# Extending CNTK¶

CNTK provides extension possibilities through
• custom operators in pure Python as so-called ‘user functions’
• custom learning algorithms (like SGD or Adam) as ‘user learners’
• custom minibatch sources as ‘user minibatch sources’

## User defined functions¶

Implementing a custom operator in pure Python is simple matter of

• inheriting from UserFunction
• implementing forward() and backward(), whose signatures dependent on the number of inputs and outputs
• specifying the outputs’ shape, data type and dynamic axes in infer_outputs()
• providing a static deserialize() method to inflate previously saved function

In the simplest case, just only one input and output, forward() takes an argument and returns a tuple of a state and the result. The state can be used to pass data from the forward to the backward pass, but can be set to None if not needed.

Let’s consider the example of a sigmoid. This is just for demonstration purposes - for real computation better use sigmoid().

As the derivative of $$\textrm{sigmoid}(x)$$ is $$\textrm{sigmoid}(x) * (1-\textrm{sigmoid}(x))$$ we pass the $$\textrm{sigmoid}(x)$$ value as the state variable, which is then later fed into backward(). Note that one can pass any Python value (including tuple, strings, etc.):

from cntk.ops.functions import UserFunction
from cntk import output_variable

class MySigmoid(UserFunction):
def __init__(self, arg, name='MySigmoid'):
super(MySigmoid, self).__init__([arg], name=name)

def forward(self, argument, device=None, outputs_to_retain=None):
sigmoid_x = 1 / (1 + np.exp(-argument))
return sigmoid_x, sigmoid_x

sigmoid_x = state
return root_gradients * sigmoid_x * (1 - sigmoid_x)

def infer_outputs(self):
return [output_variable(self.inputs[0].shape, self.inputs[0].dtype,
self.inputs[0].dynamic_axes)]

@staticmethod
def deserialize(inputs, name, state):
return = MySigmoid(inputs[0], name)


This can now be used as a normal operator like:

from cntk import user_function
s = user_function(MySigmoid(prev_node))


Note that we cannot pass the UserFunction instance directly into the graph. It is representing a primitive function, which we have to pass through user_function().

In case, the operator is initialized with multiple inputs, forward() ‘s argument will be a list of those inputs:

class MyPlus(UserFunction):
def __init__(self, arg1, arg2, name='f1'):
super(MyPlus, self).__init__([arg1, arg2], name=name)
self.forward_calls = 0
self.backward_calls = 0

def forward(self, arguments, device=None, outputs_to_retain=None):
# No state needs to be passed to backward() so we just
# pass None
self.forward_calls += 1
return None, arguments[0] + arguments[1]

self.backward_calls += 1

def infer_outputs(self):
# We just pass the meta information of the first operand. For real
# scenarios, one would want to calculate what the actual output's
# result would actually look like (considering broadcasting, etc.).
return [output_variable(self.inputs[0].shape, self.inputs[0].dtype, self.inputs[0].dynamic_axes)]

def serialize(self):
return {'forward_calls' : self.forward_calls,
'backward_calls' : self.backward_calls}

@staticmethod
def deserialize(inputs, name, state):
f = MyPlus(inputs[0], inputs[1], name)
f.forward_calls = state['forward_calls']
f.backward_calls = state['backward_calls']
return f


If the UserFunction has more than one input, backward() is invoked with an additional variables argument, which contains a dictionary of Variable to the gradient data, whose values have to be set with the proper gradients. If the gradient is not to be propagated to a particular input, the value for that input’s gradient can be left None:

def backward(self, state, root_gradients, variables):
for var in variables:
variables[var] = ... # compute the gradient for var

# no return value since all the data is already in variables


In case, the operator shall output multiple outputs, the signature of forward changes to:

self.forward(args, outputs, device, outputs_to_retain):
...


which means that there is the additional dictionary outputs, whose values have to be set with the proper data. In addition, root_gradient in backward() is a dictionary of Variable to the root_gradient.

deserialize() is invoked by CNTK to reconstruct a previously saved function. It should have the same signature as deserialize() method. In case of a stateless function, it simply needs to invoke the constructor and return an instance of the user function. However, if the function is stateful and overrides serialize() method, deserialize() also needs to properly restore the function state.

### Using user functions for debugging¶

It is now easy to just plug user function nodes into the graph to support debugging. For instance, the following operator:

class LambdaFunc(UserFunction):
def __init__(self,
arg,
when=lambda arg: True,
execute=lambda arg: print(arg),
name=''):
self.when = when
self.execute = execute

super(LambdaFunc, self).__init__([arg], name=name)

def infer_outputs(self):
return [output_variable(self.inputs[0].shape, self.inputs[0].dtype, self.inputs[0].dynamic_axes)]

def forward(self, argument, device=None, outputs_to_retain=None):
if self.when(argument):
self.execute(argument)

return None, argument



can now be used to trigger certain actions when the data in the graph shows some interesting behavior, for instance:

import pdb
import numpy as np
# ... setting up the graph
debug_node = LambdaFunc(node,
when=lambda arg: np.var(arg)>1,
execute=lambda arg: pdb.set_trace())
# out = ... using user_function(debug_node) ...
# ... training out


Now, if the variance of the input tensor exceeds 1, we will be put into debugging mode and can start inspection.

## User defined learners¶

Implementing a custom learner in pure Python is accomplished by

Here is an example, how normal stochastic gradient descent would be reimplemented in a naive way:

from cntk.learner import UserLearner

class MySgd(UserLearner):

def __init__(self, parameters, lr_schedule):
super(MySgd, self).__init__(parameters, lr_schedule)

eta = self.learning_rate() / training_sample_count
new_p = p - eta * C.constant(g)
p.set_value(new_p.eval(as_numpy=False).data())
return True


The class MySgd could then be used as a normal learner, e.g.:

# z, ce, pe = <your model, loss and evaluation functions>
# lr_per_minibatch = <your learning rate specification>
trainer = Trainer(z, (ce, pe), MySgd(z.parameters, lr_per_minibatch))


While this approach might be good enough as a one-off, it is not the fastest possible UserLearner implementation. In every call, a complete CNTK graph is created and then destructed (new_p). To speed up the parameter update, this computation can be moved to the constructor:

class MySgdFast(UserLearner):

def __init__(self, parameters, lr_schedule):
super(MySgdFast, self).__init__(parameters, lr_schedule, as_numpy=False)

self.new_p = {}

self.sample_count_input = cntk.input_variable((), name='count')

lr = lr_schedule[0]  # assuming constant learning rate
eta = lr / self.sample_count_input

# we need one graph per parameter shape
for param in parameters:
p_shape = param.shape
self.new_p[p_shape] = param - eta * self.grad_input[p_shape]

new_p = self.new_p[p.shape]

data = {
self.sample_count_input: np.asarray(training_sample_count),
}
result = new_p.eval(data, as_numpy=False)
shape = result.shape

# result has the shape of a complete minibatch, but contains
# only one tensor, which we want to write to p. This means, we
# have to slice off the leading dynamic axes.
static_tensor = result.data.slice_view([0]*len(shape),
shape[2:])
p.set_value(static_tensor)

return True


With this implementation, we keep the costly NumPy conversion to a bare minimum, while speeding up the update process considerably.

Before starting a new learner, though, please check out cntk.learners whether your learner is already available.

## User defined minibatch sources¶

In order to make use of CNTK’s training session, one has to provide the input data as an instance of MinibatchSource. Although cntk.io already provides means to read image, text, and speech data, there might be the need (e.g. in distributed scnearios) to roll out one’s own custom minibatch source. This is possible in pure Python as simple matter of

In the following example, we reimplement parts of the CNTKTextFormatReader to show how it is done in an end-to-end manner. As we can see, the majority of the lines below is scenario-specific code that deals with parsing, etc.:

import numpy as np
from cntk.io import UserMinibatchSource, StreamInformation, MinibatchData

# Our toy test data contains two sequences. 'x' is a sparse representation of the
# features (numbers representing the words in our training data). 'y' is the one-hot
# label.
MBDATA = r'''0      |x 560:1        |y 1 0 0 0 0
0   |x 0:1
0   |x 0:1
1   |x 560:1        |y 0 1 0 0 0
1   |x 0:1
1   |x 0:1
1   |x 424:1
'''

class MyDataSource(UserMinibatchSource):
def __init__(self, f_dim, l_dim):
self.f_dim, self.l_dim = f_dim, l_dim

self.fsi = StreamInformation("features", 0, 'sparse', np.float32, (self.f_dim,))
self.lsi = StreamInformation("labels", 1, 'dense', np.float32, (self.l_dim,))

# MBDATA fits into memory, so we will read it in all at once. Normally, however,
# it does not, in which case we would need to keep track of the position in the
# file until which we have already provided the data.
# It follows the CNTKTextFormat specification
#   sequence ID |feature1 data |feature2 data
# where in this case feature1's data is encoded as one-hot and we will
# convert to CSR, and feature2's data is a one-hot encoded as dense.

# We will store
#   sequence id -> "features" -> list of features
# and
#   sequence id -> "labels" -> label

self.data = {}
for line in MBDATA.split('\n'):
line = line.strip()
if not line:
continue
seq_id, data = line.split('|', 1)
data = data.split("|")
seq_id = int(seq_id.strip())

if seq_id not in self.data:
self.data[seq_id] = {'features': []}

# Processing features - expecting one per line.
features = data[0].split(" ")
vocab_idx = int(features[1].split(":")[0])
self.data[seq_id]['features'].append(vocab_idx)

# Process label, if exists
if len(data) == 2:
labels = np.asarray([data[1].split(" ")[1:]], dtype=np.float32)
self.data[seq_id]['labels'] = labels

self.sequences = sorted(self.data)
self.next_seq_idx = 0

super(MyDataSource, self).__init__()

def stream_infos(self):
return [self.fsi, self.lsi]

def next_minibatch(self, num_samples, number_of_workers=1, worker_rank=0, device=None):
# Note that in this example we do not yet make use of number_of_workers or
# worker_rank, which will limit the minibatch source to single GPU / single node
# scenarios.

features = []
labels = []

sweep_end = False

f_sample_count = l_sample_count = 0

while max(f_sample_count, l_sample_count) < num_samples:
if self.next_seq_idx == len(self.sequences):
sweep_end = True
self.next_seq_idx = 0

seq_id = self.sequences[self.sequences[self.next_seq_idx]]

f_data = self.data[seq_id]['features']
l_data = self.data[seq_id]['labels']
if (features or labels) and max(f_sample_count+len(f_data), l_sample_count+len(l_data)) > num_samples:
break
f_sample_count += len(f_data)
features.append(f_data)

l_sample_count += len(l_data)
labels.append(l_data)

self.next_seq_idx += 1

num_seq = len(features)

f_data = Value.one_hot(batch=features, num_classes=self.f_dim)
l_data = Value(batch=np.asarray(labels, dtype=np.float32))

result = {
self.fsi: MinibatchData(f_data, num_seq, f_sample_count, sweep_end),
self.lsi: MinibatchData(l_data, num_seq, l_sample_count, sweep_end)
}

return result


This can then be used wherever a MinibatchSource instance is accepted, e.g.:

input_dim = 1000
num_output_classes = 5

# instantiating the user minibatch source
mbs = MyDataSource(input_dim, num_output_classes)
feature = sequence.input_variable(shape=(input_dim,))
label = cntk.input_variable(shape=(num_output_classes,))

# setting up the model
# ...

# and train
trainer = Trainer(z, (ce, errs), [learner])
input_map = {
feature: mbs.fsi,
label: mbs.lsi
}

session = training_session(
trainer=trainer, mb_source=mbs,
model_inputs_to_streams=input_map,
mb_size=4, max_samples=20
)
session.train()


As we have noted above, this minibatch source is limited to single GPU / single node scenarios, but it can be adapted easily to be used with e.g. BlockMomentum. We simply have to use number_of_workers to cut the data in slices and then return the slices depending on which worker_rank requested the next minibatch.

Note

Please note that it is the user’s task to provide proper randomization of the training data.