pytorch:nn.Softmax()

本篇主要分析softmax函数中的dim参数
首先介绍一下softmax函数：
设 x = [1,2,3]
则softmax（x）= [$\frac{e^1}{e^1+e^2+e^3}$ ,$\frac{e^2}{e^1+e^2+e^3}$ ,$\frac{e^3}{e^1+e^2+e^3}$]

接下来分析torch.nn里面的softmax函数

y = torch.rand(size=[2,2,3])
print(y)
#y的size是2,2,3。可以看成有两张表，每张表2行3列

tensor([[[0.7536, 0.2712, 0.4176],
         [0.2008, 0.9512, 0.4904]],

        [[0.2232, 0.7459, 0.9858],
         [0.9141, 0.0604, 0.4307]]])

net_1 = nn.Softmax(dim=0)
net_2 = nn.Softmax(dim=1)
net_3 = nn.Softmax(dim=2)
print('dim=0的结果是：\n',net_1(y),"\n")
print('dim=1的结果是：\n',net_2(y),"\n")
print('dim=2的结果是：\n',net_3(y),"\n")

dim=0的结果是：
 tensor([[[0.6296, 0.3835, 0.3617],
         [0.3289, 0.7091, 0.5149]],

        [[0.3704, 0.6165, 0.6383],
         [0.6711, 0.2909, 0.4851]]]) 

dim=1的结果是：
 tensor([[[0.6348, 0.3363, 0.4818],
         [0.3652, 0.6637, 0.5182]],

        [[0.3338, 0.6650, 0.6353],
         [0.6662, 0.3350, 0.3647]]]) 

dim=2的结果是：
 tensor([[[0.4288, 0.2647, 0.3065],
         [0.2245, 0.4755, 0.3000]],

        [[0.2070, 0.3492, 0.4438],
         [0.4896, 0.2085, 0.3019]]]) 

dim = 0:

dim=0的结果是：
 tensor([[[0.6296, 0.3835, 0.3617],
         [0.3289, 0.7091, 0.5149]],

        [[0.3704, 0.6165, 0.6383],
         [0.6711, 0.2909, 0.4851]]]) 

dim = 0指第一个维度，在本例中第一个维度的size是2，如前文所说，我们把“2”看成是两张表，那么0.6296、0.3704是怎么来的呢？
这两张表中的数分别是：

for i in range(2):
    print(y[i,:,:].reshape(-1))

tensor([0.7536, 0.2712, 0.4176, 0.2008, 0.9512, 0.4904])
tensor([0.2232, 0.7459, 0.9858, 0.9141, 0.0604, 0.4307])

$$0.6296\approx \frac{e^{0.7536}}{e^{0.7536}+e^{0.2232}}$$

$$0.3704\approx \frac{e^{0.2232}}{e^{0.7536}+e^{0.2232}}$$
$$0.6296+0.3704=1$$

likewise：
$$0.3289\approx \frac{e^{0.2008}}{e^{0.2008}+e^{0.9141}}$$

$$0.6711\approx \frac{e^{0.9141}}{e^{0.2008}+e^{0.9141}}$$
$$0.3289+0.6711=1$$

dim = 1:

dim=1的结果是：
 tensor([[[0.6348, 0.3363, 0.4818],
         [0.3652, 0.6637, 0.5182]],

        [[0.3338, 0.6650, 0.6353],
         [0.6662, 0.3350, 0.3647]]]) 

dim = 1指第二个维度，在本例中第二个维度的size是2，即我们可以把原始数据中的所有数看成是2行数组成的。
这两行的数分别是：

for i in range(2):
    print(y[:,i,:].reshape(-1))

tensor([0.7536, 0.2712, 0.4176, 0.2232, 0.7459, 0.9858])
tensor([0.2008, 0.9512, 0.4904, 0.9141, 0.0604, 0.4307])

$$0.6348\approx \frac{e^{0.7536}}{e^{0.7536}+e^{0.2008}}$$

$$0.3652\approx \frac{e^{0.2008}}{e^{0.7536}+e^{0.2008}}$$
$$0.6348+0.3652=1$$

dim = 2:

dim=2的结果是：
 tensor([[[0.4288, 0.2647, 0.3065],
         [0.2245, 0.4755, 0.3000]],

        [[0.2070, 0.3492, 0.4438],
         [0.4896, 0.2085, 0.3019]]]) 

dim = 2指第三个维度，在本例中第三个维度的size是3，即我们可以把原始数据中的所有数看成是3列数组成的。
这3列数分别是：

for i in range(3):
    print(y[:,:,i].reshape(-1))

tensor([0.7536, 0.2008, 0.2232, 0.9141])
tensor([0.2712, 0.9512, 0.7459, 0.0604])
tensor([0.4176, 0.4904, 0.9858, 0.4307])

$$0.4288\approx \frac{e^{0.7536}}{e^{0.7536}+e^{0.2712}+e^{0.4176}}$$
$$0.2647\approx \frac{e^{0.2712}}{e^{0.7536}+e^{0.2712}+e^{0.4176}}$$
$$0.3065\approx \frac{e^{0.4176}}{e^{0.7536}+e^{0.2712}+e^{0.4176}}$$
$$0.4288+0.2647+0.3065=1$$