输出的梯度w.r.t网络权重，保持另一个输出常量

Question

我们假设我有一个简单的MLP

我有一个关于输出层的一些损失函数的梯度来得到G = [0，-1]（也就是说，增加第二个输出变量会减少损失函数）。

如果我根据我的网络参数采用G的渐变并应用渐变体面的权重更新，则第二个输出变量应该增加，但是没有关于第一个输出变量的说法，并且渐变的缩放应用几乎肯定会更改输出变量（无论是增加还是减少它）

如何修改损失函数或任何渐变计算，以确保第一个输出不会改变？

Answer 1

更新：我误解了这个问题。这是新的答案。

为此，您需要仅更新隐藏层和第二个输出单元之间的连接，同时保持隐藏层和第一个输出单元之间的连接完好无损。

第一种方法是引入两组变量：一组用于隐藏层和第一个输出单元之间的连接，另一组用于其余部分。然后，您可以使用tf.stack组合它们，并传递var_list以获取相应的衍生物。它就像（仅用于说明。未经测试。小心使用）：

out1 = tf.matmul(hidden, W_h_to_out1) + b_h_to_out1
out2 = tf.matmul(hidden, W_h_to_out2) + b_h_to_out2
out = tf.stack([out1, out2])
out = tf.transpose(tf.reshape(out, [2, -1]))
loss = some_function_of(out)
optimizer = tf.train.GradientDescentOptimizer(0.1)
train_op_second_unit = optimizer.minimize(loss, var_list=[W_h_to_out2, b_h_to_out2])

另一种方法是使用掩码。当你使用某些框架（比如苗条，Keras等）时，这更容易实现和更灵活，我会推荐这种方式。将第一个输出单元隐藏到损失功能的想法，同时不更改第二个输出单元。 这可以使用二进制变量来完成：如果你想保留它，可以乘以1，然后将它乘以0来删除它。这是代码：

import tensorflow as tf
import numpy as np

# let's make our tiny dataset: (x, y) pairs, where x = (x1, x2, x3), y = (y1, y2),
# and y1 = x1+x2+x3, y2 = x1^2+x2^2+x3^2

# n_sample data points
n_sample = 8
data_x = np.random.random((n_sample, 3))
data_y = np.zeros((n_sample, 2))
data_y[:, 0] += np.sum(data_x, axis=1)
data_y[:, 1] += np.sum(data_x**2, axis=1)
data_y += 0.01 * np.random.random((n_sample, 2))  # add some noise


# build graph
# suppose we have a network of shape [3, 4, 2], i.e.: one hidden layer of size 4.

x = tf.placeholder(tf.float32, shape=[None, 3], name='x')
y = tf.placeholder(tf.float32, shape=[None, 2], name='y')
mask = tf.placeholder(tf.float32, shape=[None, 2], name='mask')

W1 = tf.Variable(tf.random_normal(shape=[3, 4], stddev=0.1), name='W1')
b1 = tf.Variable(tf.random_normal(shape=[4], stddev=0.1), name='b1')
hidden = tf.nn.sigmoid(tf.matmul(x, W1) + b1)
W2 = tf.Variable(tf.random_normal(shape=[4, 2], stddev=0.1), name='W2')
b2 = tf.Variable(tf.random_normal(shape=[2], stddev=0.1), name='b2')
out = tf.matmul(hidden, W2) + b2
loss = tf.reduce_mean(tf.square(out - y))

# multiply out by mask, thus out[0] is "invisible" to loss, and its gradient will not be propagated
masked_out = mask * out
loss2 = tf.reduce_mean(tf.square(masked_out - y))

optimizer = tf.train.GradientDescentOptimizer(0.1)
train_op_all = optimizer.minimize(loss)  # update all variables in the network
train_op12 = optimizer.minimize(loss, var_list=[W2, b2])  # update hidden -> output layer
train_op2 = optimizer.minimize(loss2, var_list=[W2, b2])  # update hidden -> second output unit


sess = tf.InteractiveSession()
sess.run(tf.global_variables_initializer())
mask_out1 = np.zeros((n_sample, 2))
mask_out1[:, 1] += 1.0
# print(mask_out1)
print(sess.run([hidden, out, loss, loss2], feed_dict={x: data_x, y: data_y, mask: mask_out1}))

# In this case, only out2 is updated. You see the loss and loss2 decreases.
sess.run(train_op2, feed_dict={x: data_x, y:data_y, mask: mask_out1})
print(sess.run([hidden, out, loss, loss2], feed_dict={x: data_x, y:data_y, mask: mask_out1}))

# In this case, both out1 and out2 is updated. You see the loss and loss2 decreases.
sess.run(train_op12, feed_dict={x: data_x, y:data_y, mask: mask_out1})
print(sess.run([hidden, out, loss, loss2], feed_dict={x: data_x, y:data_y, mask: mask_out1}))

# In this case, everything is updated. You see the loss and loss2 decreases.
sess.run(train_op_all, feed_dict={x: data_x, y:data_y, mask: mask_out1})
print(sess.run([hidden, out, loss, loss2], feed_dict={x: data_x, y:data_y, mask: mask_out1}))
sess.close()

=======================以下是旧答案=================== ===========

获得衍生品w.r.t.不同的变量，您可以传递var_list来决定要更新的变量。这是一个例子：

import tensorflow as tf
import numpy as np

# let's make our tiny dataset: (x, y) pairs, where x = (x1, x2, x3), y = (y1, y2),
# and y1 = x1+x2+x3, y2 = x1^2+x2^2+x3^2

# n_sample data points
n_sample = 8
data_x = np.random.random((n_sample, 3))
data_y = np.zeros((n_sample, 2))
data_y[:, 0] += np.sum(data_x, axis=1)
data_y[:, 1] += np.sum(data_x**2, axis=1)
data_y += 0.01 * np.random.random((n_sample, 2))  # add some noise


# build graph
# suppose we have a network of shape [3, 4, 2], i.e.: one hidden layer of size 4.

x = tf.placeholder(tf.float32, shape=[None, 3], name='x')
y = tf.placeholder(tf.float32, shape=[None, 2], name='y')

W1 = tf.Variable(tf.random_normal(shape=[3, 4], stddev=0.1), name='W1')
b1 = tf.Variable(tf.random_normal(shape=[4], stddev=0.1), name='b1')
hidden = tf.nn.sigmoid(tf.matmul(x, W1) + b1)
W2 = tf.Variable(tf.random_normal(shape=[4, 2], stddev=0.1), name='W2')
b2 = tf.Variable(tf.random_normal(shape=[2], stddev=0.1), name='b2')
out = tf.matmul(hidden, W2) + b2

loss = tf.reduce_mean(tf.square(out - y))
optimizer = tf.train.GradientDescentOptimizer(0.1)
# You can pass a variable list to decide which variable(s) to minimize.
train_op_second_layer = optimizer.minimize(loss, var_list=[W2, b2])
# If there is no var_list, all variables will be updated.
train_op_all = optimizer.minimize(loss)

sess = tf.InteractiveSession()
sess.run(tf.global_variables_initializer())
print(sess.run([W1, b1, W2, b2, loss], feed_dict={x: data_x, y:data_y}))

# In this case, only W2 and b2 are updated. You see the loss decreases.
sess.run(train_op_second_layer, feed_dict={x: data_x, y:data_y})
print(sess.run([W1, b1, W2, b2, loss], feed_dict={x: data_x, y:data_y}))

# In this case, all variables are updated. You see the loss decreases.
sess.run(train_op_all, feed_dict={x: data_x, y:data_y})
print(sess.run([W1, b1, W2, b2, loss], feed_dict={x: data_x, y:data_y}))
sess.close()