python - 将 tensorflow 梯度应用于特定输入

Question

我正在尝试根据 keras 模型中的特定输入特征为某些输出变量创建雅可比矩阵。例如，如果我有一个具有 100 个输入特征和 10 个输出变量的模型，并且我想创建输出 2、3 和 4 相对于输出 50-70 的雅可比行列式，我可以像这样创建雅可比行列式:

from keras.models import Model
from keras.layers import Dense, Input
import tensorflow as tf
import keras.backend as K
import numpy as np

input_ = Input(shape=(100,))
output_ = Dense(10)(input_)

model = Model(input_,output_)

x_indices = np.arange(50,70)
y_indices = [2,3,4]

y_list = tf.unstack(model.output[0])

x = np.random.random((1,100))

jacobian_matrix = []
for i in y_indices:
    J = tf.gradients(y_list[i], model.input)
    jacobian_func = K.function([model.input, K.learning_phase()], J)
    jac = jacobian_func([x, False])[0][0,x_indices]
    jacobian_matrix.append(jac)
jacobian_matrix = np.array(jacobian_matrix)

但是对于更复杂的模型，这非常慢。我只想根据感兴趣的输入创建上面的雅可比函数。我尝试过这样的事情:

from keras.models import Model
from keras.layers import Dense, Input
import tensorflow as tf
import keras.backend as K
import numpy as np

input_ = Input(shape=(100,))
output_ = Dense(10)(input_)

model = Model(input_,output_)

x_indices = np.arange(50,60)
y_indices = [2,3,4]

y_list = tf.unstack(model.output[0])
x_list = tf.unstack(model.input[0])

x = np.random.random((1,100))

jacobian_matrix = []
for i in y_indices:
    jacobian_row = []
    for j in x_indices:
        J = tf.gradients(y_list[i], x_list[j])
        jacobian_func = K.function([model.input, K.learning_phase()], J)
        jac = jacobian_func([x, False])[0][0,:]
        jacobian_row.append(jac)
    jacobian_matrix.append(jacobian_row)

jacobian_matrix = np.array(jacobian_matrix)

并得到错误:

TypeErrorTraceback (most recent call last)
<ipython-input-33-d0d524ad0e40> in <module>()
     23     for j in x_indices:
     24         J = tf.gradients(y_list[i], x_list[j])
---> 25         jacobian_func = K.function([model.input, K.learning_phase()], J)
     26         jac = jacobian_func([x, False])[0][0,:]
     27         jacobian_row.append(jac)

/opt/conda/lib/python2.7/site-packages/keras/backend/tensorflow_backend.pyc in function(inputs, outputs, updates, **kwargs)
   2500                 msg = 'Invalid argument "%s" passed to K.function with TensorFlow backend' % key
   2501                 raise ValueError(msg)
-> 2502     return Function(inputs, outputs, updates=updates, **kwargs)
   2503 
   2504 

/opt/conda/lib/python2.7/site-packages/keras/backend/tensorflow_backend.pyc in __init__(self, inputs, outputs, updates, name, **session_kwargs)
   2443         self.inputs = list(inputs)
   2444         self.outputs = list(outputs)
-> 2445         with tf.control_dependencies(self.outputs):
   2446             updates_ops = []
   2447             for update in updates:

/opt/conda/lib/python2.7/site-packages/tensorflow/python/framework/ops.pyc in control_dependencies(control_inputs)
   4302   """
   4303   if context.in_graph_mode():
-> 4304     return get_default_graph().control_dependencies(control_inputs)
   4305   else:
   4306     return _NullContextmanager()

/opt/conda/lib/python2.7/site-packages/tensorflow/python/framework/ops.pyc in control_dependencies(self, control_inputs)
   4015       if isinstance(c, IndexedSlices):
   4016         c = c.op
-> 4017       c = self.as_graph_element(c)
   4018       if isinstance(c, Tensor):
   4019         c = c.op

/opt/conda/lib/python2.7/site-packages/tensorflow/python/framework/ops.pyc in as_graph_element(self, obj, allow_tensor, allow_operation)
   3033 
   3034     with self._lock:
-> 3035       return self._as_graph_element_locked(obj, allow_tensor, allow_operation)
   3036 
   3037   def _as_graph_element_locked(self, obj, allow_tensor, allow_operation):

/opt/conda/lib/python2.7/site-packages/tensorflow/python/framework/ops.pyc in _as_graph_element_locked(self, obj, allow_tensor, allow_operation)
   3122       # We give up!
   3123       raise TypeError("Can not convert a %s into a %s." % (type(obj).__name__,
-> 3124                                                            types_str))
   3125 
   3126   def get_operations(self):

TypeError: Can not convert a NoneType into a Tensor or Operation.

有什么想法吗？谢谢。

Answer 1

问题出在行 J = tf.gradients(y_list[i], x_list[j]) 上。 x_list[j] 派生自 model.input[0]，但没有从 x_list[j] 到 model 的定向路径.output[0]。您需要取消堆叠模型输入，重新堆叠然后运行模型，或者创建相对于整个输入的导数，然后仅选择其中的第 j 行。

第一种方式:

inputs = tf.keras.Inputs((100,))
uninteresting, interesting, more_uninteresting = tf.split(inputs, [50, 10, 40], axis=1)
inputs = tf.concat([uninteresting, interesting, more_uninteresting], axis=1)
model = Model(inputs)
...
J, = tf.gradients(y_list[i], interesting)

第二种方式:

J, = tf.gradients(y_list[i], model.input[0])
J = J[:, 50:60]

话虽如此，对于大量 y 索引来说，这仍然会很慢，所以我强烈鼓励您绝对确定您需要雅可比行列式本身(而不是，对于例如，雅可比向量乘积的结果)。