我正在尝试为keras模型中的特定输入要素创建某些输出可变量的雅可比矩阵。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，并且我想创建一个关于输出50-70的输出2,3和4的雅可比行列式，我可以像这样创建雅可比：
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)
但是使用更复杂的模型，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？感谢。
答案 0 :(得分：1)
问题在于行J = tf.gradients(y_list[i], x_list[j])。 x_list[j]源自model.input[0]，但没有从x_list[j]到model.output[0]的定向路径。您需要取消堆叠模型输入，重新堆叠然后运行模型，或者创建与整个输入相关的导数，并从那里选择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，对于大量的y指数来说，这仍然会很慢，所以我强烈建议你绝对确定你需要Jacobian本身（而不是，例如，雅可比矢量积的结果。）
答案 1 :(得分：0)
如果有人想要关于@DomJacks答案的完整解决方案：
from keras.models import Model
from keras.layers import Dense, Input, Concatenate
import tensorflow as tf
import keras.backend as K
import numpy as np
num_features = 100
input_ = Input(shape=(num_features,))
output_ = Dense(10)(input_)
model = Model(input_,output_)
# input range of interest
x_range = [50,70]
# output indices of interest
y_indices = [2,3,4]
# If model is saved, you can load using:
#model = keras.models.load_model(filepath)
# then grab the input:
input_ = model.input
# Split inputs
uninteresting, interesting, more_uninteresting = tf.split(input_, [x_range[0],
x_range[1]-x_range[0],
num_features-x_range[1]],
axis=1)
# Create new process
inputs = Concatenate()([uninteresting, interesting, more_uninteresting])
y = model(inputs)
y_list = tf.unstack(y[0])
x = np.random.random((1,num_features))
# Create Jacobian matrix
jacobian_matrix = []
for i in y_indices:
J = tf.gradients(y_list[i], interesting)
jacobian_func = K.function([input_, K.learning_phase()], J)
jac = jacobian_func([x, False])[0][0]
jacobian_matrix.append(jac)
jacobian_matrix = np.array(jacobian_matrix)