.0
Epoch: 83 w= 2.0 loss= 0.0
Epoch: 84 w= 2.0 loss= 0.0
Epoch: 85 w= 2.0 loss= 0.0
Epoch: 86 w= 2.0 loss= 0.0
Epoch: 87 w= 2.0 loss= 0.0
Epoch: 88 w= 2.0 loss= 0.0
Epoch: 89 w= 2.0 loss= 0.0
Epoch: 90 w= 2.0 loss= 0.0
Epoch: 91 w= 2.0 loss= 0.0
Epoch: 92 w= 2.0 loss= 0.0
Epoch: 93 w= 2.0 loss= 0.0
Epoch: 94 w= 2.0 loss= 0.0
Epoch: 95 w= 2.0 loss= 0.0
Epoch: 96 w= 2.0 loss= 0.0
Epoch: 97 w= 2.0 loss= 0.0
Epoch: 98 w= 2.0 loss= 0.0
Epoch: 99 w= 2.0 loss= 0.0
Predict (after training) 4 8.0

分析

假设我们有一个损失函数，我们假定一个w值，我们需要最终达到最优的w值

我们需要不断的更新w值，

在输出的日志中，w为2.0时，损失最小

绘制图表

python 复制代码

# 绘制图表
plt.plot(epoch_list, cost_list)
plt.ylabel('Cost')
plt.xlabel('Epoch')
plt.show()