Standard Function implementations¶
Chainer provides basic Function
implementations in the
chainer.functions
package. Most of them are wrapped by plain Python
functions, which users should use.
Note
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.
Activation functions¶
clipped_relu¶

chainer.functions.
clipped_relu
(x, z=20.0)[source]¶ Clipped Rectifier Unit function.
For a clipping value \(z(>0)\), it computes
Parameters:  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable. A \((s_1, s_2, ..., s_n)\)shaped float array.  z (float) – Clipping value. (default = 20.0)
Returns: Output variable. A \((s_1, s_2, ..., s_n)\)shaped float array.
Return type: Example
>>> x = np.random.uniform(100, 100, (10, 20)).astype('f') >>> z = 10.0 >>> np.any(x < 0) True >>> np.any(x > z) True >>> y = F.clipped_relu(x, z=z) >>> np.any(y.data < 0) False >>> np.any(y.data > z) False
 x (
crelu¶

chainer.functions.
crelu
(x, axis=1)[source]¶ Concatenated Rectified Linear Unit function.
This function is expressed as follows
\[f(x) = (\max(0, x), \max(0, x)).\]Here, two output values are concatenated along an axis.
See: https://arxiv.org/abs/1603.05201
Parameters:  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable. A \((s_1, s_2, ..., s_N)\)shaped float array.  axis (int) – Axis that the output values are concatenated along. Default is 1.
Returns: Output variable of concatenated array. If the axis is 1, A \((s_1, s_2 \times 2, ..., s_N)\)shaped float array.
Return type: Example
>>> x = np.array([[1, 0], [2, 3]], 'f') >>> x array([[1., 0.], [ 2., 3.]], dtype=float32) >>> y = F.crelu(x, axis=1) >>> y.data array([[ 0., 0., 1., 0.], [ 2., 0., 0., 3.]], dtype=float32)
 x (
elu¶

chainer.functions.
elu
(x, alpha=1.0)[source]¶ Exponential Linear Unit function.
For a parameter \(\alpha\), it is expressed as
\[\begin{split}f(x) = \left \{ \begin{array}{ll} x & {\rm if}~ x \ge 0 \\ \alpha (\exp(x)  1) & {\rm if}~ x < 0, \end{array} \right.\end{split}\]See: https://arxiv.org/abs/1511.07289
Parameters:  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable. A \((s_1, s_2, ..., s_N)\)shaped float array.  alpha (float) – Parameter \(\alpha\). Default is 1.0.
Returns: Output variable. A \((s_1, s_2, ..., s_N)\)shaped float array.
Return type: Example
>>> x = np.array([[1, 0], [2, 3]], 'f') >>> x array([[1., 0.], [ 2., 3.]], dtype=float32) >>> y = F.elu(x, alpha=1.) >>> y.data array([[0.63212055, 0. ], [ 2. , 0.95021296]], dtype=float32)
 x (
hard_sigmoid¶

chainer.functions.
hard_sigmoid
(x)[source]¶ Elementwise hardsigmoid function.
This function is defined as
\[\begin{split}f(x) = \left \{ \begin{array}{ll} 0 & {\rm if}~ x < 2.5 \\ 0.2 x + 0.5 & {\rm if}~ 2.5 < x < 2.5 \\ 1 & {\rm if}~ 2.5 < x. \end{array} \right.\end{split}\]Parameters: x ( Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable. A \((s_1, s_2, ..., s_N)\)shaped float array.Returns: Output variable. A \((s_1, s_2, ..., s_N)\)shaped float array. Return type: Variable Example
It maps the input values into the range of \([0, 1]\).
>>> x = np.array([2.6, 1, 0, 1, 2.6]) >>> x array([2.6, 1. , 0. , 1. , 2.6]) >>> F.hard_sigmoid(x).data array([ 0. , 0.3, 0.5, 0.7, 1. ])
leaky_relu¶

chainer.functions.
leaky_relu
(x, slope=0.2)[source]¶ Leaky Rectified Linear Unit function.
This function is expressed as
\[f(x)=\max(x, ax),\]where \(a\) is a configurable slope value.
Parameters:  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable. A \((s_1, s_2, ..., s_N)\)shaped float array.  slope (float) – Slope value \(a\).
Returns: Output variable. A \((s_1, s_2, ..., s_N)\)shaped float array.
Return type: Example
>>> x = np.array([[1, 0], [2, 3], [2, 1]], 'f') >>> x array([[1., 0.], [ 2., 3.], [2., 1.]], dtype=float32) >>> F.leaky_relu(x, slope=0.2).data array([[0.2 , 0. ], [ 2. , 0.60000002], [0.40000001, 1. ]], dtype=float32)
 x (
log_softmax¶

chainer.functions.
log_softmax
(x)[source]¶ Channelwise logsoftmax function.
This function computes its logarithm of softmax along the second axis. Let \(c = (c_1, c_2, \dots, c_D)\) be the slice of
x
along with the second axis. For each slice \(c\), it computes the logarithm of the function \(f(c)\) defined as\[f(c) = {\exp(c) \over \sum_{d} \exp(c_d)}.\]This method is theoretically equivalent to
log(softmax(x))
but is more stable.Note
log(softmax(x))
may cause underflow whenx
is too small, becausesoftmax(x)
may returns0
.log_softmax
method is more stable.Parameters: x ( Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable. A \(n\)dimensional (\(n \geq 2\)) float array.Returns: Output variable. A \(n\)dimensional (\(n \geq 2\)) float array, which is the same shape with x. Return type: Variable See also
Example
>>> x = np.array([[0, 1, 2], [0, 2, 4]], 'f') >>> x array([[ 0., 1., 2.], [ 0., 2., 4.]], dtype=float32) >>> F.log_softmax(x).data array([[2.40760589, 1.40760589, 0.40760589], [4.14293146, 2.14293146, 0.14293146]], dtype=float32) >>> np.allclose(F.log_softmax(x).data, F.log(F.softmax(x)).data) True
lstm¶

chainer.functions.
lstm
(c_prev, x)[source]¶ Long ShortTerm Memory units as an activation function.
This function implements LSTM units with forget gates. Let the previous cell state
c_prev
and the input arrayx
.First, the input array
x
is split into four arrays \(a, i, f, o\) of the same shapes along the second axis. It means thatx
‘s second axis must have 4 times thec_prev
‘s second axis.The split input arrays 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 the updated cell state
c
and the outgoing signalh
as:\[\begin{split}c &= \tanh(a) \sigma(i) + c_{\text{prev}} \sigma(f), \\ h &= \tanh(c) \sigma(o),\end{split}\]where \(\sigma\) is the elementwise sigmoid function. 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.Parameters:  c_prev (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Variable that holds the previous cell state. The cell state should be a zero array or the output of the previous call of LSTM.  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Variable that holds the sources of cell input, input gate, forget gate and output gate. It must have the second dimension whose size is four times of that of the cell state.
Returns: Two
Variable
objectsc
andh
.c
is the updated cell state.h
indicates the outgoing signal.Return type: See the original paper proposing LSTM with forget gates: Long ShortTerm Memory in Recurrent Neural Networks.
See also
Example
Assuming
y
is the current incoming signal,c
is the previous cell state, andh
is the previous outgoing 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=L.Linear(n_units, 4 * n_units), ... v=L.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 array
x
, or the input sources \(a, i, f, o\), from the current incoming signaly
and the previous outgoing signalh
. Different parameters are used for different kind of input sources.Note
We use the naming rule below.
 incoming signal
 The formal input of the formulation of LSTM (e.g. in NLP, word
vector or output of lower RNN layer). The input of
chainer.links.LSTM
is the incoming signal.
 input array
 The array which is linear transformed from incoming signal and
the previous outgoing signal. The input array contains four
sources, the sources of cell input, input gate, forget gate and
output gate. The input of
chainer.functions.LSTM
is the input array.
maxout¶

chainer.functions.
maxout
(x, pool_size, axis=1)[source]¶ 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.Parameters:  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable. A \(n\)dimensional (\(n \ge\)axis
) float array. In general, its first dimension is assumed to be the minibatch dimension. The other dimensions are treated as one concatenated dimension.  pool_size (int) – The size used for downsampling of pooling layer.
 axis (int) – The
axis
dimension to be reshaped. The size ofaxis
dimension should beM * pool_size
.
Returns: Output variable. The shape of the output is same as
x
except thataxis
dimension is transformed fromM * pool_size
toM
.Return type: See also
Example
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 = 10, 10, 10 >>> bias = np.arange(out_size * pool_size).astype('f') >>> l = L.Linear(in_size, out_size * pool_size, initial_bias=bias) >>> x = np.zeros((1, in_size), 'f') # prepare data >>> x = l(x) >>> y = F.maxout(x, pool_size) >>> x.shape (1, 100) >>> y.shape (1, 10) >>> x.reshape((out_size, pool_size)).data array([[ 0., 1., 2., 3., 4., 5., 6., 7., 8., 9.], [ 10., 11., 12., 13., 14., 15., 16., 17., 18., 19.], [ 20., 21., 22., 23., 24., 25., 26., 27., 28., 29.], [ 30., 31., 32., 33., 34., 35., 36., 37., 38., 39.], [ 40., 41., 42., 43., 44., 45., 46., 47., 48., 49.], [ 50., 51., 52., 53., 54., 55., 56., 57., 58., 59.], [ 60., 61., 62., 63., 64., 65., 66., 67., 68., 69.], [ 70., 71., 72., 73., 74., 75., 76., 77., 78., 79.], [ 80., 81., 82., 83., 84., 85., 86., 87., 88., 89.], [ 90., 91., 92., 93., 94., 95., 96., 97., 98., 99.]], dtype=float32) >>> y.data array([[ 9., 19., 29., 39., 49., 59., 69., 79., 89., 99.]], dtype=float32)
 x (
prelu¶

chainer.functions.
prelu
(x, W)[source]¶ 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.
Parameters: Returns: Output variable
Return type: See also
relu¶

chainer.functions.
relu
(x)[source]¶ Rectified Linear Unit function.
\[f(x)=\max(0, x).\]Parameters: x ( Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable. A \((s_1, s_2, ..., s_N)\)shaped float array.Returns: Output variable. A \((s_1, s_2, ..., s_N)\)shaped float array. Return type: Variable Example
>>> x = np.array([[1, 0], [2, 3], [2, 1]], 'f') >>> np.any(x < 0) True >>> y = F.relu(x) >>> np.any(y.data < 0) False >>> y.shape (3, 2)
sigmoid¶

chainer.functions.
sigmoid
(x)[source]¶ Elementwise sigmoid logistic function.
\[f(x)=(1 + \exp(x))^{1}.\]Parameters: x ( Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable. A \((s_1, s_2, ..., s_N)\)shaped float array.Returns: Output variable. A \((s_1, s_2, ..., s_N)\)shaped float array. Return type: Variable Example
It maps the input values into the range of \([0, 1]\).
>>> x = np.arange(2, 3, 2).astype('f') >>> x array([2., 0., 2.], dtype=float32) >>> F.sigmoid(x).data array([ 0.11920291, 0.5 , 0.88079709], dtype=float32)
slstm¶

chainer.functions.
slstm
(c_prev1, c_prev2, x1, x2)[source]¶ 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_prev1
andc_prev2
, and input arraysx1
andx2
.First both input arrays
x1
andx2
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 thatx1
andx2
‘s second axis must have 4 times the length ofc_prev1
andc_prev2
.The split input arrays 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 the updated cell state
c
and the outgoing signalh
as:\[\begin{split}c &= \tanh(a_1 + a_2) \sigma(i_1 + i_2) + c_{\text{prev}1} \sigma(f_1) + c_{\text{prev}2} \sigma(f_2), \\ h &= \tanh(c) \sigma(o_1 + o_2),\end{split}\]where \(\sigma\) is the elementwise sigmoid function. The function returns
c
andh
as a tuple.Parameters:  c_prev1 (
Variable
ornumpy.ndarray
orcupy.ndarray
) – 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
ornumpy.ndarray
orcupy.ndarray
) – Variable that holds the previous cell state of the second child node.  x1 (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Variable that holds the sources of cell input, input gate, forget gate and output gate from the first child node. It must have the second dimension whose size is four times of that of the cell state.  x2 (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Variable that holds the input sources from the second child node.
Returns: Two
Variable
objectsc
andh
.c
is the cell state.h
indicates the outgoing signal.Return type: See detail in paper: Long ShortTerm Memory Over Tree Structures.
Example
Assuming
c1
,c2
is the previous cell state of children, andh1
,h2
is the previous outgoing signal from children. Each ofc1
,c2
,h1
andh2
hasn_units
channels. Most typical preparation ofx1
,x2
is:>>> n_units = 100 >>> h1 = chainer.Variable(np.zeros((1, n_units), 'f')) >>> h2 = chainer.Variable(np.zeros((1, n_units), 'f')) >>> c1 = chainer.Variable(np.zeros((1, n_units), 'f')) >>> c2 = chainer.Variable(np.zeros((1, n_units), 'f')) >>> model1 = chainer.Chain(w=L.Linear(n_units, 4 * n_units), ... v=L.Linear(n_units, 4 * n_units)) >>> model2 = chainer.Chain(w=L.Linear(n_units, 4 * n_units), ... v=L.Linear(n_units, 4 * n_units)) >>> x1 = model1.w(c1) + model1.v(h1) >>> x2 = model2.w(c2) + model2.v(h2) >>> c, h = F.slstm(c1, c2, x1, x2)
It corresponds to calculate the input array
x1
, or the input sources \(a_1, i_1, f_1, o_1\) from the previous cell state of first child nodec1
, and the previous outgoing signal from first child nodeh1
. Different parameters are used for different kind of input sources.
softmax¶

chainer.functions.
softmax
(x, axis=1)[source]¶ Softmax function.
This function computes its softmax along an 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 \(p(x) = {\exp(f(x)) \over \sum_{d} \exp(f(x_d))}\).
Parameters: x (Variable) – Input variable. Returns: Output variable. Return type: Variable
softplus¶

chainer.functions.
softplus
(x, beta=1.0)[source]¶ Elementwise softplus function.
The softplus function is the smooth approximation of ReLU.
\[f(x)=\frac{1}{\beta}\log(1 + \exp(\beta x)),\]where \(\beta\) is a parameter. The function becomes curved and akin to ReLU as the \(\beta\) is increasing.
Parameters:  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable. A \((s_1, s_2, ..., s_N)\)shaped float array.  beta (float) – Parameter \(\beta\).
Returns: Output variable. A \((s_1, s_2, ..., s_N)\)shaped float array.
Return type: Example
>>> x = np.arange(2, 3, 2).astype('f') >>> x array([2., 0., 2.], dtype=float32) >>> F.softplus(x, beta=1.0).data array([ 0.126928 , 0.69314718, 2.12692809], dtype=float32)
 x (
tanh¶

chainer.functions.
tanh
(x)[source]¶ Elementwise hyperbolic tangent function.
\[f(x)=\tanh(x).\]Parameters: x ( Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable. A \((s_1, s_2, ..., s_N)\)shaped float array.Returns: Output variable. A \((s_1, s_2, ..., s_N)\)shaped float array. Return type: Variable Example
>>> x = np.arange(1, 4, 2).astype('f') >>> x array([1., 1., 3.], dtype=float32) >>> F.tanh(x).data array([0.76159418, 0.76159418, 0.99505478], dtype=float32)
Array manipulations¶
broadcast¶

chainer.functions.
broadcast
(*args)[source]¶ Broadcast given variables.
Parameters: args ( Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variables to be broadcasted. Each dimension of the shapes of the input variables must have the same size.Returns: Variable
or tuple ofVariable
objects which are broadcasted from given arguments.Return type: Variable Example
>>> x = np.random.uniform(0, 1, (3, 2)).astype('f') >>> y = F.broadcast(x) >>> np.all(x == y.data) True >>> z = np.random.uniform(0, 1, (3, 2)).astype('f') >>> y, w = F.broadcast(x, z) >>> np.all(x == y.data) & np.all(z == w.data) True
broadcast_to¶

chainer.functions.
broadcast_to
(x, shape)[source]¶ Broadcast a given variable to a given shape.
Parameters:  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable be broadcasted. A \((s_1, s_2, ..., s_N)\)shaped float array.  shape (tuple) – Tuple of
int
of the shape of the output variable.
Returns: Output variable broadcasted to the given shape.
Return type: Example
>>> x = np.arange(0, 3) >>> x array([0, 1, 2]) >>> y = F.broadcast_to(x, (3, 3)) >>> y.data array([[0, 1, 2], [0, 1, 2], [0, 1, 2]])
 x (
cast¶

chainer.functions.
cast
(x, typ)[source]¶ Cast an input variable to a given type.
Parameters:  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable to be casted. A \((s_1, s_2, ..., s_N)\)shaped float array.  typ (
str
of dtype ornumpy.dtype
) – Typecode or data type to cast.
Returns: Variable holding a casted array.
Return type: Example
>>> x = np.arange(0, 3, dtype=np.float64) >>> x.dtype dtype('float64') >>> y = F.cast(x, np.float32) >>> y.dtype dtype('float32') >>> y = F.cast(x, 'float16') >>> y.dtype dtype('float16')
 x (
concat¶

chainer.functions.
concat
(xs, axis=1)[source]¶ Concatenates given variables along an axis.
Parameters:  xs (tuple of
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variables to be concatenated. The variables must have the same shape, except in the dimension corresponding to axis.  axis (int) – The axis along which the arrays will be joined. Default is 1.
Returns: The concatenated variable.
Return type: Example
>>> x = np.arange(0, 12).reshape(3, 4) >>> x array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> y = np.arange(0, 3).reshape(3, 1) >>> y array([[0], [1], [2]]) >>> z = F.concat((x, y), axis=1) >>> z.data array([[ 0, 1, 2, 3, 0], [ 4, 5, 6, 7, 1], [ 8, 9, 10, 11, 2]])
 xs (tuple of
copy¶

chainer.functions.
copy
(x, dst)[source]¶ 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 host, from host to device, from device to device and from device to host.Parameters:  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Variable to be copied.  dst (int) – Target device specifier.
Returns: Output variable.
Return type: Example
>>> import chainer.cuda as cuda >>> x = np.random.uniform(1, 1, (5, 10)) >>> cuda.get_device_from_array(x).id 1 >>> y = F.copy(x, 0) # from host to device0 >>> cuda.get_device_from_array(y.data).id 0 >>> z = F.copy(y, 1) # from device0 to host >>> cuda.get_device_from_array(z.data).id 1
 x (
depth2space¶

chainer.functions.
depth2space
(X, r)[source]¶ Computes the depth2space transformation for subpixel calculations.
Parameters:  X (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Variable holding a 4d array of shape(batch, channel * r * r, dim1, dim2)
.  r (int) – the upscaling factor.
Returns: A variable holding the upscaled array from interspersed depth layers. The shape is
(batch, channel, dim1 * r, dim2 * r)
.Return type: Note
This can be used to compute superresolution transformations. See https://arxiv.org/abs/1609.05158 for details.
See also
Example
>>> X = np.arange(24).reshape(1, 4, 2, 3).astype('f') >>> X.shape (1, 4, 2, 3) >>> X array([[[[ 0., 1., 2.], [ 3., 4., 5.]], [[ 6., 7., 8.], [ 9., 10., 11.]], [[ 12., 13., 14.], [ 15., 16., 17.]], [[ 18., 19., 20.], [ 21., 22., 23.]]]], dtype=float32) >>> y = F.depth2space(X, 2) >>> y.shape (1, 1, 4, 6) >>> y.data array([[[[ 0., 6., 1., 7., 2., 8.], [ 12., 18., 13., 19., 14., 20.], [ 3., 9., 4., 10., 5., 11.], [ 15., 21., 16., 22., 17., 23.]]]], dtype=float32)
 X (
dstack¶

chainer.functions.
dstack
(xs)[source]¶ Concatenate variables along third axis (depth wise).
Parameters: xs (list of Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variables to be concatenated. The variables must have the samendim
. When the variables have the third axis (i.e. \(ndim \geq 3\)), the variables must have the same shape along all but the third axis. When the variables do not have the third axis(i.e. \(ndim < 3\)), the variables must have the same shape.Returns: Output variable. When the input variables have the third axis (i.e. \(ndim \geq 3\)), the shapes of inputs and output are the same along all but the third axis. The length of third axis is the sum of the lengths of inputs’ third axis. When the shape of variables are (N1, N2)
(i.e. \(ndim = 2\)), the shape of output is(N1, N2, 2)
. When the shape of variables are(N1,)
(i.e. \(ndim = 1\)), the shape of output is(1, N1, 2)
. When the shape of variables are()
(i.e. \(ndim = 0\)), the shape of output is(1, 1, 2)
.Return type: Variable Example
>>> x1 = np.array((1, 2, 3)) >>> x1.shape (3,) >>> x2 = np.array((2, 3, 4)) >>> x2.shape (3,) >>> y = F.dstack((x1, x2)) >>> y.shape (1, 3, 2) >>> y.data array([[[1, 2], [2, 3], [3, 4]]])
>>> x1 = np.arange(0, 6).reshape(3, 2) >>> x1.shape (3, 2) >>> x1 array([[0, 1], [2, 3], [4, 5]]) >>> x2 = np.arange(6, 12).reshape(3, 2) >>> x2.shape (3, 2) >>> x2 array([[ 6, 7], [ 8, 9], [10, 11]]) >>> y = F.dstack([x1, x2]) >>> y.shape (3, 2, 2) >>> y.data array([[[ 0, 6], [ 1, 7]], [[ 2, 8], [ 3, 9]], [[ 4, 10], [ 5, 11]]])
>>> x1 = np.arange(0, 12).reshape(3, 2, 2) >>> x2 = np.arange(12, 18).reshape(3, 2, 1) >>> y = F.dstack([x1, x2]) >>> y.shape (3, 2, 3) >>> y.data array([[[ 0, 1, 12], [ 2, 3, 13]], [[ 4, 5, 14], [ 6, 7, 15]], [[ 8, 9, 16], [10, 11, 17]]])
expand_dims¶

chainer.functions.
expand_dims
(x, axis)[source]¶ Expands dimensions of an input variable without copy.
Parameters:  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable.  axis (int) – Position where new axis is to be inserted. The
axis
parameter is acceptable when \(ndim  1 \leq axis \leq ndim\). (ndim
is the dimension of input variables). When \(axis < 0\), the result is the same with \(ndim + 1  axis\).
Returns: Variable that holds a expanded input. The
ndim
of output is one grater than that ofx
.Return type: Example
>>> x = np.array([1, 2, 3]) >>> x.shape (3,) >>> y = F.expand_dims(x, axis=0) >>> y.shape (1, 3) >>> y.data array([[1, 2, 3]]) >>> y = F.expand_dims(x, axis=1) >>> y.shape (3, 1) >>> y.data array([[1], [2], [3]]) >>> y = F.expand_dims(x, axis=2) >>> y.shape (1, 3) >>> y.data array([[1, 2, 3]])
 x (
flatten¶
fliplr¶
flipud¶
get_item¶

chainer.functions.
get_item
(x, slices)[source]¶ Extract elements from array with specified shape, axes and offsets.
Parameters: Returns: Variable
objectwhich contains sliced array of
x
.
Return type: Note
It only supports types that are supported by CUDA’s atomicAdd when an integer array is included in
slices
. The supported types arenumpy.float32
,numpy.int32
,numpy.uint32
,numpy.uint64
andnumpy.ulonglong
.Note
It does not support
slices
that contains multiple boolean arrays.Note
See NumPy document for details of indexing.
hstack¶

chainer.functions.
hstack
(xs)[source]¶ Concatenate variables horizontally (column wise).
Parameters: xs (list of Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variables to be concatenated. The variables must have the samendim
. When the variables have the second axis (i.e. \(ndim \geq 2\)), the variables must have the same shape along all but the second axis. When the variables do not have the second axis(i.e. \(ndim < 2\)), the variables need not to have the same shape.Returns: Output variable. When the input variables have the second axis (i.e. \(ndim \geq 2\)), the shapes of inputs and output are the same along all but the second axis. The length of second axis is the sum of the lengths of inputs’ second axis. When the variables do not have the second axis (i.e. \(ndim < 2\)), the shape of output is (N, )
(N
is the sum of the input variables’ size).Return type: Variable Example
>>> x1 = np.array((1, 2, 3)) >>> x1.shape (3,) >>> x2 = np.array((2, 3, 4)) >>> x2.shape (3,) >>> y = F.hstack((x1, x2)) >>> y.shape (6,) >>> y.data array([1, 2, 3, 2, 3, 4]) >>> x1 = np.arange(0, 12).reshape(3, 4) >>> x1.shape (3, 4) >>> x1 array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> x2 = np.arange(12, 18).reshape(3, 2) >>> x2.shape (3, 2) >>> x2 array([[12, 13], [14, 15], [16, 17]]) >>> y = F.hstack([x1, x2]) >>> y.shape (3, 6) >>> y.data array([[ 0, 1, 2, 3, 12, 13], [ 4, 5, 6, 7, 14, 15], [ 8, 9, 10, 11, 16, 17]])
im2col¶

chainer.functions.
im2col
(x, ksize, stride=1, pad=0, cover_all=False, dilate=1)[source]¶ Extract patches from an image based on the filter.
This function rearranges patches of an image and put them in the channel dimension of the output.
Patches are extracted at positions shifted by multiples of
stride
from the first positionpad
for each spatial axis. The rightmost (or bottommost) patches do not run over the padded spatial size.Notation: here is a notation.
 \(n\) is the batch size.
 \(c\) is the number of the input channels.
 \(h\) 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.
 \(s_Y\) and \(s_X\) are the strides of the filter.
 \(p_H\) and \(p_W\) are the spatial padding sizes.
 \(d_Y\) and \(d_X\) are the dilation factors of filter application.
The output size \((h_O, w_O)\) is determined by the following equations when
cover_all = False
:\[\begin{split}h_O &= (h + 2p_H  k_H  (k_H  1) * (d_Y  1)) / s_Y + 1,\\ w_O &= (w + 2p_W  k_W  (k_W  1) * (d_X  1)) / s_X + 1.\end{split}\]When
cover_all = True
, the output size is determined by the following equations:\[\begin{split}h_O &= (h + 2p_H  k_H  (k_H  1) * (d_Y  1) + s_Y  1) / s_Y + 1,\\ w_O &= (w + 2p_W  k_W  (k_W  1) * (d_X  1) + s_X  1) / s_X + 1.\end{split}\]Parameters:  x (Variable) – Input variable of shape \((n, c, h, w)\).
 ksize (int or pair of ints) – Size of filters (a.k.a. kernels).
ksize=k
andksize=(k, k)
are equivalent.  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.  cover_all (bool) – If
True
, all spatial locations are rearranged into some output pixels. It may make the output size larger.  dilate (int or pair of ints) – Dilation factor of filter applications.
dilate=d
anddilate=(d, d)
are equivalent.
Returns: Output variable whose shape is \((n, c \cdot k_H \cdot k_W, h_O, w_O)\)
Return type:
pad¶

chainer.functions.
pad
(x, pad_width, mode, **keywords)[source]¶ Pad an input variable.
Parameters:  x (chainer.Variable or :class:
numpy.ndarray
or cupy.ndarray) – Input data.  pad_width (int or arraylike) – Number of values padded to the edges of each axis.
 mode (str) – Specifies how the function fills the periphery of the array.
The mode is passed to
numpy.pad()
orcupy.pad()
. If it is'constant'
, the input is padded by a constant value specified byconstant_values
.  constant_values (int or arraylike) – Constant values to fill the periphery in the
'constant'
mode.
Returns: Output variable.
Return type:  x (chainer.Variable or :class:
permutate¶

chainer.functions.
permutate
(x, indices, axis=0, inv=False)[source]¶ 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]
.Parameters: Returns: Output variable.
Return type:
reshape¶
resize_images¶

chainer.functions.
resize_images
(x, output_shape)[source]¶ Resize images to the given shape.
This function resizes 2D data to
output_shape
. Currently, only bilinear interpolation is supported as the sampling method.Notatition: here is a notation for dimensionalities.
 \(n\) is the batch size.
 \(c_I\) is the number of the input channels.
 \(h\) and \(w\) are the height and width of the input image, respectively.
 \(h_O\) and \(w_O\) are the height and width of the output image.
Parameters: Returns: Resized image whose shape is \((n, c_I, h_O, w_O)\).
Return type:
rollaxis¶
select_item¶
separate¶

chainer.functions.
separate
(x, axis=0)[source]¶ 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()
.Parameters:  x (chainer.Variable) – Variable to be separated.
 axis (int) – Axis along which variables are separated.
Returns: Output variables.
Return type: tuple of chainer.Variable
See also
space2depth¶

chainer.functions.
space2depth
(X, r)[source]¶ Computes the space2depth transformation for subpixel calculations.
Parameters:  X (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Variable holding a 4d array of shape(batch, channel, dim1 * r, dim2 * r)
.  r (int) – the downscaling factor.
Returns: A variable holding the downscaled layer array from subpixel array sampling. The shape is
(batch, channel * r * r, dim1, dim2)
.Return type: Note
This can be used to compute inverse superresolution transformations. See https://arxiv.org/abs/1609.05158 for details.
See also
Example
>>> X = np.arange(24).reshape(1, 1, 4, 6).astype('f') >>> X.shape (1, 1, 4, 6) >>> X array([[[[ 0., 1., 2., 3., 4., 5.], [ 6., 7., 8., 9., 10., 11.], [ 12., 13., 14., 15., 16., 17.], [ 18., 19., 20., 21., 22., 23.]]]], dtype=float32) >>> y = F.space2depth(X, 2) >>> y.shape (1, 4, 2, 3) >>> y.data array([[[[ 0., 2., 4.], [ 12., 14., 16.]], [[ 1., 3., 5.], [ 13., 15., 17.]], [[ 6., 8., 10.], [ 18., 20., 22.]], [[ 7., 9., 11.], [ 19., 21., 23.]]]], dtype=float32)
 X (
spatial_transformer_grid¶

chainer.functions.
spatial_transformer_grid
(theta, output_shape, use_cudnn=True)[source]¶ 2D Spatial Transformer grid.
This function generates coordinates of the points sampled from an image to perform warping described in Spatial Transformer Networks.
Given a coordinate in the warped image \((x_i^t, y_i^t)\), the point sampled from the source image \((x_i^s, y_i^s)\) are calculated by the following equation.
\[\begin{split}\left(\begin{matrix} x_i^s \\ y_i^s \end{matrix}\right) = \left(\begin{matrix} \theta_{11} & \theta_{12} & \theta_{13} \\ \theta_{21} & \theta_{22} & \theta_{23} \end{matrix}\right) \left(\begin{matrix} x_i^t \\ y_i^t \\ 1 \end{matrix}\right)\end{split}\]Notatition: here is a notation for dimensionalities.
 \(n\) is the batch size.
 \(h_O\) and \(w_O\) are the height and the width of the output image.
Parameters:  theta (Variable) – An array of shape \((n, 2, 3)\). This is a batch of \(2 \times 3\) matrix used for the warping described above.
 output_shape (tuple) – A tuple of 2 elements: \(h_O, w_O\).
 use_cudnn (bool) – If
True
, then this function uses cuDNN if available. Note that, cuDNN supports SpatialTransformerGrid from version 5.0.0.
Returns: A variable of shape \((n, 2, h_O, w_O)\). In the 2nd dimension, the first element is the coordinate along the x axis, and the second element is the coordinate along the y axis. All the coordinates in the image are scaled to fit range \([1, 1]\). This means that the coordinate \((1, 1)\) corresponds to the upperleft corner of the input image.
Return type:
spatial_transformer_sampler¶

chainer.functions.
spatial_transformer_sampler
(x, grid, use_cudnn=True)[source]¶ 2D Spatial Transformer sampler.
This is a differentiable image sampler. With a set of sampling points
grid
and an input feature mapx
, this produces a sampled output feature map.This function currently only supports bilinear interpolation as a sampling kernel.
When coordinates in
grid
is outside range \([1, 1]\), values are sampled from a zero padded input image.Notatition: here is a notation for dimensionalities.
 \(n\) is the batch size.
 \(c_I\) is the number of the input channels.
 \(h\) and \(w\) are the height and width of the input image, respectively.
 \(h_O\) and \(w_O\) are the height and width of the output image.
See detail in the following paper: Spatial Transformer Networks.
Parameters:  x (Variable) – Input variable of shape \((n, c_I, h, w)\).
 grid (Variable) –
Coordinate variable of shape \((n, 2, h_O, w_O)\). Each coordinate defines the spatial location in the input where a sampling kernel is applied to get the value at a particular pixel in the output.
grid[idx, :, i, j]
corresponds to the coordinate that is used to sample the values for an output pixel at location \((i, j)\).In the second dimension, the first coordinate corresponds to the location along the horizontal axis, and the second coordinate corresponds to the location along the vertical axis.
The coordinate \((1, 1)\) corresponds to the upperleft corner of the input image.
 use_cudnn (bool) – If
True
, then this function uses cuDNN if available. Note that, cuDNN supports SpatialTransformerSampler from version 5.0.0.
Returns: Output feature map of shape \((n, c_I, h_O, w_O)\).
Return type:
split_axis¶

chainer.functions.
split_axis
(x, indices_or_sections, axis, force_tuple=True)[source]¶ Splits given variables along an axis.
Parameters:  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
(the default) this method returns a tuple even when the number of outputs is one. Otherwise, ifFalse
a Variable will be returned when the number of outputs is one.
Returns: Return type: Note
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)[source]¶ Remove demensions of size one from the shape of a ndarray.
Parameters:  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 raised.
Returns: Variable whose dimensions of size 1 are removed.
Return type:  x (chainer.Variable or :class:
stack¶

chainer.functions.
stack
(xs, axis=0)[source]¶ Concatenate variables along a new axis.
Parameters:  xs (list of
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variables to be concatenated. The variables must have the same shape.  axis (int) – The axis along which the arrays will be stacked. The
axis
parameter is acceptable when \(ndim  1 \leq axis \leq ndim\). (ndim
is the dimension of input variables). When \(axis < 0\), the result is the same with \(ndim + 1  axis\).
Returns: Output variable. Let
x_1, x_2, ..., x_n
andy
be the input variables and the output variable,y[:, ..., 0, ..., :]
isx_1
,y[:, ..., 1, ..., :]
isx_2
andy[:, ..., n1, ..., :]
isx_n
(The indexed axis indicates theaxis
).Return type: Example
>>> x1 = np.arange(0, 12).reshape(3, 4) >>> x1.shape (3, 4) >>> x1 array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> x2 = np.arange(12, 24).reshape(3, 4) >>> x2.shape (3, 4) >>> x2 array([[12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]]) >>> y = F.stack([x1, x2], axis=0) >>> y.shape (2, 3, 4) >>> y.data array([[[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]], [[12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]]]) >>> y = F.stack([x1, x2], axis=1) >>> y.shape (3, 2, 4) >>> y.data array([[[ 0, 1, 2, 3], [12, 13, 14, 15]], [[ 4, 5, 6, 7], [16, 17, 18, 19]], [[ 8, 9, 10, 11], [20, 21, 22, 23]]]) >>> y = F.stack([x1, x2], axis=2) >>> y.shape (3, 4, 2) >>> y.data array([[[ 0, 12], [ 1, 13], [ 2, 14], [ 3, 15]], [[ 4, 16], [ 5, 17], [ 6, 18], [ 7, 19]], [[ 8, 20], [ 9, 21], [10, 22], [11, 23]]]) >>> y = F.stack([x1, x2], axis=1) >>> y.shape (3, 4, 2)
 xs (list of
swapaxes¶
tile¶

chainer.functions.
tile
(x, reps)[source]¶ Construct an array by tiling a given array.
Parameters:  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.
Returns: Variable tiled the given array.
Return type:  x (chainer.Variable or
transpose¶

chainer.functions.
transpose
(x, axes=None)[source]¶ Permute the dimensions of an input variable without copy.
Parameters:  x (Variable) – Input variable.
 axes (tuple of ints) – By default, reverse the dimensions, otherwise permute the axes according to the values given.
Returns: Variable whose axes are permuted.
Return type:
transpose_sequence¶

chainer.functions.
transpose_sequence
(xs)[source]¶ 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
.Parameters: xs (list of ~chainer.Variable) – Variables to transpose. Returns: Transposed list. Return type: tuple or Variable
vstack¶

chainer.functions.
vstack
(xs)[source]¶ Concatenate variables vertically (row wise).
Parameters: xs (list of Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variables to be concatenated. The variables must have the samendim
. When the variables have the second axis (i.e. \(ndim \geq 2\)), the variables must have the same shape along all but the first axis. When the variables do not have the second axis(i.e. \(ndim < 2\)), the variables must have the same shape.Returns: Output variable. When the input variables have the second axis (i.e. \(ndim \geq 2\)), the shapes of inputs and output are the same along all but the first axis. The length of first axis is the sum of the lengths of inputs’ first axis. When the variables do not have the second axis (i.e. \(ndim < 2\)), the shape of output is (2, N)
(N
is the size of the input variable).Return type: Variable Example
>>> x1 = np.array((1, 2, 3)) >>> x1.shape (3,) >>> x2 = np.array((2, 3, 4)) >>> x2.shape (3,) >>> y = F.vstack((x1, x2)) >>> y.shape (2, 3) >>> y.data array([[1, 2, 3], [2, 3, 4]]) >>> x1 = np.arange(0, 12).reshape(3, 4) >>> x1.shape (3, 4) >>> x1 array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> x2 = np.arange(12, 20).reshape(2, 4) >>> x2.shape (2, 4) >>> x2 array([[12, 13, 14, 15], [16, 17, 18, 19]]) >>> y = F.vstack([x1, x2]) >>> y.shape (5, 4) >>> y.data array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11], [12, 13, 14, 15], [16, 17, 18, 19]])
Neural network connections¶
bilinear¶

chainer.functions.
bilinear
(e1, e2, W, V1=None, V2=None, b=None)[source]¶ 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.
Note
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.Note
In the original paper, \(J\) and \(K\) must be equal and the author denotes \([V^1 V^2]\) (concatenation of matrices) by \(V\).
Parameters: Returns: Output variable.
Return type:  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, cover_all=False)[source]¶ 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.
 \(h_I\) and \(w_I\) are the height and width of the input image, respectively.
 \(h_K\) and \(w_K\) are the height and width of the filters, respectively.
 \(h_P\) and \(w_P\) are the height and width of the spatial padding size, respectively.
Then the
Convolution2D
function computes correlations between filters and patches of size \((h_K, w_K)\) 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 position(h_P, w_P)
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. Then, the output size \((h_O, w_O)\) is determined by the following equations:
\[\begin{split}h_O &= (h_I + 2h_P  h_K) / s_Y + 1,\\ w_O &= (w_I + 2w_P  w_K) / s_X + 1.\end{split}\]If
cover_all
option isTrue
, the filter will cover the all spatial locations. So, if the last stride of filter does not cover the end of spatial locations, an addtional stride will be applied to the end part of spatial locations. In this case, the output size \((h_O, w_O)\) is determined by the following equations:\[\begin{split}h_O &= (h_I + 2h_P  h_K + s_Y  1) / s_Y + 1,\\ w_O &= (w_I + 2w_P  w_K + s_X  1) / s_X + 1.\end{split}\]If the bias vector is given, then it is added to all spatial locations of the output of convolution.
The output of this function can be nondeterministic when it uses cuDNN. If
chainer.configuration.config.cudnn_deterministic
isTrue
and cuDNN version is >= v3, it forces cuDNN to use a deterministic algorithm.Warning
deterministic
argument is not supported anymore since v2. Instead, usechainer.using_config('cudnn_deterministic', value)
(value is eitherTrue
orFalse
). Seechainer.using_config()
.Parameters:  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable of shape \((n, c_I, h_I, w_I)\).  W (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Weight variable of shape \((c_O, c_I, h_K, w_K)\).  b (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Bias variable of length \(c_O\) (optional).  stride (
int
or pair ofint
s) – Stride of filter applications.stride=s
andstride=(s, s)
are equivalent.  pad (
int
or pair ofint
s) – Spatial padding width for input arrays.pad=p
andpad=(p, p)
are equivalent.  cover_all (bool) – If
True
, all spatial locations are convoluted into some output pixels.
Returns: Output variable of shape \((n, c_O, h_O, w_O)\).
Return type: See also
Example
>>> n = 10 >>> c_i, c_o = 3, 1 >>> h_i, w_i = 30, 40 >>> h_k, w_k = 10, 10 >>> h_p, w_p = 5, 5 >>> x = np.random.uniform(0, 1, (n, c_i, h_i, w_i)).astype('f') >>> x.shape (10, 3, 30, 40) >>> W = np.random.uniform(0, 1, (c_o, c_i, h_k, w_k)).astype('f') >>> W.shape (1, 3, 10, 10) >>> b = np.random.uniform(0, 1, (c_o,)).astype('f') >>> b.shape (1,) >>> s_y, s_x = 5, 7 >>> y = F.convolution_2d(x, W, b, stride=(s_y, s_x), pad=(h_p, w_p)) >>> y.shape (10, 1, 7, 6) >>> h_o = int((h_i + 2 * h_p  h_k) / s_y + 1) >>> w_o = int((w_i + 2 * w_p  w_k) / s_x + 1) >>> y.shape == (n, c_o, h_o, w_o) True >>> y = F.convolution_2d(x, W, b, stride=(s_y, s_x), pad=(h_p, w_p), cover_all=True) >>> y.shape == (n, c_o, h_o, w_o + 1) True
convolution_nd¶

chainer.functions.
convolution_nd
(x, W, b=None, stride=1, pad=0, cover_all=False)[source]¶ 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.
 \(l_1, l_2, ..., l_N\) are the size of each axis of the output’s spatial dimensions, respectively.
 \(p_1, p_2, ..., p_N\) are the size of each axis of the spatial padding size, respectively.
Then the
convolution_nd
function computes correlations between filters and patches of size \((k_1, k_2, ..., k_N)\) inx
. Note that correlation here is equivalent to the inner product between expanded tensors. Patches are extracted at positions shifted by multiples ofstride
from the first position(p_1, p_2, ..., p_N)
for each spatial axis.Let \((s_1, s_2, ..., s_N)\) be the stride of filter application. Then, the output size \((l_1, l_2, ..., l_N)\) is determined by the following equations:
\[l_n = (d_n + 2p_n  k_n) / s_n + 1 \ \ (n = 1, ..., N)\]If
cover_all
option isTrue
, the filter will cover the all spatial locations. So, if the last stride of filter does not cover the end of spatial locations, an addtional stride will be applied to the end part of spatial locations. In this case, the output size is determined by the following equations:\[l_n = (d_n + 2p_n  k_n + s_n  1) / s_n + 1 \ \ (n = 1, ..., N)\]The Ndimensional convolution function is defined as follows.
Parameters:  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable of shape \((n, c_I, d_1, d_2, ..., d_N)\).  W (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Weight variable of shape \((c_O, c_I, k_1, k_2, ..., k_N)\).  b (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Onedimensional bias variable with length \(c_O\) (optional).  stride (
int
ortuple
ofint
s) – Stride of filter applications \((s_1, s_2, ..., s_N)\).stride=s
is equivalent to(s, s, ..., s)
.  pad (
int
ortuple
ofint
s) – Spatial padding width for input arrays \((p_1, p_2, ..., p_N)\).pad=p
is equivalent to(p, p, ..., p)
.  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.
Returns: Output variable of shape \((n, c_O, l_1, l_2, ..., l_N)\).
Return type: Note
This function uses cuDNN implementation for its forward and backward computation if ALL of the following conditions are satisfied:
cuda.cudnn_enabled
isTrue
chainer.config.use_cudnn
is'always'
or'auto'
 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 FP16, FP32 or FP64. (FP16 is only available when cuDNN version \(\geq\) v3.)
See also
Example
>>> n = 10 >>> c_i, c_o = 3, 1 >>> d1, d2, d3 = 30, 40, 50 >>> k1, k2, k3 = 10, 10, 10 >>> p1, p2, p3 = 5, 5, 5 >>> x = np.random.uniform(0, 1, (n, c_i, d1, d2, d3)).astype('f') >>> x.shape (10, 3, 30, 40, 50) >>> W = np.random.uniform(0, 1, (c_o, c_i, k1, k2, k3)).astype('f') >>> W.shape (1, 3, 10, 10, 10) >>> b = np.random.uniform(0, 1, (c_o)).astype('f') >>> b.shape (1,) >>> s1, s2, s3 = 2, 4, 6 >>> y = F.convolution_nd(x, W, b, stride=(s1, s2, s3), pad=(p1, p2, p3)) >>> y.shape (10, 1, 16, 11, 9) >>> l1 = int((d1 + 2 * p1  k1) / s1 + 1) >>> l2 = int((d2 + 2 * p2  k2) / s2 + 1) >>> l3 = int((d3 + 2 * p3  k3) / s3 + 1) >>> y.shape == (n, c_o, l1, l2, l3) True >>> y = F.convolution_nd(x, W, b, stride=(s1, s2, s3), pad=(p1, p2, p3), cover_all=True) >>> y.shape == (n, c_o, l1, l2, l3 + 1) True
deconvolution_2d¶

chainer.functions.
deconvolution_2d
(x, W, b=None, stride=1, pad=0, outsize=None)[source]¶ Two dimensional deconvolution function.
This is an implementation of twodimensional deconvolution. In most of deep learning frameworks and papers, this function is called transposed convolution. But because of historical reasons (e.g. paper by Ziller Deconvolutional Networks) and backward compatibility, this function is called deconvolution in Chainer.
It takes three variables: 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.
 \(h_I\) and \(w_I\) are the height and width of the input image, respectively.
 \(h_K\) and \(w_K\) are the height and width of the filters, respectively.
 \(h_P\) and \(w_P\) are the height and width of the spatial padding size, respectively.
Let \((s_Y, s_X)\) be the stride of filter application. Then, the output size \((h_O, w_O)\) is estimated by the following equations:
\[\begin{split}h_O &= s_Y (h_I  1) + h_K  2h_P,\\ w_O &= s_X (w_I  1) + w_K  2w_P.\end{split}\]The output of this function can be nondeterministic when it uses cuDNN. If
chainer.configuration.config.deterministic
isTrue
and cuDNN version is >= v3, it forces cuDNN to use a deterministic algorithm.Warning
deterministic
argument is not supported anymore since v2. Instead, usechainer.using_config('cudnn_deterministic', value)
(value is eitherTrue
orFalse
). Seechainer.using_config()
.Parameters:  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable of shape \((n, c_I, h_I, w_I)\).  W (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Weight variable of shape \((c_I, c_O, h_K, w_K)\).  b (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Bias variable of length \(c_O\) (optional).  stride (
int
or pair ofint
s) – Stride of filter applications.stride=s
andstride=(s, s)
are equivalent.  pad (
int
or pair ofint
s) – Spatial padding width for input arrays.pad=p
andpad=(p, p)
are equivalent.  outsize (
tuple
ofint
) – Expected output size of deconvolutional operation. It should be pair of height and width \((h_O, w_O)\). Default value isNone
and the outsize is estimated by input size, stride and pad.
Returns: Output variable of shape \((n, c_O, h_O, w_O)\).
Return type: Example
>>> n = 10 >>> c_i, c_o = 1, 3 >>> h_i, w_i = 5, 10 >>> h_k, w_k = 10, 10 >>> h_p, w_p = 5, 5 >>> x = np.random.uniform(0, 1, (n, c_i, h_i, w_i)).astype('f') >>> x.shape (10, 1, 5, 10) >>> W = np.random.uniform(0, 1, (c_i, c_o, h_k, w_k)).astype('f') >>> W.shape (1, 3, 10, 10) >>> b = np.random.uniform(0, 1, c_o).astype('f') >>> b.shape (3,) >>> s_y, s_x = 5, 5 >>> y = F.deconvolution_2d(x, W, b, stride=(s_y, s_x), pad=(h_p, w_p)) >>> y.shape (10, 3, 20, 45) >>> h_o = s_y * (h_i  1) + h_k  2 * h_p >>> w_o = s_x * (w_i  1) + w_k  2 * w_p >>> y.shape == (n, c_o, h_o, w_o) True
deconvolution_nd¶

chainer.functions.
deconvolution_nd
(x, W, b=None, stride=1, pad=0, outsize=None)[source]¶ Ndimensional deconvolution function.
This is an implementation of Ndimensional deconvolution which generalizes twodimensional one. In most of deep learning frameworks and papers, this function is called transposed convolution. But because of historical reasons (e.g. paper by Ziller Deconvolutional Networks) and backward compatibility, this function is called deconvolution in Chainer.
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.
 \(p_1, p_2, ..., p_N\) are the size of each axis of the spatial padding size, respectively.
 \(s_1, s_2, ..., s_N\) are the stride of each axis of filter application, respectively.
If
outsize
option isNone
, the output size \((l_1, l_2, ..., l_N)\) is determined by the following equations with the items in the above list:\[l_n = s_n (d_n  1) + k_n  2 p_n \ \ (n = 1, ..., N)\]If
outsize
option is given, the output size is determined byoutsize
. In this case, theoutsize
\((l_1, l_2, ..., l_N)\) must satisfy the following equations:\[d_n = \lfloor (l_n + 2p_n  k_n) / s_n \rfloor + 1 \ \ (n = 1, ..., N)\]Parameters:  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable of shape \((n, c_I, d_1, d_2, ..., d_N)\).  W (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Weight variable of shape \((c_I, c_O, k_1, k_2, ..., k_N)\).  b (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Onedimensional bias variable with length \(c_O\) (optional).  stride (
int
ortuple
ofint
s) – Stride of filter applications \((s_1, s_2, ..., s_N)\).stride=s
is equivalent to(s, s, ..., s)
.  pad (
int
ortuple
ofint
s) – Spatial padding width for input arrays \((p_1, p_2, ..., p_N)\).pad=p
is equivalent to(p, p, ..., p)
.  outsize (
tuple
ofint
s) – Expected output size of deconvolutional operation. It should be a tuple of ints \((l_1, l_2, ..., l_N)\). Default value isNone
and the outsize is estimated by input size, stride and pad.
Returns: Output variable of shape \((n, c_O, l_1, l_2, ..., l_N)\).
Return type: See also
links.DeconvolutionND
,deconvolution_2d()
Example
Example1: the case when
outsize
is not given.>>> n = 10 >>> c_i, c_o = 3, 1 >>> d1, d2, d3 = 5, 10, 15 >>> k1, k2, k3 = 10, 10, 10 >>> p1, p2, p3 = 5, 5, 5 >>> x = np.random.uniform(0, 1, (n, c_i, d1, d2, d3)).astype('f') >>> x.shape (10, 3, 5, 10, 15) >>> W = np.random.uniform(0, 1, (c_i, c_o, k1, k2, k3)).astype('f') >>> W.shape (3, 1, 10, 10, 10) >>> b = np.random.uniform(0, 1, (c_o)).astype('f') >>> b.shape (1,) >>> s1, s2, s3 = 2, 4, 6 >>> y = F.deconvolution_nd(x, W, b, stride=(s1, s2, s3), pad=(p1, p2, p3)) >>> y.shape (10, 1, 8, 36, 84) >>> l1 = s1 * (d1  1) + k1  2 * p1 >>> l2 = s2 * (d2  1) + k2  2 * p2 >>> l3 = s3 * (d3  1) + k3  2 * p3 >>> y.shape == (n, c_o, l1, l2, l3) True
Example2: the case when
outsize
is given.>>> n = 10 >>> c_i, c_o = 3, 1 >>> d1, d2, d3 = 5, 10, 15 >>> k1, k2, k3 = 10, 10, 10 >>> p1, p2, p3 = 5, 5, 5 >>> x = np.random.uniform(0, 1, (n, c_i, d1, d2, d3)).astype('f') >>> x.shape (10, 3, 5, 10, 15) >>> W = np.random.uniform(0, 1, (c_i, c_o, k1, k2, k3)).astype('f') >>> W.shape (3, 1, 10, 10, 10) >>> b = np.random.uniform(0, 1, (c_o)).astype('f') >>> b.shape (1,) >>> s1, s2, s3 = 2, 4, 6 >>> l1, l2, l3 = 9, 38, 87 >>> d1 == int((l1 + 2 * p1  k1) / s1) + 1 True >>> d2 == int((l2 + 2 * p2  k2) / s2) + 1 True >>> d3 == int((l3 + 2 * p3  k3) / s3) + 1 True >>> y = F.deconvolution_nd(x, W, b, stride=(s1, s2, s3), pad=(p1, p2, p3), outsize=(l1, l2, l3)) >>> y.shape (10, 1, 9, 38, 87) >>> y.shape == (n, c_o, l1, l2, l3) True
depthwise_convolution_2d¶

chainer.functions.
depthwise_convolution_2d
(x, W, b=None, stride=1, pad=0)[source]¶ Twodimensional depthwise convolution function.
This is an implementation of twodimensional depthwise convolution. It takes two or three variables: the input image
x
, the filter weightW
, and optionally, the bias vectorb
.Notation: here is a notation for dimensionalities.
 \(n\) is the batch size.
 \(c_I\) is the number of the input.
 \(c_M\) is the channel multiplier.
 \(h\) and \(w\) are the height and width of the input image, respectively.
 \(h_O\) and \(w_O\) are the height and width of the output image, respectively.
 \(k_H\) and \(k_W\) are the height and width of the filters, respectively.
Parameters:  x (chainer.Variable or
numpy.ndarray
or cupy.ndarray) – Input variable of shape \((n, c_I, h, w)\).  W (Variable) – Weight variable of shape \((c_M, c_I, k_H, k_W)\).
 b (Variable) – Bias variable of length \(c_M * c_I\) (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.
Returns: Output variable. Its shape is \((n, c_I * c_M, h_O, w_O)\).
Return type: Like
Convolution2D
,DepthwiseConvolution2D
function computes correlations between filters and patches of size \((k_H, k_W)\) inx
. But unlikeConvolution2D
,DepthwiseConvolution2D
does not add up input channels of filters but concatenates them. For that reason, the shape of outputs of depthwise convolution are \((n, c_I * c_M, h_O, w_O)\), \(c_M\) is called channel_multiplier.\((h_O, w_O)\) is determined by the equivalent equation of
Convolution2D
.If the bias vector is given, then it is added to all spatial locations of the output of convolution.
See: L. Sifre. Rigidmotion scattering for image classification
See also
Example
>>> x = np.random.uniform(0, 1, (2, 3, 4, 7)) >>> W = np.random.uniform(0, 1, (2, 3, 3, 3)) >>> b = np.random.uniform(0, 1, (6,)) >>> y = F.depthwise_convolution_2d(x, W, b) >>> y.shape (2, 6, 2, 5)
dilated_convolution_2d¶

chainer.functions.
dilated_convolution_2d
(x, W, b=None, stride=1, pad=0, dilate=1, cover_all=False)[source]¶ 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.
Parameters:  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.  cover_all (bool) – If
True
, all spatial locations are convoluted into some output pixels. It may make the output size larger.
Returns: Output variable.
Return type: 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.
See also
DilatedConvolution2D
embed_id¶

chainer.functions.
embed_id
(x, W, ignore_label=None)[source]¶ 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
.Parameters: Returns: Output variable.
Return type: See also
linear¶

chainer.functions.
linear
(x, W, b=None)[source]¶ Linear function, or affine transformation.
It accepts two or three arguments: an input minibatch
x
, a weight matrixW
, and optionally a bias vectorb
. It computes .. math:: Y = xW^top + b.Parameters:  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable, which is a \((s_B, s_1, s_2, ..., s_n)\)shaped float array. Its first dimension \((s_B)\) is assumed to be the minibatch dimension. The other dimensions are treated as concatenated one dimension whose size must be \((s_1 * ... * s_n = N)\).  W (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Weight variable of shape \((M, N)\), where \((N = s_1 * ... * s_n)\).  b (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Bias variable (optional) of shape \((M,)\).
Returns: Output variable. A float array with shape of \((s_B, M)\).
Return type: See also
Example
>>> x = np.random.uniform(0, 1, (3, 4)).astype('f') >>> W = np.random.uniform(0, 1, (5, 4)).astype('f') >>> b = np.random.uniform(0, 1, (5,)).astype('f') >>> y = F.linear(x, W, b) >>> y.shape (3, 5)
 x (
n_step_bigru¶

chainer.functions.
n_step_bigru
(n_layers, dropout_ratio, hx, ws, bs, xs)[source]¶ Stacked Bidirectional Gated Recurrent Unit function.
This function calculates stacked Bidirectional GRU with sequences. This function gets an initial hidden state \(h_0\), an input sequence \(x\), weight matrices \(W\), and bias vectors \(b\). This function calculates hidden states \(h_t\) for each time \(t\) from input \(x_t\).
\[\begin{split}r^{f}_t &= \sigma(W^{f}_0 x_t + W^{f}_3 h_{t1} + b^{f}_0 + b^{f}_3) \\ z^{f}_t &= \sigma(W^{f}_1 x_t + W^{f}_4 h_{t1} + b^{f}_1 + b^{f}_4) \\ h^{f'}_t &= \tanh(W^{f}_2 x_t + b^{f}_2 + r^{f}_t \cdot (W^{f}_5 h_{t1} + b^{f}_5)) \\ h^{f}_t &= (1  z^{f}_t) \cdot h^{f'}_t + z^{f}_t \cdot h_{t1} \\ r^{b}_t &= \sigma(W^{b}_0 x_t + W^{b}_3 h_{t1} + b^{b}_0 + b^{b}_3) \\ z^{b}_t &= \sigma(W^{b}_1 x_t + W^{b}_4 h_{t1} + b^{b}_1 + b^{b}_4) \\ h^{b'}_t &= \tanh(W^{b}_2 x_t + b^{b}_2 + r^{b}_t \cdot (W^{b}_5 h_{t1} + b^{b}_5)) \\ h^{b}_t &= (1  z^{b}_t) \cdot h^{b'}_t + z^{b}_t \cdot h_{t1} \\ h_t &= [h^{f}_t; h^{f}_t] \\\end{split}\]where \(W^{f}\) is weight matrices for forwardGRU, \(W^{b}\) is weight matrices for backwardGRU.
As the function accepts a sequence, it calculates \(h_t\) for all \(t\) with one call. Six weight matrices and six bias vectors are required for each layers. So, when \(S\) layers exists, you need to prepare \(6S\) weigth matrices and \(6S\) bias vectors.
If the number of layers
n_layers
is greather than \(1\), input ofk
th layer is hidden stateh_t
ofk1
th layer. Note that all input variables except first layer may have different shape from the first layer.Warning
train
anduse_cudnn
arguments are not supported anymore since v2. Instead, usechainer.using_config('train', train)
andchainer.using_config('use_cudnn', use_cudnn)
respectively. Seechainer.using_config()
.Parameters:  n_layers (int) – Number of layers.
 dropout_ratio (float) – Dropout ratio.
 hx (chainer.Variable) – Variable holding stacked hidden states.
Its shape is
(S, B, N)
whereS
is number of layers and is equal ton_layers
,B
is minibatch size, andN
is dimention of hidden units.  ws (list of list of chainer.Variable) – Weight matrices.
ws[i]
represents weights for ith layer. Eachws[i]
is a list containing six matrices.ws[i][j]
is corresponding withW_j
in the equation. Onlyws[0][j]
where0 <= j < 3
is(I, N)
shape as they are multiplied with input variables. All other matrices has(N, N)
shape.  bs (list of list of chainer.Variable) – Bias vectors.
bs[i]
represnents biases for ith layer. Eachbs[i]
is a list containing six vectors.bs[i][j]
is corresponding withb_j
in the equation. Shape of each matrix is(N,)
whereN
is dimention of hidden units.  xs (list of chainer.Variable) – A list of
Variable
holding input values. Each elementxs[t]
holds input value for timet
. Its shape is(B_t, I)
, whereB_t
is minibatch size for timet
, andI
is size of input units. Note that this functions supports variable length sequences. When sequneces has different lengths, sort sequences in descending order by length, and transpose the sorted sequence.transpose_sequence()
transpose a list ofVariable()
holding sequence. Soxs
needs to satisfyxs[t].shape[0] >= xs[t + 1].shape[0]
.  use_bi_direction (bool) – If
True
, this function uses Bidirection GRU.
Returns:  This functions returns a tuple concaining three elements,
hy
andys
.hy
is an updated hidden states whose shape is same ashx
.ys
is a list ofVariable
. Each elementys[t]
holds hidden states of the last layer corresponding to an inputxs[t]
. Its shape is(B_t, N)
whereB_t
is minibatch size for timet
, andN
is size of hidden units. Note thatB_t
is the same value asxs[t]
.
Return type:
n_step_bilstm¶

chainer.functions.
n_step_bilstm
(n_layers, dropout_ratio, hx, cx, ws, bs, xs)[source]¶ Stacked Bidirectional Long ShortTerm Memory function.
This function calculates stacked Bidirectional LSTM with sequences. This function gets an initial hidden state \(h_0\), an initial cell state \(c_0\), an input sequence \(x\), weight matrices \(W\), and bias vectors \(b\). This function calculates hidden states \(h_t\) and \(c_t\) for each time \(t\) from input \(x_t\).
\[\begin{split}i^{f}_t &=& \sigma(W^{f}_0 x_t + W^{f}_4 h_{t1} + b^{f}_0 + b^{f}_4), \\ f^{f}_t &=& \sigma(W^{f}_1 x_t + W^{f}_5 h_{t1} + b^{f}_1 + b^{f}_5), \\ o^{f}_t &=& \sigma(W^{f}_2 x_t + W^{f}_6 h_{t1} + b^{f}_2 + b^{f}_6), \\ a^{f}_t &=& \tanh(W^{f}_3 x_t + W^{f}_7 h_{t1} + b^{f}_3 + b^{f}_7), \\ c^{f}_t &=& f^{f}_t \cdot c^{f}_{t1} + i^{f}_t \cdot a^{f}_t, \\ h^{f}_t &=& o^{f}_t \cdot \tanh(c^{f}_t), \\ i^{b}_t &=& \sigma(W^{b}_0 x_t + W^{b}_4 h_{t1} + b^{b}_0 + b^{b}_4), \\ f^{b}_t &=& \sigma(W^{b}_1 x_t + W^{b}_5 h_{t1} + b^{b}_1 + b^{b}_5), \\ o^{b}_t &=& \sigma(W^{b}_2 x_t + W^{b}_6 h_{t1} + b^{b}_2 + b^{b}_6), \\ a^{b}_t &=& \tanh(W^{b}_3 x_t + W^{b}_7 h_{t1} + b^{b}_3 + b^{b}_7), \\ c^{b}_t &=& f^{b}_t \cdot c^{b}_{t1} + i^{b}_t \cdot a^{b}_t, \\ h^{b}_t &=& o^{b}_t \cdot \tanh(c^{b}_t), \\ h_t &=& [h^{f}; h^{b}]\end{split}\]where \(W^{f}\) is weight matrices for forwardLSTM, \(W^{b}\) is weight matrices for backwardLSTM.
As the function accepts a sequence, it calculates \(h_t\) for all \(t\) with one call. Eight weight matrices and eight bias vectors are required for each layers. So, when \(S\) layers exists, you need to prepare \(8S\) weigth matrices and \(8S\) bias vectors.
If the number of layers
n_layers
is greather than \(1\), input ofk
th layer is hidden stateh_t
ofk1
th layer. Note that all input variables except first layer may have different shape from the first layer.Warning
train
anduse_cudnn
arguments are not supported anymore since v2. Instead, usechainer.using_config('train', train)
andchainer.using_config('use_cudnn', use_cudnn)
respectively. Seechainer.using_config()
.Parameters:  n_layers (int) – Number of layers.
 dropout_ratio (float) – Dropout ratio.
 hx (chainer.Variable) – Variable holding stacked hidden states.
Its shape is
(S, B, N)
whereS
is number of layers and is equal ton_layers
,B
is minibatch size, andN
is dimention of hidden units.  cx (chainer.Variable) – Variable holding stacked cell states.
It has the same shape as
hx
.  ws (list of list of chainer.Variable) – Weight matrices.
ws[i]
represents weights for ith layer. Eachws[i]
is a list containing eight matrices.ws[i][j]
is corresponding withW_j
in the equation. Onlyws[0][j]
where0 <= j < 4
is(I, N)
shape as they are multiplied with input variables. All other matrices has(N, N)
shape.  bs (list of list of chainer.Variable) – Bias vectors.
bs[i]
represnents biases for ith layer. Eachbs[i]
is a list containing eight vectors.bs[i][j]
is corresponding withb_j
in the equation. Shape of each matrix is(N,)
whereN
is dimention of hidden units.  xs (list of chainer.Variable) – A list of
Variable
holding input values. Each elementxs[t]
holds input value for timet
. Its shape is(B_t, I)
, whereB_t
is minibatch size for timet
, andI
is size of input units. Note that this functions supports variable length sequences. When sequneces has different lengths, sort sequences in descending order by length, and transpose the sorted sequence.transpose_sequence()
transpose a list ofVariable()
holding sequence. Soxs
needs to satisfyxs[t].shape[0] >= xs[t + 1].shape[0]
.
Returns:  This functions returns a tuple concaining three elements,
hy
,cy
andys
.hy
is an updated hidden states whose shape is same ashx
.cy
is an updated cell states whose shape is same ascx
.ys
is a list ofVariable
. Each elementys[t]
holds hidden states of the last layer corresponding to an inputxs[t]
. Its shape is(B_t, N)
whereB_t
is minibatch size for timet
, andN
is size of hidden units. Note thatB_t
is the same value asxs[t]
.
Return type:
n_step_birnn¶

chainer.functions.
n_step_birnn
(n_layers, dropout_ratio, hx, ws, bs, xs, activation='tanh')[source]¶ Stacked Bidirectional RNN function for sequence inputs.
This function calculates stacked Bidirectional RNN with sequences. This function gets an initial hidden state \(h_0\), an initial cell state \(c_0\), an input sequence \(x\), weight matrices \(W\), and bias vectors \(b\). This function calculates hidden states \(h_t\) and \(c_t\) for each time \(t\) from input \(x_t\).
\[\begin{split}h^{f}_t &=& f(W^{f}_0 x_t + W^{f}_1 h_{t1} + b^{f}_0 + b^{f}_1), \\ h^{b}_t &=& f(W^{b}_0 x_t + W^{b}_1 h_{t1} + b^{b}_0 + b^{b}_1), \\ h_t &=& [h^{f}_t; h^{f}_t], \\\end{split}\]where \(f\) is an activation function.
Weight matrices \(W\) contains two matrices \(W^{f}\) and \(W^{b}\). \(W^{f}\) is weight matrices for forward directional RNN. \(W^{b}\) is weight matrices for backward directional RNN.
\(W^{f}\) contains \(W^{f}_0\) for an input sequence and \(W^{f}_1\) for a hidden state. \(W^{b}\) contains \(W^{b}_0\) for an input sequence and \(W^{b}_1\) for a hidden state.
Bias matrices \(b\) contains two matrices \(b^{f}\) and \(b^{f}\). \(b^{f}\) contains \(b^{f}_0\) for an input sequence and \(b^{f}_1\) for a hidden state. \(b^{b}\) contains \(b^{b}_0\) for an input sequence and \(b^{b}_1\) for a hidden state.
As the function accepts a sequence, it calculates \(h_t\) for all \(t\) with one call. Two weight matrices and two bias vectors are required for each layer. So, when \(S\) layers exist, you need to prepare \(2S\) weigth matrices and \(2S\) bias vectors.
If the number of layers
n_layers
is greather than \(1\), input ofk
th layer is hidden stateh_t
ofk1
th layer. Note that all input variables except first layer may have different shape from the first layer.Warning
train
anduse_cudnn
arguments are not supported anymore since v2. Instead, usechainer.using_config('train', train)
andchainer.using_config('use_cudnn', use_cudnn)
respectively. Seechainer.using_config()
.Parameters:  n_layers (int) – Number of layers.
 dropout_ratio (float) – Dropout ratio.
 hx (chainer.Variable) – Variable holding stacked hidden states.
Its shape is
(S, B, N)
whereS
is number of layers and is equal ton_layers
,B
is minibatch size, andN
is dimention of hidden units.  ws (list of list of chainer.Variable) – Weight matrices.
ws[i + di]
represents weights for ith layer. Note thatdi = 0
for forwardRNN anddi = 1
for backwardRNN. Eachws[i + di]
is a list containing two matrices.ws[i + di][j]
is corresponding withW^{f}_j
ifdi = 0
and corresponding withW^{b}_j
ifdi = 1
in the equation. Onlyws[0][j]
andws[1][j]
where0 <= j < 1
are(I, N)
shape as they are multiplied with input variables. All other matrices has(N, N)
shape.  bs (list of list of chainer.Variable) – Bias vectors.
bs[i + di]
represnents biases for ith layer. Note thatdi = 0
for forwardRNN anddi = 1
for backwardRNN. Eachbs[i + di]
is a list containing two vectors.bs[i + di][j]
is corresponding withb^{f}_j
ifdi = 0
and corresponding withb^{b}_j
ifdi = 1
in the equation. Shape of each matrix is(N,)
whereN
is dimention of hidden units.  xs (list of chainer.Variable) – A list of
Variable
holding input values. Each elementxs[t]
holds input value for timet
. Its shape is(B_t, I)
, whereB_t
is minibatch size for timet
, andI
is size of input units. Note that this functions supports variable length sequences. When sequneces has different lengths, sort sequences in descending order by length, and transpose the sorted sequence.transpose_sequence()
transpose a list ofVariable()
holding sequence. Soxs
needs to satisfyxs[t].shape[0] >= xs[t + 1].shape[0]
.  activation (str) – Activation function name.
Please select
tanh
orrelu
.
Returns:  This functions returns a tuple concaining three elements,
hy
andys
.hy
is an updated hidden states whose shape is same ashx
.ys
is a list ofVariable
. Each elementys[t]
holds hidden states of the last layer corresponding to an inputxs[t]
. Its shape is(B_t, N)
whereB_t
is minibatch size for timet
, andN
is size of hidden units. Note thatB_t
is the same value asxs[t]
.
Return type:
n_step_gru¶

chainer.functions.
n_step_gru
(n_layers, dropout_ratio, hx, ws, bs, xs)[source]¶ Stacked Unidirectional Gated Recurrent Unit function.
This function calculates stacked Unidirectional GRU with sequences. This function gets an initial hidden state \(h_0\), an input sequence \(x\), weight matrices \(W\), and bias vectors \(b\). This function calculates hidden states \(h_t\) for each time \(t\) from input \(x_t\).
\[\begin{split}r_t &= \sigma(W_0 x_t + W_3 h_{t1} + b_0 + b_3) \\ z_t &= \sigma(W_1 x_t + W_4 h_{t1} + b_1 + b_4) \\ h'_t &= \tanh(W_2 x_t + b_2 + r_t \cdot (W_5 h_{t1} + b_5)) \\ h_t &= (1  z_t) \cdot h'_t + z_t \cdot h_{t1}\end{split}\]As the function accepts a sequence, it calculates \(h_t\) for all \(t\) with one call. Six weight matrices and six bias vectors are required for each layers. So, when \(S\) layers exists, you need to prepare \(6S\) weigth matrices and \(6S\) bias vectors.
If the number of layers
n_layers
is greather than \(1\), input ofk
th layer is hidden stateh_t
ofk1
th layer. Note that all input variables except first layer may have different shape from the first layer.Warning
train
anduse_cudnn
arguments are not supported anymore since v2. Instead, usechainer.using_config('train', train)
andchainer.using_config('use_cudnn', use_cudnn)
respectively. Seechainer.using_config()
.Parameters:  n_layers (int) – Number of layers.
 dropout_ratio (float) – Dropout ratio.
 hx (chainer.Variable) – Variable holding stacked hidden states.
Its shape is
(S, B, N)
whereS
is number of layers and is equal ton_layers
,B
is minibatch size, andN
is dimention of hidden units.  ws (list of list of chainer.Variable) – Weight matrices.
ws[i]
represents weights for ith layer. Eachws[i]
is a list containing six matrices.ws[i][j]
is corresponding withW_j
in the equation. Onlyws[0][j]
where0 <= j < 3
is(I, N)
shape as they are multiplied with input variables. All other matrices has(N, N)
shape.  bs (list of list of chainer.Variable) – Bias vectors.
bs[i]
represnents biases for ith layer. Eachbs[i]
is a list containing six vectors.bs[i][j]
is corresponding withb_j
in the equation. Shape of each matrix is(N,)
whereN
is dimention of hidden units.  xs (list of chainer.Variable) – A list of
Variable
holding input values. Each elementxs[t]
holds input value for timet
. Its shape is(B_t, I)
, whereB_t
is minibatch size for timet
, andI
is size of input units. Note that this functions supports variable length sequences. When sequneces has different lengths, sort sequences in descending order by length, and transpose the sorted sequence.transpose_sequence()
transpose a list ofVariable()
holding sequence. Soxs
needs to satisfyxs[t].shape[0] >= xs[t + 1].shape[0]
.
Returns:  This functions returns a tuple concaining three elements,
hy
andys
.hy
is an updated hidden states whose shape is same ashx
.ys
is a list ofVariable
. Each elementys[t]
holds hidden states of the last layer corresponding to an inputxs[t]
. Its shape is(B_t, N)
whereB_t
is minibatch size for timet
, andN
is size of hidden units. Note thatB_t
is the same value asxs[t]
.
Return type:
n_step_lstm¶

chainer.functions.
n_step_lstm
(n_layers, dropout_ratio, hx, cx, ws, bs, xs)[source]¶ Stacked Unidirectional Long ShortTerm Memory function.
This function calculates stacked Unidirectional LSTM with sequences. This function gets an initial hidden state \(h_0\), an initial cell state \(c_0\), an input sequence \(x\), weight matrices \(W\), and bias vectors \(b\). This function calculates hidden states \(h_t\) and \(c_t\) for each time \(t\) from input \(x_t\).
\[\begin{split}i_t &= \sigma(W_0 x_t + W_4 h_{t1} + b_0 + b_4) \\ f_t &= \sigma(W_1 x_t + W_5 h_{t1} + b_1 + b_5) \\ o_t &= \sigma(W_2 x_t + W_6 h_{t1} + b_2 + b_6) \\ a_t &= \tanh(W_3 x_t + W_7 h_{t1} + b_3 + b_7) \\ c_t &= f_t \cdot c_{t1} + i_t \cdot a_t \\ h_t &= o_t \cdot \tanh(c_t)\end{split}\]As the function accepts a sequence, it calculates \(h_t\) for all \(t\) with one call. Eight weight matrices and eight bias vectors are required for each layers. So, when \(S\) layers exists, you need to prepare \(8S\) weigth matrices and \(8S\) bias vectors.
If the number of layers
n_layers
is greather than \(1\), input ofk
th layer is hidden stateh_t
ofk1
th layer. Note that all input variables except first layer may have different shape from the first layer.Warning
train
anduse_cudnn
arguments are not supported anymore since v2. Instead, usechainer.using_config('train', train)
andchainer.using_config('use_cudnn', use_cudnn)
respectively. Seechainer.using_config()
.Parameters:  n_layers (int) – Number of layers.
 dropout_ratio (float) – Dropout ratio.
 hx (chainer.Variable) – Variable holding stacked hidden states.
Its shape is
(S, B, N)
whereS
is number of layers and is equal ton_layers
,B
is minibatch size, andN
is dimention of hidden units.  cx (chainer.Variable) – Variable holding stacked cell states.
It has the same shape as
hx
.  ws (list of list of chainer.Variable) – Weight matrices.
ws[i]
represents weights for ith layer. Eachws[i]
is a list containing eight matrices.ws[i][j]
is corresponding withW_j
in the equation. Onlyws[0][j]
where0 <= j < 4
is(I, N)
shape as they are multiplied with input variables. All other matrices has(N, N)
shape.  bs (list of list of chainer.Variable) – Bias vectors.
bs[i]
represnents biases for ith layer. Eachbs[i]
is a list containing eight vectors.bs[i][j]
is corresponding withb_j
in the equation. Shape of each matrix is(N,)
whereN
is dimention of hidden units.  xs (list of chainer.Variable) – A list of
Variable
holding input values. Each elementxs[t]
holds input value for timet
. Its shape is(B_t, I)
, whereB_t
is minibatch size for timet
, andI
is size of input units. Note that this functions supports variable length sequences. When sequneces has different lengths, sort sequences in descending order by length, and transpose the sorted sequence.transpose_sequence()
transpose a list ofVariable()
holding sequence. Soxs
needs to satisfyxs[t].shape[0] >= xs[t + 1].shape[0]
.
Returns:  This functions returns a tuple concaining three elements,
hy
,cy
andys
.hy
is an updated hidden states whose shape is same ashx
.cy
is an updated cell states whose shape is same ascx
.ys
is a list ofVariable
. Each elementys[t]
holds hidden states of the last layer corresponding to an inputxs[t]
. Its shape is(B_t, N)
whereB_t
is minibatch size for timet
, andN
is size of hidden units. Note thatB_t
is the same value asxs[t]
.
Return type: See also
n_step_rnn¶

chainer.functions.
n_step_rnn
(n_layers, dropout_ratio, hx, ws, bs, xs, activation='tanh')[source]¶ Stacked Unidirectional RNN function for sequence inputs.
This function calculates stacked Unidirectional RNN with sequences. This function gets an initial hidden state \(h_0\), an initial cell state \(c_0\), an input sequence \(x\), weight matrices \(W\), and bias vectors \(b\). This function calculates hidden states \(h_t\) and \(c_t\) for each time \(t\) from input \(x_t\).
\[h_t = f(W_0 x_t + W_1 h_{t1} + b_0 + b_1)\]where \(f\) is an activation function.
Weight matrices \(W\) contains two matrices \(W_0\) and \(W_1\). \(W_0\) is a parameter for an input sequence. \(W_1\) is a parameter for a hidden state. Bias matrices \(b\) contains two matrices \(b_0\) and \(b_1\). \(b_0\) is a parameter for an input sequence. \(b_1\) is a parameter for a hidden state.
As the function accepts a sequence, it calculates \(h_t\) for all \(t\) with one call. Two weight matrices and two bias vectors are required for each layer. So, when \(S\) layers exist, you need to prepare \(2S\) weigth matrices and \(2S\) bias vectors.
If the number of layers
n_layers
is greather than \(1\), input ofk
th layer is hidden stateh_t
ofk1
th layer. Note that all input variables except first layer may have different shape from the first layer.Warning
train
anduse_cudnn
arguments are not supported anymore since v2. Instead, usechainer.using_config('train', train)
andchainer.using_config('use_cudnn', use_cudnn)
respectively. Seechainer.using_config()
.Parameters:  n_layers (int) – Number of layers.
 dropout_ratio (float) – Dropout ratio.
 hx (chainer.Variable) – Variable holding stacked hidden states.
Its shape is
(S, B, N)
whereS
is number of layers and is equal ton_layers
,B
is minibatch size, andN
is dimention of hidden units.  ws (list of list of chainer.Variable) – Weight matrices.
ws[i]
represents weights for ith layer. Eachws[i]
is a list containing two matrices.ws[i][j]
is corresponding withW_j
in the equation. Onlyws[0][j]
where0 <= j < 1
is(I, N)
shape as they are multiplied with input variables. All other matrices has(N, N)
shape.  bs (list of list of chainer.Variable) – Bias vectors.
bs[i]
represnents biases for ith layer. Eachbs[i]
is a list containing two vectors.bs[i][j]
is corresponding withb_j
in the equation. Shape of each matrix is(N,)
whereN
is dimention of hidden units.  xs (list of chainer.Variable) – A list of
Variable
holding input values. Each elementxs[t]
holds input value for timet
. Its shape is(B_t, I)
, whereB_t
is minibatch size for timet
, andI
is size of input units. Note that this functions supports variable length sequences. When sequneces has different lengths, sort sequences in descending order by length, and transpose the sorted sequence.transpose_sequence()
transpose a list ofVariable()
holding sequence. Soxs
needs to satisfyxs[t].shape[0] >= xs[t + 1].shape[0]
.  activation (str) – Activation function name.
Please select
tanh
orrelu
.
Returns:  This functions returns a tuple concaining three elements,
hy
andys
.hy
is an updated hidden states whose shape is same ashx
.ys
is a list ofVariable
. Each elementys[t]
holds hidden states of the last layer corresponding to an inputxs[t]
. Its shape is(B_t, N)
whereB_t
is minibatch size for timet
, andN
is size of hidden units. Note thatB_t
is the same value asxs[t]
.
Return type:
Evaluation functions¶
accuracy¶

chainer.functions.
accuracy
(y, t, ignore_label=None)[source]¶ Computes multiclass classification accuracy of the minibatch.
Parameters:  y (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Array whose (i, j, k, ...)th element indicates the score of the class j at the (i, k, ...)th sample. The prediction label \(\hat t\) is calculated by the formula \(\hat t(i, k, ...) = \operatorname{\mathrm{argmax}}_j y(i, j, k, ...)\).  t (
Variable
ornumpy.ndarray
orcupy.ndarray
ofnumpy.int32
) – Array of ground truth labels.  ignore_label (int or None) – Skip calculating accuracy
if the true label is
ignore_label
.
Returns: A variable holding a scalar array of the accuracy.
Return type: Note
This function is nondifferentiable.
Example
We show the most common case, when
y
is the two dimensional array.>>> y = np.array([[0.1, 0.7, 0.2], # prediction label is 1 ... [8.0, 1.0, 2.0], # prediction label is 0 ... [8.0, 1.0, 2.0], # prediction label is 2 ... [8.0, 1.0, 2.0]]) # prediction label is 1 >>> t = np.array([1, 0, 2, 1], 'i') >>> F.accuracy(y, t).data # 100% accuracy because all samples are correct array(1.0) >>> t = np.array([1, 0, 0, 0], 'i') >>> F.accuracy(y, t).data # 50% accuracy because 1st and 2nd samples are correct. array(0.5) >>> F.accuracy(y, t, ignore_label=0).data # 100% accuracy because of ignoring the 2nd, 3rd and 4th samples. array(1.0)
 y (
binary_accuracy¶
classification_summary¶

chainer.functions.
classification_summary
(y, t, label_num=None, beta=1.0, ignore_label=1)[source]¶ Calculates Precision, Recall, F beta Score, and support.
This function calculates the following quantities for each class.
 Precision: \(\frac{\mathrm{tp}}{\mathrm{tp} + \mathrm{fp}}\)
 Recall: \(\frac{\mathrm{tp}}{\mathrm{tp} + \mathrm{tn}}\)
 F beta Score: The weighted harmonic average of Precision and Recall.
 Support: The number of instances of each ground truth label.
Here,
tp
,fp
, andtn
stand for the number of true positives, false positives, and true negative, respectively.label_num
specifies the number of classes, that is, each value int
must be an integer in the range of[0, label_num)
. Iflabel_num
isNone
, this function regardslabel_num
as a maximum of int
plus one.ignore_label
determines which instances should be ignored. Specifically, instances with the given label are not taken into account for calculating the above quantities. By default, it is set to 1 so that all instances are taken into consideration, as labels are supposed to be nonnegative integers. Settingignore_label
to a nonnegative integer less thanlabel_num
is illegal and yields undefined behavior. In the current implementation, it arisesRuntimeWarning
andignore_label
th entries in output arrays do not contain correct quantities.Parameters:  y (Variable) – Variable holding a vector of scores.
 t (Variable) – Variable holding a vector of ground truth labels.
 label_num (int) – The number of classes.
 beta (float) – The parameter which determines the weight of precision in the Fbeta score.
 ignore_label (int) – Instances with this label are ignored.
Returns: 4tuple of ~chainer.Variable of size
(label_num,)
. Each element represents precision, recall, F beta score, and support of this minibatch.
r2_score¶

chainer.functions.
r2_score
(pred, true, sample_weight=None, multioutput='uniform_average')[source]¶ Computes R^2(coefficient of determination) regression score function.
Parameters:  pred (Variable) – Variable holding a vector, matrix or tensor of estimated target values.
 true (Variable) – Variable holding a vector, matrix or tensor of correct target values.
 sample_weight – This argument is for compatibility with scikitlearn’s implementation of r2_score. Current implementation admits None only.
 multioutput (string) – [‘uniform_average’, ‘raw_values’]. if ‘uniform_average’, this function returns an average of R^2 score of multiple output. If ‘raw_average’, this function return a set of R^2 score of multiple output.
Returns: A Variable holding a scalar array of the R^2 score if ‘multioutput’ is ‘uniform_average’ or a vector of R^2 scores if ‘multioutput’ is ‘raw_values’.
Return type: Note
This function is nondifferentiable.
Loss functions¶
bernoulli_nll¶

chainer.functions.
bernoulli_nll
(x, y, reduce='sum')[source]¶ Computes the negative loglikelihood of a Bernoulli distribution.
This function calculates the negative loglikelihood of a Bernoulli distribution.
\[\log B(x; p) = \sum_i \{x_i \log(p_i) + (1  x_i)\log(1  p_i)\},\]where \(p = \sigma(y)\), \(\sigma(\cdot)\) is a sigmoid function, and \(B(x; p)\) is a Bernoulli distribution.
The output is a variable whose value depends on the value of the option
reduce
. If it is'no'
, it holds the elementwise loss values. If it is'sum'
, loss values are summed up.Note
As this function uses a sigmoid function, you can pass a result of fullyconnected layer (that means
Linear
) to this function directly.Parameters:  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable.  y (
Variable
ornumpy.ndarray
orcupy.ndarray
) – A variable representing the parameter of Bernoulli distribution.  reduce (str) – Reduction option. Its value must be either
'sum'
or'no'
. Otherwise,ValueError
is raised.
Returns: A variable representing the negative loglikelihood. If
reduce
is'no'
, the output variable holds array whose shape is same as one of (hence both of) input variables. If it is'sum'
, the output variable holds a scalar value.Return type:  x (
black_out¶

chainer.functions.
black_out
(x, t, W, samples, reduce='mean')[source]¶ 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
\[p(y) = \frac{\exp(W_y^\top x)}{ \sum_{s \in samples} \exp(W_s^\top x)}.\]The output is a variable whose value depends on the value of the option
reduce
. If it is'no'
, it holds the no loss values. If it is'mean'
, this function takes a mean of loss values.Parameters:  x (Variable) – Batch of input vectors. Its shape should be \((N, D)\).
 t (Variable) – Vector of ground truth labels. Its shape should be \((N,)\). Each elements \(v\) should satisfy \(0 \geq v \geq V\) or \(1\) where \(V\) is the number of label types.
 W (Variable) – Weight matrix. Its shape should be \((V, D)\)
 samples (Variable) – Negative samples. Its shape should be \((N, S)\) where \(S\) is the number of negative samples.
 reduce (str) – Reduction option. Its value must be either
'no'
or'mean'
. Otherwise,ValueError
is raised.
Returns: A variable object holding loss value(s). If
reduce
is'no'
, the output variable holds an array whose shape is \((N,)\) . If it is'mean'
, it holds a scalar.Return type: See: BlackOut: Speeding up Recurrent Neural Network Language Models With Very Large Vocabularies
See also
connectionist_temporal_classification¶

chainer.functions.
connectionist_temporal_classification
(x, t, blank_symbol, input_length=None, label_length=None, reduce='mean')[source]¶ 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]
The output is a varialbe whose value depends on the value of the option
reduce
. If it is'no'
, it holds the samplewise loss values. If it is'mean'
, it takes the mean of loss values.Parameters:  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.  reduce (str) – Reduction option. Its value must be either
'mean'
or'no'
. Otherwise,ValueError
is raised.
Returns: A variable holding a scalar value of the CTC loss. If
reduce
is'no'
, the output varialbe holds array whose shape is (B,) where B is the number of samples. If it is'mean'
, it holds a scalar.Return type: Note
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.Note
This function is differentiable only by
x
.Note
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, reduce='mean')[source]¶ Computes contrastive loss.
It takes a pair of samples and a label as inputs. The label is \(1\) when those samples 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
x0
andx1
should be(N, K)
. The loss value of the \(n\)th sample pair \(L_n\) is\[L_n = \frac{1}{2} \left( y_n d_n^2 + (1  y_n) \max ({\rm margin}  d_n, 0)^2 \right)\]where \(d_n = \ {\bf x_0}_n  {\bf x_1}_n \_2\), \({\bf x_0}_n\) and \({\bf x_1}_n\) are \(n\)th Kdimensional vectors of
x0
andx1
.The output is a variable whose value depends on the value of the option
reduce
. If it is'no'
, it holds the elementwise loss values. If it is'mean'
, this function takes a mean of loss values.Parameters:  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.
 reduce (str) – Reduction option. Its value must be either
'mean'
or'no'
. Otherwise,ValueError
is raised.
Returns: A variable holding the loss value(s) calculated by the above equation. If
reduce
is'no'
, the output variable holds array whose shape is same as one of (hence both of) input variables. If it is'mean'
, the output variable holds a scalar value.Return type: Note
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, reduce='mean')[source]¶ 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.
Note
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 sequences:
>>> 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 mean of the negative loglikelihood of the three sequences.
The output is a variable whose value depends on the value of the option
reduce
. If it is'no'
, it holds the elementwise loss values. If it is'mean'
, it holds mean of the loss values.Parameters:  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
.  reduce (str) – Reduction option. Its value must be either
'mean'
or'no'
. Otherwise,ValueError
is raised.
Returns:  A variable holding the average negative
loglikelihood of the input sequences.
Return type: Note
See detail in the original paper: Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data.

chainer.functions.
argmax_crf1d
(cost, xs)[source]¶ Computes a state that maximizes a joint probability of the given CRF.
Parameters:  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.
Returns:  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]
.
Return type:
cross_covariance¶

chainer.functions.
cross_covariance
(y, z, reduce='half_squared_sum')[source]¶ Computes the sumsquared crosscovariance penalty between
y
andz
The output is a variable whose value depends on the value of the option
reduce
. If it is'no'
, it holds the covariant matrix that has as many rows (resp. columns) as the dimension ofy
(resp.z). If it is'half_squared_sum'
, it holds the half of the Frobenius norm (i.e. L2 norm of a matrix flattened to a vector) of the covarianct matrix.Parameters:  y (Variable) – Variable holding a matrix where the first dimension corresponds to the batches.
 z (Variable) – Variable holding a matrix where the first dimension corresponds to the batches.
 reduce (str) – Reduction option. Its value must be either
'half_squared_sum'
or'no'
. Otherwise,ValueError
is raised.
Returns: A variable holding the cross covariance loss. If
reduce
is'no'
, the output variable holds 2dimensional array matrix of shape(M, N)
whereM
(resp.N
) is the number of columns ofy
(resp.z
). If it is'half_squared_sum'
, the output variable holds a scalar value.Return type: Note
This cost can be used to disentangle variables. See https://arxiv.org/abs/1412.6583v3 for details.
gaussian_kl_divergence¶

chainer.functions.
gaussian_kl_divergence
(mean, ln_var, reduce='sum')[source]¶ Computes the KLdivergence of Gaussian variables from the standard one.
Given two variable
mean
representing \(\mu\) andln_var
representing \(\log(\sigma^2)\), this function calculates the KLdivergence in elementwise manner 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.
The output is a variable whose value depends on the value of the option
reduce
. If it is'no'
, it holds the elementwise loss values. If it is'sum'
, loss values are summed up.Parameters:  mean (
Variable
ornumpy.ndarray
orcupy.ndarray
) – A variable representing mean of given gaussian distribution, \(\mu\).  ln_var (
Variable
ornumpy.ndarray
orcupy.ndarray
) – A variable representing logarithm of variance of given gaussian distribution, \(\log(\sigma^2)\).  reduce (str) – Reduction option. Its value must be either
'sum'
or'no'
. Otherwise,ValueError
is raised.
Returns: A variable representing KLdivergence between given gaussian distribution and the standard gaussian. If
reduce
is'no'
, the output variable holds array whose shape is same as one of (hence both of) input variables. If it is'sum'
, the output variable holds a scalar value.Return type:  mean (
gaussian_nll¶

chainer.functions.
gaussian_nll
(x, mean, ln_var, reduce='sum')[source]¶ Computes the negative loglikelihood of a Gaussian distribution.
Given two variable
mean
representing \(\mu\) andln_var
representing \(\log(\sigma^2)\), this function computes in elementwise manner the negative loglikelihood of \(x\) on a Gaussianx 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 \(S_{ii} = \sigma_i^2\).
The output is a varialbe whose value depends on the value of the option
reduce
. If it is'no'
, it holds the elementwise loss values. If it is'sum'
, loss values are summed up.Parameters:  x (
Variable
ornumpy.ndarray
orcupy.ndarray
) – Input variable.  mean (
Variable
ornumpy.ndarray
orcupy.ndarray
) – A variable representing mean of a Gaussian distribution, \(\mu\).  ln_var (
Variable
ornumpy.ndarray
orcupy.ndarray
) – A variable representing logarithm of variance of a Gaussian distribution, \(\log(\sigma^2)\).  reduce (str) – Reduction option. Its value must be either
'sum'
or'no'
. Otherwise,ValueError
is raised.
Returns: A variable representing the negative loglikelihood. If
reduce
is'no'
, the output varialbe holds array whose shape is same as one of (hence both of) input variables. If it is'sum'
, the output variable holds a scalar value.Return type:  x (
hinge¶

chainer.functions.
hinge
(x, t, norm='L1', reduce='mean')[source]¶ Computes the hinge loss for a oneofmany classification task.
\[L = \frac{1}{N} \sum_{n=1}^N \sum_{k=1}^K \left[ \max(0, 1  \delta\{t_n = k\} x_{nk}) \right]^p\]where \(N\) denotes the batch size and \(K\) is the number of classes of interest,
\[\begin{split}\delta \{ {\rm condition} \} = \left \{ \begin{array}{cc} 1 & {\rm if~condition\ is\ true} \\ 1 & {\rm otherwise,} \end{array} \right.\end{split}\]and
\[\begin{split}p = \left \{ \begin{array}{cc} 1 & {\rm if~norm} = {\rm L1} \\ 2 & {\rm if~norm} = {\rm L2.} \end{array} \right.\end{split}\]The output is a variable whose value depends on the value of the option
reduce
. If it is'no'
, it holds the elementwise loss values. If it is'mean'
, it takes the mean of loss values.Parameters:  x (Variable) – Input variable. The shape of
x
should be (\(N\), \(K\)).  t (Variable) – The \(N\)dimensional label vector
with values \(t_n \in \{0, 1, 2, \dots, K1\}\).
The shape of
t
should be (\(N\),).  norm (string) – Specifies norm type. Either
'L1'
or'L2'
is acceptable.  reduce (str) – Reduction option. Its value must be either
'mean'
or'no'
. Otherwise,ValueError
is raised.
Returns: A variable object holding a scalar array of the hinge loss \(L\). If
reduce
is'no'
, the output variable holds array whose shape is same as one of (hence both of) input variables. If it is'mean'
, the output variable holds a scalar value.Return type:  x (Variable) – Input variable. The shape of
huber_loss¶

chainer.functions.
huber_loss
(x, t, delta, reduce='sum_along_second_axis')[source]¶ Loss function which is less sensitive to outliers in data than MSE.
\[a = x  t\]and
\[\begin{split}L_{\delta}(a) = \left \{ \begin{array}{cc} \frac{1}{2} a^2 & {\rm if~a \leq \delta} \\ \delta (a  \frac{1}{2} \delta) & {\rm otherwise,} \end{array} \right.\end{split}\]The output is a variable whose value depends on the value of the option
reduce
. If it is'no'
, it holds the elementwise loss values. If it is'sum_along_second_axis'
, loss values are summed up along the second axis (i.e.axis=1
).Parameters:  x (Variable) – Input variable.
The shape of
x
should be (\(N\), \(K\)).  t (Variable) – Target variable for regression.
The shape of
t
should be (\(N\), \(K\)).  delta (float) – Constant variable for huber loss function as used in definition.
 reduce (str) – Reduction option. Its value must be either
'sum_along_second_axis'
or'no'
. Otherwise,ValueError
is raised.
Returns: A variable object holding a scalar array of the huber loss \(L_{\delta}\). If
reduce
is'no'
, the output variable holds array whose shape is same as one of (hence both of) input variables. If it is'sum_along_second_axis'
, the shape of the array is same as the input variables, except the second axis is removed.Return type:  See:
 Huber loss  Wikipedia.
 x (Variable) – Input variable.
The shape of
mean_absolute_error¶
mean_squared_error¶
negative_sampling¶

chainer.functions.
negative_sampling
(x, t, W, sampler, sample_size, reduce='sum')[source]¶ 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.
Parameters:  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.
 reduce (str) – Reduction option. Its value must be either
'sum'
or'no'
. Otherwise,ValueError
is raised.
Returns: A variable holding the loss value(s) calculated by the above equation. If
reduce
is'no'
, the output variable holds array whose shape is same as one of (hence both of) input variables. If it is'sum'
, the output variable holds a scalar value.Return type: See: Distributed Representations of Words and Phrases and their Compositionality
See also
sigmoid_cross_entropy¶

chainer.functions.
sigmoid_cross_entropy
(x, t, normalize=True, reduce='mean')[source]¶ Computes cross entropy loss for presigmoid activations.
Parameters:  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.
 reduce (str) – Variable holding a
str
which determines whether to reduce the shape of the input. If it is'mean'
, it computes the sum of cross entropy and normalize it according tonormalize
option. If is is'no'
, this function computes cross entropy for each instance and does not normalize it (normalize
option is ignored). In this case, the loss value of the ignored instance, which has1
as its target value, is set to0
.
Returns: A variable object holding an array of the cross entropy. If
reduce
is'mean'
, it is a scalar array. Ifreduce
is'no'
, the shape is same asx
.Return type: Note
This function is differentiable only by
x
.
softmax_cross_entropy¶

chainer.functions.
softmax_cross_entropy
(x, t, normalize=True, cache_score=True, class_weight=None, ignore_label=1, reduce='mean')[source]¶ Computes cross entropy loss for presoftmax activations.
Parameters:  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] == ignore_label
, 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.  class_weight (ndarray or ndarray) – An array
that contains constant weights that will be multiplied with the
loss values along with the second dimension. The shape of this
array should be
(x.shape[1],)
. If this is notNone
, each class weightclass_weight[i]
is actually multiplied toy[:, i]
that is the corresponding logsoftmax output ofx
and has the same shape asx
before calculating the actual loss value.  ignore_label (int) – Label value you want to ignore. Its default value
is
1
. See description of the argument t.  reduce (str) – A string that determines whether to reduce the loss
values. If it is
'mean'
, it computes the sum of the individual cross entropy and normalize it according tonormalize
option. If it is'no'
, this function computes cross entropy for each instance and does not normalize it (normalize
option is ignored). In this case, the loss value of the ignored instance, which hasignore_label
as its target value, is set to0
.
Returns: A variable holding a scalar array of the cross entropy loss. If
reduce
is'mean'
, it is a scalar array. Ifreduce
is'no'
, the shape is same as that ofx
.Return type: Note
This function is differentiable only by
x
.
triplet¶

chainer.functions.
triplet
(anchor, positive, negative, margin=0.2, reduce='mean')[source]¶ 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 \(d(x_i, y_i) = \ {\bf x}_i  {\bf y}_i \_2^2\).
The output is a variable whose value depends on the value of the option
reduce
. If it is'no'
, it holds the elementwise loss values. If it is'mean'
, this function takes a mean of loss values.Parameters:  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.
 reduce (str) – Reduction option. Its value must be either
'mean'
or'no'
. Otherwise,ValueError
is raised.
Returns: A variable holding a scalar that is the loss value calculated by the above equation. If
reduce
is'no'
, the output variable holds array whose shape is same as one of (hence both of) input variables. If it is'mean'
, the output variable holds a scalar value.Return type: Note
This cost can be used to train triplet networks. See Learning Finegrained Image Similarity with Deep Ranking for details.
Mathematical functions¶
arccos¶
arcsin¶
arctan¶
argmax¶
argmin¶
average¶

chainer.functions.
average
(x, axis=None, weights=None, keepdims=False)[source]¶ Calculate weighted average of array elements over a given axis.
Parameters:  x (Variable) – Elements to sum.
 axis (None or int) – Axis which the method is performed. With the default (axis = None) it performs a mean over all the dimensions of the input array.
 weights (None or chainer.Variable) – An array holding weights to
calculate weighted average. If it is
None
, all weights are assumed to be one. Whenaxis
isNone
,weights
must have the same shape ofx
. And whenaxis
isint
, it must be 1D array satisfingweights.shape == (x.shape[axis],)
.  keepdims (bool) – If
True
, the specified axes are remained as axes of length one.
Returns: Output variable.
Return type:
batch_inv¶

chainer.functions.
batch_inv
(a)[source]¶ Computes the inverse of a batch of square matrices.
Parameters: 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.Returns: Inverse of every matrix in the batch of matrices. Return type: Variable
batch_l2_norm_squared¶

chainer.functions.
batch_l2_norm_squared
(x)[source]¶ 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.
Parameters: 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.Returns: Two dimensional output variable. Return type: Variable
batch_matmul¶

chainer.functions.
batch_matmul
(a, b, transa=False, transb=False)[source]¶ Computes the batch matrix multiplications of two sets of arrays.
Parameters:  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
.
Returns:  The result of the batch matrix multiplications as a
3D array.
Return type:  a (Variable) – The left operand of the batch matrix multiplications.
A 2D array of shape
bias¶

chainer.functions.
bias
(x, y, axis=1)[source]¶ 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
.Parameters: Returns: Output variable.
Return type:
ceil¶
clip¶
cosh¶
fmod¶
floor¶
inv¶
linear_interpolate¶
log10¶
log2¶
logsumexp¶
matmul¶

chainer.functions.
matmul
(a, b, transa=False, transb=False)[source]¶ Computes the matrix multiplication of two arrays.
Parameters:  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
.
Returns:  The result of the matrix multiplication as a 2D
array.
Return type:  a (Variable) – The left operand of the matrix multiplication.
A 1D array of shape
max¶
maximum¶
mean¶

chainer.functions.
mean
(x, axis=None, weights=None, keepdims=False)¶ Calculate weighted average of array elements over a given axis.
Parameters:  x (Variable) – Elements to sum.
 axis (None or int) – Axis which the method is performed. With the default (axis = None) it performs a mean over all the dimensions of the input array.
 weights (None or chainer.Variable) – An array holding weights to
calculate weighted average. If it is
None
, all weights are assumed to be one. Whenaxis
isNone
,weights
must have the same shape ofx
. And whenaxis
isint
, it must be 1D array satisfingweights.shape == (x.shape[axis],)
.  keepdims (bool) – If
True
, the specified axes are remained as axes of length one.
Returns: Output variable.
Return type:
min¶
minimum¶
rsqrt¶
scale¶

chainer.functions.
scale
(x, y, axis=1)[source]¶ 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
.Parameters: Returns: Output variable.
Return type:
sinh¶
sqrt¶
square¶

chainer.functions.
square
(x)[source]¶ Elementwise square function.
\[y_i = x_i ^ 2.\]Parameters: x (chainer.Variable or numpy.ndarray
or cupy.ndarray) – Input variable.Returns: Output variable. Return type: Variable
squared_difference¶
Noise injections¶
dropout¶

chainer.functions.
dropout
(x, ratio=.5)[source]¶ 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
.Warning
train
argument is not supported anymore since v2. Instead, usechainer.using_config('train', train)
. Seechainer.using_config()
.Parameters: Returns: Output variable.
Return type: See the paper by G. Hinton: Improving neural networks by preventing coadaptation of feature detectors.
gaussian¶
simplified_dropconnect¶

chainer.functions.
simplified_dropconnect
(x, W, b=None, ratio=0.5, train=True, mask=None)[source]¶ Linear unit regularized by simplified dropconnect.
Simplified dropconnect drops weight matrix elements randomly with probability
ratio
and scales the remaining elements by factor1 / (1  ratio)
. Which element is dropped depends on each sample. It accepts two or three arguments: an input minibatchx
, a weight matrixW
, and optionally a bias vectorb
. It computes \(Y = xW^\top + b\).In testing mode, zero will be used as simplified dropconnect ratio instead of
ratio
.Notice: This implementation cannot be used for reproduction of the paper. There is a difference between the current implementation and the original one. The original version uses sampling with gaussian distribution before passing activation function, whereas the current implementation averages before activation.
Parameters:  x (chainer.Variable or
numpy.ndarray
or cupy.ndarray) – Input variable. Its first dimensionn
is assumed to be the minibatch dimension. The other dimensions are treated as concatenated one dimension whose size must beN
.  W (Variable) – Weight variable of shape
(M, N)
.  b (Variable) – Bias variable (optional) of shape
(M,)
.  ratio (float) – Dropconnect ratio.
 train (bool) – If
True
, executes simplified dropconnect. Otherwise, simplified dropconnect function works as a linear function.  mask (None or chainer.Variable or numpy.ndarray or cupy.ndarray) – If
None
, randomized dropconnect mask is generated. Otherwise, The mask must be(n, M, N)
shaped array. Main purpose of this option is debugging. mask array will be used as a dropconnect mask.
Returns: Output variable.
Return type: See also
Dropconnect
See also
Li, W., Matthew Z., Sixin Z., Yann L., Rob F. (2013). Regularization of Neural Network using DropConnect. International Conference on Machine Learning. URL
 x (chainer.Variable or
Normalization functions¶
batch_normalization¶

chainer.functions.
batch_normalization
(x, gamma, beta, eps=2e5, running_mean=None, running_var=None, decay=0.9)[source]¶ Batch normalization function.
It takes the input variable
x
and two parameter variablesgamma
andbeta
. The parameter variables must both have the same dimensionality, which is referred to as the channel shape. This channel shape corresponds to the dimensions in the input which are not averaged over. Since the first dimension of the input corresponds to the batch size, the second dimension of x will correspond to the first dimension of the channel shape, the third dimension of x will correspond to the second channel dimension (if it exists) and so on. Therefore, the dimensionality of the input must be at least one plus the number of channel dimensions. The total effective “batch size” will then be considered to be the product of all dimensions in x except for the channel dimensions.As an example, if the input is four dimensional and the parameter variables are one dimensional, then it is assumed that the first dimension of the input is the batch size, the second dimension is the channel size, and the remaining two dimensions are considered to be spatial dimensions that will be averaged over along with the batch size in the batch normalization computations. That is, the total batch size will be considered to be the product of all input 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.
Warning
train
argument is not supported anymore since v2. Instead, usechainer.using_config('train', train)
. Seechainer.using_config()
.Parameters:  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.
See: Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
See also
links.BatchNormalization
fixed_batch_normalization¶

chainer.functions.
fixed_batch_normalization
(x, gamma, beta, mean, var, eps=2e05)[source]¶ 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.
Parameters:  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.
See also
functions.batch_normalization()
,links.BatchNormalization
local_response_normalization¶

chainer.functions.
local_response_normalization
(x, n=5, k=2, alpha=0.0001, beta=0.75)[source]¶ 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:
\[y_i = {x_i \over \left( k + \ \alpha \sum_{j=\max{1, i  n/2}}^{\min{N, i + n/2}} \ x_j^2 \right)^\beta}.\]Parameters: Returns: Output variable.
Return type: See: Section 3.3 of ImageNet Classification with Deep Convolutional Neural Networks
normalize¶

chainer.functions.
normalize
(x, eps=1e05, axis=1)[source]¶ L2 norm squared (a.k.a. Euclidean norm).
This function implements L2 normalization on a vector along the given axis. No reduction is done along the normalization axis.
In the case when
axis=1
and \(x\) is a vector of dimension \((N, K)\), where \(N\) and \(K\) denote minibatch size and the dimension of the input variable, this function computes an output vector \(y\) by the following equation:\[y_i = {x_i \over \ x_i \_2 + \epsilon}\]eps
is used to avoid division by zero when norm of \(x\) along the given axis is zero.The default value of
axis
is determined for backward compatibility.Parameters: Returns: The output variable which has the same shape as \(x\).
Return type:
Spatial pooling¶
average_pooling_2d¶

chainer.functions.
average_pooling_2d
(x, ksize, stride=None, pad=0)[source]¶ 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.Parameters:  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.
Returns: Output variable.
Return type: Note
This function currently does not support
cover_all
mode asmax_pooling_2d()
. Average pooling runs in noncoverall mode.
average_pooling_nd¶

chainer.functions.
average_pooling_nd
(x, ksize, stride=None, pad=0)[source]¶ Ndimensionally spatial average pooling function.
This function provides a Ndimensionally generalized version of
average_pooling_2d()
. This acts similarly toConvolutionND
, but it computes the average of input spatial patch for each channel without any parameter instead of computing the inner products.Parameters:  x (Variable) – Input variable.
 ksize (int or tuple of ints) – Size of pooling window.
ksize=k
andksize=(k, k, ..., k)
are equivalent.  stride (int or tuple of ints or None) – Stride of pooling applications.
stride=s
andstride=(s, s, ..., s)
are equivalent. IfNone
is specified, then it uses same stride as the pooling window size.  pad (int or tuple of ints) – Spatial padding width for the input array.
pad=p
andpad=(p, p, ..., p)
are equivalent.
Returns: Output variable.
Return type: Note
This function currently does not support
cover_all
mode asmax_pooling_nd()
. Average pooling runs in noncoverall mode.
max_pooling_2d¶

chainer.functions.
max_pooling_2d
(x, ksize, stride=None, pad=0, cover_all=True)[source]¶ 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.Parameters:  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.
Returns: Output variable.
Return type:
max_pooling_nd¶

chainer.functions.
max_pooling_nd
(x, ksize, stride=None, pad=0, cover_all=True)[source]¶ Ndimensionally spatial max pooling function.
This function provides a Ndimensionally generalized version of
max_pooling_2d()
. This acts similarly toConvolutionND
, but it computes the maximum of input spatial patch for each channel without any parameter instead of computing the inner products.Parameters:  x (Variable) – Input variable.
 ksize (int or tuple of ints) – Size of pooling window.
ksize=k
andksize=(k, k, ..., k)
are equivalent.  stride (int or tuple of ints or None) – Stride of pooling applications.
stride=s
andstride=(s,s, ..., s)
are equivalent. IfNone
is specified, then it uses same stride as the pooling window size.  pad (int or tuple of ints) – Spatial padding width for the input array.
pad=p
andpad=(p, 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.
Returns: Output variable.
Return type:
roi_pooling_2d¶

chainer.functions.
roi_pooling_2d
(x, rois, outh, outw, spatial_scale)[source]¶ 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.Parameters:  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.
Returns: Output variable.
Return type: See the original paper proposing ROIPooling: Fast RCNN.
spatial_pyramid_pooling_2d¶

chainer.functions.
spatial_pyramid_pooling_2d
(x, pyramid_height, pooling_class)[source]¶ 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.
Parameters: Returns:  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.
Return type: Note
This function uses some pooling classes as components to perform spatial pyramid pooling. Now it supports only
MaxPooling2D
as elemental pooling operator so far.
unpooling_2d¶

chainer.functions.
unpooling_2d
(x, ksize, stride=None, pad=0, outsize=None, cover_all=True)[source]¶ 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.Parameters:  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()
.
Returns: Output variable.
Return type:
upsampling_2d¶

chainer.functions.
upsampling_2d
(x, indexes, ksize, stride=None, pad=0, outsize=None, cover_all=True)[source]¶ Upsampling using pooling indices.
This function produces an upsampled image using pooling indices.
Example
It should be noted that you need to turn off
chainer.config.use_cudnn
flag when you create MaxPooling2D object because if cuDNN used for operating max pooling,indexes
is never created and stored in the MaxPooling2D object.>>> with chainer.using_config('use_cudnn', 'never'): ... p = F.MaxPooling2D(2, 2) >>> x = np.arange(1, 37).reshape(1, 1, 6, 6).astype('f') >>> x = chainer.Variable(x) >>> x.data array([[[[ 1., 2., 3., 4., 5., 6.], [ 7., 8., 9., 10., 11., 12.], [ 13., 14., 15., 16., 17., 18.], [ 19., 20., 21., 22., 23., 24.], [ 25., 26., 27., 28., 29., 30.], [ 31., 32., 33., 34., 35., 36.]]]], dtype=float32)
This is the original
x
before max pooling.>>> pooled_x = p(x) >>> pooled_x.data array([[[[ 8., 10., 12.], [ 20., 22., 24.], [ 32., 34., 36.]]]], dtype=float32)
This is the output of the max pooling operation.
upsampling_2d
needsindexes
array stored in the max pooling objectp
.>>> upsampled_x = F.upsampling_2d( ... pooled_x, p.indexes, p.kh, p.sy, p.ph, x.shape[2:]) >>> upsampled_x.shape (1, 1, 6, 6) >>> upsampled_x.data array([[[[ 0., 0., 0., 0., 0., 0.], [ 0., 8., 0., 10., 0., 12.], [ 0., 0., 0., 0., 0., 0.], [ 0., 20., 0., 22., 0., 24.], [ 0., 0., 0., 0., 0., 0.], [ 0., 32., 0., 34., 0., 36.]]]], dtype=float32)
Parameters:  x (Variable) – Input variable.
 indexes (ndarray or ndarray) – Index array that was used to calculate x with MaxPooling2D.
 ksize (int or (int, int)) – ksize attribute of MaxPooling2D object that is used to calculate x
 stride (int or (int, int)) – stride attribute of MaxPooling2D object that is used to calculate x
 pad (int or (int, int)) – pad attribute of MaxPooling2D object that is used to calculate x
 outsize ((int, int)) – Expected output size (height, width).
 cover_all (bool) – Whether cover_all is used in the MaxPooling2D object or not.
Returns: Output variable.
Return type:
Utility functions¶
forget¶

chainer.functions.
forget
(func, *xs)[source]¶ 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.
Example
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.Note
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.Parameters: Returns: A variable
func
returns. If it returns a tuple, the method returns a tuple too.Return type: