nn.Linear
nn.Linear —— 全连接层本质
nn.Linear(in_features, out_features)
fc = nn.Linear(4, 3)
含义：
输入: 4维向量
输出: 3维向量
数学公式：y = x @ weight.T + bias
其中：
x shape = (batch, in_features)
batch = 5
in_features = 4
那么 x shape = (5, 4)
可以理解为： 5个样本， 每个样本4个特征
x =
[1 2 3 4]
[5 6 7 8]
[9 1 2 3]
[4 5 6 7]
[8 9 1 2]
weight shape = (out_features, in_features)
out_features = 3
in_features = 4
那么： weight shape = (3, 4)
表示： 3个神经元， 每个神经元有4个权重
weight =
[w11 w12 w13 w14]
[w21 w22 w23 w24]
[w31 w32 w33 w34]
weight.T
为什么要转置 weight.T？
因为矩阵乘法规则：
(batch, in_features)@(in_features, out_features)=(batch, out_features)
但 weight 存储为：
(out_features, in_features)
所以需要转置：
转置规则：
行 → 列
列 → 行weight.T shape = (in_features, out_features)
b shape = (out_features)
bias shape = (3,)
例如： bias = [b1 b2 b3]
y shape = (batch, out_features)
y shape = (5,3)
表示： 5个样本，每个样本输出3个特征
完整数值例子
x shape = (2, 4)
x =
[1 2 3 4]
[5 6 7 8]weight shape = (3, 4)
weight =
[1 0 0 0]
[0 1 0 0]
[0 0 1 0]weight.T =
[1 0 0]
[0 1 0]
[0 0 1]
[0 0 0]
计算 y = x @ weight.T
y =
[1 2 3]
[5 6 7]
神经元角度理解
一个神经元：
y1 = w11x1 + w12x2 + w13x3 + w14x4 + b1
第二个神经元：
y2 = w21x1 + w22x2 + w23x3 + w24x4 + b2
第三个神经元：
y3 = w31x1 + w32x2 + w33x3 + w34x4 + b3
