Developer Guide and Reference

  • 2022.1
  • 04/11/2022
  • Public Content



The PReLU primitive (Leaky ReLU with trainable alpha parameter) performs forward or backward operation on data tensor. Weights (alpha) tensor supports broadcast-semantics. Broadcast configuration is assumed based on src and weights dimensions.
Example broadcasts:
broadcast type
src dimensions
weights dimensions
LaTex Math image.
LaTex Math image.
LaTex Math image.
LaTex Math image.
LaTex Math image.
LaTex Math image.
LaTex Math image.
LaTex Math image.
Shared-axes indicates broadcast with any combination of shared dimensions.
The PReLU operation is defined by the following formulas. We show formulas only for 2D spatial data which are straightforward to generalize to cases of higher and lower dimensions. Variable names follow the standard Naming Conventions. For no broadcast case, results are calculated using formula:
LaTex Math image.
Depending on broadcast configuration, result is calculated taking into account shared dimensions of weights tensor.
Difference Between Forward Training and Forward Inference
There is no difference between the dnnl_forward_training and dnnl_forward_inference propagation kinds.
The backward propagation computes LaTex Math image. and LaTex Math image.. For no broadcast case, results are calculated using formula:
ERROR processing math
Similar to forward propagation, result is calculated taking into account shared dimensions of weights tensor. LaTex Math image. results are accumulated according to weights tensor shared dimensions, since LaTex Math image. tensor must match LaTex Math image. tensor.

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
LaTex Math image.
LaTex Math image.
LaTex Math image.
LaTex Math image.
LaTex Math image.
LaTex Math image.

Implementation Details

General Notes
  • Prelu primitive requires all input/output tensors to have the same number of dimensions. Dimension sizes can differ however.
  • LaTex Math image. tensor dimensions sizes must follow broadcast semantics. Each dimension can either equal corresponding data dimension or equal 1 - to indicate that dimension is shared.
  • Prelu primitive requires that LaTex Math image. tensor has exact same dimensions sizes as LaTex Math image. tensor, LaTex Math image. as src and LaTex Math image. as dst.
  • LaTex Math image. tensor can be initialized with format_tag::any primitive will match it to data tensor format.
Data Type Support
The PReLU primitive supports the following combinations of data types:
Source / Destination
forward / backward
f32, s32, bf16, s8, u8
Data Representation
The PReLU primitive works with arbitrary data tensors. There is no special meaning associated with any logical dimensions.

Implementation Limitations

Current implementation supports all tensors up to 3D spatial (n, c, d, h, w).

Performance Tips

Its recommended to allow PReLU primitive to choose the appropriate weights memory format by passing weights_md with format_tag::any. For best performance, the weights memory format should match data memory format.


This C++ API example demonstrates how to create and execute an PReLU primitive in forward training propagation mode.

Product and Performance Information


Performance varies by use, configuration and other factors. Learn more at