理解keras中的K.batch_dot和TensorFlow的tf.matmul

概述

在使用keras中的keras.backend.batch_dot和tf.matmul实现功能其实是一样的智能矩阵乘法，比如$A,B,C,D,E,F,G,H，I, J,K,L$A,B,C,D,E,F,G,H，I,J,K,L都是二维矩阵，中间点表示矩阵乘法，$AG$AG表示矩阵$A$A和$G$G矩阵乘法（$A$A的列维度等于$G$G行维度），$WX=Z$WX=Z

import keras.backend as K
import tensorflow as tf
import numpy as np

w = K.variable(np.random.randint(10,size=(10,12,4,5)))
k = K.variable(np.random.randint(10,size=(10,12,5,8)))
z = K.batch_dot(w,k)
print(z.shape) #(10, 12, 4, 8)

import keras.backend as K
import tensorflow as tf
import numpy as np

w = tf.Variable(np.random.randint(10,size=(10,12,4,5)),dtype=tf.float32)
k = tf.Variable(np.random.randint(10,size=(10,12,5,8)),dtype=tf.float32)
z = tf.matmul(w,k)
print(z.shape) #(10, 12, 4, 8)

示例

from keras import backend as K
a = K.ones((3,4,5,2))
b = K.ones((2,5,3,7))
c = K.dot(a, b)
print(c.shape)

会输出：
ValueError: Dimensions must be equal, but are 2 and 3 for ‘MatMul’ (op: ‘MatMul’) with input shapes: [60,2], [3,70].

from keras import backend as K
a = K.ones((3,4))
b = K.ones((4,5))
c = K.dot(a, b)
print(c.shape)#(3,5)

或者

import tensorflow as tf
a = tf.ones((3,4))
b = tf.ones((4,5))
c = tf.matmul(a, b)
print(c.shape)#(3,5)

如果增加维度：

from keras import backend as K
a = K.ones((2,3,4))
b = K.ones((7,4,5))
c = K.dot(a, b)
print(c.shape)#(2, 3, 7, 5)

这个矩阵乘法会沿着两个矩阵最后两个维度进行乘法，不是element-wise矩阵乘法

from keras import backend as K
a = K.ones((1, 2, 3 , 4))
b = K.ones((8, 7, 4, 5))
c = K.dot(a, b)
print(c.shape)#(1, 2, 3, 8, 7, 5)

$c_{a,b,c,i,j,k}=\sum_rw_{a,b,c,r}x_{i,j,r,k}$ca,b,c,i,j,k​=∑r​wa,b,c,r​xi,j,r,k​

keras的dot方法是Theano中的复制

from keras import backend as K
a = K.ones((1, 2, 4))
b = K.ones((8, 7, 4, 5))
c = K.dot(a, b)
print(c.shape)# (1, 2, 8, 7, 5).

from keras import backend as K
a = K.ones((9, 8, 7, 4, 2))
b = K.ones((9, 8, 7, 2, 5))
c = K.batch_dot(a, b)
print(c.shape) #(9, 8, 7, 4, 5)

或者

import tensorflow as tf
a = tf.ones((9, 8, 7, 4, 2))
b = tf.ones((9, 8, 7, 2, 5))
c = tf.matmul(a, b)
print(c.shape) #(9, 8, 7, 4, 5)

参考

[1]: tf.keras.backend.batch_dot函数
[2]: keras batch_dot
[3]: Understand batch matrix multiplication
[4]: batch_dot