mx.symbol.RNN

Description

Applies recurrent layers to input data. Currently, vanilla RNN, LSTM and GRU are implemented, with both multi-layer and bidirectional support.

When the input data is of type float32 and the environment variables MXNET_CUDA_ALLOW_TENSOR_CORE and MXNET_CUDA_TENSOR_OP_MATH_ALLOW_CONVERSION are set to 1, this operator will try to use pseudo-float16 precision (float32 math with float16 I/O) precision in order to use Tensor Cores on suitable NVIDIA GPUs. This can sometimes give significant speedups.

Vanilla RNN

Applies a single-gate recurrent layer to input X. Two kinds of activation function are supported: ReLU and Tanh.

With ReLU activation function:

\[h_t = relu(W_{ih} * x_t + b_{ih} + W_{hh} * h_{(t-1)} + b_{hh})\]

With Tanh activtion function:

\[h_t = \tanh(W_{ih} * x_t + b_{ih} + W_{hh} * h_{(t-1)} + b_{hh})\]

Reference paper: Finding structure in time - Elman, 1988. https://crl.ucsd.edu/~elman/Papers/fsit.pdf

LSTM

Long Short-Term Memory - Hochreiter, 1997. http://www.bioinf.jku.at/publications/older/2604.pdf

\[\begin{split}\begin{array}{ll} i_t = \mathrm{sigmoid}(W_{ii} x_t + b_{ii} + W_{hi} h_{(t-1)} + b_{hi}) \\ f_t = \mathrm{sigmoid}(W_{if} x_t + b_{if} + W_{hf} h_{(t-1)} + b_{hf}) \\ g_t = \tanh(W_{ig} x_t + b_{ig} + W_{hc} h_{(t-1)} + b_{hg}) \\ o_t = \mathrm{sigmoid}(W_{io} x_t + b_{io} + W_{ho} h_{(t-1)} + b_{ho}) \\ c_t = f_t * c_{(t-1)} + i_t * g_t \\ h_t = o_t * \tanh(c_t) \end{array}\end{split}\]

With the projection size being set, LSTM could use the projection feature to reduce the parameters size and give some speedups without significant damage to the accuracy.

Long Short-Term Memory Based Recurrent Neural Network Architectures for Large Vocabulary Speech Recognition - Sak et al. 2014. https://arxiv.org/abs/1402.1128

\[\begin{split}\begin{array}{ll} i_t = \mathrm{sigmoid}(W_{ii} x_t + b_{ii} + W_{ri} r_{(t-1)} + b_{ri}) \\ f_t = \mathrm{sigmoid}(W_{if} x_t + b_{if} + W_{rf} r_{(t-1)} + b_{rf}) \\ g_t = \tanh(W_{ig} x_t + b_{ig} + W_{rc} r_{(t-1)} + b_{rg}) \\ o_t = \mathrm{sigmoid}(W_{io} x_t + b_{o} + W_{ro} r_{(t-1)} + b_{ro}) \\ c_t = f_t * c_{(t-1)} + i_t * g_t \\ h_t = o_t * \tanh(c_t) r_t = W_{hr} h_t \end{array}\end{split}\]

GRU

Gated Recurrent Unit - Cho et al. 2014. http://arxiv.org/abs/1406.1078

The definition of GRU here is slightly different from paper but compatible with CUDNN.

\[\begin{split}\begin{array}{ll} r_t = \mathrm{sigmoid}(W_{ir} x_t + b_{ir} + W_{hr} h_{(t-1)} + b_{hr}) \\ z_t = \mathrm{sigmoid}(W_{iz} x_t + b_{iz} + W_{hz} h_{(t-1)} + b_{hz}) \\ n_t = \tanh(W_{in} x_t + b_{in} + r_t * (W_{hn} h_{(t-1)}+ b_{hn})) \\ h_t = (1 - z_t) * n_t + z_t * h_{(t-1)} \\ \end{array}\end{split}\]

Usage

mx.symbol.RNN(...)

Arguments

Argument	Description
data	NDArray-or-Symbol. Input data to RNN
parameters	NDArray-or-Symbol. Vector of all RNN trainable parameters concatenated
state	NDArray-or-Symbol initial hidden state of the RNN
state.cell	NDArray-or-Symbol initial cell state for LSTM networks (only for LSTM)
sequence.length	NDArray-or-Symbol. Vector of valid sequence lengths for each element in batch. (Only used if use_sequence_length kwarg is True)
state.size	int (non-negative), required. size of the state for each layer
num.layers	int (non-negative), required. number of stacked layers
bidirectional	boolean, optional, default=0. whether to use bidirectional recurrent layers
mode	{‘gru’, ‘lstm’, ‘rnn_relu’, ‘rnn_tanh’}, required. the type of RNN to compute
p	float, optional, default=0. drop rate of the dropout on the outputs of each RNN layer, except the last layer.
state.outputs	boolean, optional, default=0. Whether to have the states as symbol outputs.
projection.size	int or None, optional, default=’None’ size of project size
lstm.state.clip.min	double or None, optional, default=None. Minimum clip value of LSTM states. This option must be used together with lstm_state_clip_max.
lstm.state.clip.max	double or None, optional, default=None. Maximum clip value of LSTM states. This option must be used together with lstm_state_clip_min.
lstm.state.clip.nan	boolean, optional, default=0. Whether to stop NaN from propagating in state by clipping it to min/max. If clipping range is not specified, this option is ignored.
use.sequence.length	boolean, optional, default=0. If set to true, this layer takes in an extra input parameter sequence_length to specify variable length sequence
name	string, optional. Name of the resulting symbol.

Value

out The result mx.symbol

Link to Source Code: http://github.com/apache/incubator-mxnet/blob/1.6.0/src/operator/rnn.cc#L377