実装されている標準関数¶
Chainer provides basic Function
implementations in the
chainer.functions
package. Most of them are wrapped by plain Python
functions, which users should use.
注釈
As of v1.5, the concept of parameterized functions are gone, and they are
replaced by corresponding Link
implementations. They are
still put in the functions
namespace for backward
compatibility, though it is strongly recommended to use them via the
chainer.links
package.
活性化関数¶
clipped_relu¶
crelu¶

chainer.functions.
crelu
(x, axis=1)[ソース]¶ Concatenated Rectified Linear Unit function.
This function is expressed as \(f(x) = (\max(0, x), \max(0, x))\), where two output values are concatenated along an axis.
See: http://arxiv.org/abs/1603.05201
パラメータ: 戻り値: Output variable.
戻り値の型:
elu¶

chainer.functions.
elu
(x, alpha=1.0)[ソース]¶ Exponential Linear Unit function.
This function is expressed as
\[\begin{split}f(x) = \left \{ \begin{array}{ll} x & {\rm if}~ x \ge 0 \\ \alpha (\exp(x)  1) & {\rm if}~ x < 0, \end{array} \right.\end{split}\]where \(\alpha\) is a parameter. See: http://arxiv.org/abs/1511.07289
パラメータ: 戻り値: Output variable.
戻り値の型:
hard_sigmoid¶

chainer.functions.
hard_sigmoid
(x)[ソース]¶ Elementwise hardsigmoid function.
This function is defined as
\[\begin{split}f(x) = \left \{ \begin{array}{ll} 0 & {\rm if}~ x < 0.25 \\ 0.2 x + 0.5 & {\rm if}~ 0.25 < x < 0.25 \\ 1 & {\rm if}~ 0.25 < x. \end{array} \right.\end{split}\]パラメータ: x (Variable) – Input variable. 戻り値: Output variable. 戻り値の型: Variable
leaky_relu¶
log_softmax¶

chainer.functions.
log_softmax
(x, use_cudnn=True)[ソース]¶ Channelwise logsoftmax function.
This function computes its logarithm of softmax along the second axis. Let \(i = (i_1, i_2, \dots, i_d)^{\top}\) be the d dimensional index array and \(x = f(i)\) be the corresponding d dimensional input array. For each index \(i\) of the input array \(f(i)\), it computes the logarithm of the probability \(\log p(x)\) defined as
\[p(i) = {\exp(f(i)) \over \sum_{i'_2} \exp(f(i'))},\]where \(i' = (i_1, i'_2, \dots, i_d)\).
\[p(x) = {\exp(f(x)) \over \sum_{x'} \exp(f(x'))}.\]This method is theoretically equivalent to
log(softmax(x))
but is more stable.注釈
log(softmax(x))
may cause underflow whenx
is too small, becausesoftmax(x)
may returns0
.log_softmax
method is more stable.パラメータ: 戻り値: Output variable.
戻り値の型: 参考
lstm¶

chainer.functions.
lstm
(c_prev, x)[ソース]¶ Long ShortTerm Memory units as an activation function.
This function implements LSTM units with forget gates. Let the previous cell state \(c_{\text{prev}}\) and the incoming signal \(x\).
First, the incoming signal \(x\) is split into four arrays \(a, i, f, o\) of the same shapes along the second axis. It means that \(x\) ‘s second axis must have 4 times the length of \(c_{\text{prev}}\).
The split input signals are corresponding to:
 \(a\) : sources of cell input
 \(i\) : sources of input gate
 \(f\) : sources of forget gate
 \(o\) : sources of output gate
Second, it computes outputs as:
\[\begin{split}c &= \tanh(a) \text{sigmoid}(i) + c_{\text{prev}} \text{sigmoid}(f), \\ h &= \tanh(c) \text{sigmoid}(o).\end{split}\]These are returned as a tuple of two variables.
This function supports variable length inputs. The minibatch size of the current input must be equal to or smaller than that of the previous one. When minibatch size of
x
is smaller than that ofc
, this function only updatesc[0:len(x)]
and doesn’t change the rest ofc
,c[len(x):]
. So, please sort input sequences in descending order of lengths before applying the function.パラメータ: 戻り値:  Two
Variable
objectsc
andh
.c
is the updated cell state.
h
indicates the outgoing signal.
戻り値の型: See the original paper proposing LSTM with forget gates: Long ShortTerm Memory in Recurrent Neural Networks.
例
Assuming
y
is the current input signal,c
is the previous cell state, andh
is the previous output signal from anlstm
function. Each ofy
,c
andh
hasn_units
channels. Most typical preparation ofx
is:>>> n_units = 100 >>> y = chainer.Variable(np.zeros((1, n_units), 'f')) >>> h = chainer.Variable(np.zeros((1, n_units), 'f')) >>> c = chainer.Variable(np.zeros((1, n_units), 'f')) >>> model = chainer.Chain(w=F.Linear(n_units, 4 * n_units), ... v=F.Linear(n_units, 4 * n_units),) >>> x = model.w(y) + model.v(h) >>> c, h = F.lstm(c, x)
It corresponds to calculate the input sources \(a, i, f, o\) from the current input
y
and the previous outputh
. Different parameters are used for different kind of input sources.
maxout¶

chainer.functions.
maxout
(x, pool_size, axis=1)[ソース]¶ Maxout activation function.
It accepts an input tensor
x
, reshapes theaxis
dimension (say the size beingM * pool_size
) into two dimensions(M, pool_size)
, and takes maximum along theaxis
dimension. The output of this function is same asx
except thataxis
dimension is transformed fromM * pool_size
toM
.Typically,
x
is the output of a linear layer or a convolution layer. The following is the example where we usemaxout()
in combination with a Linear link.>>> in_size, out_size, pool_size = 100, 100, 100 >>> l = L.Linear(in_size, out_size * pool_size) >>> x = chainer.Variable(np.zeros((1, in_size), 'f')) # prepare data >>> x = l(x) >>> y = F.maxout(x, pool_size)
パラメータ: x (Variable) – Input variable. Its first dimension is assumed to be the minibatch dimension. The other dimensions are treated as one concatenated dimension. 戻り値: Output variable. 戻り値の型: Variable 参考
prelu¶

chainer.functions.
prelu
(x, W)[ソース]¶ Parametric ReLU function.
It accepts two arguments: an input
x
and a weight arrayW
and computes the output as \(PReLU(x) = \max(x, W*x)\), where \(*\) is an elementwise multiplication for each sample in the batch.When the PReLU function is combined with twodimensional convolution, the elements of parameter \(a\) are typically shared across the same filter of different pixels. In order to support such usage, this function supports the shape of parameter array that indicates leading dimensions of input arrays except the batch dimension.
For example \(W\) has the shape of \((2, 3, 4)\), \(x\) must have the shape of \((B, 2, 3, 4, S1, ..., SN)\) where B is batch size and the number of trailing S’s is arbitrary nonnegative integer.
パラメータ: 戻り値: Output variable
戻り値の型: 参考
relu¶
sigmoid¶
slstm¶

chainer.functions.
slstm
(c_prev1, c_prev2, x1, x2)[ソース]¶ SLSTM units as an activation function.
This function implements SLSTM unit. It is an extension of LSTM unit applied to tree structures. The function is applied to binary trees. Each node has two child nodes. It gets four arguments, previous cell states \(c_1\) and \(c_2\), and incoming signals \(x_1\) and \(x_2\).
First both input signals \(x_1\) and \(x_2\) are split into eight arrays \(a_1, i_1, f_1, o_1\), and \(a_2, i_2, f_2, o_2\). They have the same shape along the second axis. It means that \(x_1\) and \(x_2\) ‘s second axis must have 4 times the length of \(c_{1 \text{prev}}\) and \(c_{2 \text{prev}}\).
The split input signals are corresponding to:
 \(a_i\) : sources of cell input
 \(i_i\) : sources of input gate
 \(f_i\) : sources of forget gate
 \(o_i\) : sources of output gate
It computes outputs as:
\[\begin{split}c &= \tanh(a_1 + a_2) \sigma(i_1 + i_2) + c_{1 \text{prev}} \sigma(f_1) + c_{2 \text{prev}} \sigma(f_2), \\ h &= \tanh(c) \sigma(o_1 + o_2),\end{split}\]where \(\sigma\) is the elementwise sigmoid function. The function returns \(c\) and \(h\) as a tuple.
パラメータ:  c_prev1 (Variable) – Variable that holds the previous cell state of the first child node. The cell state should be a zero array or the output of the previous call of LSTM.
 c_prev2 (Variable) – Variable that holds the previous cell state of the second child node.
 x1 (Variable) – Variable that holds the incoming signal from the first child node. It must have the second dimension four times of that of the cell state,
 x2 (Variable) – Variable that holds the incoming signal from the second child node.
戻り値:  Two
Variable
objectsc
andh
.c
is the cell state.
h
indicates the outgoing signal.
戻り値の型: See detail in paper: Long ShortTerm Memory Over Tree Structures.
softmax¶

chainer.functions.
softmax
(x, use_cudnn=True)[ソース]¶ Channelwise softmax function.
This function computes its softmax along the second axis. Let \(x = (x_1, x_2, \dots, x_d)^{\top}\) be the d dimensional index array and \(f(x)\) be the d dimensional input array. For each index \(x\) of the input array \(f(x)\), it computes the probability \(p(x)\) defined as \(p(x) = {\exp(f(x)) \over \sum_{x_2} \exp(f(x))}\).
パラメータ: 戻り値: Output variable.
戻り値の型:
softplus¶
配列の操作¶
broadcast¶
broadcast_to¶
cast¶
concat¶
copy¶

chainer.functions.
copy
(x, dst)[ソース]¶ Copies the input variable onto the specified device.
This function copies the array of input variable onto the device specified by
dst
. Whendst == 1
, it copies the array onto the host memory. This function supports copies from host to device, from device to device and from device to host.パラメータ:  x (Variable) – Variable to be copied.
 dst – Target device specifier.
戻り値: Output variable.
戻り値の型:
dstack¶
expand_dims¶
flatten¶
get_item¶
hstack¶
permutate¶

chainer.functions.
permutate
(x, indices, axis=0, inv=False)[ソース]¶ Permutates a given variable along an axis.
This function permutate
x
with givenindices
. That meansy[i] = x[indices[i]]
for alli
. Note that this result is same asy = x.take(indices)
.indices
must be a permutation of[0, 1, ..., len(x)  1]
.When
inv
isTrue
,indices
is treated as its inverse. That meansy[indices[i]] = x[i]
.パラメータ: 戻り値: Output variable.
戻り値の型:
reshape¶
rollaxis¶
select_item¶
separate¶

chainer.functions.
separate
(x, axis=0)[ソース]¶ Separates an array along a given axis.
This function separates an array along a given axis. For example, shape of an array is
(2, 3, 4)
. When it separates the array withaxis=1
, it returns three(2, 4)
arrays.This function is an inverse of
chainer.functions.stack()
.パラメータ:  x (chainer.Variable) – Variable to be separated.
 axis (int) – Axis along which variables are separated.
戻り値: Output variables.
戻り値の型: tuple of chainer.Variable
split_axis¶

chainer.functions.
split_axis
(x, indices_or_sections, axis, force_tuple=False)[ソース]¶ Splits given variables along an axis.
パラメータ:  x (tuple of Variables) – Variables to be split.
 indices_or_sections (int or 1D array) – If this argument is an integer, N, the array will be divided into N equal arrays along axis. If it is a 1D array of sorted integers, it indicates the positions where the array is split.
 axis (int) – Axis that the input array is split along.
 force_tuple (bool) – If
True
, this method returns a tuple even when the number of outputs is one.
戻り値: 戻り値の型: 注釈
This function raises
ValueError
if at least one of the outputs is split to zerosize (i.e.axis
th value of its shape is zero).
squeeze¶

chainer.functions.
squeeze
(x, axis=None)[ソース]¶ Remove demensions of size one from the shape of a ndarray.
パラメータ:  x (chainer.Variable or :class:``numpy.ndarray` or cupy.ndarray) – Input data.
 axis (None or int or tuple of ints) – A subset of the singledimensional
entries in the shape to remove. If
None
is supplied, all of them are removed. The dimension index starts at zero. If an axis with dimension greater than one is selected, an error is raiseed.
戻り値: Variable whose dimensions of size 1 are removed.
戻り値の型:
stack¶
swapaxes¶
tile¶

chainer.functions.
tile
(x, reps)[ソース]¶ Construct an array by tiling a given array.
パラメータ:  x (chainer.Variable or
numpy.ndarray
or cupy.ndarray) – Input data.  reps (int or tuple of ints) – The number of times for each axis with which x is replicated.
戻り値: Variable tiled the given array.
戻り値の型:  x (chainer.Variable or
transpose¶

chainer.functions.
transpose
(x, axes=None)[ソース]¶ Permute the dimensions of an input variable without copy.
パラメータ:  x (Variable) – Input variable.
 axes (tuple of ints) – By default, reverse the dimensions, otherwise permute the axes according to the values given.
戻り値: Variable whose axes are permuted.
戻り値の型:
transpose_sequence¶

chainer.functions.
transpose_sequence
(xs)[ソース]¶ Transpose a list of Variables.
This function transposes a list of
Variable
s and returns a list ofVariable
s. For example a user gives[(0, 1, 2, 3), (4, 5), (6)]
, the function returns[(0, 4, 6), (1, 5), (2), (3)]
. Note that a given list needs to be sorted by each length ofVariable
.パラメータ: xs (list of ~chainer.Variable) – Variables to transpose. 戻り値: Transposed list. 戻り値の型: tuple or Variable
vstack¶
ニューラルネットワーク接続¶
bilinear¶

chainer.functions.
bilinear
(e1, e2, W, V1=None, V2=None, b=None)[ソース]¶ Applies a bilinear function based on given parameters.
This is a building block of Neural Tensor Network (see the reference paper below). It takes two input variables and one or four parameters, and outputs one variable.
To be precise, denote six input arrays mathematically by \(e^1\in \mathbb{R}^{I\cdot J}\), \(e^2\in \mathbb{R}^{I\cdot K}\), \(W\in \mathbb{R}^{J \cdot K \cdot L}\), \(V^1\in \mathbb{R}^{J \cdot L}\), \(V^2\in \mathbb{R}^{K \cdot L}\), and \(b\in \mathbb{R}^{L}\), where \(I\) is minibatch size. In this document, we call \(V^1\), \(V^2\), and \(b\) linear parameters.
The output of forward propagation is calculated as
\[y_{il} = \sum_{jk} e^1_{ij} e^2_{ik} W_{jkl} + \ \sum_{j} e^1_{ij} V^1_{jl} + \sum_{k} e^2_{ik} V^2_{kl} + b_{l}.\]Note that V1, V2, b are optional. If these are not given, then this function omits the last three terms in the above equation.
注釈
This function accepts an input variable
e1
ore2
of a nonmatrix array. In this case, the leading dimension is treated as the batch dimension, and the other dimensions are reduced to one dimension.注釈
In the original paper, \(J\) and \(K\) must be equal and the author denotes \([V^1 V^2]\) (concatenation of matrices) by \(V\).
パラメータ: 戻り値: Output variable.
戻り値の型:  See:
 Reasoning With Neural Tensor Networks for Knowledge Base Completion [Socher+, NIPS2013].
convolution_2d¶

chainer.functions.
convolution_2d
(x, W, b=None, stride=1, pad=0, use_cudnn=True, cover_all=False, deterministic=False)[ソース]¶ Twodimensional convolution function.
This is an implementation of twodimensional convolution in ConvNets. It takes three variables: the input image
x
, the filter weightW
, and the bias vectorb
.Notation: here is a notation for dimensionalities.
 \(n\) is the batch size.
 \(c_I\) and \(c_O\) are the number of the input and output channels, respectively.
 \(h\) and \(w\) are the height and width of the input image, respectively.
 \(k_H\) and \(k_W\) are the height and width of the filters, respectively.
パラメータ:  x (Variable) – Input variable of shape \((n, c_I, h, w)\).
 W (Variable) – Weight variable of shape \((c_O, c_I, k_H, k_W)\).
 b (Variable) – Bias variable of length \(c_O\) (optional).
 stride (int or pair of ints) – Stride of filter applications.
stride=s
andstride=(s, s)
are equivalent.  pad (int or pair of ints) – Spatial padding width for input arrays.
pad=p
andpad=(p, p)
are equivalent.  use_cudnn (bool) – If
True
, then this function uses cuDNN if available.  cover_all (bool) – If True, all spatial locations are convoluted into some output pixels. It may make the output size larger.
 deterministic (bool) – The output of this function can be
nondeterministic when it uses cuDNN.
If this option is
True
, then it forces cuDNN to use a deterministic algorithm. This option is only available for cuDNN version >= v4.
戻り値: Output variable.
戻り値の型: The twodimensional convolution function is defined as follows. Then the
Convolution2D
function computes correlations between filters and patches of size \((k_H, k_W)\) inx
. Note that correlation here is equivalent to the inner product between expanded vectors. Patches are extracted at positions shifted by multiples ofstride
from the first positionpad
for each spatial axis. The rightmost (or bottommost) patches do not run over the padded spatial size.Let \((s_Y, s_X)\) be the stride of filter application, and \((p_H, p_W)\) the spatial padding size. Then, the output size \((h_O, w_O)\) is determined by the following equations:
\[\begin{split}h_O &= (h + 2p_H  k_H) / s_Y + 1,\\ w_O &= (w + 2p_W  k_W) / s_X + 1.\end{split}\]If the bias vector is given, then it is added to all spatial locations of the output of convolution.
convolution_nd¶

chainer.functions.
convolution_nd
(x, W, b=None, stride=1, pad=0, use_cudnn=True, cover_all=False)[ソース]¶ Ndimensional convolution function.
This is an implementation of Ndimensional convolution which is generalized twodimensional convolution in ConvNets. It takes three variables: the input
x
, the filter weightW
and the bias vectorb
.Notation: here is a notation for dimensionalities.
 \(N\) is the number of spatial dimensions.
 \(n\) is the batch size.
 \(c_I\) and \(c_O\) are the number of the input and output channels, respectively.
 \(d_1, d_2, ..., d_N\) are the size of each axis of the input’s spatial dimensions, respectively.
 \(k_1, k_2, ..., k_N\) are the size of each axis of the filters, respectively.
パラメータ:  x (Variable) – Input variable of shape \((n, c_I, d_1, d_2, ..., d_N)\).
 W (Variable) – Weight variable of shape \((c_O, c_I, k_1, k_2, ..., k_N)\).
 b (Variable) – Onedimensional bias variable with length \(c_O\) (optional).
 stride (int or tuple of ints) – Stride of filter applications
\((s_1, s_2, ..., s_N)\).
stride=s
is equivalent to(s, s, ..., s)
.  pad (int or tuple of ints) – Spatial padding width for input arrays
\((p_1, p_2, ..., p_N)\).
pad=p
is equivalent to(p, p, ..., p)
.  use_cudnn (bool) – If
True
, then this function uses cuDNN if available. See below for the excact conditions.  cover_all (bool) – If
True
, all spatial locations are convoluted into some output pixels. It may make the output size larger. cover_all needs to beFalse
if you want to use cuDNN.
戻り値: Output variable.
戻り値の型: This function uses cuDNN implementation for its forward and backward computation if ALL of the following conditions are satisfied:
cuda.cudnn_enabled
isTrue
use_cudnn
isTrue
 The number of spatial dimensions is more than one.
cover_all
isFalse
 The input’s
dtype
is equal to the filter weight’s.  The
dtype
is FP32, FP64 or FP16(cuDNN version is equal to or greater than v3)
deconvolution_2d¶

chainer.functions.
deconvolution_2d
(x, W, b=None, stride=1, pad=0, outsize=None, use_cudnn=True, deterministic=False)[ソース]¶ Two dimensional deconvolution function.
This is an implementation of twodimensional deconvolution. It takes three variables: input image
x
, the filter weightW
, and the bias vectorb
.パラメータ:  x (Variable) – Input variable of shape \((n, c_I, h, w)\).
 W (Variable) – Weight variable of shape \((c_I, c_O, k_H, k_W)\).
 b (Variable) – Bias variable of length \(c_O\) (optional).
 stride (int or pair of ints) – Stride of filter applications.
stride=s
andstride=(s, s)
are equivalent.  pad (int or pair of ints) – Spatial padding width for input arrays.
pad=p
andpad=(p, p)
are equivalent.  outsize (tuple) – Expected output size of deconvolutional operation.
It should be pair of height and width \((out_H, out_W)\).
Default value is
None
and the outsize is estimated by input size, stride and pad.  use_cudnn (bool) – If
True
, then this function uses cuDNN if available.  deterministic (bool) – The output of this function can be
nondeterministic when it uses cuDNN.
If this option is
True
, then it forces cuDNN to use a deterministic algorithm. This option is only available for cuDNN version >= v4.
The filter weight has four dimensions \((c_I, c_O, k_H, k_W)\) which indicate the number of input channels, output channels, height and width of the kernels, respectively.
The bias vector is of size \(c_O\).
Let \(X\) be the input tensor of dimensions \((n, c_I, h, w)\), \((s_Y, s_X)\) the stride of filter application, and \((p_H, p_W)\) the spatial padding size. Then, the output size \((h_O, w_O)\) is determined by the following equations:
\[\begin{split}h_O &= s_Y (h  1) + k_H  2p_H,\\ w_O &= s_X (w  1) + k_W  2p_W.\end{split}\]
deconvolution_nd¶

chainer.functions.
deconvolution_nd
(x, W, b=None, stride=1, pad=0, outsize=None, use_cudnn=True)[ソース]¶ Ndimensional deconvolution function.
This is an implementation of Ndimensional deconvolution which generalizes twodimensional one. It takes three variables: input
x
, the filter weightW
, and the bias vectorb
.パラメータ:  x (chainer.Variable or
numpy.ndarray
or cupy.ndarray) – Input data of shape \((n, c_I, d_1, d_2, ..., d_N)\).  W (chainer.Variable or
numpy.ndarray
or cupy.ndarray) – Weight data of shape \((c_I, c_O, k_1, k_2, ..., k_N)\).  b (chainer.Variable or
numpy.ndarray
or cupy.ndarray) – Bias vector of length \(c_O\) (optional).  stride (int or tuple of ints) – Stride of filter applications
\((s_1, s_2, ..., s_N)\).
stride=s
is equivalent to(s, s, ..., s)
.  pad (int or tuple of ints) – Spatial padding size for input arrays
\((p_1, p_2, ..., p_N)\).
pad=p
is equivalent to(p, p, ..., p)
.  outsize (tuple of ints) – Expected output size of deconvolutional
operation. It should be a tuple of ints
\((out_1, out_2, ..., out_N)\). Default value is
None
and the outsize is estimated by input size, stride and pad.  use_cudnn (bool) – If
True
, then this function uses cuDNN if available. Note that cuDNN supports more than onedimensional deconvolution operations only.
戻り値: Output variable.
戻り値の型: The filter weight has the following dimensions \((c_I, c_O, k_1, k_2, ..., k_N)\) which indicate the number of input channels, that of output channels and the filter’s spatial sizes, respectively.
The onedimensional bias vector is of size \(c_O\).
Let \(X\) be the input tensor of dimensions \((n, c_I, d_1, d_2, ..., d_N)\), \((s_1, s_2, ..., s_N)\) the stride of filter applications, and \((p_1, p_2, ..., p_N)\) the spacial padding size. Then the output size \((out_1, out_2, ..., out_N)\) is determined by the following equations:
\[\begin{split}out_1 &= s_1 (d_1  1) + k_1  2 p_1,\\ out_2 &= s_2 (d_2  1) + k_2  2 p_2,\\ ...,\\ out_N &= s_N (d_N  1) + k_N  2 p_N.\end{split}\]参考
links.DeconvolutionND
,deconvolution_2d()
 x (chainer.Variable or
dilated_convolution_2d¶

chainer.functions.
dilated_convolution_2d
(x, W, b=None, stride=1, pad=0, dilate=1, use_cudnn=True, cover_all=False)[ソース]¶ Twodimensional dilated convolution function.
This is an implementation of twodimensional dilated convolution in ConvNets. It takes three variables: the input image
x
, the filter weightW
, and the bias vectorb
.Notation: here is a notation for dimensionalities.
 \(n\) is the batch size.
 \(c_I\) and \(c_O\) are the number of the input and output, respectively.
 \(h\) and \(w\) are the height and width of the input image, respectively.
 \(k_H\) and \(k_W\) are the height and width of the filters, respectively.
パラメータ:  x (Variable) – Input variable of shape \((n, c_I, h, w)\).
 W (Variable) – Weight variable of shape \((c_O, c_I, k_H, k_W)\).
 b (Variable) – Bias variable of length \(c_O\) (optional).
 stride (int or pair of ints) – Stride of filter applications.
stride=s
andstride=(s, s)
are equivalent.  pad (int or pair of ints) – Spatial padding width for input arrays.
pad=p
andpad=(p, p)
are equivalent.  dilate (int or pair of ints) – Dilation factor of filter applications.
dilate=d
anddilate=(d, d)
are equivalent.  use_cudnn (bool) – If
True
, then this function uses cuDNN if available.  cover_all (bool) – If True, all spatial locations are convoluted into some output pixels. It may make the output size larger.
戻り値: Output variable.
戻り値の型: The twodimensional dilated convolution function is defined as follows. Then the
DilatedConvolution2D
function computes correlations between filters and patches of size \((k_H, k_W)\) inx
. Patches here are extracted at intervals of the dilation factor. Note that correlation here is equivalent to the inner product between expanded vectors. Patches are extracted at intervals of the dilation factor and at positions shifted by multiples ofstride
from the first positionpad
for each spatial axis. The rightmost (or bottommost) patches do not run over the padded spatial size.Let \((s_Y, s_X)\) be the stride of filter application, \((p_H, p_W)\) the spatial padding size, and \((d_Y, d_X)\) the dilation factor of filter application. Then, the output size \((h_O, w_O)\) is determined by the following equations:
\[\begin{split}h_O &= (h + 2p_H  k_H  (k_H  1) * (d_Y  1)) / s_Y + 1,\\ w_O &= (w + 2p_W  k_W  (k_W  1) * (d_X  1)) / s_X + 1.\end{split}\]If the bias vector is given, then it is added to all spatial locations of the output of convolution.
参考
DilatedConvolution2D
embed_id¶

chainer.functions.
embed_id
(x, W, ignore_label=None)[ソース]¶ Efficient linear function for onehot input.
This function implements so called word embedding. It takes two arguments: a set of IDs (words)
x
in \(B\) dimensional integer vector, and a set of all ID (word) embeddingsW
in \(V \times d\) float32 matrix. It outputs \(B \times d\) matrix whosei
th column is thex[i]
th column ofW
.This function is only differentiable on the input
W
.パラメータ: 戻り値: Output variable.
戻り値の型: 参考
評価関数¶
accuracy¶
損失関数¶
bernoulli_nll¶

chainer.functions.
bernoulli_nll
(x, y)[ソース]¶ Computes the negative loglikelihood of a Bernoulli distribution.
This function calculates the negative loglikelihood of a Bernoulli distribution.
\[B(x; p) = \sum_i {x_i \log(p_i) + (1  x_i)\log(1  p_i)},\]where \(p = \sigma(y)\), and \(\sigma(\cdot)\) is a sigmoid function.
注釈
As this function uses a sigmoid function, you can pass a result of fullyconnected layer (that means
Linear
) to this function directly.パラメータ: 戻り値: A variable representing negative loglikelihood.
戻り値の型:
black_out¶

chainer.functions.
black_out
(x, t, W, samples)[ソース]¶ BlackOut loss function.
BlackOut loss function is defined as
\[\log(p(t))  \sum_{s \in S} \log(1  p(s)),\]where \(t\) is the correct label, \(S\) is a set of negative examples and \(p(\cdot)\) is likelihood of a given label. And, \(p\) is defined as
\[p(y) = \frac{\exp(W_y^\top x)}{ \sum_{s \in samples} \exp(W_s^\top x)}.\]パラメータ: 戻り値: Loss value.
戻り値の型: See: BlackOut: Speeding up Recurrent Neural Network Language Models With Very Large Vocabularies
参考
connectionist_temporal_classification¶

chainer.functions.
connectionist_temporal_classification
(x, t, blank_symbol, input_length=None, label_length=None)[ソース]¶ Connectionist Temporal Classification loss function.
Connectionist Temporal Classification(CTC) [Graves2006] is a loss function of sequence labeling where the alignment between the inputs and target is unknown. See also [Graves2012]
パラメータ:  x (sequence of Variable) – RNN output at each time.
x
must be a list ofVariable
s. Each element ofx
,x[i]
is aVariable
representing output of RNN at timei
.  t (Variable) – Expected label sequence.
 blank_symbol (int) – Index of blank_symbol. This value must be nonnegative.
 input_length (Variable) – Length of valid sequence for each of mini
batch
x
(optional). If input_length is skipped, It regards that all ofx
is valid input.  label_length (Variable) – Length of valid sequence for each of mini
batch
t
(optional). If label_length is skipped, It regards that all oft
is valid input.
戻り値: A variable holding a scalar value of the CTC loss.
戻り値の型: 注釈
You need to input
x
without applying to activation functions(e.g. softmax function), because this function applies softmax functions tox
before calculating CTC loss to avoid numerical limitations. You also need to apply softmax function to forwarded values before you decode it.注釈
This function is differentiable only by
x
.注釈
This function supports (batch, sequence, 1dimensional input)data.
[Graves2006] Alex Graves, Santiago Fernandez, Faustino Gomez, Jurgen Schmidhuber, Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks [Graves2012] Alex Graves, Supervised Sequence Labelling with Recurrent Neural Networks  x (sequence of Variable) – RNN output at each time.
contrastive¶

chainer.functions.
contrastive
(x0, x1, y, margin=1)[ソース]¶ Computes contrastive loss.
It takes a pair of variables and a label as inputs. The label is 1 when those two input variables are similar, or 0 when they are dissimilar. Let \(N\) and \(K\) denote minibatch size and the dimension of input variables, respectively. The shape of both input variables should be
(N, K)
.\[L = \frac{1}{2N} \left( \sum_{n=1}^N y_n d_n^2 + (1  y_n) \max ({\rm margin}  d_n, 0)^2 \right)\]where \(d_n = \ {\bf x_0}_n  {\bf x_1}_n \_2\). \(N\) denotes the minibatch size. Input variables, x0 and x1, have \(N\) vectors, and each vector is Kdimensional. Therefore, \({\bf x_0}_n\) and \({\bf x_1}_n\) are \(n\)th Kdimensional vectors of x0 and x1.
パラメータ:  x0 (Variable) – The first input variable. The shape should be
(N, K), where N denotes the minibatch size, and K denotes the
dimension of
x0
.  x1 (Variable) – The second input variable. The shape should be
the same as
x0
.  y (Variable) – Labels. All values should be 0 or 1. The shape
should be
(N,)
, where N denotes the minibatch size.  margin (float) – A parameter for contrastive loss. It should be positive value.
戻り値:  A variable holding a scalar that is the loss value
calculated by the above equation.
戻り値の型: 注釈
This cost can be used to train siamese networks. See Learning a Similarity Metric Discriminatively, with Application to Face Verification for details.
 x0 (Variable) – The first input variable. The shape should be
(N, K), where N denotes the minibatch size, and K denotes the
dimension of
crf1d¶

chainer.functions.
crf1d
(cost, xs, ys)[ソース]¶ Calculates negative loglikelihood of linearchain CRF.
It takes a transition cost matrix, a sequence of costs, and a sequence of labels. Let \(c_{st}\) be a transition cost from a label \(s\) to a label \(t\), \(x_{it}\) be a cost of a label \(t\) at position \(i\), and \(y_i\) be an expected label at position \(i\). The negative loglikelihood of linearchain CRF is defined as
\[L = \left( \sum_{i=1}^l x_{iy_i} + \ \sum_{i=1}^{l1} c_{y_i y_{i+1}}  {\log(Z)} \right) ,\]where \(l\) is the length of the input sequence and \(Z\) is the normalizing constant called partition function.
注釈
When you want to calculate the negative loglikelihood of sequences which have different lengths, sort the sequences in descending order of lengths and transpose the sequences. For example, you have three input seuqnces:
>>> a1 = a2 = a3 = a4 = np.random.uniform(1, 1, 3).astype('f') >>> b1 = b2 = b3 = np.random.uniform(1, 1, 3).astype('f') >>> c1 = c2 = np.random.uniform(1, 1, 3).astype('f')
>>> a = [a1, a2, a3, a4] >>> b = [b1, b2, b3] >>> c = [c1, c2]
where
a1
and all other variables are arrays with(K,)
shape. Make a transpose of the sequences:>>> x1 = np.stack([a1, b1, c1]) >>> x2 = np.stack([a2, b2, c2]) >>> x3 = np.stack([a3, b3]) >>> x4 = np.stack([a4])
and make a list of the arrays:
>>> xs = [x1, x2, x3, x4]
You need to make label sequences in the same fashion. And then, call the function:
>>> cost = chainer.Variable( ... np.random.uniform(1, 1, (3, 3)).astype('f')) >>> ys = [np.zeros(x.shape[0:1], dtype='i') for x in xs] >>> loss = F.crf1d(cost, xs, ys)
It calculates sum of the negative loglikelihood of the three sequences.
パラメータ:  cost (Variable) – A \(K \times K\) matrix which holds transition cost between two labels, where \(K\) is the number of labels.
 xs (list of Variable) – Input vector for each label.
len(xs)
denotes the length of the sequence, and eachVariable
holds a \(B \times K\) matrix, where \(B\) is minibatch size, \(K\) is the number of labels. Note that \(B\) s in all the variables are not necessary the same, i.e., it accepts the input sequences with different lengths.  ys (list of Variable) – Expected output labels. It needs to have the
same length as
xs
. EachVariable
holds a \(B\) integer vector. Whenx
inxs
has the different \(B\), correspodingy
has the same \(B\). In other words,ys
must satisfyys[i].shape == xs[i].shape[0:1]
for alli
.
戻り値:  A variable holding the average negative
loglikelihood of the input sequences.
戻り値の型: 注釈
See detail in the original paper: Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data.

chainer.functions.
argmax_crf1d
(cost, xs)[ソース]¶ Computes a state that maximizes a joint probability of the given CRF.
パラメータ:  cost (Variable) – A \(K \times K\) matrix which holds transition cost between two labels, where \(K\) is the number of labels.
 xs (list of Variable) – Input vector for each label.
len(xs)
denotes the length of the sequence, and eachVariable
holds a \(B \times K\) matrix, where \(B\) is minibatch size, \(K\) is the number of labels. Note that \(B\) s in all the variables are not necessary the same, i.e., it accepts the input sequences with different lengths.
戻り値:  A tuple of
Variable
objects
and a list
ps
. The shape ofs
is(B,)
, whereB
is the minibatch size. ith element ofs
,s[i]
, represents loglikelihood of ith data.ps
is a list ofnumpy.ndarray
orcupy.ndarray
, and denotes the state that maximizes the point probability.len(ps)
is equal tolen(xs)
, and shape of eachps[i]
is the minibatch size of the correspondingxs[i]
. That means,ps[i].shape == xs[i].shape[0:1]
.
戻り値の型:
cross_covariance¶

chainer.functions.
cross_covariance
(y, z)[ソース]¶ Computes the sumsquared crosscovariance penalty between
y
andz
パラメータ: 戻り値: A variable holding a scalar of the cross covariance loss.
戻り値の型: 注釈
This cost can be used to disentangle variables. See http://arxiv.org/abs/1412.6583v3 for details.
gaussian_kl_divergence¶

chainer.functions.
gaussian_kl_divergence
(mean, ln_var)[ソース]¶ Computes the KLdivergence of Gaussian variables from the standard one.
Given two variable
mean
representing \(\mu\) andln_var
representing \(\log(\sigma^2)\), this function returns a variable representing the KLdivergence between the given multidimensional Gaussian \(N(\mu, S)\) and the standard Gaussian \(N(0, I)\)\[D_{\mathbf{KL}}(N(\mu, S) \ N(0, I)),\]where \(S\) is a diagonal matrix such that \(S_{ii} = \sigma_i^2\) and \(I\) is an identity matrix.
パラメータ: 戻り値:  A variable representing KLdivergence between
given gaussian distribution and the standard gaussian.
戻り値の型:
gaussian_nll¶

chainer.functions.
gaussian_nll
(x, mean, ln_var)[ソース]¶ Computes the negative loglikelihood of a Gaussian distribution.
Given two variable
mean
representing \(\mu\) andln_var
representing \(\log(\sigma^2)\), this function returns the negative loglikelihood of \(x\) on a Gaussian distribution \(N(\mu, S)\),\[\log N(x; \mu, \sigma^2) = \log\left(\sqrt{(2\pi)^D S}\right) + \frac{1}{2}(x  \mu)^\top S^{1}(x  \mu),\]where \(D\) is a dimension of \(x\) and \(S\) is a diagonal matrix where \(S_{ii} = \sigma_i^2\).
パラメータ: 戻り値: A variable representing the negative loglikelihood.
戻り値の型:
hinge¶

chainer.functions.
hinge
(x, t, norm='L1')[ソース]¶ Computes the hinge loss for a oneofmany classification task.
\[L = \frac{1}{N} \sum_{n=1}^N \sum_{k=1}^K \left[ \max(0, 1  \delta\{l_n = k\} t_{nk}) \right]^p\]where \(N\) denotes the batch size, \(K\) is the number of classes of interest,
\[\begin{split}\delta \{ {\rm condition} \} = \left \{ \begin{array}{cc} 1 & {\rm if~condition} \\ 1 & {\rm otherwise,} \end{array} \right.\end{split}\]and
\[\begin{split}p = \left \{ \begin{array}{cc} 1 & {\rm if~norm} = {\rm 'L1'} \\ 2 & {\rm if~norm} = {\rm 'L2'.} \end{array} \right.\end{split}\]パラメータ: 戻り値:  A variable object holding a scalar array of the
hinge loss \(L\).
戻り値の型:
huber_loss¶

chainer.functions.
huber_loss
(x, t, delta)[ソース]¶ Loss function which is less sensitive to outliers in data than MSE.
\[a = x  t\]and
\[\begin{split}L_{\delta}(a) = \left \{ \begin{array}{cc} \frac{1}{2} a^2 & {\rm if~a \leq \delta} \\ \delta (a  \frac{1}{2} \delta) & {\rm otherwise,} \end{array} \right.\end{split}\]パラメータ: 戻り値:  A variable object holding a scalar array of the
huber loss \(L_{\delta}\).
戻り値の型:  See:
 Huber loss  Wikipedia.
mean_absolute_error¶
mean_squared_error¶
negative_sampling¶

chainer.functions.
negative_sampling
(x, t, W, sampler, sample_size)[ソース]¶ Negative sampling loss function.
In natural language processing, especially language modeling, the number of words in a vocabulary can be very large. Therefore, you need to spend a lot of time calculating the gradient of the embedding matrix.
By using the negative sampling trick you only need to calculate the gradient for a few sampled negative examples.
The objective function is below:
\[f(x, p) = \log \sigma(x^\top w_p) + \ k E_{i \sim P(i)}[\log \sigma( x^\top w_i)],\]where \(\sigma(\cdot)\) is a sigmoid function, \(w_i\) is the weight vector for the word \(i\), and \(p\) is a positive example. It is approximated with \(k\) examples \(N\) sampled from probability \(P(i)\), like this:
\[f(x, p) \approx \log \sigma(x^\top w_p) + \ \sum_{n \in N} \log \sigma(x^\top w_n).\]Each sample of \(N\) is drawn from the word distribution \(P(w)\). This is calculated as \(P(w) = \frac{1}{Z} c(w)^\alpha\), where \(c(w)\) is the unigram count of the word \(w\), \(\alpha\) is a hyperparameter, and \(Z\) is the normalization constant.
パラメータ:  x (Variable) – Batch of input vectors.
 t (Variable) – Vector of ground truth labels.
 W (Variable) – Weight matrix.
 sampler (FunctionType) – Sampling function. It takes a shape and
returns an integer array of the shape. Each element of this array
is a sample from the word distribution.
A
WalkerAlias
object built with the power distribution of word frequency is recommended.  sample_size (int) – Number of samples.
See: Distributed Representations of Words and Phrases and their Compositionality
参考
sigmoid_cross_entropy¶

chainer.functions.
sigmoid_cross_entropy
(x, t, use_cudnn=True, normalize=True)[ソース]¶ Computes cross entropy loss for presigmoid activations.
パラメータ:  x (Variable) – A variable object holding a matrix whose (i, j)th element indicates the unnormalized log probability of the jth unit at the ith example.
 t (Variable) – Variable holding an int32 vector of ground truth labels.
If
t[i] == 1
, correspondingx[i]
is ignored. Loss is zero if all ground truth labels are1
.  normalize (bool) – Variable holding a boolean value which determines the normalization constant. If true, this function normalizes the cross entropy loss across all instances. If else, it only normalizes along a batch size.
戻り値:  A variable object holding a scalar array of the cross entropy
loss.
戻り値の型: 注釈
This function is differentiable only by
x
.
softmax_cross_entropy¶

chainer.functions.
softmax_cross_entropy
(x, t, use_cudnn=True, normalize=True, cache_score=True)[ソース]¶ Computes cross entropy loss for presoftmax activations.
パラメータ:  x (Variable) – Variable holding a multidimensional array whose element indicates unnormalized log probability: the first axis of the variable represents the number of samples, and the second axis represents the number of classes. While this function computes a usual softmax cross entropy if the number of dimensions is equal to 2, it computes a cross entropy of the replicated softmax if the number of dimensions is greater than 2.
 t (Variable) – Variable holding an int32 vector of ground truth labels.
If
t[i] == 1
, correspondingx[i]
is ignored.  normalize (bool) – If
True
, this function normalizes the cross entropy loss across all instances. IfFalse
, it only normalizes along a batch size.  cache_score (bool) – When it is
True
, the function stores result of forward computation to use it on backward computation. It reduces computational cost though consumes more memory.
戻り値: A variable holding a scalar array of the cross entropy loss.
戻り値の型: 注釈
This function is differentiable only by
x
.
triplet¶

chainer.functions.
triplet
(anchor, positive, negative, margin=0.2)[ソース]¶ Computes triplet loss.
It takes a triplet of variables as inputs, \(a\), \(p\) and \(n\): anchor, positive example and negative example respectively. The triplet defines a relative similarity between samples. Let \(N\) and \(K\) denote minibatch size and the dimension of input variables, respectively. The shape of all input variables should be \((N, K)\).
\[L(a, p, n) = \frac{1}{N} \left( \sum_{i=1}^N \max \{d(a_i, p_i)  d(a_i, n_i) + {\rm margin}, 0\} \right)\]where \(d(x_i, y_i) = \ {\bf x}_i  {\bf y}_i \_2^2\).
パラメータ:  anchor (Variable) – The anchor example variable. The shape should be \((N, K)\), where \(N\) denotes the minibatch size, and \(K\) denotes the dimension of the anchor.
 positive (Variable) – The positive example variable. The shape should be the same as anchor.
 negative (Variable) – The negative example variable. The shape should be the same as anchor.
 margin (float) – A parameter for triplet loss. It should be a positive value.
戻り値:  A variable holding a scalar that is the loss value
calculated by the above equation.
戻り値の型: 注釈
This cost can be used to train triplet networks. See Learning Finegrained Image Similarity with Deep Ranking for details.
数学関数¶
arccos¶
arcsin¶
arctan¶
argmax¶
argmin¶
batch_inv¶

chainer.functions.
batch_inv
(a)[ソース]¶ Computes the inverse of a batch of square matrices.
パラメータ: a (Variable) – Input array to compute the inverse for. Shape of the array should be (m, n, n)
wherem
is the number of matrices in the batch, andn
is the dimensionality of a square matrix.戻り値: Inverse of every matrix in the batch of matrices. 戻り値の型: Variable
batch_l2_norm_squared¶

chainer.functions.
batch_l2_norm_squared
(x)[ソース]¶ L2 norm (a.k.a. Euclidean norm) squared.
This function implements the square of L2 norm on a vector. No reduction along batch axis is done.
パラメータ: x (Variable) – Input variable. The first dimension is assumed to be the minibatch dimension. If x
has more than two dimensions all but the first dimension are flattened to one dimension.戻り値: Two dimensional output variable. 戻り値の型: Variable
batch_matmul¶

chainer.functions.
batch_matmul
(a, b, transa=False, transb=False)[ソース]¶ Computes the batch matrix multiplications of two sets of arrays.
パラメータ:  a (Variable) – The left operand of the batch matrix multiplications.
A 2D array of shape
(B, N)
is considered as B \(N \times 1\) matrices. A 3D array of shape(B, M, N)
is considered as B \(M \times N\) matrices.  b (Variable) – The right operand of the batch matrix multiplications.
Its array is treated as matrices in the same way as
a
‘s array.  transa (bool) – If
True
, transpose each matrix ina
.  transb (bool) – If
True
, transpose each matrix inb
.
戻り値:  The result of the batch matrix multiplications as a
3D array.
戻り値の型:  a (Variable) – The left operand of the batch matrix multiplications.
A 2D array of shape
bias¶

chainer.functions.
bias
(x, y, axis=1)[ソース]¶ Elementwise summation with broadcasting.
Computes a elementwise summation of two input variables, with the shape of the latter variable broadcasted to match the shape of the former.
axis
is the first axis of the first variable along which the second variable is applied.The term “broadcasting” here comes from Caffe’s bias layer so the “broadcasting” with the following arguments:
x : 100 x 3 x 40 x 60 y : 3 x 40 axis : 1
is equivalent to the following numpy broadcasting:
x : 100 x 3 x 40 x 60 y : 1 x 3 x 40 x 1
Note that how the
axis
indicates to which axis ofx
we applyy
.パラメータ: 戻り値: Output variable.
戻り値の型:
ceil¶
clip¶
cosh¶
floor¶
inv¶
linear_interpolate¶
log10¶
log2¶
logsumexp¶
matmul¶

chainer.functions.
matmul
(a, b, transa=False, transb=False)[ソース]¶ Computes the matrix multiplication of two arrays.
パラメータ:  a (Variable) – The left operand of the matrix multiplication.
A 1D array of shape
(N,)
is considered as an \(N \times 1\) matrix. A 2D array of shape(M, N)
is considered as an \(M \times N\) matrix.  b (Variable) – The right operand of the matrix multiplication.
Its array is treated as a matrix in the same way as
a
‘s array.  transa (bool) – If
True
, transposea
.  transb (bool) – If
True
, transposeb
.
戻り値:  The result of the matrix multiplication as a 2D
array.
戻り値の型:  a (Variable) – The left operand of the matrix multiplication.
A 1D array of shape
max¶
maximum¶
min¶
minimum¶
rsqrt¶
scale¶

chainer.functions.
scale
(x, y, axis=1)[ソース]¶ Elementwise product with broadcasting.
Computes a elementwise product of two input variables, with the shape of the latter variable broadcasted to match the shape of the former.
axis
is the first axis of the first variable along which the second variable is applied.The term “broadcasting” here comes from Caffe’s scale layer so the “broadcasting” with the following arguments:
x : 100 x 3 x 40 x 60 y : 3 x 40 axis : 1
is equivalent to the following numpy broadcasting:
x : 100 x 3 x 40 x 60 y : 1 x 3 x 40 x 1
Note that how the
axis
indicates to which axis ofx
we applyy
.パラメータ: 戻り値: Output variable.
戻り値の型:
sinh¶
sqrt¶
square¶

chainer.functions.
square
(x)[ソース]¶ Elementwise square function.
\[y_i = x_i ^ 2.\]パラメータ: x (chainer.Variable or numpy.ndarray
or cupy.ndarray) – Input variable.戻り値: Output variable. 戻り値の型: Variable
squared_difference¶
ノイズ注入¶
dropout¶

chainer.functions.
dropout
(x, ratio=0.5, train=True)[ソース]¶ Drops elements of input variable randomly.
This function drops input elements randomly with probability
ratio
and scales the remaining elements by factor1 / (1  ratio)
. In testing mode, it does nothing and just returnsx
.パラメータ: 戻り値: Output variable.
戻り値の型: See the paper by G. Hinton: Improving neural networks by preventing coadaptation of feature detectors.
正規化関数¶
batch_normalization¶

chainer.functions.
batch_normalization
(x, gamma, beta, eps=2e05, running_mean=None, running_var=None, decay=0.9, use_cudnn=True)[ソース]¶ Batch normalization function.
It takes the input variable
x
and two parameter variablesgamma
andbeta
. The input must have the batch size and the features (or channels) as the first two dimensions of its shape. The input can have more than two dimensions, where the remaining dimensions are considered as spatial dimensions, which are considered as a part of the batch size. That is, the total batch size will be considered to be the product of all dimensions except the second dimension.Note: If this function is called, it will not be possible to access the updated running mean and variance statistics, because they are members of the function object, which cannot be accessed by the caller. If it is desired to access the updated running statistics, it is necessary to get a new instance of the function object, call the object, and then access the running_mean and/or running_var attributes. See the corresponding Link class for an example of how to do this.
パラメータ:  x (Variable) – Input variable.
 gamma (Variable) – Scaling parameter of normalized data.
 beta (Variable) – Shifting parameter of scaled normalized data.
 eps (float) – Epsilon value for numerical stability.
 running_mean (array) – Running average of the mean. This is a
running average of the mean over several minibatches using
the decay parameter. If
None
, the running average is not computed. If this isNone
, thenrunnng_var
must also beNone
.  running_var (array) – Running average of the variance. This is a
running average of the variance over several minibatches using
the decay parameter. If
None
, the running average is not computed. If this isNone
, thenrunning_mean
must also beNone
.  decay (float) – Decay rate of moving average. It is used during training.
 use_cudnn (bool) – If
True
and cuDNN is enabled, then this function uses cuDNN as the core implementation.
See: Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
参考
links.BatchNormalization
fixed_batch_normalization¶

chainer.functions.
fixed_batch_normalization
(x, gamma, beta, mean, var, eps=2e05, use_cudnn=True)[ソース]¶ Batch normalization function with fixed statistics.
This is a variant of batch normalization, where the mean and variance statistics are given by the caller as fixed variables. This is used on testing mode of the batch normalization layer, where batch statistics cannot be used for prediction consistency.
パラメータ:  x (Variable) – Input variable.
 gamma (Variable) – Scaling parameter of normalized data.
 beta (Variable) – Shifting parameter of scaled normalized data.
 mean (Variable) – Shifting parameter of input.
 var (Variable) – Square of scaling parameter of input.
 eps (float) – Epsilon value for numerical stability.
 use_cudnn (bool) – If
True
and cuDNN is enabled, then this function uses cuDNN as the core implementation.
参考
functions.batch_normalization()
,links.BatchNormalization
local_response_normalization¶

chainer.functions.
local_response_normalization
(x, n=5, k=2, alpha=0.0001, beta=0.75)[ソース]¶ Local response normalization across neighboring channels.
This function implements normalization across channels. Let \(x\) an input image with \(N\) channels. Then, this function computes an output image \(y\) by following formula:
\[y_i = {x_i \over \left( k + \ \alpha \sum_{j=\max{1, i  n/2}}^{\min{N, i + n/2}} \ x_j^2 \right)^\beta}.\]パラメータ: 戻り値: Output variable.
戻り値の型: See: Section 3.3 of ImageNet Classification with Deep Convolutional Neural Networks
normalize¶

chainer.functions.
normalize
(x, eps=1e05)[ソース]¶ L2 norm squared (a.k.a. Euclidean norm).
This function implements L2 normalization on a 1D vector. No reduction is done along batch axis. Let \(x\) be an input vector of dimension \((N, K)\), where \(N\) and \(K\) denote minibatch size and the dimension of the input variable. Then, this function computes an output vector \(y\) by the following equation:
\[y_i = {x_i \over \ x_i \_2}\]\(eps\) is used to avoid division by zero when \(x_i=0\)
パラメータ: 戻り値:  Two dimensional output variable, the same shape
as \(x\).
戻り値の型:
空間プーリング¶
average_pooling_2d¶

chainer.functions.
average_pooling_2d
(x, ksize, stride=None, pad=0, use_cudnn=True)[ソース]¶ Spatial average pooling function.
This function acts similarly to
Convolution2D
, but it computes the average of input spatial patch for each channel without any parameter instead of computing the inner products.パラメータ:  x (Variable) – Input variable.
 ksize (int or pair of ints) – Size of pooling window.
ksize=k
andksize=(k, k)
are equivalent.  stride (int or pair of ints or None) – Stride of pooling applications.
stride=s
andstride=(s, s)
are equivalent. IfNone
is specified, then it uses same stride as the pooling window size.  pad (int or pair of ints) – Spatial padding width for the input array.
pad=p
andpad=(p, p)
are equivalent.  use_cudnn (bool) – If
True
and cuDNN is enabled, then this function uses cuDNN as the core implementation.
戻り値: Output variable.
戻り値の型: 注釈
This function currently does not support
cover_all
mode asmax_pooling_2d()
. Average pooling runs in noncoverall mode.
max_pooling_2d¶

chainer.functions.
max_pooling_2d
(x, ksize, stride=None, pad=0, cover_all=True, use_cudnn=True)[ソース]¶ Spatial max pooling function.
This function acts similarly to
Convolution2D
, but it computes the maximum of input spatial patch for each channel without any parameter instead of computing the inner products.パラメータ:  x (Variable) – Input variable.
 ksize (int or pair of ints) – Size of pooling window.
ksize=k
andksize=(k, k)
are equivalent.  stride (int or pair of ints or None) – Stride of pooling applications.
stride=s
andstride=(s, s)
are equivalent. IfNone
is specified, then it uses same stride as the pooling window size.  pad (int or pair of ints) – Spatial padding width for the input array.
pad=p
andpad=(p, p)
are equivalent.  cover_all (bool) – If
True
, all spatial locations are pooled into some output pixels. It may make the output size larger.  use_cudnn (bool) – If
True
and cuDNN is enabled, then this function uses cuDNN as the core implementation.
戻り値: Output variable.
戻り値の型:
roi_pooling_2d¶

chainer.functions.
roi_pooling_2d
(x, rois, outh, outw, spatial_scale)[ソース]¶ Spatial Region of Interest (ROI) pooling function.
This function acts similarly to
MaxPooling2D
, but it computes the maximum of input spatial patch for each channel with the region of interest.パラメータ:  x (Variable) – Input variable. The shape is expected to be 4 dimentional: (n: batch, c: channel, h, height, w: width).
 rois (Variable) – Input roi variable. The shape is expected to be (n: data size, 5), and each datum is set as below: (batch_index, x_min, y_min, x_max, y_max).
 outh (int) – Height of output image after pooled.
 outw (int) – Width of output image after pooled.
 spatial_scale (float) – Scale of the roi is resized.
戻り値: Output variable.
戻り値の型: See the original paper proposing ROIPooling: Fast RCNN.
spatial_pyramid_pooling_2d¶

chainer.functions.
spatial_pyramid_pooling_2d
(x, pyramid_height, pooling_class, use_cudnn=True)[ソース]¶ Spatial pyramid pooling function.
It outputs a fixedlength vector regardless of input feature map size.
It performs pooling operation to the input 4Darray
x
with different kernel sizes and padding sizes, and then flattens all dimensions except first dimension of all pooling results, and finally concatenates them along second dimension.At \(i\)th pyramid level, the kernel size \((k_h^{(i)}, k_w^{(i)})\) and padding size \((p_h^{(i)}, p_w^{(i)})\) of pooling operation are calculated as below:
\[\begin{split}k_h^{(i)} &= \lceil b_h / 2^i \rceil, \\ k_w^{(i)} &= \lceil b_w / 2^i \rceil, \\ p_h^{(i)} &= (2^i k_h^{(i)}  b_h) / 2, \\ p_w^{(i)} &= (2^i k_w^{(i)}  b_w) / 2,\end{split}\]where \(\lceil \cdot \rceil\) denotes the ceiling function, and \(b_h, b_w\) are height and width of input variable
x
, respectively. Note that index of pyramid level \(i\) is zerobased.See detail in paper: Spatial Pyramid Pooling in Deep Convolutional Networks for Visual Recognition.
パラメータ:  x (Variable) – Input variable. The shape of
x
should be(batchsize, # of channels, height, width)
.  pyramid_height (int) – Number of pyramid levels
 pooling_class (MaxPooling2D or AveragePooling2D) – Only MaxPooling2D class can be available for now.
 use_cudnn (bool) – If
True
and cuDNN is enabled, then this function uses cuDNN as the core implementation.
戻り値:  Output variable. The shape of the output variable
will be \((batchsize, c \sum_{h=0}^{H1} 2^{2h}, 1, 1)\), where \(c\) is the number of channels of input variable
x
and \(H\) is the number of pyramid levels.
戻り値の型: 注釈
This function uses some pooling classes as components to perform spatial pyramid pooling. Now it supports only
MaxPooling2D
as elemental pooling operator so far. x (Variable) – Input variable. The shape of
unpooling_2d¶

chainer.functions.
unpooling_2d
(x, ksize, stride=None, pad=0, outsize=None, cover_all=True)[ソース]¶ Inverse operation of pooling for 2d array.
This function acts similarly to
Deconvolution2D
, but it spreads input 2d array’s value without any parameter instead of computing the inner products.パラメータ:  x (Variable) – Input variable.
 ksize (int or pair of ints) – Size of pooling window.
ksize=k
andksize=(k, k)
are equivalent.  stride (int, pair of ints or None) – Stride of pooling applications.
stride=s
andstride=(s, s)
are equivalent. IfNone
is specified, then it uses same stride as the pooling window size.  pad (int or pair of ints) – Spatial padding width for the input array.
pad=p
andpad=(p, p)
are equivalent.  outsize (None or pair of ints) – Expected output size (height, width)
of array after the operation. If
None
, the size (height or width) is estimated from the size of input array in first batch withget_deconv_outsize()
. If outsize is notNone
, the result of outsize applied toget_conv_outsize()
must be equal to the shape of the 2d array in the input batchx
.  cover_all (bool) – If
True
, the output size may be smaller than the size ifcover_all
isFalse
. This flag serves to align behavior to the pooling functions which can cover all input locations, seemax_pooling_2d()
andconvolution_2d()
.
戻り値: Output variable.
戻り値の型:
ユーティリティ関数¶
forget¶

chainer.functions.
forget
(func, *xs)[ソース]¶ Call a function without storing internal results.
On a forward propagation Chainer stores all internal results of
Function
on a computational graph as they are required on backwardpropagation. These results consume too much memory when the internal results are too large. This method forgets such internal results on forward propagation, and still supports backpropagation with recalculation.In a forward propagation, this method calls a given function with given variables without creating a computational graph. That means, no internal results are stored. In a backward propagation this method calls the given function again to create a computational graph to execute backpropagation.
This method reduces internal memory usage. Instead it requires more calculation time as it calls the function twice.
例
Let
f
be a function defined as:>>> def f(a, b): ... return a + b + a
and,
x
andy
beVariable
:>>> x = chainer.Variable(np.random.uniform(1, 1, 5).astype('f')) >>> y = chainer.Variable(np.random.uniform(1, 1, 5).astype('f'))
When
z
is calculated asz = f(x, y)
, its internal resultx + y
is stored in memory. Instead if you callf
withforget()
:>>> z = F.forget(f, x, y)
internal
x + y
is forgotten.注釈
The method does not support functions behaving randomly, such as
dropout()
andnegative_sampling()
. It is because first results of these function differ from the second one.パラメータ: 戻り値: A variable
func
returns. If it returns a tuple, the method returns a tuple too.戻り値の型: