python - Calculating gradient norm wrt weights with keras

Question

I am attempting to calculate the gradient norm with respect to the weights of a neural network with keras (as a diagnostic tool). Eventually, I want to create a callback for this, but on the way there I have been working on just creating a function that can compute the gradient and return actual values in the form of a numpy array/scalar value (and not just a tensorflow tensor). The code is as follows:

import numpy as np
import keras.backend as K
from keras.layers import Dense
from keras.models import Sequential


def get_gradient_norm_func(model):
    grads = K.gradients(model.total_loss, model.trainable_weights)
    summed_squares = [K.sum(K.square(g)) for g in grads]
    norm = K.sqrt(sum(summed_squares))
    func = K.function([model.input], [norm])
    return func


def main():
    x = np.random.random((128,)).reshape((-1, 1))
    y = 2 * x
    model = Sequential(layers=[Dense(2, input_shape=(1,)),
                               Dense(1)])
    model.compile(loss='mse', optimizer='RMSprop')
    get_gradient = get_gradient_norm_func(model)
    history = model.fit(x, y, epochs=1)
    print(get_gradient([x]))

if  __name__ == '__main__':
    main()

The code fails on the call to get_gradient(). The traceback is lengthy, involving a lot about shapes, but little information on what is the correct shape. How can I correct this?

Ideally, I would like a backend-agnostic solution, but a tensorflow-based solution is also an option.

2017-08-15 15:39:14.914388: W tensorflow/core/framework/op_kernel.cc:1148] Invalid argument: Shape [-1,-1] has negative dimensions
2017-08-15 15:39:14.914414: E tensorflow/core/common_runtime/executor.cc:644] Executor failed to create kernel. Invalid argument: Shape [-1,-1] has negative dimensions
         [[Node: dense_2_target = Placeholder[dtype=DT_FLOAT, shape=[?,?], _device="/job:localhost/replica:0/task:0/cpu:0"]()]]
2017-08-15 15:39:14.915026: W tensorflow/core/framework/op_kernel.cc:1148] Invalid argument: Shape [-1,-1] has negative dimensions
2017-08-15 15:39:14.915038: E tensorflow/core/common_runtime/executor.cc:644] Executor failed to create kernel. Invalid argument: Shape [-1,-1] has negative dimensions
         [[Node: dense_2_target = Placeholder[dtype=DT_FLOAT, shape=[?,?], _device="/job:localhost/replica:0/task:0/cpu:0"]()]]
2017-08-15 15:39:14.915310: W tensorflow/core/framework/op_kernel.cc:1148] Invalid argument: Shape [-1] has negative dimensions
2017-08-15 15:39:14.915321: E tensorflow/core/common_runtime/executor.cc:644] Executor failed to create kernel. Invalid argument: Shape [-1] has negative dimensions
         [[Node: dense_2_sample_weights = Placeholder[dtype=DT_FLOAT, shape=[?], _device="/job:localhost/replica:0/task:0/cpu:0"]()]]
Traceback (most recent call last):
  File "/home/josteb/.local/opt/anaconda3/envs/timeseries/lib/python3.6/site-packages/tensorflow/python/client/session.py", line 1139, in _do_call
    return fn(*args)
  File "/home/josteb/.local/opt/anaconda3/envs/timeseries/lib/python3.6/site-packages/tensorflow/python/client/session.py", line 1121, in _run_fn
    status, run_metadata)
  File "/home/josteb/.local/opt/anaconda3/envs/timeseries/lib/python3.6/contextlib.py", line 89, in __exit__
    next(self.gen)
  File "/home/josteb/.local/opt/anaconda3/envs/timeseries/lib/python3.6/site-packages/tensorflow/python/framework/errors_impl.py", line 466, in raise_exception_on_not_ok_status
    pywrap_tensorflow.TF_GetCode(status))
tensorflow.python.framework.errors_impl.InvalidArgumentError: Shape [-1] has negative dimensions
         [[Node: dense_2_sample_weights = Placeholder[dtype=DT_FLOAT, shape=[?], _device="/job:localhost/replica:0/task:0/cpu:0"]()]]

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File "gradientlog.py", line 45, in <module>
    main()
  File "gradientlog.py", line 42, in main
    print(get_gradient([x]))
  File "/home/josteb/sandbox/keras/keras/backend/tensorflow_backend.py", line 2251, in __call__
    **self.session_kwargs)
  File "/home/josteb/.local/opt/anaconda3/envs/timeseries/lib/python3.6/site-packages/tensorflow/python/client/session.py", line 789, in run
    run_metadata_ptr)
  File "/home/josteb/.local/opt/anaconda3/envs/timeseries/lib/python3.6/site-packages/tensorflow/python/client/session.py", line 997, in _run
    feed_dict_string, options, run_metadata)
  File "/home/josteb/.local/opt/anaconda3/envs/timeseries/lib/python3.6/site-packages/tensorflow/python/client/session.py", line 1132, in _do_run
    target_list, options, run_metadata)
  File "/home/josteb/.local/opt/anaconda3/envs/timeseries/lib/python3.6/site-packages/tensorflow/python/client/session.py", line 1152, in _do_call
    raise type(e)(node_def, op, message)
tensorflow.python.framework.errors_impl.InvalidArgumentError: Shape [-1] has negative dimensions
         [[Node: dense_2_sample_weights = Placeholder[dtype=DT_FLOAT, shape=[?], _device="/job:localhost/replica:0/task:0/cpu:0"]()]]

Caused by op 'dense_2_sample_weights', defined at:
  File "gradientlog.py", line 45, in <module>
    main()
  File "gradientlog.py", line 39, in main
    model.compile(loss='mse', optimizer='RMSprop')
  File "/home/josteb/sandbox/keras/keras/models.py", line 783, in compile
    **kwargs)
  File "/home/josteb/sandbox/keras/keras/engine/training.py", line 799, in compile
    name=name + '_sample_weights'))
  File "/home/josteb/sandbox/keras/keras/backend/tensorflow_backend.py", line 435, in placeholder
    x = tf.placeholder(dtype, shape=shape, name=name)
  File "/home/josteb/.local/opt/anaconda3/envs/timeseries/lib/python3.6/site-packages/tensorflow/python/ops/array_ops.py", line 1530, in placeholder
    return gen_array_ops._placeholder(dtype=dtype, shape=shape, name=name)
  File "/home/josteb/.local/opt/anaconda3/envs/timeseries/lib/python3.6/site-packages/tensorflow/python/ops/gen_array_ops.py", line 1954, in _placeholder
    name=name)
  File "/home/josteb/.local/opt/anaconda3/envs/timeseries/lib/python3.6/site-packages/tensorflow/python/framework/op_def_library.py", line 767, in apply_op
    op_def=op_def)
  File "/home/josteb/.local/opt/anaconda3/envs/timeseries/lib/python3.6/site-packages/tensorflow/python/framework/ops.py", line 2506, in create_op
    original_op=self._default_original_op, op_def=op_def)
  File "/home/josteb/.local/opt/anaconda3/envs/timeseries/lib/python3.6/site-packages/tensorflow/python/framework/ops.py", line 1269, in __init__
    self._traceback = _extract_stack()

InvalidArgumentError (see above for traceback): Shape [-1] has negative dimensions
         [[Node: dense_2_sample_weights = Placeholder[dtype=DT_FLOAT, shape=[?], _device="/job:localhost/replica:0/task:0/cpu:0"]()]]

Answer 1

There are several placeholders related to the gradient computation process in Keras:

1. Input x
2. Target y
3. Sample weights: even if you don't provide it in model.fit(), Keras still generates a placeholder for sample weights, and feed np.ones((y.shape[0],), dtype=K.floatx()) into the graph during training.
4. Learning phase: this placeholder will be connected to the gradient tensor only if there's any layer using it (e.g. Dropout).

So, in your provided example, in order to compute the gradients, you need to feed x, y and sample_weights into the graph. That's the underlying reason of the error.

Inside Model._make_train_function() there are the following lines showing how to construct the necessary inputs to K.function() in this case:

inputs = self._feed_inputs + self._feed_targets + self._feed_sample_weights
if self.uses_learning_phase and not isinstance(K.learning_phase(), int):
    inputs += [K.learning_phase()]

with K.name_scope('training'):
    ...
    self.train_function = K.function(inputs,
                                     [self.total_loss] + self.metrics_tensors,
                                     updates=updates,
                                     name='train_function',
                                     **self._function_kwargs)

By mimicking this function, you should be able to get the norm value:

def get_gradient_norm_func(model):
    grads = K.gradients(model.total_loss, model.trainable_weights)
    summed_squares = [K.sum(K.square(g)) for g in grads]
    norm = K.sqrt(sum(summed_squares))
    inputs = model.model._feed_inputs + model.model._feed_targets + model.model._feed_sample_weights
    func = K.function(inputs, [norm])
    return func

def main():
    x = np.random.random((128,)).reshape((-1, 1))
    y = 2 * x
    model = Sequential(layers=[Dense(2, input_shape=(1,)),
                               Dense(1)])
    model.compile(loss='mse', optimizer='rmsprop')
    get_gradient = get_gradient_norm_func(model)
    history = model.fit(x, y, epochs=1)
    print(get_gradient([x, y, np.ones(len(y))]))

Execution output:

Epoch 1/1
128/128 [==============================] - 0s - loss: 2.0073     
[4.4091368]

Note that since you're using Sequential instead of Model, model.model._feed_* is required instead of model._feed_*.

Answer 2

Extending josteinb's comment, I'm sharing the version that I have used.

Basically same with the previous answer, but this version integrates norm computation into the usual training routine.

import keras.backend as K

# Get a "l2 norm of gradients" tensor
def get_gradient_norm(model):
    with K.name_scope('gradient_norm'):
        grads = K.gradients(model.total_loss, model.trainable_weights)
        norm = K.sqrt(sum([K.sum(K.square(g)) for g in grads]))
    return norm

# Build a model
model = Model(...)

# Compile the model
model.compile(
    loss="categorical_crossentropy",
    optimizer="adam",
    metrics=["categorical_accuracy"],
)

# Append the "l2 norm of gradients" tensor as a metric
model.metrics_names.append("gradient_norm")
model.metrics_tensors.append(get_gradient_norm(model))

# You can compute the norm within the usual training routine
loss, acc, gradient_norm = model.train_on_batch(batch, label)