def scatter(seq, condition, new_sequence_axis_typeinfo=None, name=''):
'''
Performs the inverse of gather. The sequence ``seq`` must have as many
elements as the number of True values in the sequence ``condition``.
It will return a sequence whose length is the same as the ``condition``
sequence with zeroes everywhere except for the locations where ``condition``
evaluates to True in which case it will copy the elements from ``seq``
preserving their order.
Example:
>>> x = C.sequence.input_variable(shape=(3,2))
>>> t = C.sequence.last(x)
>>> b = C.sequence.is_first(x)
>>> y = C.sequence.scatter(t, b)
>>> # create one sequence of 4 tensors each with shape (3,2)
>>> x0 = np.reshape(np.arange(24.0,dtype=np.float32),(1,4,3,2))
>>> y.eval({x:x0})
[array([[[ 18., 19.],
[ 20., 21.],
[ 22., 23.]],
<BLANKLINE>
[[ 0., 0.],
[ 0., 0.],
[ 0., 0.]],
<BLANKLINE>
[[ 0., 0.],
[ 0., 0.],
[ 0., 0.]],
<BLANKLINE>
[[ 0., 0.],
[ 0., 0.],
[ 0., 0.]]], dtype=float32)]
Args:
seq: the symbolic sequence from which elements will be copied in the
output
condition: the symbolic sequence which denotes the locations where
elements should be copied
new_sequence_axis_typeinfo: tuple of integers indicating
the scaling and additive factors for the length of the new sequence axis
w.r.t. the condition sequence. This is used to determine the sequence axis
to be used for the output of the gather operation. If this argument is left
unspecified a new independent sequence axis is created.
name (str): the name of the node in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import scatter
seq = sanitize_input(seq, get_data_type(seq))
condition = sanitize_input(condition, get_data_type(condition))
if new_sequence_axis_typeinfo is None:
return scatter(seq, condition, name)
else:
return scatter(seq, condition, new_sequence_axis_typeinfo, name)
def squared_error(output, target, name=''):
'''
This operation computes the sum of the squared difference between elements
in the two input matrices. The result is a scalar (i.e., one by one matrix).
This is often used as a training criterion.
Example:
>>> i1 = C.input_variable((1,2))
>>> i2 = C.input_variable((1,2))
>>> C.squared_error(i1,i2).eval({i1:np.asarray([[[2., 1.]]], dtype=np.float32), i2:np.asarray([[[4., 6.]]], dtype=np.float32)})
array([ 29.], dtype=float32)
>>> C.squared_error(i1,i2).eval({i1:np.asarray([[[1., 2.]]], dtype=np.float32), i2:np.asarray([[[1., 2.]]], dtype=np.float32)})
array([ 0.], dtype=float32)
Args:
output: the output values from the network
target: it is usually a one-hot vector where the hot bit
corresponds to the label index
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import squared_error
dtype = get_data_type(output, target)
output = sanitize_input(output, dtype)
target = sanitize_input(target, dtype)
return squared_error(output, target, name)
def cosine_distance(x, y, name=''):
'''
Computes the cosine distance between ``x`` and ``y``:
Example:
>>> a = np.asarray([-1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1]).reshape(3,2,2)
>>> b = np.asarray([1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1]).reshape(3,2,2)
>>> x = C.sequence.input_variable(shape=(2,))
>>> y = C.sequence.input_variable(shape=(2,))
>>> np.round(C.cosine_distance(x,y).eval({x:a,y:b}),5)
array([[-1., 1.],
[ 1., 0.],
[ 0., -1.]], dtype=float32)
Args:
x: numpy array or any :class:`~cntk.ops.functions.Function` that outputs a tensor
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import cosine_distance
dtype = get_data_type(x, y)
x = sanitize_input(x, dtype)
y = sanitize_input(y, dtype)
return cosine_distance(x, y, name)
def broadcast_as(operand, broadcast_as_operand, name=''):
'''
Creates a sequence out of a non-sequence by endowing the ``operand``
with dynamic axes of the same type as the ``broadcast_as_operand``
and broadcasting the value of the ``operand`` along those dynamic axes.
Example:
>>> x = C.sequence.input_variable(shape=(3,2))
>>> t = C.sequence.last(x)
>>> b = C.sequence.is_first(x)
>>> y = C.sequence.broadcast_as(t, b)
>>> # create one sequence of 4 tensors each with shape (3,2)
>>> x0 = np.reshape(np.arange(24.0,dtype=np.float32),(1,4,3,2))
>>> y.eval({x:x0})
[array([[[ 18., 19.],
[ 20., 21.],
[ 22., 23.]],
<BLANKLINE>
[[ 18., 19.],
[ 20., 21.],
[ 22., 23.]],
<BLANKLINE>
[[ 18., 19.],
[ 20., 21.],
[ 22., 23.]],
<BLANKLINE>
[[ 18., 19.],
[ 20., 21.],
[ 22., 23.]]], dtype=float32)]
Args:
operand: the symbolic tensor whose value will be broadcast
broadcast_as_operand: the symbolic tensor whose dynamic axes will
be used to broadcast the operand
name (str): the name of the node in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import broadcast_as
operand = sanitize_input(operand, get_data_type(operand, broadcast_as_operand))
broadcast_as_operand = sanitize_input(
broadcast_as_operand, get_data_type(broadcast_as_operand))
return broadcast_as(operand, broadcast_as_operand, name)
def gather(seq, condition, new_sequence_axis_typeinfo=None, name=''):
'''
Takes two sequences of the same length and returns a new sequence whose
elements are those elements of sequence ``seq`` whose corresponding element
in ``condition`` is True, preserving the ordering of ``seq``.
This operation is also known as stream compaction, or copy_if.
Example:
>>> x = C.sequence.input_variable(shape=(3,2))
>>> z = C.greater(C.reduce_sum(x),60)
>>> y = C.sequence.gather(x,z)
>>> # create one sequence of 4 tensors each with shape (3,2)
>>> x0 = np.reshape(np.arange(24.0,dtype=np.float32),(1,4,3,2))
>>> y.eval({x:x0})
[array([[[ 12., 13.],
[ 14., 15.],
[ 16., 17.]],
<BLANKLINE>
[[ 18., 19.],
[ 20., 21.],
[ 22., 23.]]], dtype=float32)]
Args:
seq: the symbolic sequence from which elements will be selected
condition: the symbolic sequence of booleans which indicate which
elements should be selected
new_sequence_axis_typeinfo: tuple of integers indicating
the scaling and additive factors for the length of the new sequence axis
w.r.t. the operand sequence. This is used to determine the sequence axis
to be used for the output of the gather operation. If this argument is left
unspecified, a new independent sequence axis is created.
name (str): the name of the node in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import gather
seq = sanitize_input(seq, get_data_type(seq))
condition = sanitize_input(condition, get_data_type(condition))
if new_sequence_axis_typeinfo is None:
return gather(seq, condition, name)
else:
return gather(seq, condition, new_sequence_axis_typeinfo, name)
def lattice_sequence_with_softmax(label, prediction, loglikelihood, lattice, symListPath, phonePath, stateListPath, transProbPath, latticeConfigPath="LatticeNode.config",
hSmoothingWeight = 0.95, frameDropThresh = 1e-10, doReferenceAlign = False, seqGammarUsesMBR = False,
seqGammarAMF = 14.0, seqGammarLMF = 14.0, seqGammarBMMIFactor = 0.0, seqGammarWordPen = 0.0, name=''):
from cntk.cntk_py import lattice_sequence_with_softmax
dtype = get_data_type(label, prediction, loglikelihood, lattice)
label = sanitize_input(label, dtype)
prediction = sanitize_input(prediction, dtype)
loglikelihood = sanitize_input(loglikelihood, dtype)
lattice = sanitize_input(lattice, dtype)
return lattice_sequence_with_softmax(label, prediction, loglikelihood, lattice, symListPath, phonePath, stateListPath, transProbPath, latticeConfigPath, hSmoothingWeight, frameDropThresh, doReferenceAlign, seqGammarUsesMBR, seqGammarAMF, seqGammarLMF, seqGammarBMMIFactor, seqGammarWordPen, name)
def lambda_rank(output, gain, group, name=''):
r'''
Groups samples according to ``group``, sorts
them within each group based on ``output`` and
computes the Normalized Discounted Cumulative Gain
(NDCG) at infinity for each group. Concretely,
the Discounted Cumulative Gain (DCG) at infinity is:
:math:`\mathrm{DCG_{\infty}}()=\sum_{i=0}^{\infty} \frac{gain_{(i)}}{\log(i+2)}`
where :math:`gain_{(i)}` means the gain of the :math:`i`-th ranked sample.
The NDCG is just the DCG divided by the maximum achievable DCG (obtained
by placing the samples with the largest gain at the top of the ranking).
Samples in the same group must appear in order of decreasing gain.
It returns 1 minus the average NDCG across all the groups in the minibatch
multiplied by 100 times the number of samples in the minibatch.
In the backward direction it back-propagates LambdaRank gradients.
Example:
>>> group = C.input_variable((1,))
>>> score = C.input_variable((1,), needs_gradient=True)
>>> gain = C.input_variable((1,))
>>> g = np.array([1, 1, 2, 2], dtype=np.float32).reshape(4,1)
>>> s = np.array([1, 2, 3, 4], dtype=np.float32).reshape(4,1)
>>> n = np.array([7, 1, 3, 1], dtype=np.float32).reshape(4,1)
>>> f = C.lambda_rank(score, gain, group)
>>> np.round(f.grad({score:s, gain:n, group: g}, wrt=[score]),4)
array([[-0.2121],
<BLANKLINE>
[ 0.2121],
<BLANKLINE>
[-0.1486],
<BLANKLINE>
[ 0.1486]], dtype=float32)
Args:
output: score of each sample
gain: gain of each sample
group: group of each sample
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import lambda_rank
dtype = get_data_type(output, gain, group)
output = sanitize_input(output, dtype)
gain = sanitize_input(gain, dtype)
group = sanitize_input(group, dtype)
return lambda_rank(output, gain, group, name)
def softmax(seq, name = ''):
'''
Computes the softmax of the input across the sequence axis.
Args:
seq: sequence input tensor
name (`str`, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import sequence_softmax
seq = sanitize_input(seq, get_data_type(seq))
return sequence_softmax(seq, name)
def edit_distance_error(input_a, input_b, subPen=1, delPen=1, insPen=1, squashInputs=False, tokensToIgnore=[], name=''):
'''
Edit distance error evaluation function with the option of specifying penalty of substitution, deletion and insertion, as well as squashing the input sequences and ignoring certain samples.
Using the classic DP algorithm as described in https://en.wikipedia.org/wiki/Edit_distance, adjusted to take into account the penalties.
Each sequence in the inputs is expected to be a matrix. Prior to computation of the edit distance, the operation extracts the indices of maximum element in each column.
For example, a sequence matrix
1 2 9 1
3 0 3 2
will be represented as the vector of labels (indices) as [1, 0, 0, 1], on which edit distance will be actually evaluated.
The function allows to squash sequences of repeating labels and ignore certain labels. For example, if squashInputs is true and tokensToIgnore contains index of label '-' then
given first input sequence as s1="1-12-" and second as s2="-11--122" the edit distance will be computed against s1' = "112" and s2' = "112".
When used as an evaluation criterion, the Trainer will aggregate all values over an epoch and report the average, i.e. the error rate.
Primary objective of this node is for error evaluation of CTC training, see formula (1) in "Connectionist Temporal Classification: Labelling Unsegmented
Sequence Data with Recurrent Neural Networks", ftp://ftp.idsia.ch/pub/juergen/icml2006.pdf
Example:
>>> i1 = C.input(shape=(2,))
>>> i2 = C.input(shape=(2,))
>>> arguments = {i1 : [[1, 3], [2, 0]], i2 : [[2, 0], [2, 0]]}
>>> a = C.edit_distance_error(i1, i2, 0, 1, 1, True, [1])
>>> a.eval(arguments)
array(1.0, dtype=float32)
Args:
input_a: first input sequence
input_b: second input sequence
subPen: substitution penalty
delPen: deletion penalty
insPen: insertion penalty
squashInputs: whether to merge sequences of identical samples (in both input sequences). If true and tokensToIgnore contains label '-' then
given first input sequence as s1="a-ab-" and second as s2="-aa--abb" the edit distance will be computed against s1' = "aab" and s2' = "aab".
tokensToIgnore: list of indices of samples to ignore during edit distance evaluation (in both sequences)
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import edit_distance_error
dtype = get_data_type(input_a, input_b)
input_a = sanitize_input(input_a, dtype)
input_b = sanitize_input(input_b, dtype)
return edit_distance_error(input_a, input_b, subPen, delPen, insPen, squashInputs, tokensToIgnore, name)
def ndcg_at_1(output, gain, group, name=''):
r'''
Groups samples according to ``group``, sorts
them within each group based on ``output`` and
computes the Normalized Discounted Cumulative Gain
(NDCG) at 1 for each group. Concretely,
the NDCG at 1 is:
:math:`\mathrm{NDCG_1} = \frac{gain_{(1)}}{\max_i gain_i}`
where :math:`gain_{(1)}` means the gain of the first ranked sample.
Samples in the same group must appear in order of decreasing gain.
It returns the average NDCG at 1 across all the groups in the minibatch
multiplied by 100 times the number of samples in the minibatch.
This is a forward-only operation, there is no gradient for it.
Example:
>>> group = C.input_variable((1,))
>>> score = C.input_variable((1,))
>>> gain = C.input_variable((1,))
>>> g = np.array([1, 1, 2, 2], dtype=np.float32).reshape(4,1,1)
>>> s = np.array([2, 1, 3, 1], dtype=np.float32).reshape(4,1,1)
>>> n = np.array([7, 1, 3, 1], dtype=np.float32).reshape(4,1,1)
>>> C.ndcg_at_1(score, gain, group).eval({score:s, gain:n, group: g})
array(400.0, dtype=float32)
Args:
output: score of each sample
gain: gain of each sample
group: group of each sample
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import ndcg_at_1
dtype = get_data_type(output, gain, group)
output = sanitize_input(output, dtype)
gain = sanitize_input(gain, dtype)
group = sanitize_input(group, dtype)
return ndcg_at_1(output, gain, group, name)
def binary_cross_entropy(output, target, name=''):
r'''
Computes the binary cross entropy (aka logistic loss) between the ``output`` and ``target``.
Args:
output: the computed posterior probability for a variable to be 1 from the network (typ. a ``sigmoid``)
target: ground-truth label, 0 or 1
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
Todo:
add an example
'''
from cntk.cntk_py import binary_cross_entropy
dtype = get_data_type(output, target)
output = sanitize_input(output, dtype)
target = sanitize_input(target, dtype)
return binary_cross_entropy(output, target, name)
def where(condition, name=''):
'''
Given a symbolic sequence ``condition`` of boolean-like (1/0) values, it will return
a new sequence containing the indices for which the values were true.
If ``condition`` has a value other than 0 or 1, it will denote a repeat factor.
If a repeat factor is fractional, it will round up but deduct the overshoot from the
next repeat factor.
Example:
>>> x = C.sequence.input_variable(shape=(3,2))
>>> z = C.greater(C.reduce_sum(x), 60)
>>> # create one sequence of 4 tensors each with shape (3,2)
>>> x0 = np.reshape(np.arange(24.0, dtype=np.float32), (1,4,3,2))
>>> z.eval({x:x0})
[array([ 0., 0., 1., 1.], dtype=float32)]
>>> y = C.sequence.where(z)
>>> y.eval({x:x0})
[array([ 2., 3.], dtype=float32)]
>>> # repeat frame[1] twice, frame[3] three times, and frame[4] twice
>>> C.sequence.where(C.sequence.input_variable(1)).eval([[[1], [2], [1], [3], [2]]])
[array([ 0., 1., 1., 2., 3., 3., 3., 4., 4.], dtype=float32)]
>>> # note that the above are the indices that are passed to
>>> # repeat frames with a fractional factor
>>> C.sequence.where(C.sequence.input_variable(1)).eval([[[1.2]]*10])
[array([ 0., 0., 1., 2., 3., 4., 5., 5., 6., 7., 8., 9.],
dtype=float32)]
>>> # as a result, a 1.2 times stretch is realized by duplicating frame[0] and frame[5]
Args:
condition: sequence of 0 or 1 values for filtering, or other positive values for repetition (also fractional)
name (str): the name of the node in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import where
condition = sanitize_input(condition, get_data_type(condition))
return where(condition, name)
def cosine_distance_with_negative_samples(x, y, shift, num_negative_samples, name=''):
'''
Given minibatches for ``x`` and ``y``, this function computes for each element in `x` the cosine distance between
it and the corresponding `y` and additionally the cosine distance between ``x`` and some other elements of ``y``
(referred to a negative samples). The ``x`` and ``y`` pairs are samples often derived
from embeddings of textual data, though the function can be used for any form of numeric encodings.
When using this function to compute textual similarity, ``x`` represents search query term embedding
and ``y`` represents a document embedding. The negative samples are formed on the fly by shifting
the right side (``y``). The ``shift`` indicates how many samples in ``y`` one should shift while
forming each negative sample pair. It is often chosen to be 1. As the name suggests
``num_negative_samples`` indicates how many negative samples one would want to generate.
Example:
>>> qry = np.asarray([1., 1., 0., 0., 0., 1., 1., 0., 0., 0., 1., 1.], dtype=np.float32).reshape(3, 1, 4)
>>> doc = np.asarray([1., 1., 0., 0., 0., 1., 1., 0., 0., 0., 1., 1.], dtype=np.float32).reshape(3, 1, 4)
>>> x = C.sequence.input_variable(shape=(4,))
>>> y = C.sequence.input_variable(shape=(4,))
>>> model = C.cosine_distance_with_negative_samples(x, y, shift=1, num_negative_samples=2)
>>> np.round(model.eval({x: qry, y: doc}), decimals=4)
array([[[ 1. , 0.5, 0. ]],
<BLANKLINE>
[[ 1. , 0.5, 0.5]],
<BLANKLINE>
[[ 1. , 0. , 0.5]]], dtype=float32)
Args:
x: numpy array or any :class:`~cntk.ops.functions.Function` that outputs a tensor
y: numpy array or any :class:`~cntk.ops.functions.Function` that outputs a tensor
shift: non-zero positive integer representing number of shift to generate a negative sample
num_negative_samples: number of negative samples to generate, a non-zero positive integer
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import cosine_distance_with_negative_samples
dtype = get_data_type(x, y)
x = sanitize_input(x, dtype)
y = sanitize_input(y, dtype)
return cosine_distance_with_negative_samples(x, y, shift, num_negative_samples, name)
def slice(seq, begin_index, end_index, name=''):
'''
Slice the input sequence.
Examples:
TBA
Args:
seq: sequence input tensor
begin_index (`int`): the index along sequence axis where the slicing starts
end_index (`int`): the index along sequence axis where the slicing ends
name (`str`, optional): the name of the Function instance in the network
See also:
Indexing in NumPy: https://docs.scipy.org/doc/numpy/reference/arrays.indexing.html
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import sequence_slice
seq = sanitize_input(seq, get_data_type(seq))
return sequence_slice(seq, begin_index, end_index, name)
def weighted_binary_cross_entropy(output, target, weight, name=''):
r'''
This operation computes the weighted binary cross entropy (aka logistic loss) between the ``output`` and ``target``.
Example:
TBA
Args:
output: the computed posterior probability from the network
target: ground-truth label, 0 or 1
weight: weight of each example
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import weighted_binary_cross_entropy
dtype = get_data_type(output, target, weight)
output = sanitize_input(output, dtype)
target = sanitize_input(target, dtype)
weight = sanitize_input(weight, dtype)
return weighted_binary_cross_entropy(output, target, weight, name)
def classification_error(output_vector,
target_vector,
axis=-1,
topN=1,
name=''):
'''
This operation computes the classification error. It finds the index of the highest
value in the output_vector and compares it to the actual ground truth label
(the index of the hot bit in the target vector). The result is a scalar
(i.e., one by one matrix). This is often used as an evaluation criterion.
It cannot be used as a training criterion though since the gradient is not
defined for it.
Example:
>>> C.classification_error([[1., 2., 3., 4.]], [[0., 0., 0., 1.]]).eval()
array([[ 0.]], dtype=float32)
>>> C.classification_error([[1., 2., 3., 4.]], [[0., 0., 1., 0.]]).eval()
array([[ 1.]], dtype=float32)
>>> # Note that non-1 values are treated as 0
>>> C.classification_error([[1., 2., 3., 4.]], [[5., 0., 1., 0.]]).eval()
array([[ 1.]], dtype=float32)
Args:
output_vector: the output values from the network
target_vector: it is one-hot vector where the hot bit corresponds to
the label index.
axis (int or :class:`~cntk.axis.Axis`): axis along which the
classification error will be computed.
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import classification_error
dtype = get_data_type(output_vector, target_vector)
output_vector = sanitize_input(output_vector, dtype)
target_vector = sanitize_input(target_vector, dtype)
axis = sanitize_axis(axis)
return classification_error(output_vector, target_vector, topN, axis, name)
def slice(seq, begin_index, end_index, name=''):
'''
Slice the input sequence.
Args:
seq: sequence input tensor
begin_index (`int`): the index along sequence axis where the slicing starts
end_index (`int`): the index along sequence axis where the slicing ends
name (`str`, optional): the name of the Function instance in the network
See also:
Indexing in NumPy: https://docs.scipy.org/doc/numpy/reference/arrays.indexing.html
Returns:
:class:`~cntk.ops.functions.Function`
Todo:
add an example
'''
from cntk.cntk_py import sequence_slice
seq = sanitize_input(seq, get_data_type(seq))
return sequence_slice(seq, begin_index, end_index, name)
def weighted_binary_cross_entropy(output, target, weight, name=''):
r'''
This operation computes the weighted binary cross entropy (aka logistic loss) between the ``output`` and ``target``.
Args:
output: the computed posterior probability from the network
target: ground-truth label, 0 or 1
weight: weight of each example
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
Todo:
add an example
'''
from cntk.cntk_py import weighted_binary_cross_entropy
dtype = get_data_type(output, target, weight)
output = sanitize_input(output, dtype)
target = sanitize_input(target, dtype)
weight = sanitize_input(weight, dtype)
return weighted_binary_cross_entropy(output, target, weight, name)
def cross_entropy_with_softmax(output_vector, target_vector, axis=-1, name=''):
r'''
This operation computes the cross entropy between the ``target_vector`` and
the softmax of the ``output_vector``. The elements of ``target_vector``
have to be non-negative and should sum to 1. The ``output_vector`` can
contain any values. The function will internally compute the softmax of
the ``output_vector``. Concretely,
:math:`\mathrm{softmax}(x)=\left[\frac{\exp(x_1)}{\sum_i\exp(x_i)}\quad\frac{\exp(x_1)}{\sum_i\exp(x_i)}\quad\ldots\quad\frac{\exp(x_1)}{\sum_i\exp(x_i)}\right]`
:math:`\mathrm{cross\_entropy\_with\_softmax}(o, t) = -\sum_{i} t_i \log(\mathrm{softmax}(o)_i)`
with the understanding that the implementation can use equivalent formulas
for efficiency and numerical stability.
Example:
>>> C.cross_entropy_with_softmax([[1., 1., 1., 50.]], [[0., 0., 0., 1.]]).eval()
array([[ 0.]], dtype=float32)
>>> C.cross_entropy_with_softmax([[1., 2., 3., 4.]], [[0.35, 0.15, 0.05, 0.45]]).eval()
array([[ 1.84019]], dtype=float32)
Args:
output_vector: the unscaled computed output values from the network
target_vector: usually it is one-hot vector where the hot bit
corresponds to the label index. But it can be any probability
distribution over the labels.
axis (int or :class:`~cntk.axis.Axis`, optional): if given, cross entropy will be computed
along this axis
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import cross_entropy_with_softmax
dtype = get_data_type(output_vector, target_vector)
output_vector = sanitize_input(output_vector, dtype)
target_vector = sanitize_input(target_vector, dtype)
axis = sanitize_axis(axis)
return cross_entropy_with_softmax(output_vector, target_vector, axis, name)
def cross_entropy_with_softmax(output_vector, target_vector, axis=-1, name=''):
r'''
This operation computes the cross entropy between the ``target_vector`` and
the softmax of the ``output_vector``. The elements of ``target_vector``
have to be non-negative and should sum to 1. The ``output_vector`` can
contain any values. The function will internally compute the softmax of
the ``output_vector``. Concretely,
:math:`\mathrm{softmax}(x)=\left[\frac{\exp(x_1)}{\sum_i\exp(x_i)}\quad\frac{\exp(x_1)}{\sum_i\exp(x_i)}\quad\ldots\quad\frac{\exp(x_1)}{\sum_i\exp(x_i)}\right]`
:math:`\mathrm{cross\_entropy\_with\_softmax}(o, t) = -\sum_{i} t_i \log(\mathrm{softmax}(o)_i)`
with the understanding that the implementation can use equivalent formulas
for efficiency and numerical stability.
Example:
>>> C.cross_entropy_with_softmax([[1., 1., 1., 50.]], [[0., 0., 0., 1.]]).eval()
array([[ 0.]], dtype=float32)
>>> C.cross_entropy_with_softmax([[1., 2., 3., 4.]], [[0.35, 0.15, 0.05, 0.45]]).eval()
array([[ 1.84019]], dtype=float32)
Args:
output_vector: the unscaled computed output values from the network
target_vector: usually it is one-hot vector where the hot bit
corresponds to the label index. But it can be any probability
distribution over the labels.
axis (int or :class:`~cntk.axis.Axis`, optional): if given, cross entropy will be computed
along this axis
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import cross_entropy_with_softmax
dtype = get_data_type(output_vector, target_vector)
output_vector = sanitize_input(output_vector, dtype)
target_vector = sanitize_input(target_vector, dtype)
axis = sanitize_axis(axis)
return cross_entropy_with_softmax(output_vector, target_vector, axis, name)
def is_last(seq, name=''):
'''
Returns a symbolic sequence of booleans with the same length as ``seq``. The
last element of the sequence is 1 and all others are 0.
Example:
>>> x = C.sequence.input_variable(shape=(3,2))
>>> y = C.sequence.is_last(x)
>>> # create one sequence of 4 tensors each with shape (3,2)
>>> x0 = np.reshape(np.arange(24.0,dtype=np.float32),(1,4,3,2))
>>> y.eval({x:x0})
[array([ 0., 0., 0., 1.], dtype=float32)]
Args:
seq: the symbolic tensor denoting a sequence
name (str): the name of the node in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import is_last
seq = sanitize_input(seq, get_data_type(seq))
return is_last(seq, name)
def first(seq, name=''):
'''
Returns the first element of its symbolic input sequence ``seq``
Example:
>>> x = C.sequence.input_variable(shape=(3,2))
>>> y = C.sequence.first(x)
>>> # create one sequence of 4 tensors each with shape (3,2)
>>> x0 = np.reshape(np.arange(24.0,dtype=np.float32),(1,4,3,2))
>>> y.eval({x:x0})
array([[[ 0., 1.],
[ 2., 3.],
[ 4., 5.]]], dtype=float32)
Args:
seq: the symbolic tensor denoting a sequence
name (str): the name of the node in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import first
seq = sanitize_input(seq, get_data_type(seq))
return first(seq, name)
def first(seq, name=''):
'''
Returns the first element of its symbolic input sequence ``seq``
Example:
>>> x = C.sequence.input(shape=(3,2))
>>> y = C.sequence.first(x)
>>> # create one sequence of 4 tensors each with shape (3,2)
>>> x0 = np.reshape(np.arange(24.0,dtype=np.float32),(1,4,3,2))
>>> y.eval({x:x0})
array([[[ 0., 1.],
[ 2., 3.],
[ 4., 5.]]], dtype=float32)
Args:
seq: the symbolic tensor denoting a sequence
name (str): the name of the node in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import first
seq = sanitize_input(seq, get_data_type(seq))
return first(seq, name)
def is_last(seq, name=''):
'''
Returns a symbolic sequence of booleans with the same length as ``seq``. The
last element of the sequence is 1 and all others are 0.
Example:
>>> x = C.sequence.input(shape=(3,2))
>>> y = C.sequence.is_last(x)
>>> # create one sequence of 4 tensors each with shape (3,2)
>>> x0 = np.reshape(np.arange(24.0,dtype=np.float32),(1,4,3,2))
>>> y.eval({x:x0})
[array([ 0., 0., 0., 1.], dtype=float32)]
Args:
seq: the symbolic tensor denoting a sequence
name (str): the name of the node in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import is_last
seq = sanitize_input(seq, get_data_type(seq))
return is_last(seq, name)
def classification_error(output_vector, target_vector, axis=-1, topN=1, name=''):
'''
This operation computes the classification error. It finds the index of the highest
value in the output_vector and compares it to the actual ground truth label
(the index of the hot bit in the target vector). The result is a scalar
(i.e., one by one matrix). This is often used as an evaluation criterion.
It cannot be used as a training criterion though since the gradient is not
defined for it.
Example:
>>> C.classification_error([[1., 2., 3., 4.]], [[0., 0., 0., 1.]]).eval()
array([[ 0.]], dtype=float32)
>>> C.classification_error([[1., 2., 3., 4.]], [[0., 0., 1., 0.]]).eval()
array([[ 1.]], dtype=float32)
>>> # Note that non-1 values are treated as 0
>>> C.classification_error([[1., 2., 3., 4.]], [[5., 0., 1., 0.]]).eval()
array([[ 1.]], dtype=float32)
Args:
output_vector: the output values from the network
target_vector: it is one-hot vector where the hot bit corresponds to
the label index.
axis (int or :class:`~cntk.axis.Axis`): axis along which the
classification error will be computed.
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import classification_error
dtype = get_data_type(output_vector, target_vector)
output_vector = sanitize_input(output_vector, dtype)
target_vector = sanitize_input(target_vector, dtype)
axis = sanitize_axis(axis)
return classification_error(output_vector, target_vector, topN, axis, name)
def reduce_sum(seq, name=''):
'''
Computes the sum of the input sequence's elements across the sequence axis.
Examples:
>>> x = C.sequence.input_variable(shape=(3,2))
>>> # create one sequence of 4 tensors each with shape (3,2)
>>> x0 = np.reshape(np.arange(24.0,dtype=np.float32),(1,4,3,2))
>>> y = C.sequence.reduce_sum(x)
>>> y.eval({x:x0})
array([[[ 36., 40.],
[ 44., 48.],
[ 52., 56.]]], dtype=float32)
Args:
seq: sequence input tensor
name (`str`, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import sequence_reduce_sum
seq = sanitize_input(seq, get_data_type(seq))
return sequence_reduce_sum(seq, name)
def reduce_sum(seq, name=''):
'''
Computes the sum of the input sequence's elements across the sequence axis.
Examples:
>>> x = C.sequence.input(shape=(3,2))
>>> # create one sequence of 4 tensors each with shape (3,2)
>>> x0 = np.reshape(np.arange(24.0,dtype=np.float32),(1,4,3,2))
>>> y = C.sequence.reduce_sum(x)
>>> y.eval({x:x0})
array([[[ 36., 40.],
[ 44., 48.],
[ 52., 56.]]], dtype=float32)
Args:
seq: sequence input tensor
name (`str`, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
'''
from cntk.cntk_py import sequence_reduce_sum
seq = sanitize_input(seq, get_data_type(seq))
return sequence_reduce_sum(seq, name)
def nce_loss(weights, biases, inputs, labels, noise_distribution, num_samples=32, allow_duplicates=True, seed=auto_select, name=''):
'''nce_loss(weights, biases, inputs, labels, noise_distribution, num_samples=32, allow_duplicates=True, seed=auto_select, name='')
Computes the noise contrastive estimation loss. This implementation mostly
follows Chris Dyer's notes [1]. At a high level, this layer draws
`num_samples` random labels from `noise_distribution` and then forms
`num_samples`+1 binary classification problems where the true label is
considered a positive example and the random labels are considered negative
examples. The negatives are shared among all the examples in the
minibatch. This operation only computes the logits for the labels in the
minibatch and the random labels drawn from `noise_distribution`. The
gradients will be sparse if the labels are sparse.
The `noise_distribution` is read once and certain quantities are
precomputed based on it. This operation will need to be reinstantiated if
the `noise_distribution` changes.
Shape inference for the weights is currently not supported when inputs are
placeholders. Either a concrete input must be used or the weights must be
provided without any inferred dimensions.
Example:
>>> import scipy
>>> # dimensions of input, number of noise labels, batch size, number of classes
>>> xdim = 10
>>> samples = 32
>>> batch = 4
>>> classes = 100
>>> # some variables; typically x will be the output of a layer
>>> x = C.input_variable(xdim)
>>> y = C.input_variable(classes, is_sparse=True)
>>> # dummy data
>>> x0 = np.arange(batch * xdim, dtype=np.float32).reshape((batch, xdim))/(batch * xdim)
>>> data = np.ones(batch, dtype=np.float32)
>>> indices = list(range(10, 10*batch+1, 10))
>>> indptr = list(range(batch + 1))
>>> y0 = scipy.sparse.csr_matrix((data, indices, indptr), shape=(batch, classes))
>>> # a dummy noise distribution
>>> q = np.arange(classes, dtype=np.float32) + 1 # normalization not necessary
>>> # the parameters
>>> b = C.parameter((classes, 1), init=-np.log(classes))
>>> W = C.parameter((classes, C.InferredDimension), init=C.glorot_uniform(seed=98052))
>>> # the loss
>>> loss = C.nce_loss(W, b, x, y, q, seed=98052)
>>> # evaluate the loss at our dummy data
>>> np.round(loss.eval({x:x0, y:y0}), decimals=3)
array([ 2.385, 3.035, 3.886, 3.868], dtype=float32)
>>> # after training, use the logits for predictions
>>> logits = C.times_transpose(x, W) + C.reshape(b, -1)
Args:
weights: parameter (or variable in general) containing the weights with
which inputs will be multiplied. Its shape must be
(number of classes, dimension of input)
biases: parameter (or variable in general) containing the biases that
will be added to the product of weights and inputs. Its shape must be
(number of classes, 1)
inputs: vector of inputs to this layer. Multiplying by the weights and
adding the biases gives the logits.
labels: a one-hot vector with the ground-truth labels.
noise_distribution: a constant vector with dimension equal to the number
of classes. The entries must be positive numbers but do not have to
sum to 1. random labels will be drawn according to the normalized
distribution.
num_samples: number of random labels that will be drawn from the
`noise_distribution`.
allow_duplicates: boolean. If True (default), the random labels can
contain duplicates. Compared to `allow_duplicates=False` it is faster
but the quality of the approximations is slightly worse for the same
number of samples.
seed: random seed. The default value selects a unique random seed.
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
See also:
[1] C. Dyer. `Notes on Noise Contrastive Estimation and Negative Sampling [pdf] <http://demo.clab.cs.cmu.edu/cdyer/nce_notes.pdf>`_.
'''
from cntk.cntk_py import nce_loss
dtype = get_data_type(inputs, labels, noise_distribution)
inputs = sanitize_input(inputs, dtype)
labels = sanitize_input(labels, dtype)
noise_distribution = sanitize_input(noise_distribution, dtype)
return nce_loss(weights, biases, inputs, labels, noise_distribution,
num_samples, allow_duplicates, seed, name)
def test_get_data_type():
pa32 = C.parameter(init=np.asarray(2, dtype=np.float32))
pa64 = C.parameter(init=np.asarray(2, dtype=np.float64))
pl = C.placeholder(shape=(2))
c = C.constant(value=3.0)
n32 = AA(1, dtype=np.float32)
n64 = AA(1, dtype=np.float64)
assert get_data_type(pa32) == np.float32
assert get_data_type(pa32, n32) == np.float32
assert get_data_type(n32, n32) == np.float32
assert get_data_type(n32, n64) == np.float64
assert get_data_type(pl, n64) == np.float64
assert get_data_type(pl, n32) == np.float32
assert get_data_type(pl, pl) is None
# variable's type shall take precedence over provided data
assert get_data_type(pa32, n64) == np.float32
assert get_data_type(pa64, n64) == np.float64
assert get_data_type(pa32, pl, n64) == np.float32
assert get_data_type(pa64, pl, n64) == np.float64
def nce_loss(weights,
biases,
inputs,
labels,
noise_distribution,
num_samples=32,
allow_duplicates=True,
seed=auto_select,
name=''):
'''nce_loss(weights, biases, inputs, labels, noise_distribution, num_samples=32, allow_duplicates=True, seed=auto_select, name='')
Computes the noise contrastive estimation loss. This implementation mostly
follows Chris Dyer's notes [1]. At a high level, this layer draws
`num_samples` random labels from `noise_distribution` and then forms
`num_samples`+1 binary classification problems where the true label is
considered a positive example and the random labels are considered negative
examples. The negatives are shared among all the examples in the
minibatch. This operation only computes the logits for the labels in the
minibatch and the random labels drawn from `noise_distribution`. The
gradients will be sparse if the labels are sparse.
The `noise_distribution` is read once and certain quantities are
precomputed based on it. This operation will need to be reinstantiated if
the `noise_distribution` changes.
Shape inference for the weights is currently not supported when inputs are
placeholders. Either a concrete input must be used or the weights must be
provided without any inferred dimensions.
Example:
>>> import scipy
>>> # dimensions of input, number of noise labels, batch size, number of classes
>>> xdim = 10
>>> samples = 32
>>> batch = 4
>>> classes = 100
>>> # some variables; typically x will be the output of a layer
>>> x = C.input_variable(xdim)
>>> y = C.input_variable(classes, is_sparse=True)
>>> # dummy data
>>> x0 = np.arange(batch * xdim, dtype=np.float32).reshape((batch, xdim))/(batch * xdim)
>>> data = np.ones(batch, dtype=np.float32)
>>> indices = list(range(10, 10*batch+1, 10))
>>> indptr = list(range(batch + 1))
>>> y0 = scipy.sparse.csr_matrix((data, indices, indptr), shape=(batch, classes))
>>> # a dummy noise distribution
>>> q = np.arange(classes, dtype=np.float32) + 1 # normalization not necessary
>>> # the parameters
>>> b = C.parameter((classes, 1), init=-np.log(classes))
>>> W = C.parameter((classes, C.InferredDimension), init=C.glorot_uniform(seed=98052))
>>> # the loss
>>> loss = C.nce_loss(W, b, x, y, q, seed=98052)
>>> # evaluate the loss at our dummy data
>>> np.round(loss.eval({x:x0, y:y0}), decimals=3)
array([ 2.385, 3.035, 3.886, 3.868], dtype=float32)
>>> # after training, use the logits for predictions
>>> logits = C.times(W, C.reshape(x, (xdim, 1))) + b
Args:
weights: parameter (or variable in general) containing the weights with
which inputs will be multiplied. Its shape must be
(number of classes, dimension of input)
biases: parameter (or variable in general) containing the biases that
will be added to the product of weights and inputs. Its shape must be
(number of classes, 1)
inputs: vector of inputs to this layer. Multiplying by the weights and
adding the biases gives the logits.
labels: a one-hot vector with the ground-truth labels.
noise_distribution: a constant vector with dimension equal to the number
of classes. The entries must be positive numbers but do not have to
sum to 1. random labels will be drawn according to the normalized
distribution.
num_samples: number of random labels that will be drawn from the
`noise_distribution`.
allow_duplicates: boolean. If True (default), the random labels can
contain duplicates. Compared to `allow_duplicates=False` it is faster
but the quality of the approximations is slightly worse for the same
number of samples.
seed: random seed. The default value selects a unique random seed.
name (str, optional): the name of the Function instance in the network
Returns:
:class:`~cntk.ops.functions.Function`
See also:
[1] C. Dyer. `Notes on Noise Contrastive Estimation and Negative Sampling [pdf] <http://demo.clab.cs.cmu.edu/cdyer/nce_notes.pdf>`_.
'''
from cntk.cntk_py import nce_loss
dtype = get_data_type(inputs, labels, noise_distribution)
inputs = sanitize_input(inputs, dtype)
labels = sanitize_input(labels, dtype)
noise_distribution = sanitize_input(noise_distribution, dtype)
return nce_loss(weights, biases, inputs, labels, noise_distribution,
num_samples, allow_duplicates, seed, name)
def test_get_data_type():
pa32 = C.parameter(init=np.asarray(2, dtype=np.float32))
pa64 = C.parameter(init=np.asarray(2, dtype=np.float64))
pl = C.placeholder(shape=(2))
c = C.constant(value=3.0)
n32 = AA(1, dtype=np.float32)
n64 = AA(1, dtype=np.float64)
assert get_data_type(pa32) == np.float32
assert get_data_type(pa32, n32) == np.float32
assert get_data_type(n32, n32) == np.float32
assert get_data_type(n32, n64) == np.float64
assert get_data_type(pl, n64) == np.float64
assert get_data_type(pl, n32) == np.float32
assert get_data_type(pl, pl) is None
# variable's type shall take precedence over provided data
assert get_data_type(pa32, n64) == np.float32
assert get_data_type(pa64, n64) == np.float64
assert get_data_type(pa32, pl, n64) == np.float32
assert get_data_type(pa64, pl, n64) == np.float64
