一、问题
如何使用Pytorch计算样本张量的基本梯度呢？考虑一个样本数据集，且有两个展示变量，在给定初始权重的基础上，如何在每次迭代中计算梯度呢？
二、如何运行
假设有x_data 和 y_data 列表，计算两个列表需要计算损失函数，一个forward通道以及一个循环中的训练。
forward函数计算权重矩阵和输入张量的乘积。
from torch import FloatTensor
from torch.autograd import Variable ＃ 引入Variable方法是为了计算变量的梯度
a = Variable(FloatTensor([5]))
weights = [Variable(FloatTensor([i]), requires_grad=True) for i in (12, 53, 91, 73)]w1, w2, w3, w4 = weights ＃权重赋值
b = w1 * a
c = w2 * a
d = w3 * b + w4 * c
Loss = (10 - d)
Loss.backward() ＃从loss 开始反向传播for index, weight in enumerate(weights, start=1):gradient, *_ = weight.grad.data ＃取出梯度print(f"Gradient of w{index} w.r.t to Loss: {gradient}")Gradient of w1 w.r.t to Loss: -455.0
Gradient of w2 w.r.t to Loss: -365.0
Gradient of w3 w.r.t to Loss: -60.0
Gradient of w4 w.r.t to Loss: -265.0# 使用forward
def forward(x):return x * w #forwar过程import torch
from torch.autograd import Variable
x_data = [11.0, 22.0, 33.0]
y_data = [21.0, 14.0, 64.0]w = Variable(torch.Tensor([1.0]), requires_grad=True) # 初始化为任意值;# 训练前打印
print("predict (before training)", 4, forward(4).data[0])
# 定义损失函数
def loss(x, y):y_pred = forward(x)return (y_pred - y) * (y_pred - y)
#运行训练循环
for epoch in range(10):for x_val, y_val in zip(x_data, y_data):l = loss(x_val, y_val)l.backward()print("\tgrad: ", x_val, y_val, w.grad.data[0])w.data = w.data - 0.01 * w.grad.data# 训练后，人工设置梯度为０,否则梯度会累加；w.grad.data.zero_()print("progress:", epoch, l.data[0])＃结果
grad: 11.0 21.0 tensor(-220.)
grad: 22.0 14.0 tensor(2481.6001)
grad: 33.0 64.0 tensor(-51303.6484)progress: 0 tensor(604238.8125)
progress: １ …………………………………………
………………………………………………………………………………
＃训练后的预测 权重已更新
print("predict (after training)", 4, forward(4).data[0])＃结果
predict (after training) 4 tensor(-9.2687e+24)
下面的程序展示了如何用Ｖariable 变量从损失函数计算梯度：
a = Variable(FloatTensor([5]))
weights = [Variable(FloatTensor([i]), requires_grad=True) for i in (12, 53, 91, 73)]
w1, w2, w3, w4 = weights
b = w1 * a
c = w2 * a
d = w3 * b + w4 * c
Loss = (10 - d)
Loss.backward()
