将张量流梯度应用于特定输入

Question

I am trying to create a Jacobian matrix for certain output vairables with respect to specific input features in a keras model. For instance If I have a model with 100 input features and 10 output variables and I want to create a Jacobian of outputs 2, 3, and 4 with respect to outputs 50-70, I can create the jacobian like this:

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)

but with a much more complex model, this is extremely slow. I only want to create the Jacobian functions above with respect to the inputs of interest. I tried something like this:

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)

and got the Error:

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.

Any ideas? Thanks.

Answer 1

The issue is with the line J = tf.gradients(y_list[i], x_list[j]) . x_list[j] was derived from model.input[0] , but there's no directed path from x_list[j] to model.output[0] . You need to either unstack the model input, restack then run the model, or create the derivative with respect to the entire input and just select the j th row from there.

First way:

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)

Second way:

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

Having said that, this is still going to be slow for a large number of y indices, so I'd strongly encourage you to be absolutely sure you need the Jacobian itself (and not, for example, the result of a Jacobian-vector product).

Answer 2

In case anyone is wanting a full solution regarding @DomJacks answer:

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)