张量乘规则与代码

import tensorflow as tf
import numpy as np

t=4*64*20

feats = np.ones((t)).reshape((4,64,20))

g = tf.Graph()
device_t='/gpu:0'
soft_config = tf.compat.v1.ConfigProto(allow_soft_placement=True)
soft_config.gpu_options.allow_growth = True
with g.as_default(), g.device(device_t), \
    tf.compat.v1.Session(config=soft_config) as sess:
    feats_T = tf.transpose(a=feats, perm=[0,2,1])
    print(feats_T.shape)
    print(feats.shape)
    grams = tf.matmul(feats_T, feats) 
    print(grams.shape)

(4, 20, 64)
(4, 64, 20)
(4, 20, 20)

import tensorflow as tf
import numpy as np

t=4*64*20*16

t1 = 64*20

feats = np.ones((t)).reshape((4,t1,16))

g = tf.Graph()
device_t='/gpu:0'
soft_config = tf.compat.v1.ConfigProto(allow_soft_placement=True)
soft_config.gpu_options.allow_growth = True
with g.as_default(), g.device(device_t), \
    tf.compat.v1.Session(config=soft_config) as sess:
    feats_T = tf.transpose(a=feats, perm=[0,2,1])
    print(feats_T.shape)
    print(feats.shape)
    grams = tf.matmul(feats_T, feats) 
    print(grams.shape)

(4, 16, 1280)
(4, 1280, 16)
(4, 16, 16)

grams = np.ones((4*16*16)).reshape((4,16,16))
grams_1 = np.ones((16*16)).reshape((16,16))

g = tf.Graph()
device_t='/gpu:0'
soft_config = tf.compat.v1.ConfigProto(allow_soft_placement=True)
soft_config.gpu_options.allow_growth = True
with g.as_default(), g.device(device_t), \
    tf.compat.v1.Session(config=soft_config) as sess:
    grams = tf.reshape(grams,(4,16,16))
    loss = grams - grams_1
    loss1 = tf.nn.l2_loss(grams - grams_1)
    print(loss.shape)
    print(sess.run(loss))
    print(sess.run(loss1))

[[[0. 0. 0. ... 0. 0. 0.]
  [0. 0. 0. ... 0. 0. 0.]
  [0. 0. 0. ... 0. 0. 0.]
  ...
  [0. 0. 0. ... 0. 0. 0.]
  [0. 0. 0. ... 0. 0. 0.]
  [0. 0. 0. ... 0. 0. 0.]]

 [[0. 0. 0. ... 0. 0. 0.]
  [0. 0. 0. ... 0. 0. 0.]
  [0. 0. 0. ... 0. 0. 0.]
  ...
  [0. 0. 0. ... 0. 0. 0.]
  [0. 0. 0. ... 0. 0. 0.]
  [0. 0. 0. ... 0. 0. 0.]]

 [[0. 0. 0. ... 0. 0. 0.]
  [0. 0. 0. ... 0. 0. 0.]
  [0. 0. 0. ... 0. 0. 0.]
  ...
  [0. 0. 0. ... 0. 0. 0.]
  [0. 0. 0. ... 0. 0. 0.]
  [0. 0. 0. ... 0. 0. 0.]]

 [[0. 0. 0. ... 0. 0. 0.]
  [0. 0. 0. ... 0. 0. 0.]
  [0. 0. 0. ... 0. 0. 0.]
  ...
  [0. 0. 0. ... 0. 0. 0.]
  [0. 0. 0. ... 0. 0. 0.]
  [0. 0. 0. ... 0. 0. 0.]]]
0.0

可见上面计算发生了广播。

grams = np.ones((4*16*16)).reshape((4,16,16))
grams_1 = np.ones((4*16*16)).reshape((4,16,16))

g = tf.Graph()
device_t='/gpu:0'
soft_config = tf.compat.v1.ConfigProto(allow_soft_placement=True)
soft_config.gpu_options.allow_growth = True
with g.as_default(), g.device(device_t), \
    tf.compat.v1.Session(config=soft_config) as sess:
    grams = tf.reshape(grams,(4,16,16))
    loss = grams - grams_1
    loss1 = tf.nn.l2_loss(grams - grams_1)
    print(loss.shape)
    print(sess.run(loss))
    print(sess.run(loss1))

计算结果一样。