RNN¶
General¶
The RNN primitive computes a stack of unrolled recurrent cells, as depicted in Figure 1. \(\bias\), \(\srciter\) and \(\dstiter\) are optional parameters (the variable names follow the standard Naming Conventions). If not provided, \(\bias\) and \(\srciter\) will default to 0.
The RNN primitive supports four modes for evaluation direction:
left2right
will process the input data timestamps by increasing orderright2left
will process the input data timestamps by decreasing orderbidirectional_concat
will process all the stacked layers fromleft2right
and fromright2left
independently, and will concatenate the output in \(\dstlayer\) over the channel dimension.bidirectional_sum
will process all the stacked layers fromleft2right
and fromright2left
independently, and will sum the two outputs to \(\dstlayer\).
Even though the RNN primitive supports passing a different number of channels for \(\srclayer\), \(\srciter\), \(\dstlayer\), and \(\dstiter\), we always require the following conditions in order for the dimension to be consistent:
\(channels(\dstlayer) = channels(\dstiter)\),
when \(T > 1\), \(channels(\srciter) = channels(\dstiter)\),
when \(L > 1\), \(channels(\srclayer) = channels(\dstlayer)\),
when using the
bidirectional_concat
direction, \(channels(\dstlayer) = 2 * channels(\dstiter)\).
The general formula for the execution of a stack of unrolled recurrent cells depends on the current iteration of the previous layer (\(h_{t,l1}\) and \(c_{t,l1}\)) and the previous iteration of the current layer (\(h_{t1, l}\)). Here is the exact equation for nonLSTM cells:
where \(t,l\) are the indices of the timestamp and the layer of the cell being executed.
And here is the equation for LSTM cells:
where \(t,l\) are the indices of the timestamp and the layer of the cell being executed.
Cell Functions¶
The RNN API provides four cell functions:
Vanilla RNN, a singlegate recurrent cell,
LSTM, a fourgate long shortterm memory cell,
GRU, a threegate gated recurrent unit cell,
Linearbeforereset GRU, a threegate recurrent unit cell with the linear layer before the reset gate.
Vanilla RNN¶
A singlegate recurrent cell initialized with dnnl::vanilla_rnn_forward::desc::desc() or dnnl::vanilla_rnn_forward::desc::desc() as in the following example.
auto vanilla_rnn_desc = dnnl::vanilla_rnn_forward::desc( aprop, activation, direction, src_layer_desc, src_iter_desc, weights_layer_desc, weights_iter_desc, bias_desc, dst_layer_desc, dst_iter_desc);
The Vanilla RNN cell supports the ReLU, Tanh and Sigmoid activation functions. The following equations defines the mathematical operation performed by the Vanilla RNN cell for the forward pass:
LSTM¶
LSTM (or Vanilla LSTM)¶
A fourgate long shortterm memory recurrent cell initialized with dnnl::lstm_forward::desc::desc() or dnnl::lstm_backward::desc::desc() as in the following example.
auto lstm_desc = lstm_forward::desc( aprop, direction, src_layer_desc, src_iter_h_desc, src_iter_c_desc, weights_layer_desc, weights_iter_desc, bias_desc, dst_layer_desc, dst_iter_h_desc, dst_iter_c_desc);
Note that for all tensors with a dimension depending on the gates number, we implicitly require the order of these gates to be i
, f
, \(\tilde c\), and o
. The following equation gives the mathematical description of these gates and output for the forward pass:
where \(W_*\) are stored in \(\weightslayer\), \(U_*\) are stored in \(\weightsiter\) and \(B_*\) are stored in \(\bias\).
Note
In order for the dimensions to be consistent, we require \(channels(\srciterc) = channels(\dstiterc) = channels(\dstiter)\).
LSTM with Peephole¶
A fourgate long shortterm memory recurrent cell with peephole initialized with dnnl::lstm_forward::desc::desc() or dnnl::lstm_backward::desc::desc() as in the following example.
auto lstm_desc = dnnl::lstm_forward::desc( aprop, direction, src_layer_desc, src_iter_h_desc, src_iter_c_desc, weights_layer_desc, weights_iter_desc, weights_peephole_desc, bias_desc, dst_layer_desc, dst_iter_h_desc, dst_iter_c_desc);
Similarly to vanilla LSTM, we implicitly require the order of the gates to be i
, f
, \(\tilde c\), and o
for all tensors with a dimension depending on the gates. For peephole weights, the gates order is i
, f
, o
. The following equation gives the mathematical description of these gates and output for the forward pass:
where \(P_*\) are stored in weights_peephole
, and the other parameters are the same as in vanilla LSTM.
Note
If the weights_peephole_desc
passed to the operation descriptor constructor is a zero memory desciptor, the primitive will behave the same as in LSTM primitive without peephole.
LSTM with Projection (or LSTMP)¶
A fourgate long shortterm memory recurrent cell with projection initialized with dnnl::lstm_forward::desc::desc() or dnnl::lstm_backward::desc::desc() as in the following example.
auto lstm_desc = dnnl::lstm_forward::desc( aprop, direction, src_layer_desc, src_iter_h_desc, src_iter_c_desc, weights_layer_desc, weights_iter_desc, weights_peephole_desc, weights_projection_desc, bias_desc, dst_layer_desc, dst_iter_h_desc, dst_iter_c_desc);
Similarly to vanilla LSTM, we implicitly require the order of the gates to be i
, f
, \(\tilde c\), and o
for all tensors with a dimension depending on the gates. The following equation gives the mathematical description of these gates and output for the forward pass (for simplicity, LSTM without peephole is shown):
where \(R\) is stored in weights_projection
, and the other parameters are the same as in vanilla LSTM.
Note
If the weights_projection_desc
passed to the operation descriptor constructor is a zero memory desciptor, the primitive will behave the same as in LSTM primitive without projection.
GRU¶
A threegate gated recurrent unit cell, initialized with dnnl::gru_forward::desc::desc() or dnnl::gru_backward::desc::desc() as in the following example.
auto gru_desc = dnnl::gru_forward::desc( aprop, direction, src_layer_desc, src_iter_desc, weights_layer_desc, weights_iter_desc, bias_desc, dst_layer_desc, dst_iter_desc);
Note that for all tensors with a dimension depending on the gates number, we implicitly require the order of these gates to be u
, r
, and o
. The following equation gives the mathematical definition of these gates.
where \(W_*\) are in \(\weightslayer\), \(U_*\) are in \(\weightsiter\), and \(B_*\) are stored in \(\bias\).
Note
If you need to replace u_t by (1u_t) when computing h_t, you can achieve this by multiplying \(W_u\), \(U_u\) and \(B_u\) by \(1\). This is possible as \(u_t = \sigma(W_u \cdot h_{t,l1} + U_u \cdot h_{t1, l} + B_u)\), and \(1 – \sigma(a) = \sigma(a)\).
LinearBeforeReset GRU¶
A threegate gated recurrent unit cell with linear layer applied before the reset gate, initialized with dnnl::lbr_gru_forward::desc::desc() or dnnl::lbr_gru_backward::desc::desc() as in the following example.
auto lbr_gru_desc = dnnl::lbr_gru_forward::desc( aprop, direction, src_layer_desc, src_iter_desc, weights_layer_desc, weights_iter_desc, bias_desc, dst_layer_desc, dst_iter_desc);
The following equation describes the mathematical behavior of the LinearBeforeReset GRU cell.
Note that for all tensors with a dimension depending on the gates number, except the bias, we implicitly require the order of these gates to be u
, r
, and o
. For the \(\bias\) tensor, we implicitly require the order of the gates to be u
, r
, o
, and u'
.
Note
If you need to replace u_t by (1u_t) when computing h_t, you can achieve this by multiplying \(W_u\), \(U_u\) and \(B_u\) by \(1\). This is possible as \(u_t = \sigma(W_u \cdot h_{t,l1} + U_u \cdot h_{t1, l} + B_u)\), and \(1 – \sigma(a) = \sigma(a)\).
Considerations for Training¶
When using the RNN API for training, the forward pass should use the forward_training
propagation kind, and a workspace should be passed to both the forward pass and the backward pass. Note that after executing the backward pass, the workspace is no more valid and should be populated once again by another forward pass.
The RNN primitive backward pass accumulates gradients to its weight outputs (namely \(\diffweightslayer\), \(\diffweightsiter\), \(\diffweightspeephole\), \(\diffweightsprojection\), \(\diffbias\)). Hence, these tensors should be properly initialized to zero before their first use, and can be reused across calls to accumulate gradients if need be.
Execution Arguments¶
When executed, the inputs and outputs should be mapped to an execution argument index as specified by the following table.
Primitive input/output 
Execution argument index 

\(\srclayer\) 
DNNL_ARG_SRC_LAYER 
\(\srciter\) 
DNNL_ARG_SRC_ITER 
\(\srciterc\) 
DNNL_ARG_SRC_ITER_C 
\(\weightslayer\) 
DNNL_ARG_WEIGHTS_LAYER 
\(\weightsiter\) 
DNNL_ARG_WEIGHTS_ITER 
\(\weightspeephole\) 
DNNL_ARG_WEIGHTS_PEEPHOLE 
\(\weightsprojection\) 
DNNL_ARG_WEIGHTS_PROJECTION 
\(\bias\) 
DNNL_ARG_BIAS 
\(\dstlayer\) 
DNNL_ARG_DST_LAYER 
\(\dstiter\) 
DNNL_ARG_DST_ITER 
\(\dstiterc\) 
DNNL_ARG_DST_ITER_C 
\(\workspace\) 
DNNL_WORKSPACE 
\(\diffsrclayer\) 
DNNL_ARG_DIFF_SRC_LAYER 
\(\diffsrciter\) 
DNNL_ARG_DIFF_SRC_ITER 
\(\diffsrciterc\) 
DNNL_ARG_DIFF_SRC_ITER_C 
\(\diffweightslayer\) 
DNNL_ARG_DIFF_WEIGHTS_LAYER 
\(\diffweightsiter\) 
DNNL_ARG_DIFF_WEIGHTS_ITER 
\(\diffweightspeephole\) 
DNNL_ARG_DIFF_WEIGHTS_PEEPHOLE 
\(\diffweightsprojection\) 
DNNL_ARG_DIFF_WEIGHTS_PROJECTION 
\(\diffbias\) 
DNNL_ARG_DIFF_BIAS 
\(\diffdstlayer\) 
DNNL_ARG_DIFF_DST_LAYER 
\(\diffdstiter\) 
DNNL_ARG_DIFF_DST_ITER 
\(\diffdstiterc\) 
DNNL_ARG_DIFF_DST_ITER_C 
Implementation details¶
Data Type Support¶
The following table lists the combination of data types supported by the RNN primitive for each input and output memory object.
Propagation 
Cell Function 
Input data 
Recurrent data (1) 
Weights 
Bias 
Output Data 

Forward / Backward 
All 
f32 
f32 
f32 
f32 
f32 
Forward / Backward (2) 
All (3) 
bf16 
bf16 
bf16 
f32 
bf16 
Forward 
All (3) 
f16 
f16 
f16 
f16 
f16 
Forward inference 
Vanilla LSTM, LSTMP and GRU 
u8 
u8 
s8 
f32 
u8, f32 
Forward inference 
Vanilla LSTM, LSTMP 
s8 
s8 
s8 
f32 
s8, f32 
With LSTM and Peephole LSTM cells, the cell state datatype is f32, except for the f16 configuration.
In backward propagation, all
diff_*
tensors are in f32.Projection LSTM is not supported.
Warning
There might be hardware and/or implementation specific restrictions. Check Implementation Limitations section below.
Data Representation¶
In the oneDNN programming model, the RNN primitive is one of a few that support the placeholder memory format dnnl::memory::format_tag::any (shortened to any
from now on) and can define data and weight memory objects format based on the primitive parameters.
The following table summarizes the data layouts supported by the RNN primitive.
Propagation 
Input/Output Data 
Recurrent Data 
Layer and Iteration Weights 
Peephole Weights and Bias 
Projection LSTM Weights 

Forward / Backward 

Forward 

Backward 
While an RNN primitive can be created with memory formats specified explicitly, the performance is likely to be suboptimal. When using any
it is necessary to first create an RNN primitive descriptor and then query it for the actual data and weight memory objects formats.
Note
The RNN primitive supports padded tensors and views. So even if two memory descriptors share the same data layout, they might still be different.
Postops and Attributes¶
Currently postops and attributes are only used by the int8 variants of LSTM and GRU. See the markdown RNN int8 inference example for more details on how to use and set these quantization parameters.
Implementation Limitations¶
Refer to Data Types for limitations related to data types support.
CPU
Bias must always be present (that is, the corresponding memory descriptor argument cannot be zero memory descriptor when the RNN operation descriptor is initialized).
oneDNN supports s8 as input data only on systems with Advanced Matrix Extension(AMX) support.
GPU
No support for GRU
No support for Peephole LSTM and Projection LSTM
Bias must always be present (that is, the corresponding memory descriptor argument cannot be zero memory descriptor when the RNN operation descriptor is initialized).
Examples¶
Engine 
Name 
Comments 


CPU/GPU 
This C++ API example demonstrates how to create and execute an LSTM RNN primitive in forward training propagation mode. 
Key optimizations included in this example: 