深度学习核对矩阵的维数对w权重矩阵的维数的计算

墨蓝 2024-03-16 11:09 53阅读 0赞

![57c77894fac447faa062b7766d2f5927.png][]

(n,m)：n为神经节点数，m为样本数

由上图我们可以设几个例子：

已知：

![z ^\{\[1\]\} =w ^\{\[1\]\} x+b ^\{\[1\]\}][z _1_ _w _1_ x_b _1]

![z ^\{\[1\]\}:(3,1),x:(2,1),b^\{\[1\]\}: ( 3 , 1 )][z _1_3_1_x_2_1_b_1_ _ 3 _ 1]

可知：![w^\{\[1\]\}:(3,2)][w_1_3_2]

x可以看做是a^\[0\]

已知：

![z ^\{\[2\]\} =w ^\{\[2\]\} a^\{\[1\]\}+b ^\{\[2\]\}][z _2_ _w _2_ a_1_b _2]

![z ^\{\[2\]\}:(5,1),a^\{\[2\]\}:(3,1),b^\{\[1\]\}: ( 5 , 1 )][z _2_5_1_a_2_3_1_b_1_ _ 5 _ 1]

可知：![w^\{\[2\]\}:(5,3)][w_2_5_3]

分析第一个例子，由行列矩阵相乘理解因为z是(3,1)的，而x是(2,1)的，要变成z(3,1)，w只能是(3,2)。

因此可得结论(建议直接记) ：

![z ^\{\[l\]\} ,a ^\{\[l\]\},b ^\{\[l\]\}:(n^\{\[l\]\},1)][z _l_ _a _l_b _l_n_l_1]

![w^\{\[l\]\} :(n^\{\[l\]\},n^\{\[l-1\]\})][w_l_ _n_l_n_l-1]

![dw^\{\[l\]\} :(n^\{\[l\]\},n^\{\[l-1\]\})][dw_l_ _n_l_n_l-1]

![db ^\{\[l\]\}:(n^\{\[l\]\},1)][db _l_n_l_1]

[57c77894fac447faa062b7766d2f5927.png]: https://image.dandelioncloud.cn/pgy_files/images/2024/03/16/fc1c70ca38fc405a99d4bb3f74d735ed.png
[z _1_ _w _1_ x_b _1]: https://latex.csdn.net/eq?z%20%5E%7B%5B1%5D%7D%20%3Dw%20%5E%7B%5B1%5D%7D%20x&plus;b%20%5E%7B%5B1%5D%7D
[z _1_3_1_x_2_1_b_1_ _ 3 _ 1]: https://latex.csdn.net/eq?z%20%5E%7B%5B1%5D%7D%3A%283%2C1%29%2Cx%3A%282%2C1%29%2Cb%5E%7B%5B1%5D%7D%3A%20%28%203%20%2C%201%20%29
[w_1_3_2]: https://latex.csdn.net/eq?w%5E%7B%5B1%5D%7D%3A%283%2C2%29
[z _2_ _w _2_ a_1_b _2]: https://latex.csdn.net/eq?z%20%5E%7B%5B2%5D%7D%20%3Dw%20%5E%7B%5B2%5D%7D%20a%5E%7B%5B1%5D%7D&plus;b%20%5E%7B%5B2%5D%7D
[z _2_5_1_a_2_3_1_b_1_ _ 5 _ 1]: https://latex.csdn.net/eq?z%20%5E%7B%5B2%5D%7D%3A%285%2C1%29%2Ca%5E%7B%5B2%5D%7D%3A%283%2C1%29%2Cb%5E%7B%5B1%5D%7D%3A%20%28%205%20%2C%201%20%29
[w_2_5_3]: https://latex.csdn.net/eq?w%5E%7B%5B2%5D%7D%3A%285%2C3%29
[z _l_ _a _l_b _l_n_l_1]: https://latex.csdn.net/eq?z%20%5E%7B%5Bl%5D%7D%20%2Ca%20%5E%7B%5Bl%5D%7D%2Cb%20%5E%7B%5Bl%5D%7D%3A%28n%5E%7B%5Bl%5D%7D%2C1%29
[w_l_ _n_l_n_l-1]: https://latex.csdn.net/eq?w%5E%7B%5Bl%5D%7D%20%3A%28n%5E%7B%5Bl%5D%7D%2Cn%5E%7B%5Bl-1%5D%7D%29
[dw_l_ _n_l_n_l-1]: https://latex.csdn.net/eq?dw%5E%7B%5Bl%5D%7D%20%3A%28n%5E%7B%5Bl%5D%7D%2Cn%5E%7B%5Bl-1%5D%7D%29
[db _l_n_l_1]: https://latex.csdn.net/eq?db%20%5E%7B%5Bl%5D%7D%3A%28n%5E%7B%5Bl%5D%7D%2C1%29