pytorch中bilinear的理解

直接参考官方文档，x1和x2是两个输入，A是参数矩阵，如下表达式

但仔细看实现发现这个表达式并不是简单连乘的关系。假设x1(shape是b,n)和x2(shape是b,m)是二维，那么A是个三维tensor(shape是a,n,m)。具体实现时，A先拆成a个(n,m)形状的tensor，x1分别与之矩阵乘后再点乘（公式里的两次乘法），得到了a个(b,m)形状的tensor，然后在axis=1的维度上求和，最终输出成(b,a)的shape，用爱因斯坦表示法就是bn,anm,bm->ba，下面上一下code：

import torch
import torch.nn as nn
import numpy as np

l = torch.ones(2,5)
A = torch.ones(3,5,4)
r = torch.ones(2,4)
print(torch.einsum('bn,anm,bm->ba', l, A, r))
print(torch.nn.functional.bilinear(l,r,A))

x = torch.ones(2,5)
w = torch.ones(3,5)
print(torch.einsum('ij,kj->ik', x,w))
print(torch.nn.functional.linear(x,w))

print('learn nn.Bilinear')
m = nn.Bilinear(5, 4, 3)

output = m(l, r)
print(output.size())
arr_output = output.data.cpu().numpy()

weight = m.weight.data.cpu().numpy()
bias = m.bias.data.cpu().numpy()
x1 = l.data.cpu().numpy()
x2 = r.data.cpu().numpy()
print(x1.shape, weight.shape, x2.shape, bias.shape)
y = np.zeros((x1.shape[0], weight.shape[0]))
for k in range(weight.shape[0]):
    buff = np.dot(x1, weight[k])
    buff = buff * x2
    buff = np.sum(buff, axis=1)
    y[:, k] = buff
y += bias
dif = y - arr_output
print(np.mean(np.abs(dif.flatten())))