# Layers

## Data layer

### data

class `paddle.v2.layer.``data`(name, type, **kwargs)

  Define DataLayer For NeuralNetwork.

  The example usage is:

      data = paddle.layer.data(name="input", type=paddle.data_type.dense_vector(1000))

  Parameters: | name (basestring) – Name of this data layer. type – Data type of this data layer height (int|None) – Height of this data layer, used for image width (int|None) – Width of this data layer, used for image layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

## Fully Connected Layers

### fc

class `paddle.v2.layer.``fc`(*args, **kwargs)

  Helper for declare fully connected layer.

  The example usage is:

      fc = fc(input=layer,
                    size=1024,
                    act=paddle.v2.Activation.Linear(),
                    bias_attr=False)

  which is equal to:

      with mixed(size=1024) as fc:
          fc += full_matrix_projection(input=layer)

  Parameters: | name (basestring) – The Layer Name. input (paddle.v2.config_base.Layer|list|tuple) – The input layer. Could be a list/tuple of input layer. size (int) – The layer dimension. act (paddle.v2.Activation.Base) – Activation Type. Default is tanh. param_attr (paddle.v2.attr.ParameterAttribute) – The Parameter Attribute|list. bias_attr (paddle.v2.attr.ParameterAttribute|None|Any) – The Bias Attribute. If no bias, then pass False or something not type of paddle.v2.attr.ParameterAttribute. None will get a default Bias. layer_attr (paddle.v2.attr.ExtraAttributeNone) – Extra Layer config.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### selective_fc

class `paddle.v2.layer.``selective_fc`(*args, **kwargs)

  Selectived fully connected layer. Different from fc, the output of this layer maybe sparse. It requires an additional input to indicate several selected columns for output. If the selected columns is not specified, selective_fc acts exactly like fc.

  The simple usage is:

      sel_fc = selective_fc(input=input, size=128, act=paddle.v2.Activation.Tanh())

  Parameters: | name (basestring) – The Layer Name. input (paddle.v2.config_base.Layer|list|tuple) – The input layer. select (paddle.v2.config_base.Layer) – The select layer. The output of select layer should be a sparse binary matrix, and treat as the mask of selective fc. If is None, acts exactly like fc. size (int) – The layer dimension. act (paddle.v2.Activation.Base) – Activation Type. Default is tanh. param_attr (paddle.v2.attr.ParameterAttribute) – The Parameter Attribute. bias_attr (paddle.v2.attr.ParameterAttribute|None|Any) – The Bias Attribute. If no bias, then pass False or something not type of paddle.v2.attr.ParameterAttribute. None will get a default Bias. layer_attr (paddle.v2.attr.ExtraAttributeNone) – Extra Layer config.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

## Conv Layers

### conv_operator

class `paddle.v2.layer.``conv_operator`(**kwargs)

  Different from img_conv, conv_op is an Operator, which can be used in mixed. And conv_op takes two inputs to perform convolution. The first input is the image and the second is filter kernel. It only support GPU mode.

  The example usage is:

      op = conv_operator(img=input1,
                         filter=input2,
                         filter_size=3,
                         num_filters=64,
                         num_channels=64)

  Parameters: | img (paddle.v2.config_base.Layer) – input image filter (paddle.v2.config_base.Layer) – input filter filter_size (int) – The x dimension of a filter kernel. filter_size_y (int) – The y dimension of a filter kernel. Since PaddlePaddle now supports rectangular filters, the filter’s shape can be (filter_size, filter_size_y). num_filters (int) – channel of output data. num_channels (int) – channel of input data. stride (int) – The x dimension of the stride. stride_y (int) – The y dimension of the stride. padding (int) – The x dimension of padding. padding_y (int) – The y dimension of padding.
  Returns: | A ConvOperator Object.
  Return type: | ConvOperator

### conv_projection

class `paddle.v2.layer.``conv_projection`(**kwargs)

  Different from img_conv and conv_op, conv_projection is an Projection, which can be used in mixed and conat. It use cudnn to implement conv and only support GPU mode.

  The example usage is:

      proj = conv_projection(input=input1,
                             filter_size=3,
                             num_filters=64,
                             num_channels=64)

  Parameters: | input (paddle.v2.config_base.Layer) – input layer filter_size (int) – The x dimension of a filter kernel. filter_size_y (int) – The y dimension of a filter kernel. Since PaddlePaddle now supports rectangular filters, the filter’s shape can be (filter_size, filter_size_y). num_filters (int) – channel of output data. num_channels (int) – channel of input data. stride (int) – The x dimension of the stride. stride_y (int) – The y dimension of the stride. padding (int) – The x dimension of padding. padding_y (int) – The y dimension of padding. groups (int) – The group number. param_attr (paddle.v2.attr.ParameterAttribute) – Convolution param attribute. None means default attribute trans (boolean) – whether it is convTrans or conv
  Returns: | A DotMulProjection Object.
  Return type: | DotMulProjection

### conv_shift

class `paddle.v2.layer.``conv_shift`(*args, **kwargs)
  This layer performs cyclic convolution for two input. For example:
    - a[in]: contains M elements.
    - b[in]: contains N elements (N should be odd).
    - c[out]: contains M elements.
  \[c[i] = \sum_{j=-(N-1)/2}^{(N-1)/2}a_{i+j} * b_{j}\]
  In this formular:
    - a’s index is computed modulo M. When it is negative, then get item from the right side (which is the end of array) to the left.
    - b’s index is computed modulo N. When it is negative, then get item from the right size (which is the end of array) to the left.

  The example usage is:

      conv_shift = conv_shift(a=layer1, b=layer2)

  Parameters: | name (basestring) – layer name a (paddle.v2.config_base.Layer) – Input layer a. b (paddle.v2.config_base.Layer) – input layer b. layer_attr (paddle.v2.attr.ExtraAttribute) – layer’s extra attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### img_conv

class `paddle.v2.layer.``img_conv`(*args, **kwargs)

  Convolution layer for image. Paddle can support both square and non-square input currently.

  The details of convolution layer, please refer UFLDL’s convolution .

  Convolution Transpose (deconv) layer for image. Paddle can support both square and non-square input currently.

  The details of convolution transpose layer, please refer to the following explanation and references therein <http://datascience.stackexchange.com/questions/6107/ what-are-deconvolutional-layers/>`_ . The num_channel means input image’s channel number. It may be 1 or 3 when input is raw pixels of image(mono or RGB), or it may be the previous layer’s num_filters * num_group.

  There are several group of filter in PaddlePaddle implementation. Each group will process some channel of the inputs. For example, if an input num_channel = 256, group = 4, num_filter=32, the PaddlePaddle will create 32*4 = 128 filters to process inputs. The channels will be split into 4 pieces. First 256/4 = 64 channels will process by first 32 filters. The rest channels will be processed by rest group of filters.

  The example usage is:

      conv = img_conv(input=data, filter_size=1, filter_size_y=1,
                            num_channels=8,
                            num_filters=16, stride=1,
                            bias_attr=False,
                            act=paddle.v2.Activation.Relu())

  Parameters: | name (basestring) – Layer name. input (paddle.v2.config_base.Layer) – Layer Input. filter_size (int|tuple|list) – The x dimension of a filter kernel. Or input a tuple for two image dimension. filter_size_y (int|None) – The y dimension of a filter kernel. Since PaddlePaddle currently supports rectangular filters, the filter’s shape will be (filter_size, filter_size_y). num_filters – Each filter group’s number of filter act (paddle.v2.Activation.Base) – Activation type. Default is tanh groups (int) – Group size of filters. stride (int|tuple|list) – The x dimension of the stride. Or input a tuple for two image dimension. stride_y (int) – The y dimension of the stride. padding (int|tuple|list) – The x dimension of the padding. Or input a tuple for two image dimension padding_y (int) – The y dimension of the padding. bias_attr (paddle.v2.attr.ParameterAttribute|False) – Convolution bias attribute. None means default bias. False means no bias. num_channels (int) – number of input channels. If None will be set automatically from previous output. param_attr (paddle.v2.attr.ParameterAttribute) – Convolution param attribute. None means default attribute shared_biases (bool) – Is biases will be shared between filters or not. layer_attr (paddle.v2.attr.ExtraAttribute) – Layer Extra Attribute. trans (bool) – true if it is a convTransLayer, false if it is a convLayer layer_type (String) – specify the layer_type, default is None. If trans=True, layer_type has to be “exconvt” or “cudnn_convt”, otherwise layer_type has to be either “exconv” or “cudnn_conv”
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### context_projection

class `paddle.v2.layer.``context_projection`(**kwargs)

  Context Projection.

  It just simply reorganizes input sequence, combines “context_len” sequence to one context from context_start. “context_start” will be set to -(context_len - 1) / 2 by default. If context position out of sequence length, padding will be filled as zero if padding_attr = False, otherwise it is trainable.

  For example, origin sequence is [A B C D E F G], context len is 3, then after context projection and not set padding_attr, sequence will be [ 0AB ABC BCD CDE DEF EFG FG0 ].

  Parameters: | input (paddle.v2.config_base.Layer) – Input Sequence. context_len (int) – context length. context_start (int) – context start position. Default is -(context_len - 1)/2 padding_attr (bool|paddle.v2.attr.ParameterAttribute) – Padding Parameter Attribute. If false, it means padding always be zero. Otherwise Padding is learnable, and parameter attribute is set by this parameter.
  Returns: | Projection
  Return type: | Projection

## Image Pooling Layer

### img_pool

class `paddle.v2.layer.``img_pool`(*args, **kwargs)

  Image pooling Layer.

  The details of pooling layer, please refer ufldl’s pooling .

  - ceil_mode=True:
  \[w = 1 + int(ceil(input\_width + 2 * padding - pool\_size) / float(stride)) h = 1 + int(ceil(input\_height + 2 * padding\_y - pool\_size\_y) / float(stride\_y))\]
  - ceil_mode=False:
  \[w = 1 + int(floor(input\_width + 2 * padding - pool\_size) / float(stride)) h = 1 + int(floor(input\_height + 2 * padding\_y - pool\_size\_y) / float(stride\_y))\]

  The example usage is:

      maxpool = img_pool(input=conv,
                               pool_size=3,
                               pool_size_y=5,
                               num_channels=8,
                               stride=1,
                               stride_y=2,
                               padding=1,
                               padding_y=2,
                               pool_type=MaxPooling())

  Parameters: | padding (int) – pooling padding width. padding_y (int|None) – pooling padding height. It’s equal to padding by default. name (basestring.) – name of pooling layer input (paddle.v2.config_base.Layer) – layer’s input pool_size (int) – pooling window width pool_size_y (int|None) – pooling window height. It’s eaqual to pool_size by default. num_channels (int) – number of input channel. pool_type (BasePoolingType) – pooling type. MaxPooling or AvgPooling. Default is MaxPooling. stride (int) – stride width of pooling. stride_y (int|None) – stride height of pooling. It is equal to stride by default. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer attribute. ceil_mode (bool) – Wether to use ceil mode to calculate output height and with. Defalut is True. If set false, Otherwise use floor.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### spp

class `paddle.v2.layer.``spp`(*args, **kwargs)

  Spatial Pyramid Pooling in Deep Convolutional Networks for Visual Recognition. The details please refer to Kaiming He’s paper.

  The example usage is:

      spp = spp(input=data,
                      pyramid_height=2,
                      num_channels=16,
                      pool_type=MaxPooling())

  Parameters: | name (basestring) – layer name. input (paddle.v2.config_base.Layer) – layer’s input. num_channels (int) – number of input channel. pool_type – Pooling type. MaxPooling or AveragePooling. Default is MaxPooling. pyramid_height (int) – pyramid height. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### maxout

class `paddle.v2.layer.``maxout`(*args, **kwargs)
  A layer to do max out on conv layer output.
    - Input: output of a conv layer.
    - Output: feature map size same as input. Channel is (input channel) / groups.

  So groups should be larger than 1, and the num of channels should be able to devided by groups.

  Please refer to Paper:
    - Maxout Networks: http://www.jmlr.org/proceedings/papers/v28/goodfellow13.pdf
    - Multi-digit Number Recognition from Street View Imagery using Deep Convolutional Neural Networks: https://arxiv.org/pdf/1312.6082v4.pdf

  The simple usage is:

      maxout = maxout(input,
                            num_channels=128,
                            groups=4)

  Parameters: | input (paddle.v2.config_base.Layer) – The input layer. num_channels (int|None) – The channel number of input layer. If None will be set automatically from previous output. groups (int) – The group number of input layer. name (None|basestring.) – The name of this layer, which can not specify. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

## Norm Layer

### img_cmrnorm

class `paddle.v2.layer.``img_cmrnorm`(*args, **kwargs)

  Response normalization across feature maps. The details please refer to Alex’s paper.

  The example usage is:

      norm = img_cmrnorm(input=net, size=5)

  Parameters: | name (None|basestring) – layer name. input (paddle.v2.config_base.Layer) – layer’s input. size (int) – Normalize in number of \(size\) feature maps. scale (float) – The hyper-parameter. power (float) – The hyper-parameter. num_channels – input layer’s filers number or channels. If num_channels is None, it will be set automatically. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### batch_norm

class `paddle.v2.layer.``batch_norm`(*args, **kwargs)

  Batch Normalization Layer. The notation of this layer as follow.

  \(x\) is the input features over a mini-batch.

  \[\begin{split}\mu_{\beta} &\gets \frac{1}{m} \sum_{i=1}^{m} x_i \qquad &//\ \ mini-batch\ mean \\ \sigma_{\beta}^{2} &\gets \frac{1}{m} \sum_{i=1}^{m}(x_i - \ \mu_{\beta})^2 \qquad &//\ mini-batch\ variance \\ \hat{x_i} &\gets \frac{x_i - \mu_\beta} {\sqrt{\ \sigma_{\beta}^{2} + \epsilon}} \qquad &//\ normalize \\ y_i &\gets \gamma \hat{x_i} + \beta \qquad &//\ scale\ and\ shift\end{split}\]

  The details of batch normalization please refer to this paper.

  The example usage is:

      norm = batch_norm(input=net, act=paddle.v2.Activation.Relu())

  Parameters: | name (basestring) – layer name. input (paddle.v2.config_base.Layer) – batch normalization input. Better be linear activation. Because there is an activation inside batch_normalization. batch_norm_type (None|string, None or "batch_norm" or "cudnn_batch_norm") – We have batch_norm and cudnn_batch_norm. batch_norm supports both CPU and GPU. cudnn_batch_norm requires cuDNN version greater or equal to v4 (>=v4). But cudnn_batch_norm is faster and needs less memory than batch_norm. By default (None), we will automaticly select cudnn_batch_norm for GPU and batch_norm for CPU. Otherwise, select batch norm type based on the specified type. If you use cudnn_batch_norm, we suggested you use latest version, such as v5.1. act (paddle.v2.Activation.Base) – Activation Type. Better be relu. Because batch normalization will normalize input near zero. num_channels (int) – num of image channels or previous layer’s number of filters. None will automatically get from layer’s input. bias_attr (paddle.v2.attr.ParameterAttribute) – \(\beta\), better be zero when initialize. So the initial_std=0, initial_mean=1 is best practice. param_attr (paddle.v2.attr.ParameterAttribute) – \(\gamma\), better be one when initialize. So the initial_std=0, initial_mean=1 is best practice. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute. use_global_stats (bool|None.) – whether use moving mean/variance statistics during testing peroid. If None or True, it will use moving mean/variance statistics during testing. If False, it will use the mean and variance of current batch of test data for testing. moving_average_fraction (float.) – Factor used in the moving average computation, referred to as facotr, \(runningMean = newMean*(1-factor) + runningMean*factor\)
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### sum_to_one_norm

class `paddle.v2.layer.``sum_to_one_norm`(*args, **kwargs)

  A layer for sum-to-one normalization, which is used in NEURAL TURING MACHINE.

  \[out[i] = \frac {in[i]} {\sum_{k=1}^N in[k]}\]

  where \(in\) is a (batchSize x dataDim) input vector, and \(out\) is a (batchSize x dataDim) output vector.

  The example usage is:

      sum_to_one_norm = sum_to_one_norm(input=layer)

  Parameters: | input (paddle.v2.config_base.Layer) – Input layer. name (basestring) – Layer name. layer_attr (paddle.v2.attr.ExtraAttribute) – extra layer attributes.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### cross_channel_norm

class `paddle.v2.layer.``cross_channel_norm`(*args, **kwargs)

  Normalize a layer’s output. This layer is necessary for ssd. This layer applys normalize across the channels of each sample to a conv layer’s output and scale the output by a group of trainable factors which dimensions equal to the channel’s number.

  Parameters: | name (basestring) – The Layer Name. input (paddle.v2.config_base.Layer) – The input layer. param_attr (paddle.v2.attr.ParameterAttribute) – The Parameter Attribute|list.
  Returns: | paddle.v2.config_base.Layer

## Recurrent Layers

### recurrent

class `paddle.v2.layer.``recurrent`(*args, **kwargs)

  Simple recurrent unit layer. It is just a fully connect layer through both time and neural network.

  For each sequence [start, end] it performs the following computation:

  \[\begin{split}out_{i} = act(in_{i}) \ \ \text{for} \ i = start \\ out_{i} = act(in_{i} + out_{i-1} * W) \ \ \text{for} \ start < i <= end\end{split}\]

  If reversed is true, the order is reversed:

  \[\begin{split}out_{i} = act(in_{i}) \ \ \text{for} \ i = end \\ out_{i} = act(in_{i} + out_{i+1} * W) \ \ \text{for} \ start <= i < end\end{split}\]

  Parameters: | input (paddle.v2.config_base.Layer) – Input Layer act (paddle.v2.Activation.Base) – activation. bias_attr (paddle.v2.attr.ParameterAttribute) – bias attribute. param_attr (paddle.v2.attr.ParameterAttribute) – parameter attribute. name (basestring) – name of the layer layer_attr (paddle.v2.attr.ExtraAttribute) – Layer Attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### lstmemory

class `paddle.v2.layer.``lstmemory`(*args, **kwargs)

  Long Short-term Memory Cell.

  The memory cell was implemented as follow equations.

  \[ \begin{align}\begin{aligned}i_t & = \sigma(W_{xi}x_{t} + W_{hi}h_{t-1} + W_{ci}c_{t-1} + b_i)\\f_t & = \sigma(W_{xf}x_{t} + W_{hf}h_{t-1} + W_{cf}c_{t-1} + b_f)\\c_t & = f_tc_{t-1} + i_t tanh (W_{xc}x_t+W_{hc}h_{t-1} + b_c)\\o_t & = \sigma(W_{xo}x_{t} + W_{ho}h_{t-1} + W_{co}c_t + b_o)\\h_t & = o_t tanh(c_t)\end{aligned}\end{align} \]

  NOTE: In PaddlePaddle’s implementation, the multiplications \(W_{xi}x_{t}\) , \(W_{xf}x_{t}\), \(W_{xc}x_t\), \(W_{xo}x_{t}\) are not done in the lstmemory layer, so an additional mixed with full_matrix_projection or a fc must be included in the configuration file to complete the input-to-hidden mappings before lstmemory is called.

  NOTE: This is a low level user interface. You can use network.simple_lstm to config a simple plain lstm layer.

  Please refer to Generating Sequences With Recurrent Neural Networks for more details about LSTM.

  Link goes as below.

  Parameters: | name (basestring) – The lstmemory layer name. input (paddle.v2.config_base.Layer) – input layer name. reverse (bool) – is sequence process reversed or not. act (paddle.v2.Activation.Base) – activation type, paddle.v2.Activation.Tanh by default. \(h_t\) gate_act (paddle.v2.Activation.Base) – gate activation type, paddle.v2.Activation.Sigmoid by default. state_act (paddle.v2.Activation.Base) – state activation type, paddle.v2.Activation.Tanh by default. bias_attr (paddle.v2.attr.ParameterAttribute|None|False) – Bias attribute. None means default bias. False means no bias. param_attr (paddle.v2.attr.ParameterAttribute|None|False) – Parameter Attribute. layer_attr (paddle.v2.attr.ExtraAttributeNone) – Extra Layer attribute
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### grumemory

class `paddle.v2.layer.``grumemory`(*args, **kwargs)

  Gate Recurrent Unit Layer.

  The memory cell was implemented as follow equations.

  1. update gate \(z\): defines how much of the previous memory to keep around or the unit updates its activations. The update gate is computed by:

  \[z_t = \sigma(W_{z}x_{t} + U_{z}h_{t-1} + b_z)\]

  2. reset gate \(r\): determines how to combine the new input with the previous memory. The reset gate is computed similarly to the update gate:

  \[r_t = \sigma(W_{r}x_{t} + U_{r}h_{t-1} + b_r)\]

  3. The candidate activation \(\tilde{h_t}\) is computed similarly to that of the traditional recurrent unit:

  \[{\tilde{h_t}} = tanh(W x_{t} + U (r_{t} \odot h_{t-1}) + b)\]

  4. The hidden activation \(h_t\) of the GRU at time t is a linear interpolation between the previous activation \(h_{t-1}\) and the candidate activation \(\tilde{h_t}\):

  \[h_t = (1 - z_t) h_{t-1} + z_t {\tilde{h_t}}\]

  NOTE: In PaddlePaddle’s implementation, the multiplication operations \(W_{r}x_{t}\), \(W_{z}x_{t}\) and \(W x_t\) are not computed in gate_recurrent layer. Consequently, an additional mixed with full_matrix_projection or a fc must be included before grumemory is called.

  More details can be found by referring to Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling.

  The simple usage is:

      gru = grumemory(input)

  Parameters: | name (None|basestring) – The gru layer name. input (paddle.v2.config_base.Layer.) – input layer. reverse (bool) – Whether sequence process is reversed or not. act (paddle.v2.Activation.Base) – activation type, paddle.v2.Activation.Tanh by default. This activation affects the \({\tilde{h_t}}\). gate_act (paddle.v2.Activation.Base) – gate activation type, paddle.v2.Activation.Sigmoid by default. This activation affects the \(z_t\) and \(r_t\). It is the \(\sigma\) in the above formula. bias_attr (paddle.v2.attr.ParameterAttribute|None|False) – Bias attribute. None means default bias. False means no bias. param_attr (paddle.v2.attr.ParameterAttribute|None|False) – Parameter Attribute. layer_attr (paddle.v2.attr.ExtraAttributeNone) – Extra Layer attribute size (None) – Stub parameter of size, but actually not used. If set this size will get a warning.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

## Recurrent Layer Group

### memory

`paddle.v2.layer.``memory`

  alias of `MemoryV2`

### recurrent_group

class `paddle.v2.layer.``recurrent_group`

### lstm_step

class `paddle.v2.layer.``lstm_step`(*args, **kwargs)

  LSTM Step Layer. It used in recurrent_group. The lstm equations are shown as follow.

  \[ \begin{align}\begin{aligned}i_t & = \sigma(W_{xi}x_{t} + W_{hi}h_{t-1} + W_{ci}c_{t-1} + b_i)\\f_t & = \sigma(W_{xf}x_{t} + W_{hf}h_{t-1} + W_{cf}c_{t-1} + b_f)\\c_t & = f_tc_{t-1} + i_t tanh (W_{xc}x_t+W_{hc}h_{t-1} + b_c)\\o_t & = \sigma(W_{xo}x_{t} + W_{ho}h_{t-1} + W_{co}c_t + b_o)\\h_t & = o_t tanh(c_t)\end{aligned}\end{align} \]

  The input of lstm step is \(Wx_t + Wh_{t-1}\), and user should use `mixed` and `full_matrix_projection` to calculate these input vector.

  The state of lstm step is \(c_{t-1}\). And lstm step layer will do

  \[ \begin{align}\begin{aligned}i_t = \sigma(input + W_{ci}c_{t-1} + b_i)\\...\end{aligned}\end{align} \]

  This layer contains two outputs. Default output is \(h_t\). The other output is \(o_t\), which name is ‘state’ and can use `get_output` to extract this output.

  Parameters: | name (basestring) – Layer’s name. size (int) – Layer’s size. NOTE: lstm layer’s size, should be equal as `input.size/4`, and should be equal as `state.size`. input (paddle.v2.config_base.Layer) – input layer. \(Wx_t + Wh_{t-1}\) state (paddle.v2.config_base.Layer) – State Layer. \(c_{t-1}\) act (paddle.v2.Activation.Base) – Activation type. Default is tanh gate_act (paddle.v2.Activation.Base) – Gate Activation Type. Default is sigmoid, and should be sigmoid only. state_act (paddle.v2.Activation.Base) – State Activation Type. Default is sigmoid, and should be sigmoid only. bias_attr (paddle.v2.attr.ParameterAttribute) – Bias Attribute. layer_attr (paddle.v2.attr.ExtraAttribute) – layer’s extra attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### gru_step

class `paddle.v2.layer.``gru_step`(*args, **kwargs)

  Parameters: | input (paddle.v2.config_base.Layer) – output_mem – size – act – name – gate_act – bias_attr – param_attr – the parameter_attribute for transforming the output_mem from previous step. layer_attr –
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### beam_search

class `paddle.v2.layer.``beam_search`

### get_output

class `paddle.v2.layer.``get_output`(*args, **kwargs)

  Get layer’s output by name. In PaddlePaddle, a layer might return multiple values, but returns one layer’s output. If the user wants to use another output besides the default one, please use get_output first to get the output from input.

  Parameters: | name (basestring) – Layer’s name. input (paddle.v2.config_base.Layer) – get output layer’s input. And this layer should contains multiple outputs. arg_name (basestring) – Output name from input. layer_attr – Layer’s extra attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

## Mixed Layer

### mixed

class `paddle.v2.layer.``mixed`

### embedding

class `paddle.v2.layer.``embedding`(*args, **kwargs)

  Define a embedding Layer.

  Parameters: | name (basestring) – Name of this embedding layer. input (paddle.v2.config_base.Layer) – The input layer for this embedding. NOTE: must be Index Data. size (int) – The embedding dimension. param_attr (paddle.v2.attr.ParameterAttribute|None) – The embedding parameter attribute. See paddle.v2.attr.ParameterAttribute for details. layer_attr (paddle.v2.attr.ExtraAttributeNone) – Extra layer Config. Default is None.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### scaling_projection

class `paddle.v2.layer.``scaling_projection`(**kwargs)

  scaling_projection multiplies the input with a scalar parameter and add to the output.

  \[out += w * in\]

  The example usage is:

      proj = scaling_projection(input=layer)

  Parameters: | input (paddle.v2.config_base.Layer) – Input Layer. param_attr (paddle.v2.attr.ParameterAttribute) – Parameter config, None if use default.
  Returns: | A ScalingProjection object
  Return type: | ScalingProjection

### dotmul_projection

class `paddle.v2.layer.``dotmul_projection`(**kwargs)

  DotMulProjection with a layer as input. It performs element-wise multiplication with weight.

  \[out.row[i] += in.row[i] .* weight\]

  where \(.*\) means element-wise multiplication.

  The example usage is:

      proj = dotmul_projection(input=layer)

  Parameters: | input (paddle.v2.config_base.Layer) – Input layer. param_attr (paddle.v2.attr.ParameterAttribute) – Parameter config, None if use default.
  Returns: | A DotMulProjection Object.
  Return type: | DotMulProjection

### dotmul_operator

class `paddle.v2.layer.``dotmul_operator`(**kwargs)

  DotMulOperator takes two inputs and performs element-wise multiplication:

  \[out.row[i] += scale * (a.row[i] .* b.row[i])\]

  where \(.*\) means element-wise multiplication, and scale is a config scalar, its default value is one.

  The example usage is:

      op = dotmul_operator(a=layer1, b=layer2, scale=0.5)

  Parameters: | a (paddle.v2.config_base.Layer) – Input layer1 b (paddle.v2.config_base.Layer) – Input layer2 scale (float) – config scalar, default value is one.
  Returns: | A DotMulOperator Object.
  Return type: | DotMulOperator

### full_matrix_projection

class `paddle.v2.layer.``full_matrix_projection`(**kwargs)

  Full Matrix Projection. It performs full matrix multiplication.

  \[out.row[i] += in.row[i] * weight\]

  There are two styles of usage.

  1. When used in mixed like this, you can only set the input:

      with mixed(size=100) as m:
          m += full_matrix_projection(input=layer)

  2. When used as an independant object like this, you must set the size:

      proj = full_matrix_projection(input=layer,
                                    size=100,
                                    param_attr=ParamAttr(name='_proj'))

  Parameters: | input (paddle.v2.config_base.Layer) – input layer size (int) – The parameter size. Means the width of parameter. param_attr (paddle.v2.attr.ParameterAttribute) – Parameter config, None if use default.
  Returns: | A FullMatrixProjection Object.
  Return type: | FullMatrixProjection

### identity_projection

class `paddle.v2.layer.``identity_projection`(**kwargs)
  1. IdentityProjection if offset=None. It performs:
  \[out.row[i] += in.row[i]\]

  The example usage is:

      proj = identity_projection(input=layer)

  2. IdentityOffsetProjection if offset!=None. It likes IdentityProjection, but layer size may be smaller than input size. It select dimesions [offset, offset+layer_size) from input:

  \[out.row[i] += in.row[i + \textrm{offset}]\]

  The example usage is:

      proj = identity_projection(input=layer,
                                 offset=10)

  Note that both of two projections should not have any parameter.

  Parameters: | input (paddle.v2.config_base.Layer) – Input Layer. offset (int) – Offset, None if use default.
  Returns: | A IdentityProjection or IdentityOffsetProjection object
  Return type: | IdentityProjection or IdentityOffsetProjection

### table_projection

class `paddle.v2.layer.``table_projection`(**kwargs)

  Table Projection. It selects rows from parameter where row_id is in input_ids.

  \[out.row[i] += table.row[ids[i]]\]

  where \(out\) is output, \(table\) is parameter, \(ids\) is input_ids, and \(i\) is row_id.

  There are two styles of usage.

  1. When used in mixed like this, you can only set the input:

      with mixed(size=100) as m:
          m += table_projection(input=layer)

  2. When used as an independant object like this, you must set the size:

      proj = table_projection(input=layer,
                              size=100,
                              param_attr=ParamAttr(name='_proj'))

  Parameters: | input (paddle.v2.config_base.Layer) – Input layer, which must contains id fields. size (int) – The parameter size. Means the width of parameter. param_attr (paddle.v2.attr.ParameterAttribute) – Parameter config, None if use default.
  Returns: | A TableProjection Object.
  Return type: | TableProjection

### trans_full_matrix_projection

class `paddle.v2.layer.``trans_full_matrix_projection`(**kwargs)

  Different from full_matrix_projection, this projection performs matrix multiplication, using transpose of weight.

  \[out.row[i] += in.row[i] * w^\mathrm{T}\]

  \(w^\mathrm{T}\) means transpose of weight. The simply usage is:

      proj = trans_full_matrix_projection(input=layer,
                                          size=100,
                                          param_attr=ParamAttr(
                                               name='_proj',
                                               initial_mean=0.0,
                                               initial_std=0.01))

  Parameters: | input (paddle.v2.config_base.Layer) – input layer size (int) – The parameter size. Means the width of parameter. param_attr (paddle.v2.attr.ParameterAttribute) – Parameter config, None if use default.
  Returns: | A TransposedFullMatrixProjection Object.
  Return type: | TransposedFullMatrixProjection

## Aggregate Layers

### pooling

class `paddle.v2.layer.``pooling`(*args, **kwargs)

  Pooling layer for sequence inputs, not used for Image.

  The example usage is:

      seq_pool = pooling(input=layer,
                               pooling_type=AvgPooling(),
                               agg_level=AggregateLevel.EACH_SEQUENCE)

  Parameters: | agg_level (AggregateLevel) – AggregateLevel.EACH_TIMESTEP or AggregateLevel.EACH_SEQUENCE name (basestring) – layer name. input (paddle.v2.config_base.Layer) – input layer name. pooling_type (BasePoolingType|None) – Type of pooling, MaxPooling(default), AvgPooling, SumPooling, SquareRootNPooling. bias_attr (paddle.v2.attr.ParameterAttribute|None|False) – Bias parameter attribute. False if no bias. layer_attr (paddle.v2.attr.ExtraAttributeNone) – The Extra Attributes for layer, such as dropout.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### last_seq

class `paddle.v2.layer.``last_seq`(*args, **kwargs)

  Get Last Timestamp Activation of a sequence.

  If stride > 0, this layer slides a window whose size is determined by stride, and return the last value of the window as the output. Thus, a long sequence will be shorten. Note that for sequence with sub-sequence, the default value of stride is -1.

  The simple usage is:

      seq = last_seq(input=layer)

  Parameters: | agg_level – Aggregated level name (basestring) – Layer name. input (paddle.v2.config_base.Layer) – Input layer name. stride (Int) – window size. layer_attr (paddle.v2.attr.ExtraAttribute) – extra layer attributes.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### first_seq

class `paddle.v2.layer.``first_seq`(*args, **kwargs)

  Get First Timestamp Activation of a sequence.

  If stride > 0, this layer slides a window whose size is determined by stride, and return the first value of the window as the output. Thus, a long sequence will be shorten. Note that for sequence with sub-sequence, the default value of stride is -1.

  The simple usage is:

      seq = first_seq(input=layer)

  Parameters: | agg_level – aggregation level name (basestring) – Layer name. input (paddle.v2.config_base.Layer) – Input layer name. stride (Int) – window size. layer_attr (paddle.v2.attr.ExtraAttribute) – extra layer attributes.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### concat

class `paddle.v2.layer.``concat`(*args, **kwargs)

  Concat all input vector into one huge vector. Inputs can be list of paddle.v2.config_base.Layer or list of projection.

  The example usage is:

      concat = concat(input=[layer1, layer2])

  Parameters: | name (basestring) – Layer name. input (list|tuple|collections.Sequence) – input layers or projections act (paddle.v2.Activation.Base) – Activation type. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### seq_concat

class `paddle.v2.layer.``seq_concat`(*args, **kwargs)

  Concat sequence a with sequence b.

  Inputs:
    - a = [a1, a2, ..., an]
    - b = [b1, b2, ..., bn]
    - Note that the length of a and b should be the same.

  Output: [a1, b1, a2, b2, ..., an, bn]

  The example usage is:

      concat = seq_concat(a=layer1, b=layer2)

  Parameters: | name (basestring) – Layer name. a (paddle.v2.config_base.Layer) – input sequence layer b (paddle.v2.config_base.Layer) – input sequence layer act (paddle.v2.Activation.Base) – Activation type. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute. bias_attr (paddle.v2.attr.ParameterAttribute or None or bool) – The Bias Attribute. If no bias, then pass False or something not type of paddle.v2.attr.ParameterAttribute. None will get a default Bias.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

## Reshaping Layers

### block_expand

class `paddle.v2.layer.``block_expand`(*args, **kwargs)
  Expand feature map to minibatch matrix.
    - matrix width is: block_y * block_x * num_channels
    - matirx height is: outputH * outputW
  \[ \begin{align}\begin{aligned}outputH = 1 + (2 * padding_y + imgSizeH - block_y + stride_y - 1) / stride_y\\outputW = 1 + (2 * padding_x + imgSizeW - block_x + stride_x - 1) / stride_x\end{aligned}\end{align} \]

  The expand method is the same with ExpandConvLayer, but saved the transposed value. After expanding, output.sequenceStartPositions will store timeline. The number of time steps are outputH * outputW and the dimension of each time step is block_y * block_x * num_channels. This layer can be used after convolution neural network, and before recurrent neural network.

  The simple usage is:

      block_expand = block_expand(input=layer,
                                        num_channels=128,
                                        stride_x=1,
                                        stride_y=1,
                                        block_x=1,
                                        block_x=3)

  Parameters: | input (paddle.v2.config_base.Layer) – The input layer. num_channels (int|None) – The channel number of input layer. block_x (int) – The width of sub block. block_y (int) – The width of sub block. stride_x (int) – The stride size in horizontal direction. stride_y (int) – The stride size in vertical direction. padding_x (int) – The padding size in horizontal direction. padding_y (int) – The padding size in vertical direction. name (None|basestring.) – The name of this layer, which can not specify. layer_attr (paddle.v2.attr.ExtraAttributeNone) – Extra Layer config.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### expand

class `paddle.v2.layer.``expand`(*args, **kwargs)

  A layer for “Expand Dense data or (sequence data where the length of each sequence is one) to sequence data.”

  The example usage is:

      expand = expand(input=layer1,
                            expand_as=layer2,
                            expand_level=ExpandLevel.FROM_TIMESTEP)

  Parameters: | input (paddle.v2.config_base.Layer) – Input layer expand_as (paddle.v2.config_base.Layer) – Expand as this layer’s sequence info. name (basestring) – Layer name. bias_attr (paddle.v2.attr.ParameterAttribute|None|False) – Bias attribute. None means default bias. False means no bias. expand_level (ExpandLevel) – whether input layer is timestep(default) or sequence. layer_attr (paddle.v2.attr.ExtraAttribute) – extra layer attributes.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### repeat

class `paddle.v2.layer.``repeat`(*args, **kwargs)

  A layer for repeating the input for num_repeats times. This is equivalent to apply concat() with num_repeats same input.

  \[y = [x, x, \cdots, x]\]

  The example usage is:

      expand = repeat(input=layer, num_repeats=4)

  Parameters: | input (paddle.v2.config_base.Layer) – Input layer num_repeats (int) – Repeat the input so many times name (basestring) – Layer name. layer_attr (paddle.v2.attr.ExtraAttribute) – extra layer attributes.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### rotate

class `paddle.v2.layer.``rotate`(*args, **kwargs)

  A layer for rotating 90 degrees (clock-wise) for each feature channel, usually used when the input sample is some image or feature map.

  \[y(j,i,:) = x(M-i-1,j,:)\]

  where \(x\) is (M x N x C) input, and \(y\) is (N x M x C) output.

  The example usage is:

      rot = rotate(input=layer,
                         height=100,
                         width=100)

  Parameters: | input (paddle.v2.config_base.Layer) – Input layer. height (int) – The height of the sample matrix name (basestring) – Layer name. layer_attr (paddle.v2.attr.ExtraAttribute) – extra layer attributes.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### seq_reshape

class `paddle.v2.layer.``seq_reshape`(*args, **kwargs)

  A layer for reshaping the sequence. Assume the input sequence has T instances, the dimension of each instance is M, and the input reshape_size is N, then the output sequence has T*M/N instances, the dimension of each instance is N.

  Note that T*M/N must be an integer.

  The example usage is:

      reshape = seq_reshape(input=layer, reshape_size=4)

  Parameters: | input (paddle.v2.config_base.Layer) – Input layer. reshape_size (int) – the size of reshaped sequence. name (basestring) – Layer name. act (paddle.v2.Activation.Base) – Activation type. layer_attr (paddle.v2.attr.ExtraAttribute) – extra layer attributes. bias_attr (paddle.v2.attr.ParameterAttribute or None or bool) – The Bias Attribute. If no bias, then pass False or something not type of paddle.v2.attr.ParameterAttribute. None will get a default Bias.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

## Math Layers

### addto

class `paddle.v2.layer.``addto`(*args, **kwargs)

  AddtoLayer.

  \[y = f(\sum_{i} x_i + b)\]

  where \(y\) is output, \(x\) is input, \(b\) is bias, and \(f\) is activation function.

  The example usage is:

      addto = addto(input=[layer1, layer2],
                          act=paddle.v2.Activation.Relu(),
                          bias_attr=False)

  This layer just simply add all input layers together, then activate the sum inputs. Each input of this layer should be the same size, which is also the output size of this layer.

  There is no weight matrix for each input, because it just a simple add operation. If you want a complicated operation before add, please use mixed.

  It is a very good way to set dropout outside the layers. Since not all PaddlePaddle layer support dropout, you can add an add_to layer, set dropout here. Please refer to dropout for details.

  Parameters: | name (basestring) – Layer name. input (paddle.v2.config_base.Layer|list|tuple) – Input layers. It could be a paddle.v2.config_base.Layer or list/tuple of paddle.v2.config_base.Layer. act (paddle.v2.Activation.Base) – Activation Type, default is tanh. bias_attr (paddle.v2.attr.ParameterAttribute|bool) – Bias attribute. If False, means no bias. None is default bias. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### linear_comb

class `paddle.v2.layer.``linear_comb`(*args, **kwargs)
  A layer for weighted sum of vectors takes two inputs.
    - Input: size of weights is M
        size of vectors is M*N
    - Output: a vector of size=N
  \[z(i) = \sum_{j=0}^{M-1} x(j) y(i+Nj)\]

  where \(0 \le i \le N-1\)

  Or in the matrix notation:

  \[z = x^\mathrm{T} Y\]
  In this formular:
    - \(x\): weights
    - \(y\): vectors.
    - \(z\): the output.

  Note that the above computation is for one sample. Multiple samples are processed in one batch.

  The simple usage is:

      linear_comb = linear_comb(weights=weight, vectors=vectors,
                                      size=elem_dim)

  Parameters: | weights (paddle.v2.config_base.Layer) – The weight layer. vectors (paddle.v2.config_base.Layer) – The vector layer. size (int) – the dimension of this layer. name (basestring) – The Layer Name. layer_attr (paddle.v2.attr.ExtraAttributeNone) – Extra Layer config.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### interpolation

class `paddle.v2.layer.``interpolation`(*args, **kwargs)

  This layer is for linear interpolation with two inputs, which is used in NEURAL TURING MACHINE.

  \[y.row[i] = w[i] * x_1.row[i] + (1 - w[i]) * x_2.row[i]\]

  where \(x_1\) and \(x_2\) are two (batchSize x dataDim) inputs, \(w\) is (batchSize x 1) weight vector, and \(y\) is (batchSize x dataDim) output.

  The example usage is:

      interpolation = interpolation(input=[layer1, layer2], weight=layer3)

  Parameters: | input (list|tuple) – Input layer. weight (paddle.v2.config_base.Layer) – Weight layer. name (basestring) – Layer name. layer_attr (paddle.v2.attr.ExtraAttribute) – extra layer attributes.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### bilinear_interp

class `paddle.v2.layer.``bilinear_interp`(*args, **kwargs)

  This layer is to implement bilinear interpolation on conv layer output.

  Please refer to Wikipedia: https://en.wikipedia.org/wiki/Bilinear_interpolation

  The simple usage is:

      bilinear = bilinear_interp(input=layer1, out_size_x=64, out_size_y=64)

  Parameters: | input (paddle.v2.config_base.Layer.) – A input layer. out_size_x (int|None) – bilinear interpolation output width. out_size_y (int|None) – bilinear interpolation output height. name (None|basestring) – The layer’s name, which cna not be specified. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### power

class `paddle.v2.layer.``power`(*args, **kwargs)

  This layer applies a power function to a vector element-wise, which is used in NEURAL TURING MACHINE.

  \[y = x^w\]

  where \(x\) is a input vector, \(w\) is scalar weight, and \(y\) is a output vector.

  The example usage is:

      power = power(input=layer1, weight=layer2)

  Parameters: | input (paddle.v2.config_base.Layer) – Input layer. weight (paddle.v2.config_base.Layer) – Weight layer. name (basestring) – Layer name. layer_attr (paddle.v2.attr.ExtraAttribute) – extra layer attributes.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### scaling

class `paddle.v2.layer.``scaling`(*args, **kwargs)

  A layer for multiplying input vector by weight scalar.

  \[y = w x\]

  where \(x\) is size=dataDim input, \(w\) is size=1 weight, and \(y\) is size=dataDim output.

  Note that the above computation is for one sample. Multiple samples are processed in one batch.

  The example usage is:

      scale = scaling(input=layer1, weight=layer2)

  Parameters: | input (paddle.v2.config_base.Layer) – Input layer. weight (paddle.v2.config_base.Layer) – Weight layer. name (basestring) – Layer name. layer_attr (paddle.v2.attr.ExtraAttribute) – extra layer attributes.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### slope_intercept

class `paddle.v2.layer.``slope_intercept`(*args, **kwargs)

  This layer for applying a slope and an intercept to the input element-wise. There is no activation and weight.

  \[y = slope * x + intercept\]

  The simple usage is:

      scale = slope_intercept(input=input, slope=-1.0, intercept=1.0)

  Parameters: | input (paddle.v2.config_base.Layer) – The input layer. name (basestring) – The Layer Name. slope (float.) – the scale factor. intercept (float.) – the offset. layer_attr (paddle.v2.attr.ExtraAttributeNone) – Extra Layer config.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### tensor

class `paddle.v2.layer.``tensor`(*args, **kwargs)

  This layer performs tensor operation for two input. For example, each sample:

  \[y_{i} = a * W_{i} * {b^\mathrm{T}}, i=0,1,...,K-1\]
  In this formular:
    - \(a\): the first input contains M elements.
    - \(b\): the second input contains N elements.
    - \(y_{i}\): the i-th element of y.
    - \(W_{i}\): the i-th learned weight, shape if [M, N]
    - \(b^\mathrm{T}\): the transpose of \(b_{2}\).

  The simple usage is:

      tensor = tensor(a=layer1, b=layer2, size=1000)

  Parameters: | name (basestring) – layer name a (paddle.v2.config_base.Layer) – Input layer a. b (paddle.v2.config_base.Layer) – input layer b. size (int.) – the layer dimension. act (paddle.v2.Activation.Base) – Activation Type. Default is tanh. param_attr (paddle.v2.attr.ParameterAttribute) – The Parameter Attribute. bias_attr (paddle.v2.attr.ParameterAttribute|None|Any) – The Bias Attribute. If no bias, then pass False or something not type of paddle.v2.attr.ParameterAttribute. None will get a default Bias. layer_attr (paddle.v2.attr.ExtraAttributeNone) – Extra Layer config.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### cos_sim

class `paddle.v2.layer.``cos_sim`(*args, **kwargs)

  Cosine Similarity Layer. The cosine similarity equation is here.

  \[similarity = cos(\theta) = {\mathbf{a} \cdot \mathbf{b} \over \|\mathbf{a}\| \|\mathbf{b}\|}\]

  The size of a is M, size of b is M*N, Similarity will be calculated N times by step M. The output size is N. The scale will be multiplied to similarity.

  Note that the above computation is for one sample. Multiple samples are processed in one batch.

  The example usage is:

      cos = cos_sim(a=layer1, b=layer2, size=3)

  Parameters: | name (basestring) – layer name a (paddle.v2.config_base.Layer) – input layer a b (paddle.v2.config_base.Layer) – input layer b scale (float) – scale for cosine value. default is 5. size (int) – layer size. NOTE size_a * size should equal size_b. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### trans

class `paddle.v2.layer.``trans`(*args, **kwargs)

  A layer for transposing a minibatch matrix.

  \[y = x^\mathrm{T}\]

  where \(x\) is (M x N) input, and \(y\) is (N x M) output.

  The example usage is:

      trans = trans(input=layer)

  Parameters: | input (paddle.v2.config_base.Layer) – Input layer. name (basestring) – Layer name. layer_attr (paddle.v2.attr.ExtraAttribute) – extra layer attributes.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

## Sampling Layers

### maxid

class `paddle.v2.layer.``max_id`(*args, **kwargs)

  A layer for finding the id which has the maximal value for each sample. The result is stored in output.ids.

  The example usage is:

      maxid = maxid(input=layer)

  Parameters: | input (paddle.v2.config_base.Layer) – Input layer name. name (basestring) – Layer name. layer_attr (paddle.v2.attr.ExtraAttribute) – extra layer attributes.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### sampling_id

class `paddle.v2.layer.``sampling_id`(*args, **kwargs)

  A layer for sampling id from multinomial distribution from the input layer. Sampling one id for one sample.

  The simple usage is:

      samping_id = sampling_id(input=input)

  Parameters: | input (paddle.v2.config_base.Layer) – The input layer. name (basestring) – The Layer Name. layer_attr (paddle.v2.attr.ExtraAttributeNone) – Extra Layer config.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

## Slicing and Joining Layers

### pad

class `paddle.v2.layer.``pad`(*args, **kwargs)

  This operation pads zeros to the input data according to pad_c,pad_h and pad_w. pad_c, pad_h, pad_w specifies the which dimension and size of padding. And the input data shape is NCHW.

  For example, pad_c=[2,3] means padding 2 zeros before the input data and 3 zeros after the input data in channel dimension. pad_h means padding zeros in height dimension. pad_w means padding zeros in width dimension.

  For example,

      input(2,2,2,3)  = [
                          [ [[1,2,3], [3,4,5]],
                            [[2,3,5], [1,6,7]] ],
                          [ [[4,3,1], [1,8,7]],
                            [[3,8,9], [2,3,5]] ]
                        ]

      pad_c=[1,1], pad_h=[0,0], pad_w=[0,0]

      output(2,4,2,3) = [
                          [ [[0,0,0], [0,0,0]],
                            [[1,2,3], [3,4,5]],
                            [[2,3,5], [1,6,7]],
                            [[0,0,0], [0,0,0]] ],
                          [ [[0,0,0], [0,0,0]],
                            [[4,3,1], [1,8,7]],
                            [[3,8,9], [2,3,5]],
                            [[0,0,0], [0,0,0]] ]
                        ]

  The simply usage is:

      pad = pad(input=ipt,
                      pad_c=[4,4],
                      pad_h=[0,0],
                      pad_w=[2,2])

  Parameters: | input (paddle.v2.config_base.Layer) – layer’s input. pad_c (list|None) – padding size in channel dimension. pad_h (list|None) – padding size in height dimension. pad_w (list|None) – padding size in width dimension. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute. name (basestring) – layer name.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

## Cost Layers

### cross_entropy_cost

class `paddle.v2.layer.``cross_entropy_cost`(*args, **kwargs)

  A loss layer for multi class entropy.

      cost = cross_entropy(input=input,
                           label=label)

  Parameters: | input (paddle.v2.config_base.Layer.) – The first input layer. label – The input label. name (None|basestring.) – The name of this layers. It is not necessary. coeff (float.) – The cost is multiplied with coeff. The coefficient affects the gradient in the backward. weight (LayerOutout) – The cost of each sample is multiplied with each weight. The weight should be a layer with size=1. Note that gradient will not be calculated for weight. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer.

### cross_entropy_with_selfnorm_cost

class `paddle.v2.layer.``cross_entropy_with_selfnorm_cost`(*args, **kwargs)

  A loss layer for multi class entropy with selfnorm. Input should be a vector of positive numbers, without normalization.

      cost = cross_entropy_with_selfnorm(input=input,
                                         label=label)

  Parameters: | input (paddle.v2.config_base.Layer.) – The first input layer. label – The input label. name (None|basestring.) – The name of this layers. It is not necessary. coeff (float.) – The coefficient affects the gradient in the backward. softmax_selfnorm_alpha (float.) – The scale factor affects the cost. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer.

### multi_binary_label_cross_entropy_cost

class `paddle.v2.layer.``multi_binary_label_cross_entropy_cost`(*args, **kwargs)

  A loss layer for multi binary label cross entropy.

      cost = multi_binary_label_cross_entropy(input=input,
                                              label=label)

  Parameters: | input (paddle.v2.config_base.Layer) – The first input layer. label – The input label. name (None|basestring) – The name of this layers. It is not necessary. coeff (float) – The coefficient affects the gradient in the backward. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### huber_cost

class `paddle.v2.layer.``huber_cost`(*args, **kwargs)

  A loss layer for huber loss.

      cost = huber_cost(input=input,
                        label=label)

  Parameters: | input (paddle.v2.config_base.Layer.) – The first input layer. label – The input label. name (None|basestring.) – The name of this layers. It is not necessary. coeff (float.) – The coefficient affects the gradient in the backward. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer.

### lambda_cost

class `paddle.v2.layer.``lambda_cost`(*args, **kwargs)

  lambdaCost for lambdaRank LTR approach.

  The simple usage:

      cost = lambda_cost(input=input,
                         score=score,
                         NDCG_num=8,
                         max_sort_size=-1)

  Parameters: | input (paddle.v2.config_base.Layer) – Samples of the same query should be loaded as sequence. score – The 2nd input. Score of each sample. NDCG_num (int) – The size of NDCG (Normalized Discounted Cumulative Gain), e.g., 5 for NDCG@5. It must be less than for equal to the minimum size of lists. max_sort_size (int) – The size of partial sorting in calculating gradient. If max_sort_size = -1, then for each list, the algorithm will sort the entire list to get gradient. In other cases, max_sort_size must be greater than or equal to NDCG_num. And if max_sort_size is greater than the size of a list, the algorithm will sort the entire list of get gradient. name (None|basestring) – The name of this layers. It is not necessary. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### mse_cost

class `paddle.v2.layer.``mse_cost`(*args, **kwargs)

  > mean squared error cost:

  > \[\]

  rac{1}{N}sum_{i=1}^N(t_i-y_i)^2

  > param name: | layer name.
  > type name: | basestring
  > param input: | Network prediction.
  > type input: | paddle.v2.config_base.Layer
  > param label: | Data label.
  > type label: | paddle.v2.config_base.Layer
  > param weight: | The weight affects the cost, namely the scale of cost. It is an optional argument.
  > type weight: | paddle.v2.config_base.Layer
  > param layer_attr:
  > | layer’s extra attribute.
  > type layer_attr:
  > | paddle.v2.attr.ExtraAttribute
  > return: | paddle.v2.config_base.Layer object.
  > rtype: | paddle.v2.config_base.Layer

### rank_cost

class `paddle.v2.layer.``rank_cost`(*args, **kwargs)

  A cost Layer for learning to rank using gradient descent. Details can refer to papers. This layer contains at least three inputs. The weight is an optional argument, which affects the cost.

  \[ \begin{align}\begin{aligned}C_{i,j} & = -\tilde{P_{ij}} * o_{i,j} + log(1 + e^{o_{i,j}})\\o_{i,j} & = o_i - o_j\\\tilde{P_{i,j}} & = \{0, 0.5, 1\} \ or \ \{0, 1\}\end{aligned}\end{align} \]
  In this formula:
    - \(C_{i,j}\) is the cross entropy cost.
    - \(\tilde{P_{i,j}}\) is the label. 1 means positive order and 0 means reverse order.
    - \(o_i\) and \(o_j\): the left output and right output. Their dimension is one.

  The simple usage:

      cost = rank_cost(left=out_left,
                       right=out_right,
                       label=label)

  Parameters: | left (paddle.v2.config_base.Layer) – The first input, the size of this layer is 1. right (paddle.v2.config_base.Layer) – The right input, the size of this layer is 1. label (paddle.v2.config_base.Layer) – Label is 1 or 0, means positive order and reverse order. weight (paddle.v2.config_base.Layer) – The weight affects the cost, namely the scale of cost. It is an optional argument. name (None|basestring) – The name of this layers. It is not necessary. coeff (float) – The coefficient affects the gradient in the backward. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### sum_cost

class `paddle.v2.layer.``sum_cost`(*args, **kwargs)

  A loss layer which calculate the sum of the input as loss

      cost = sum_cost(input=input)

  Parameters: | input (paddle.v2.config_base.Layer.) – The first input layer. name (None|basestring.) – The name of this layers. It is not necessary. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer.

### crf

class `paddle.v2.layer.``crf`(*args, **kwargs)

  A layer for calculating the cost of sequential conditional random field model.

  The simple usage:

      crf = crf(input=input,
                      label=label,
                      size=label_dim)

  Parameters: | input (paddle.v2.config_base.Layer) – The first input layer is the feature. label (paddle.v2.config_base.Layer) – The second input layer is label. size (int) – The category number. weight (paddle.v2.config_base.Layer) – The third layer is “weight” of each sample, which is an optional argument. param_attr (paddle.v2.attr.ParameterAttribute) – Parameter attribute. None means default attribute name (None|basestring) – The name of this layers. It is not necessary. layer_attr (paddle.v2.attr.ExtraAttributeNone) – Extra Layer config.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### crf_decoding

class `paddle.v2.layer.``crf_decoding`(*args, **kwargs)

  A layer for calculating the decoding sequence of sequential conditional random field model. The decoding sequence is stored in output.ids. If a second input is provided, it is treated as the ground-truth label, and this layer will also calculate error. output.value[i] is 1 for incorrect decoding or 0 for correct decoding.

  The simple usage:

      crf_decoding = crf_decoding(input=input,
                                        size=label_dim)

  Parameters: | input (paddle.v2.config_base.Layer) – The first input layer. size (int) – size of this layer. label (paddle.v2.config_base.Layer or None) – None or ground-truth label. param_attr (paddle.v2.attr.ParameterAttribute) – Parameter attribute. None means default attribute name (None|basestring) – The name of this layers. It is not necessary. layer_attr (paddle.v2.attr.ExtraAttributeNone) – Extra Layer config.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### ctc

class `paddle.v2.layer.``ctc`(*args, **kwargs)

  Connectionist Temporal Classification (CTC) is designed for temporal classication task. That is, for sequence labeling problems where the alignment between the inputs and the target labels is unknown.

  More details can be found by referring to Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks

  Note

  Considering the ‘blank’ label needed by CTC, you need to use (num_classes + 1) as the input size. num_classes is the category number. And the ‘blank’ is the last category index. So the size of ‘input’ layer, such as fc with softmax activation, should be num_classes + 1. The size of ctc should also be num_classes + 1.

  The simple usage:

      ctc = ctc(input=input,
                      label=label,
                      size=9055,
                      norm_by_times=True)

  Parameters: | input (paddle.v2.config_base.Layer) – The input layer. label (paddle.v2.config_base.Layer) – The data layer of label with variable length. size (int) – category numbers + 1. name (basestring|None) – The name of this layer norm_by_times (bool) – Whether to normalization by times. False by default. layer_attr (paddle.v2.attr.ExtraAttributeNone) – Extra Layer config.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### warp_ctc

class `paddle.v2.layer.``warp_ctc`(*args, **kwargs)

  A layer intergrating the open-source warp-ctc <https://github.com/baidu-research/warp-ctc> library, which is used in Deep Speech 2: End-toEnd Speech Recognition in English and Mandarin <https://arxiv.org/pdf/1512.02595v1.pdf>, to compute Connectionist Temporal Classification (CTC) loss.

  More details of CTC can be found by referring to Connectionist Temporal Classification: Labelling Unsegmented Sequence Data with Recurrent Neural Networks

  Note

  - Let num_classes represent the category number. Considering the ‘blank’ label needed by CTC, you need to use (num_classes + 1) as the input size. Thus, the size of both warp_ctc and ‘input’ layer should be set to num_classes + 1.
  - You can set ‘blank’ to any value ranged in [0, num_classes], which should be consistent as that used in your labels.
  - As a native ‘softmax’ activation is interated to the warp-ctc library, ‘linear’ activation is expected instead in the ‘input’ layer.

  The simple usage:

      ctc = warp_ctc(input=input,
                           label=label,
                           size=1001,
                           blank=1000,
                           norm_by_times=False)

  Parameters: | input (paddle.v2.config_base.Layer) – The input layer. label (paddle.v2.config_base.Layer) – The data layer of label with variable length. size (int) – category numbers + 1. name (basestring|None) – The name of this layer, which can not specify. blank (int) – the ‘blank’ label used in ctc norm_by_times (bool) – Whether to normalization by times. False by default. layer_attr (paddle.v2.attr.ExtraAttributeNone) – Extra Layer config.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### nce

class `paddle.v2.layer.``nce`(*args, **kwargs)

  Noise-contrastive estimation. Implements the method in the following paper: A fast and simple algorithm for training neural probabilistic language models.

  The example usage is:

      cost = nce(input=layer1, label=layer2, weight=layer3,
                       num_classes=3, neg_distribution=[0.1,0.3,0.6])

  Parameters: | name (basestring) – layer name input (paddle.v2.config_base.Layer|list|tuple|collections.Sequence) – input layers. It could be a paddle.v2.config_base.Layer of list/tuple of paddle.v2.config_base.Layer. label (paddle.v2.config_base.Layer) – label layer weight (paddle.v2.config_base.Layer) – weight layer, can be None(default) num_classes (int) – number of classes. act (paddle.v2.Activation.Base) – Activation, default is Sigmoid. num_neg_samples (int) – number of negative samples. Default is 10. neg_distribution (list|tuple|collections.Sequence|None) – The distribution for generating the random negative labels. A uniform distribution will be used if not provided. If not None, its length must be equal to num_classes. bias_attr (paddle.v2.attr.ParameterAttribute|None|False) – Bias parameter attribute. True if no bias. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute.
  Returns: | layer name.
  Return type: | paddle.v2.config_base.Layer

### hsigmoid

class `paddle.v2.layer.``hsigmoid`(*args, **kwargs)

  Organize the classes into a binary tree. At each node, a sigmoid function is used to calculate the probability of belonging to the right branch. This idea is from “F. Morin, Y. Bengio (AISTATS 05): Hierarchical Probabilistic Neural Network Language Model.”

  The example usage is:

      cost = hsigmoid(input=[layer1, layer2],
                      label=data)

  Parameters: | input (paddle.v2.config_base.Layer|list|tuple) – Input layers. It could be a paddle.v2.config_base.Layer or list/tuple of paddle.v2.config_base.Layer. label (paddle.v2.config_base.Layer) – Label layer. num_classes (int|None) – number of classes. name (basestring) – layer name bias_attr (paddle.v2.attr.ParameterAttribute|False) – Bias attribute. None means default bias. False means no bias. param_attr (paddle.v2.attr.ParameterAttribute|None) – Parameter Attribute. None means default parameter. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

### smooth_l1_cost

class `paddle.v2.layer.``smooth_l1_cost`(*args, **kwargs)

  This is a L1 loss but more smooth. It requires that the size of input and label are equal. The formula is as follows,

  \[L = \sum_{i} smooth_{L1}(input_i - label_i)\]

  in which

  \[\begin{split}smooth_{L1}(x) = \begin{cases} 0.5x^2& \text{if} \ |x| < 1 \\ |x|-0.5& \text{otherwise} \end{cases}\end{split}\]

  More details can be found by referring to Fast R-CNN

      cost = smooth_l1_cost(input=input,
                            label=label)

  Parameters: | input (paddle.v2.config_base.Layer) – The input layer. label – The input label. name (None|basestring) – The name of this layers. It is not necessary. layer_attr (paddle.v2.attr.ExtraAttribute) – Extra Layer Attribute.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer

## Check Layer

### eos

class `paddle.v2.layer.``eos`(*args, **kwargs)

  A layer for checking EOS for each sample: - output_id = (input_id == conf.eos_id)

  The result is stored in output_.ids. It is used by recurrent layer group.

  The example usage is:

      eos = eos(input=layer, eos_id=id)

  Parameters: | name (basestring) – Layer name. input (paddle.v2.config_base.Layer) – Input layer name. eos_id (int) – end id of sequence layer_attr (paddle.v2.attr.ExtraAttribute) – extra layer attributes.
  Returns: | paddle.v2.config_base.Layer object.
  Return type: | paddle.v2.config_base.Layer