1PReLU {#dev_guide_prelu} 2============================ 3 4> 5> [API Reference](@ref dnnl_api_prelu) 6> 7 8## General 9 10The PReLU primitive (Leaky ReLU with trainable alpha parameter) performs 11forward or backward operation on data tensor. Weights (alpha) tensor supports 12broadcast-semantics. Broadcast configuration is assumed based on src and 13weights dimensions. 14 15Example broadcasts: 16 17| broadcast type | src dimensions | weights dimensions | 18| --- | --- | --- | 19| Channel-shared | \f$\{n, c, h ,w\}\f$ | \f$\{1, 1, 1 ,1\}\f$ | 20| Channel-wise | \f$\{n, c, h ,w\}\f$ | \f$\{1, c, 1 ,1\}\f$ | 21| Whole-tensor | \f$\{n, c, h ,w\}\f$ | \f$\{n, c, h ,w\}\f$ | 22| Shared-axes | \f$\{n, c, h ,w\}\f$ | \f$\{n, 1, h ,1\}\f$ | 23 24@note 25 Shared-axes indicates broadcast with any combination of shared 26dimensions. 27 28### Forward 29 30The PReLU operation is defined by the following formulas. 31We show formulas only for 2D spatial data which are straightforward to 32generalize to cases of higher and lower dimensions. Variable names follow the 33standard @ref dev_guide_conventions. 34For no broadcast case, results are calculated using formula: 35 36\f[ 37 \dst(n, c, h, w) = 38 \begin{cases} 39 \src(n, c, h, w) & \mbox{if } \src(n, c, h, w) > 0 \\ 40 \src(n, c, h, w) \cdot \weights(n, c, h, w) & \mbox{if } 41 \src(n, c, h, w) \leq 0 42 \end{cases} 43\f] 44 45Depending on broadcast configuration, result is calculated taking into account 46shared dimensions of weights tensor. 47 48#### Difference Between Forward Training and Forward Inference 49 50There is no difference between the #dnnl_forward_training 51and #dnnl_forward_inference propagation kinds. 52 53### Backward 54 55The backward propagation computes \f$\diffsrc\f$ and \f$\diffweights\f$. 56For no broadcast case, results are calculated using formula: 57 58\f[ 59 \begin{align} 60 \mbox{diff_src}(n, c, h, w) &= 61 \begin{cases} 62 \mbox{diff_dst}(n, c, h, w) & \mbox{if } \src(n, c, h, w) > 0 \\ 63 \mbox{diff_dst}(n, c, h, w) \cdot \weights(n, c, h, w) & 64 \mbox{if } \src(n, c, h, w) \leq 0 65 \end{cases}\\\\ 66 \mbox{diff_weights}(n, c, h, w) &= 67 \min(\src(n, c, h, w), 0) \cdot \mbox{diff_dst}(n, c, h, w) 68 \end{align} 69\f] 70 71Similar to forward propagation, result is calculated taking into 72account shared dimensions of weights tensor. 73\f$\diffweights\f$ results are accumulated according to weights tensor shared 74dimensions, since \f$\diffweights\f$ tensor must match \f$\weights\f$ tensor. 75 76 77## Execution Arguments 78 79When executed, the inputs and outputs should be mapped to an execution 80argument index as specified by the following table. 81 82| Primitive input/output | Execution argument index | 83| --- | --- | 84| \f$\src\f$ | DNNL_ARG_SRC | 85| \f$\dst\f$ | DNNL_ARG_DST | 86| \f$\weights\f$ | DNNL_ARG_WEIGHTS | 87| \f$\diffsrc\f$ | DNNL_ARG_DIFF_SRC | 88| \f$\diffdst\f$ | DNNL_ARG_DIFF_DST | 89| \f$\diffweights\f$ | DNNL_ARG_DIFF_WEIGHTS | 90 91 92## Implementation Details 93 94### General Notes 95 96 * Prelu primitive requires all input/output tensors to have the 97 same number of dimensions. Dimension sizes can differ however. 98 99 * \weights tensor dimensions sizes must follow broadcast semantics. 100 Each dimension can either equal corresponding data dimension or 101 equal 1 - to indicate that dimension is shared. 102 103 * Prelu primitive requires that \diffweights tensor has exact same dimensions 104 sizes as \weights tensor, \diffsrc as src and \diffdst as dst. 105 106 * \weights tensor can be initialized with format_tag::any 107 primitive will match it to data tensor format. 108 109### Data Type Support 110 111The PReLU primitive supports the following combinations of data types: 112 113| Propagation | Source / Destination | 114| :-- | :-- | 115| forward / backward | f32, s32, bf16, s8, u8 | 116 117### Data Representation 118 119The PReLU primitive works with arbitrary data tensors. There is no special 120meaning associated with any logical dimensions. 121 122## Implementation Limitations 123 124Current implementation supports all tensors up to 3D spatial (n, c, d, h, w). 125 126## Performance Tips 127 128Its recommended to allow PReLU primitive to choose the appropriate weights 129memory format by passing weights_md with format_tag::any. 130For best performance, the weights memory format should match 131data memory format. 132 133## Example 134 135[PReLU Primitive Example](@ref prelu_example_cpp) 136 137@copydetails prelu_example_cpp_short 138