# cntk.layers.higher_order_layers module¶

Higher-order functions, like Sequential() and ResNetBlock(). Note that sequential higher-order functions like Recurrence() are in cntk.layers.sequence.

For(what_range, constructor, name='')[source]

Layer factory function to create a composite through a pattern similar to Python’s for statement.

This layer factory loops over the given range and passes each value to the constructor function. It is equivalent to Sequential([constructor(i) for i in what_range]).

It is acceptable that constructor takes no argument.

Example

>>> from cntk.layers import *
>>> from cntk.ops import relu

>>> # stack of 3 Dense relu layers
>>> model = For(range(3), lambda: Dense(2000, activation=relu))

>>> # version of the above that has no activation for the last layer
>>> model = For(range(3), lambda i: Dense(2000, activation=relu if i < 2 else identity))

>>> # complex example that uses For() inside Sequential()
>>> with default_options(activation=relu, pad=True):  # default activation is relu
...     model = Sequential([
...          For(range(2), lambda : [
...              Convolution2D((3,3), 64),
...              Convolution2D((3,3), 64),
...              MaxPooling((3,3), strides=2)
...          ]),
...          Label('ndfeat'),              # name this specific value
...          For(range(2), lambda i: [     # this passes a nested list to Sequential
...              Dense([256,128][i]),      # layer index i used to index into an array of parameters
...              Dropout(0.5)
...          ]),
...          Label('hidden'),
...          Dense(10, activation=None)    # activation parameter overrides default (which was set to relu)
...      ])
>>> model.update_signature((3,32,32))      # RGB, 32 x 32 pixels
>>> model.ndfeat.shape                     # shape at top of convo/pooling pyramid
(64, 8, 8)
>>> model.hidden.shape                     # shape before classifier
(128,)

Parameters: what_range (range) – a Python range to loop over constructor (Python function/lambda with 1 or 0 arguments) – lambda that constructs a layer A function that accepts one argument and applies the layers as constructed by constructor one after another. cntk.ops.functions.Function
ResNetBlock(f, name='')[source]

Layer factory function to create a composite that adds a skip connection to a function. This is equivalent to Sequential((f, identity), plus).

Example

>>> # a ResNet layer
>>> from cntk.layers import *
>>> from cntk.ops import relu
>>> resnet_layer = Sequential([ResNetBlock(Convolution((3,3), 64, activation=None)), relu])

Parameters: f (Function or equivalent Python function) – the function to add the skip connection to. A function that accepts one argument, applies f to it, and adds the original argument. cntk.ops.functions.Function
Sequential(layers, name='')[source]

Layer factory function to create a composite that applies a sequence of layers (or any functions) onto an input. Sequential ([F, G, H])(x) means the same as H(G(F(x))).

The list of functions may also include tuples of functions. In that case, each function in a tuple is applied to the input, and the result is a tuple containing the results of these function applications. If followed by another function (typ. plus or splice), the tuple items form the arguments to that function.

Intermediate values in the chain can be accessed by name by inserting a Label(name=...) layer.

Note: An equivalent way of writing Sequential ([F, G, H])(x) is F >> G >> H.

Example

>>> from cntk.layers import *

>>> # sequence classifier. Maps a one-hot word sequence to a scalar probability value.
>>> # The recurrence is a Fold(), meaning only the final hidden state is produced.
>>> # The Label() layer allows to access the final hidden layer by name.
>>> model = Sequential([Embedding(300), Fold(LSTM(500)), Label('hidden'), Dense(1, activation=sigmoid)])
>>> model.update_signature(Sequence[Tensor[30000]])
>>> model.hidden.shape
(500,)

>>> # simple example that squares an input value
>>> f = Sequential([C.log, lambda x: 2 * x, C.exp])  # the second function is a Python lambda
>>> f.update_signature(1)
>>> f([np.array([2])])     # log, times 2, exp is the same as computing the square
array([[ 4.]], dtype=float32)

>>> # using function tuples to implement a bidirectional LSTM
>>> bi_lstm = Sequential([(Recurrence(LSTM(250)),                      # first tuple entry: forward pass
...                        Recurrence(LSTM(250), go_backwards=True)),  # second: backward pass
...                       splice])                                     # splice both on top of each other

>>> # using function tuple to implement a ResNet block
>>> # The function tuple applies all items to the input, and emits a tuple with the results
>>> # that then act as the arguments to the next one.
>>> # Here we say (Convolution(), identity), which generates two arguments to the next function,
>>> # the first being the convolution, the second being the input passed through.
>>> # Following that with plus() implements the ResNet formula.
>>> from cntk.ops import plus, relu
>>> resnet_layer = Sequential([(Convolution((3,3), 64, activation=None), # first tuple entry
...                             identity),                               # second tuple entry is a pass-through
...                            plus,                                     # this sums both
...                            relu])                                    # activation applied afterwards

>>> # simple function-tuples example with values
>>> f = Sequential([(lambda x: x * x, identity), splice])  # computes tuple (x^2, x) and splices both values
>>> f.update_signature(1)
>>> f([np.array([2])])
array([[ 4.,  2.]], dtype=float32)

Parameters: layers (list of Function, equivalent Python functions, tuples of functions, or lists thereof) – the list of functions to apply in sequence. A tuple aplies each of its items to the input and results in a tuple value. An item that is a list will be flattened. A function that accepts one argument and applies the given functions one after another. cntk.ops.functions.Function
SequentialClique(functions, name='')[source]

Layer factory function to create a composite that applies a sequence of functions onto an input, with skip connections between all function. I.e. each function receives a sum of the input and all prior functions’ outputs.

Example

>>> from cntk.layers import *
>>> from cntk.ops import abs, sqrt, square
>>> x = C.input_variable(2)
>>> seq_clique = SequentialClique([abs, sqrt, square])
>>> seq_clique(x).eval(np.array([2, 8], np.float32)) # 400 = square((8 + abs(8)) + sqrt(8 + abs(8)))
array([[  36.,  400.]], dtype=float32)

Parameters: functions (single or list of Function) – functions to be applied. A function that accepts one argument and applies the sequence of functions. cntk.ops.functions.Function