# RNN¶

API Reference

## 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 order

• right2left will process the input data timestamps by decreasing order

• bidirectional_concat will process all the stacked layers from left2right and from right2left independently, and will concatenate the output in $$\dstlayer$$ over the channel dimension.

• bidirectional_sum will process all the stacked layers from left2right and from right2left 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 ($$h_{t,l-1}$$ and $$c_{t,l-1}$$) and the previous iteration of the current layer ($$h_{t-1, l}$$). Here is the exact equation for non-LSTM cells:

\begin{align} h_{t, l} = Cell(h_{t, l-1}, h_{t-1, l}) \end{align}

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:

$\begin{equation*} (h_{t, l},c_{t,l}) = Cell(h_{t, l-1}, h_{t-1, l}, c_{t-1,l}) \end{equation*}$

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 single-gate recurrent cell,

• LSTM, a four-gate long short-term memory cell,

• GRU, a three-gate gated recurrent unit cell,

• Linear-before-reset GRU, a three-gate recurrent unit cell with the linear layer before the reset gate.

### Vanilla RNN¶

A single-gate 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:

\begin{split}\begin{align} a_t &= W \cdot h_{t,l-1} + U \cdot h_{t-1, l} + B \\ h_t &= activation(a_t) \end{align}\end{split}

### LSTM¶

#### LSTM (or Vanilla LSTM)¶

A four-gate long short-term 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:

\begin{split}\begin{align} i_t &= \sigma(W_i \cdot h_{t,l-1} + U_i \cdot h_{t-1, l} + B_i) \\ f_t &= \sigma(W_f \cdot h_{t,l-1} + U_f \cdot h_{t-1, l} + B_f) \\ \\ \tilde c_t &= \tanh(W_{\tilde c} \cdot h_{t,l-1} + U_{\tilde c} \cdot h_{t-1, l} + B_{\tilde c}) \\ c_t &= f_t * c_{t-1} + i_t * \tilde c_t \\ \\ o_t &= \sigma(W_o \cdot h_{t,l-1} + U_o \cdot h_{t-1, l} + B_o) \\ h_t &= \tanh(c_t) * o_t \end{align}\end{split}

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 four-gate long short-term 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:

\begin{split}\begin{align} i_t &= \sigma(W_i \cdot h_{t,l-1} + U_i \cdot h_{t-1, l} + P_i \cdot c_{t-1} + B_i) \\ f_t &= \sigma(W_f \cdot h_{t,l-1} + U_f \cdot h_{t-1, l} + P_f \cdot c_{t-1} + B_f) \\ \\ \tilde c_t &= \tanh(W_{\tilde c} \cdot h_{t,l-1} + U_{\tilde c} \cdot h_{t-1, l} + B_{\tilde c}) \\ c_t &= f_t * c_{t-1} + i_t * \tilde c_t \\ \\ o_t &= \sigma(W_o \cdot h_{t,l-1} + U_o \cdot h_{t-1, l} + P_o \cdot c_t + B_o) \\ h_t &= \tanh(c_t) * o_t \end{align}\end{split}

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 four-gate long short-term 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):

\begin{split}\begin{align} i_t &= \sigma(W_i \cdot h_{t,l-1} + U_i \cdot h_{t-1,l} + B_i) \\ f_t &= \sigma(W_f \cdot h_{t,l-1} + U_f \cdot h_{t-1,l} + B_f) \\ & \\ \tilde{c}_t &= \tanh(W_{\tilde{c}} \cdot h_{t,l-1} + U_{\tilde{c}} \cdot h_{t-1,l} + B_{\tilde{c}}) \\ c_t &= f_t * c_{t-1} + i_t * \tilde{c}_t \\ & \\ o_t &= \sigma(W_o \cdot h_{t,l-1} + U_o \cdot h_{t-1,l} + B_o) \\ h_t &= R \cdot (\tanh(c_t) * o_t) \end{align}\end{split}

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 three-gate 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.

\begin{split}\begin{align} u_t &= \sigma(W_u \cdot h_{t,l-1} + U_u \cdot h_{t-1, l} + B_u) \\ r_t &= \sigma(W_r \cdot h_{t,l-1} + U_r \cdot h_{t-1, l} + B_r) \\ o_t &= \tanh(W_o \cdot h_{t,l-1} + U_o \cdot (r_t * h_{t-1, l}) + B_o) \\ h_t &= u_t * h_{t-1, l} + (1 - u_t) * o_t \end{align}\end{split}

where $$W_*$$ are in $$\weightslayer$$, $$U_*$$ are in $$\weightsiter$$, and $$B_*$$ are stored in $$\bias$$.

Note

If you need to replace u_t by (1-u_t) when computing h_t, you can achieve this by multiplying $$W_u$$, $$U_u$$ and $$B_u$$ by $$-1$$. This is possible as $$u_t = \sigma(W_u \cdot h_{t,l-1} + U_u \cdot h_{t-1, l} + B_u)$$, and $$1 – \sigma(a) = \sigma(-a)$$.

### Linear-Before-Reset GRU¶

A three-gate 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 Linear-Before-Reset GRU cell.

\begin{split}\begin{align} u_t &= \sigma(W_u \cdot h_{t,l-1} + U_u \cdot h_{t-1, l} + B_u) \\ r_t &= \sigma(W_r \cdot h_{t,l-1} + U_r \cdot h_{t-1, l} + B_r) \\ o_t &= \tanh(W_o \cdot h_{t,l-1} + r_t *(U_o \cdot h_{t-1, l} + B_{u'}) + B_o) \\ h_t &= u_t * h_{t-1, l} + (1 - u_t) * o_t \end{align}\end{split}

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 (1-u_t) when computing h_t, you can achieve this by multiplying $$W_u$$, $$U_u$$ and $$B_u$$ by $$-1$$. This is possible as $$u_t = \sigma(W_u \cdot h_{t,l-1} + U_u \cdot h_{t-1, l} + B_u)$$, 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

1. With LSTM and Peephole LSTM cells, the cell state datatype is f32, except for the f16 configuration.

2. In backward propagation, all diff_* tensors are in f32.

3. 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

dnnl_format_tag_any

dnnl_format_tag_any

dnnl_format_tag_any

dnnl_ldgo

dnnl_format_tag_any

Forward

dnnl_ldnc

dnnl_ldigo

dnnl_ldgo

dnnl_ldio

Backward

dnnl_ldnc

dnnl_ldgoi

dnnl_ldgo

dnnl_ldoi

While an RNN primitive can be created with memory formats specified explicitly, the performance is likely to be sub-optimal. 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.

### Post-ops and Attributes¶

Currently post-ops 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¶

1. Refer to Data Types for limitations related to data types support.

2. 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.

3. 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

CPU/GPU

LSTM RNN Primitive Example

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: