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 |
---|---|---|
Channel-shared | \(\{n, c, h ,w\}\) | \(\{1, 1, 1 ,1\}\) |
Channel-wise | \(\{n, c, h ,w\}\) | \(\{1, c, 1 ,1\}\) |
Whole-tensor | \(\{n, c, h ,w\}\) | \(\{n, c, h ,w\}\) |
Shared-axes | \(\{n, c, h ,w\}\) | \(\{n, 1, h ,1\}\) |
note: 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:
\[ \dst(n, c, h, w) = \begin{cases} \src(n, c, h, w) & \mbox{if } \src(n, c, h, w) > 0 \\ \src(n, c, h, w) \cdot \weights(n, c, h, w) & \mbox{if } \src(n, c, h, w) \leq 0 \end{cases} \]
Depending on broadcast configuration, result is calculated taking into account shared dimensions of weights tensor.
There is no difference between the dnnl_forward_training and dnnl_forward_inference propagation kinds.
The backward propagation computes \(\diffsrc\) and \(\diffweights\). For no broadcast case, results are calculated using formula:
\[ \begin{align} \mbox{diff_src}(n, c, h, w) &= \begin{cases} \mbox{diff_dst}(n, c, h, w) & \mbox{if } \src(n, c, h, w) > 0 \\ \mbox{diff_dst}(n, c, h, w) \cdot \weights(n, c, h, w) & \mbox{if } \src(n, c, h, w) \leq 0 \end{cases}\\\\ \mbox{diff_weights}(n, c, h, w) &= \min(\src(n, c, h, w), 0) \cdot \mbox{diff_dst}(n, c, h, w) \end{align} \]
Similar to forward propagation, result is calculated taking into account shared dimensions of weights tensor. \(\diffweights\) results are accumulated according to weights tensor shared dimensions, since \(\diffweights\) tensor must match \(\weights\) tensor.
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 |
---|---|
\(\src\) | DNNL_ARG_SRC |
\(\dst\) | DNNL_ARG_DST |
\(\weights\) | DNNL_ARG_WEIGHTS |
\(\diffsrc\) | DNNL_ARG_DIFF_SRC |
\(\diffdst\) | DNNL_ARG_DIFF_DST |
\(\diffweights\) | DNNL_ARG_DIFF_WEIGHTS |
The PReLU primitive supports the following combinations of data types:
Propagation | Source / Destination |
---|---|
forward / backward | f32, s32, bf16, s8, u8 |
The PReLU primitive works with arbitrary data tensors. There is no special meaning associated with any logical dimensions.
Current implementation supports all tensors up to 3D spatial (n, c, d, h, w).
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.
Engine | Name | Comments |
---|---|---|
CPU/GPU | Primitive Example | This C++ API example demonstrates how to create and execute an PReLU primitive in forward training propagation mode. |