我正在尝试为keras模型中的特定输出变量相对于特定输入特征创建雅可比矩阵。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的雅可比矩阵，我可以这样创建雅可比矩阵:

from keras.models import Modelfrom keras.layers import Dense, Inputimport tensorflow as tfimport keras.backend as Kimport numpy as npinput_ = 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)

但是对于一个复杂得多的模型，这非常慢。我只想创建上述雅可比函数相对于感兴趣的输入。我尝试了这样的方法:

from keras.models import Modelfrom keras.layers import Dense, Inputimport tensorflow as tfimport keras.backend as Kimport numpy as npinput_ = 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)

但得到了错误:

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。

回答：

问题出在J = tf.gradients(y_list[i], x_list[j])这行。x_list[j]是从model.input[0]派生出来的，但是从x_list[j]到model.output[0]之间没有直接路径。你需要要么拆分模型输入，然后重新组合并运行模型，要么相对于整个输入创建导数，然后只选择其中的第j行。

第一种方法:

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)

第二种方法:

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

尽管如此，对于大量的y索引，这仍然会很慢，所以我强烈建议你确定你确实需要雅可比矩阵本身（例如，不是雅可比-向量乘积的结果）。