pytorch中torch.einsum函数的详细计算过程图解

第一次见到 rel_h = torch.einsum("bhwc,hkc->bhwk", r_q, Rh)这行代码时，属实是懵了，网上找了很多博主的介绍，但都没有详细的说明函数内部的计算过程，看得我是一头雾水，只知道计算结果的维度是如何变化的，却不明白函数内部是如何计算的。话不多说，直接上示例代码

示例代码

import torch
r_q = torch.tensor([[[[1, 2, 3, 4, 5],
                      [6, 7, 8, 9, 10],
                      [11, 12, 13, 14, 15],
                      [16, 17, 18, 19, 20]],
                     [[21, 22, 23, 24, 25],
                      [26, 27, 28, 29, 30],
                      [31, 32, 33, 34, 35],
                      [36, 37, 38, 39, 40]],
                     [[41, 42, 43, 44, 45],
                      [46, 47, 48, 49, 50],
                      [51, 52, 53, 54, 55],
                      [56, 57, 58, 59, 60]]]])

Rh = torch.tensor([[[1, 2, 3, 4, 5,],
                      [7, 8, 9, 10, 11, ],
                      [13, 14, 15, 16, 17, ],
                      [19, 20, 21, 22, 23, ],
                        [1, 2, 3, 4, 5,],
                    [1, 2, 3, 4, 5,],],
                     [[25, 26, 27, 28, 29, ],
                      [31, 32, 33, 34, 35, ],
                      [37, 38, 39, 40, 41, ],
                      [43, 44, 45, 46, 47, ],
                      [1, 2, 3, 4, 5,],
                      [1, 2, 3, 4, 5,],],
                     [[49, 50, 51, 52, 53, ],
                      [55, 56, 57, 58, 59, ],
                      [61, 62, 63, 64, 65, ],
                      [67, 68, 69, 70, 71, ],
                      [1, 2, 3, 4, 5,],
                      [1, 2, 3, 4, 5,],]])

rel_h = torch.einsum("bhwc,hkc->bhwk", r_q, Rh)
print(rel_h)

输出结果：

结果解释

文字很难解释清楚，直接上图。r_q的维度为(1, 3, 4, 5)， Rh的维度为(3, 6, 5)，函数torch.einsum("bhwc,hkc->bhwk", r_q, Rh)中b=1, h=3, w=4, c=5。所以最终结果Rel_h的维度为bhwk，即(1, 3, 4, 5)。具体计算过程如下图。

这回看懂了吧。还不理解的或者讲的不对的地方，欢迎在评论区留言。创作不易，喜欢的话点个关注吧