Python 一维数据的带Logits的TensorFlow S形交叉熵 上下文

假设我们有一些1D数据（例如时间序列），其中所有序列都有固定长度l：

我们想用n个类执行语义分割：

然后，单个示例的输出具有shape

[n，l]

（即

数据格式不是
“channels\u last”
），并且批处理的输出具有shape
[b，n，l]
，其中
b
是批处理中的示例数

这些类是独立的，因此我的理解是，使用sigmoid交叉熵作为损失而不是softmax交叉熵在这里是适用的


问题:
关于
tf.nn.sigmoid\u cross\u entropy\u with\u logits的预期格式和使用，我有几个相关的小问题：

由于网络输出的张量与成批标签的形状相同，我应该在假设网络输出Logit的情况下对网络进行训练，还是采用keras方法（参见keras的
二进制交叉熵
）并假设它输出概率

考虑到1d分割问题，我是否应该调用
tf.nn.sigmoid\u cross\u entropy\u，并启用\u logits
：


data\u format='channels\u first'
（如上所示），或
data\u format='channels\u last'
（示例.T）

如果我想每个频道单独分配标签

传递给优化器的丢失操作应为：


tf.nn.sigmoid\u cross\u entropy\u与logits（标签、logits）
tf.reduce\u mean（tf.nn.sigmoid\u cross\u entropy\u with\u logits（标签、logits））
，或
tf.loss.sigmoid\u cross\u entropy


代码
这突出了我的困惑，并证明了
数据\u格式
实际上很重要…，但文档没有明确说明预期的格式

虚拟数据
tf.缩减平均值（tf.nn）
tf.损失
测试等效性
数据格式等效性
tf.reduce\u mean（tf.nn.sigmoid\u cross\u entropy\u with\u logits（…）
和
tf.loss.sigmoid\u cross\u entropy（…）
（带有默认参数）都在计算相同的东西。问题在于测试中使用
==
比较两个浮点数。相反，使用方法检查两个浮点数是否相等：

# loss _should_(?) be the same for 'channels_first' and 'channels_last' data_format
# test example_1
e1 = np.isclose(l1, t_l1.T).all()
# test example 2
e2 = np.isclose(l2, t_l2.T).all()

# loss calculated for each example and then batched together should be the same 
# as the loss calculated on the batched examples
ea = np.isclose(np.array([l1, l2]), bl).all()
t_ea = np.isclose(np.array([t_l1, t_l2]), t_bl).all()

# loss calculated on the batched examples for 'channels_first' should be the same
# as loss calculated on the batched examples for 'channels_last'
eb = np.isclose(bl, np.transpose(t_bl, (0, 2, 1))).all()


e1, e2, ea, t_ea, eb
# (True, True, True, True, True)

以及：

我想可能会对你有所帮助。@今天我之前读过这个答案，但我仍然不太清楚，因为独立性的维度没有得到明确的证明，而且我在Colab中的结果与该答案所暗示的不同，这是有道理的。。。那么，如果每个类都应该是独立的，那么为什么数据格式不重要呢？还是每个类中的每个项都是独立的？@sumneuro分别计算每个元素的sigomoid和交叉熵损失（这是因为您的假设：每个元素可能属于多个类，因此类是独立的）。因此，
data\u格式
在这里并不重要，只是澄清一下，在sigmoid\u交叉熵损失之前是否应该有激活函数？或者图形应该有两个输出节点？一个是用sigmoid交叉熵计算损失的，另一个是返回输出层的sigmoid？@sumneurn都
tf.nn.sigmoid\u交叉熵\u和
tf.loss.sigmoid\u交叉熵
首先应用sigmoid（这就是为什么他们假定logits为输入），然后计算交叉熵损失。因此，您不应该单独应用乙状结肠。好吧，现在我有点困惑（对此感到抱歉）。我在读马克西姆的答案，他说网络的输出被认为是“逻辑”（而凯拉斯默认假设概率）。如果是这种情况，那么我将输出层传递给sigmoid C.E.以计算损失，但我能否在返回概率的图形中添加另一个输出节点？
          # [ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11]    index            
labeled = [
            [ 0,  1,  1,  0,  0,  0,  0,  0,  0,  0,  0,  0], # class 1
            [ 0,  0,  0,  0,  1,  1,  1,  1,  0,  0,  0,  0], # class 2
            [ 0,  0,  0,  0,  0,  0,  0,  1,  1,  1,  0,  0], # class 3
           #[                     ...                      ],
            [ 1,  1,  1,  0,  0,  0,  0,  0,  1,  1,  1,  1], # class n
 ]

c = 5  # number of channels (label classes)
p = 10 # number of positions ('pixels')


# data_format = 'channels_first', shape = [classes, pixels]
# 'logits' for 2 examples
pred_1 = np.array([[random.random() for v in range(p)]for n in range(c)]).astype(float)
pred_2 = np.array([[random.random() for v in range(p)]for n in range(c)]).astype(float)

# 'ground truth' for the above 2 examples
targ_1 = np.array([[0 if random.random() < 0.8 else 1 for v in range(p)]for n in range(c)]).astype(float)
targ_2 = np.array([[0 if random.random() < 0.8 else 1 for v in range(p)]for n in range(c)]).astype(float)

# batched form of the above examples
preds = np.array([pred_1, pred_2])
targs = np.array([targ_1, targ_2])


# data_format = 'channels_last', shape = [pixels, classes]
t_pred_1 = pred_1.T
t_pred_2 = pred_2.T
t_targ_1 = targ_1.T
t_targ_2 = targ_2.T

t_preds = np.array([t_pred_1, t_pred_2])
t_targs = np.array([t_targ_1, t_targ_2])

# calculate individual losses for 'channels_first'
loss_1 = tf.nn.sigmoid_cross_entropy_with_logits(labels=targ_1, logits=pred_1)
loss_2 = tf.nn.sigmoid_cross_entropy_with_logits(labels=targ_2, logits=pred_2)
# calculate batch loss for 'channels_first'
b_loss = tf.nn.sigmoid_cross_entropy_with_logits(labels=targs, logits=preds)

# calculate individual losses for 'channels_last'
t_loss_1 = tf.nn.sigmoid_cross_entropy_with_logits(labels=t_targ_1, logits=t_pred_1)
t_loss_2 = tf.nn.sigmoid_cross_entropy_with_logits(labels=t_targ_2, logits=t_pred_2)
# calculate batch loss for 'channels_last'
t_b_loss = tf.nn.sigmoid_cross_entropy_with_logits(labels=t_targs, logits=t_preds)
# get actual tensors
with tf.Session() as sess:
  # loss for 'channels_first'
  l1   = sess.run(loss_1)
  l2   = sess.run(loss_2)
  # batch loss for 'channels_first'
  bl   = sess.run(b_loss)

  # loss for 'channels_last'
  t_l1 = sess.run(t_loss_1)
  t_l2 = sess.run(t_loss_2)

  # batch loss for 'channels_last'
  t_bl = sess.run(t_b_loss)

# calculate individual losses for 'channels_first'
rm_loss_1 = tf.reduce_mean(loss_1)
rm_loss_2 = tf.reduce_mean(loss_2)
# calculate batch loss for 'channels_first'
rm_b_loss = tf.reduce_mean(b_loss)

# calculate individual losses for 'channels_last'
rm_t_loss_1 = tf.reduce_mean(t_loss_1)
rm_t_loss_2 = tf.reduce_mean(t_loss_2)
# calculate batch loss for 'channels_last'
rm_t_b_loss = tf.reduce_mean(t_b_loss)
# get actual tensors
with tf.Session() as sess:
  # loss for 'channels_first'
  rm_l1   = sess.run(rm_loss_1)
  rm_l2   = sess.run(rm_loss_2)
  # batch loss for 'channels_first'
  rm_bl   = sess.run(rm_b_loss)

  # loss for 'channels_last'
  rm_t_l1 = sess.run(rm_t_loss_1)
  rm_t_l2 = sess.run(rm_t_loss_2)

  # batch loss for 'channels_last'
  rm_t_bl = sess.run(rm_t_b_loss)

# calculate individual losses for 'channels_first'
tf_loss_1 = tf.losses.sigmoid_cross_entropy(multi_class_labels=targ_1, logits=pred_1)
tf_loss_2 = tf.losses.sigmoid_cross_entropy(multi_class_labels=targ_2, logits=pred_2)
# calculate batch loss for 'channels_first'
tf_b_loss = tf.losses.sigmoid_cross_entropy(multi_class_labels=targs, logits=preds)

# calculate individual losses for 'channels_last'
tf_t_loss_1 = tf.losses.sigmoid_cross_entropy(multi_class_labels=t_targ_1, logits=t_pred_1)
tf_t_loss_2 = tf.losses.sigmoid_cross_entropy(multi_class_labels=t_targ_2, logits=t_pred_2)
# calculate batch loss for 'channels_last'
tf_t_b_loss = tf.losses.sigmoid_cross_entropy(multi_class_labels=t_targs, logits=t_preds)
# get actual tensors
with tf.Session() as sess:
  # loss for 'channels_first'
  tf_l1   = sess.run(tf_loss_1)
  tf_l2   = sess.run(tf_loss_2)
  # batch loss for 'channels_first'
  tf_bl   = sess.run(tf_b_loss)

  # loss for 'channels_last'
  tf_t_l1 = sess.run(tf_t_loss_1)
  tf_t_l2 = sess.run(tf_t_loss_2)

  # batch loss for 'channels_last'
  tf_t_bl = sess.run(tf_t_b_loss)

# loss _should_(?) be the same for 'channels_first' and 'channels_last' data_format
# test example_1
e1 = (l1 == t_l1.T).all()
# test example 2
e2 = (l2 == t_l2.T).all()

# loss calculated for each example and then batched together should be the same 
# as the loss calculated on the batched examples
ea = (np.array([l1, l2]) == bl).all()
t_ea = (np.array([t_l1, t_l2]) == t_bl).all()

# loss calculated on the batched examples for 'channels_first' should be the same
# as loss calculated on the batched examples for 'channels_last'
eb = (bl == np.transpose(t_bl, (0, 2, 1))).all()


e1, e2, ea, t_ea, eb
# (True, False, False, False, True) <- changes every time, so True is happenstance

l_e1 = tf_l1 == rm_l1
l_e2 = tf_l2 == rm_l2
l_eb = tf_bl == rm_bl

l_t_e1 = tf_t_l1 == rm_t_l1
l_t_e2 = tf_t_l2 == rm_t_l2
l_t_eb = tf_t_bl == rm_t_bl

l_e1, l_e2, l_eb, l_t_e1, l_t_e2, l_t_eb
# (False, False, False, False, False, False)

# loss _should_(?) be the same for 'channels_first' and 'channels_last' data_format
# test example_1
e1 = np.isclose(l1, t_l1.T).all()
# test example 2
e2 = np.isclose(l2, t_l2.T).all()

# loss calculated for each example and then batched together should be the same 
# as the loss calculated on the batched examples
ea = np.isclose(np.array([l1, l2]), bl).all()
t_ea = np.isclose(np.array([t_l1, t_l2]), t_bl).all()

# loss calculated on the batched examples for 'channels_first' should be the same
# as loss calculated on the batched examples for 'channels_last'
eb = np.isclose(bl, np.transpose(t_bl, (0, 2, 1))).all()


e1, e2, ea, t_ea, eb
# (True, True, True, True, True)

l_e1 = np.isclose(tf_l1, rm_l1)
l_e2 = np.isclose(tf_l2, rm_l2)
l_eb = np.isclose(tf_bl, rm_bl)

l_t_e1 = np.isclose(tf_t_l1, rm_t_l1)
l_t_e2 = np.isclose(tf_t_l2, rm_t_l2)
l_t_eb = np.isclose(tf_t_bl, rm_t_bl)

l_e1, l_e2, l_eb, l_t_e1, l_t_e2, l_t_eb
# (True, True, True, True, True, True)