Intel® oneAPI Deep Neural Network Developer Guide and Reference
                    
                        ID
                        768875
                    
                
                
                    Date
                    2/28/2024
                
                
                    Public
                
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                                                        Abs
                                                    
                                                    
                                                
                                                    
                                                    
                                                        AbsBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Add
                                                    
                                                    
                                                
                                                    
                                                    
                                                        AvgPool
                                                    
                                                    
                                                
                                                    
                                                    
                                                        AvgPoolBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        BatchNormForwardTraining
                                                    
                                                    
                                                
                                                    
                                                    
                                                        BatchNormInference
                                                    
                                                    
                                                
                                                    
                                                    
                                                        BatchNormTrainingBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        BiasAdd
                                                    
                                                    
                                                
                                                    
                                                    
                                                        BiasAddBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Clamp
                                                    
                                                    
                                                
                                                    
                                                    
                                                        ClampBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Concat
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Convolution
                                                    
                                                    
                                                
                                                    
                                                    
                                                        ConvolutionBackwardData
                                                    
                                                    
                                                
                                                    
                                                    
                                                        ConvolutionBackwardWeights
                                                    
                                                    
                                                
                                                    
                                                    
                                                        ConvTranspose
                                                    
                                                    
                                                
                                                    
                                                    
                                                        ConvTransposeBackwardData
                                                    
                                                    
                                                
                                                    
                                                    
                                                        ConvTransposeBackwardWeights
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Dequantize
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Divide
                                                    
                                                    
                                                
                                                    
                                                    
                                                        DynamicDequantize
                                                    
                                                    
                                                
                                                    
                                                    
                                                        DynamicQuantize
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Elu
                                                    
                                                    
                                                
                                                    
                                                    
                                                        EluBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        End
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Exp
                                                    
                                                    
                                                
                                                    
                                                    
                                                        GELU
                                                    
                                                    
                                                
                                                    
                                                    
                                                        GELUBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        HardSigmoid
                                                    
                                                    
                                                
                                                    
                                                    
                                                        HardSigmoidBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        HardSwish
                                                    
                                                    
                                                
                                                    
                                                    
                                                        HardSwishBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Interpolate
                                                    
                                                    
                                                
                                                    
                                                    
                                                        InterpolateBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        LayerNorm
                                                    
                                                    
                                                
                                                    
                                                    
                                                        LayerNormBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        LeakyReLU
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Log
                                                    
                                                    
                                                
                                                    
                                                    
                                                        LogSoftmax
                                                    
                                                    
                                                
                                                    
                                                    
                                                        LogSoftmaxBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        MatMul
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Maximum
                                                    
                                                    
                                                
                                                    
                                                    
                                                        MaxPool
                                                    
                                                    
                                                
                                                    
                                                    
                                                        MaxPoolBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Minimum
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Mish
                                                    
                                                    
                                                
                                                    
                                                    
                                                        MishBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Multiply
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Pow
                                                    
                                                    
                                                
                                                    
                                                    
                                                        PReLU
                                                    
                                                    
                                                
                                                    
                                                    
                                                        PReLUBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Quantize
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Reciprocal
                                                    
                                                    
                                                
                                                    
                                                    
                                                        ReduceL1
                                                    
                                                    
                                                
                                                    
                                                    
                                                        ReduceL2
                                                    
                                                    
                                                
                                                    
                                                    
                                                        ReduceMax
                                                    
                                                    
                                                
                                                    
                                                    
                                                        ReduceMean
                                                    
                                                    
                                                
                                                    
                                                    
                                                        ReduceMin
                                                    
                                                    
                                                
                                                    
                                                    
                                                        ReduceProd
                                                    
                                                    
                                                
                                                    
                                                    
                                                        ReduceSum
                                                    
                                                    
                                                
                                                    
                                                    
                                                        ReLU
                                                    
                                                    
                                                
                                                    
                                                    
                                                        ReLUBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Reorder
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Round
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Select
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Sigmoid
                                                    
                                                    
                                                
                                                    
                                                    
                                                        SigmoidBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        SoftMax
                                                    
                                                    
                                                
                                                    
                                                    
                                                        SoftMaxBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        SoftPlus
                                                    
                                                    
                                                
                                                    
                                                    
                                                        SoftPlusBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Sqrt
                                                    
                                                    
                                                
                                                    
                                                    
                                                        SqrtBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Square
                                                    
                                                    
                                                
                                                    
                                                    
                                                        SquaredDifference
                                                    
                                                    
                                                
                                                    
                                                    
                                                        StaticReshape
                                                    
                                                    
                                                
                                                    
                                                    
                                                        StaticTranspose
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Subtract
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Tanh
                                                    
                                                    
                                                
                                                    
                                                    
                                                        TanhBackward
                                                    
                                                    
                                                
                                                    
                                                    
                                                        TypeCast
                                                    
                                                    
                                                
                                                    
                                                    
                                                        Wildcard
                                                    
                                                    
                                                
                                            
                                        
                                                            
                                                            
                                                                
                                                                
                                                                    enum dnnl_alg_kind_t
                                                                
                                                                
                                                            
                                                                
                                                                
                                                                    enum dnnl_normalization_flags_t
                                                                
                                                                
                                                            
                                                                
                                                                
                                                                    enum dnnl_primitive_kind_t
                                                                
                                                                
                                                            
                                                                
                                                                
                                                                    enum dnnl_prop_kind_t
                                                                
                                                                
                                                            
                                                                
                                                                
                                                                    enum dnnl_query_t
                                                                
                                                                
                                                            
                                                                
                                                                
                                                                    enum dnnl::normalization_flags
                                                                
                                                                
                                                            
                                                                
                                                                
                                                                    enum dnnl::query
                                                                
                                                                
                                                            
                                                                
                                                                
                                                                    struct dnnl_exec_arg_t
                                                                
                                                                
                                                            
                                                                
                                                                
                                                                    struct dnnl_primitive
                                                                
                                                                
                                                            
                                                                
                                                                
                                                                    struct dnnl_primitive_desc
                                                                
                                                                
                                                            
                                                                
                                                                    struct dnnl::primitive
                                                                
                                                                
                                                                
                                                            
                                                                
                                                                
                                                                    struct dnnl::primitive_desc
                                                                
                                                                
                                                            
                                                                
                                                                
                                                                    struct dnnl::primitive_desc_base
                                                                
                                                                
                                                            
                                                        
                                                    
                                                            
                                                            
                                                                
                                                                
                                                                    enum dnnl_rnn_direction_t
                                                                
                                                                
                                                            
                                                                
                                                                
                                                                    enum dnnl_rnn_flags_t
                                                                
                                                                
                                                            
                                                                
                                                                
                                                                    enum dnnl::rnn_direction
                                                                
                                                                
                                                            
                                                                
                                                                
                                                                    enum dnnl::rnn_flags
                                                                
                                                                
                                                            
                                                                
                                                                    struct dnnl::augru_backward
                                                                
                                                                
                                                                
                                                            
                                                                
                                                                    struct dnnl::augru_forward
                                                                
                                                                
                                                                
                                                            
                                                                
                                                                    struct dnnl::gru_backward
                                                                
                                                                
                                                                
                                                            
                                                                
                                                                    struct dnnl::gru_forward
                                                                
                                                                
                                                                
                                                            
                                                                
                                                                    struct dnnl::lbr_augru_backward
                                                                
                                                                
                                                                
                                                            
                                                                
                                                                    struct dnnl::lbr_augru_forward
                                                                
                                                                
                                                                
                                                            
                                                                
                                                                    struct dnnl::lbr_gru_backward
                                                                
                                                                
                                                                
                                                            
                                                                
                                                                    struct dnnl::lbr_gru_forward
                                                                
                                                                
                                                                
                                                            
                                                                
                                                                    struct dnnl::lstm_backward
                                                                
                                                                
                                                                
                                                            
                                                                
                                                                    struct dnnl::lstm_forward
                                                                
                                                                
                                                                
                                                            
                                                                
                                                                
                                                                    struct dnnl::rnn_primitive_desc_base
                                                                
                                                                
                                                            
                                                                
                                                                    struct dnnl::vanilla_rnn_backward
                                                                
                                                                
                                                                
                                                            
                                                                
                                                                    struct dnnl::vanilla_rnn_forward
                                                                
                                                                
                                                                
                                                            
                                                        
                                                    cnn_training_bf16 cpp
This C++ API example demonstrates how to build an AlexNet model training using the bfloat16 data type. Annotated version: CNN bf16 training example
This C++ API example demonstrates how to build an AlexNet model training using the bfloat16 data type. Annotated version: CNN bf16 training example
/*******************************************************************************
* Copyright 2019-2022 Intel Corporation
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
*     http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*******************************************************************************/
#include <cassert>
#include <cmath>
#include <iostream>
#include <stdexcept>
#include "oneapi/dnnl/dnnl.hpp"
#include "example_utils.hpp"
using namespace dnnl;
void simple_net(engine::kind engine_kind) {
    using tag = memory::format_tag;
    using dt = memory::data_type;
    auto eng = engine(engine_kind, 0);
    stream s(eng);
    // Vector of primitives and their execute arguments
    std::vector<primitive> net_fwd, net_bwd;
    std::vector<std::unordered_map<int, memory>> net_fwd_args, net_bwd_args;
    const int batch = 32;
    // float data type is used for user data
    std::vector<float> net_src(batch * 3 * 227 * 227);
    // initializing non-zero values for src
    for (size_t i = 0; i < net_src.size(); ++i)
        net_src[i] = sinf((float)i);
    // AlexNet: conv
    // {batch, 3, 227, 227} (x) {96, 3, 11, 11} -> {batch, 96, 55, 55}
    // strides: {4, 4}
    memory::dims conv_src_tz = {batch, 3, 227, 227};
    memory::dims conv_weights_tz = {96, 3, 11, 11};
    memory::dims conv_bias_tz = {96};
    memory::dims conv_dst_tz = {batch, 96, 55, 55};
    memory::dims conv_strides = {4, 4};
    memory::dims conv_padding = {0, 0};
    // float data type is used for user data
    std::vector<float> conv_weights(product(conv_weights_tz));
    std::vector<float> conv_bias(product(conv_bias_tz));
    // initializing non-zero values for weights and bias
    for (size_t i = 0; i < conv_weights.size(); ++i)
        conv_weights[i] = sinf((float)i);
    for (size_t i = 0; i < conv_bias.size(); ++i)
        conv_bias[i] = sinf((float)i);
    // create memory for user data
    auto conv_user_src_memory
            = memory({{conv_src_tz}, dt::f32, tag::nchw}, eng);
    write_to_dnnl_memory(net_src.data(), conv_user_src_memory);
    auto conv_user_weights_memory
            = memory({{conv_weights_tz}, dt::f32, tag::oihw}, eng);
    write_to_dnnl_memory(conv_weights.data(), conv_user_weights_memory);
    auto conv_user_bias_memory = memory({{conv_bias_tz}, dt::f32, tag::x}, eng);
    write_to_dnnl_memory(conv_bias.data(), conv_user_bias_memory);
    // create memory descriptors for bfloat16 convolution data w/ no specified
    // format tag(`any`)
    // tag `any` lets a primitive(convolution in this case)
    // chose the memory format preferred for best performance.
    auto conv_src_md = memory::desc({conv_src_tz}, dt::bf16, tag::any);
    auto conv_weights_md = memory::desc({conv_weights_tz}, dt::bf16, tag::any);
    auto conv_dst_md = memory::desc({conv_dst_tz}, dt::bf16, tag::any);
    // here bias data type is set to bf16.
    // additionally, f32 data type is supported for bf16 convolution.
    auto conv_bias_md = memory::desc({conv_bias_tz}, dt::bf16, tag::any);
    // create a convolution primitive descriptor
    // check if bf16 convolution is supported
    try {
        convolution_forward::primitive_desc(eng, prop_kind::forward,
                algorithm::convolution_direct, conv_src_md, conv_weights_md,
                conv_bias_md, conv_dst_md, conv_strides, conv_padding,
                conv_padding);
    } catch (error &e) {
        if (e.status == dnnl_unimplemented)
            throw example_allows_unimplemented {
                    "No bf16 convolution implementation is available for this "
                    "platform.\n"
                    "Please refer to the developer guide for details."};
        // on any other error just re-throw
        throw;
    }
    auto conv_pd = convolution_forward::primitive_desc(eng, prop_kind::forward,
            algorithm::convolution_direct, conv_src_md, conv_weights_md,
            conv_bias_md, conv_dst_md, conv_strides, conv_padding,
            conv_padding);
    // create reorder primitives between user input and conv src if needed
    auto conv_src_memory = conv_user_src_memory;
    if (conv_pd.src_desc() != conv_user_src_memory.get_desc()) {
        conv_src_memory = memory(conv_pd.src_desc(), eng);
        net_fwd.push_back(reorder(conv_user_src_memory, conv_src_memory));
        net_fwd_args.push_back({{DNNL_ARG_FROM, conv_user_src_memory},
                {DNNL_ARG_TO, conv_src_memory}});
    }
    auto conv_weights_memory = conv_user_weights_memory;
    if (conv_pd.weights_desc() != conv_user_weights_memory.get_desc()) {
        conv_weights_memory = memory(conv_pd.weights_desc(), eng);
        net_fwd.push_back(
                reorder(conv_user_weights_memory, conv_weights_memory));
        net_fwd_args.push_back({{DNNL_ARG_FROM, conv_user_weights_memory},
                {DNNL_ARG_TO, conv_weights_memory}});
    }
    // convert bias from f32 to bf16 as convolution descriptor is created with
    // bias data type as bf16.
    auto conv_bias_memory = conv_user_bias_memory;
    if (conv_pd.bias_desc() != conv_user_bias_memory.get_desc()) {
        conv_bias_memory = memory(conv_pd.bias_desc(), eng);
        net_fwd.push_back(reorder(conv_user_bias_memory, conv_bias_memory));
        net_fwd_args.push_back({{DNNL_ARG_FROM, conv_user_bias_memory},
                {DNNL_ARG_TO, conv_bias_memory}});
    }
    // create memory for conv dst
    auto conv_dst_memory = memory(conv_pd.dst_desc(), eng);
    // finally create a convolution primitive
    net_fwd.push_back(convolution_forward(conv_pd));
    net_fwd_args.push_back({{DNNL_ARG_SRC, conv_src_memory},
            {DNNL_ARG_WEIGHTS, conv_weights_memory},
            {DNNL_ARG_BIAS, conv_bias_memory},
            {DNNL_ARG_DST, conv_dst_memory}});
    // AlexNet: relu
    // {batch, 96, 55, 55} -> {batch, 96, 55, 55}
    memory::dims relu_data_tz = {batch, 96, 55, 55};
    const float negative_slope = 0.0f;
    // create relu primitive desc
    // keep memory format tag of source same as the format tag of convolution
    // output in order to avoid reorder
    auto relu_pd = eltwise_forward::primitive_desc(eng, prop_kind::forward,
            algorithm::eltwise_relu, conv_pd.dst_desc(), conv_pd.dst_desc(),
            negative_slope);
    // create relu dst memory
    auto relu_dst_memory = memory(relu_pd.dst_desc(), eng);
    // finally create a relu primitive
    net_fwd.push_back(eltwise_forward(relu_pd));
    net_fwd_args.push_back(
            {{DNNL_ARG_SRC, conv_dst_memory}, {DNNL_ARG_DST, relu_dst_memory}});
    // AlexNet: lrn
    // {batch, 96, 55, 55} -> {batch, 96, 55, 55}
    // local size: 5
    // alpha: 0.0001
    // beta: 0.75
    // k: 1.0
    memory::dims lrn_data_tz = {batch, 96, 55, 55};
    const uint32_t local_size = 5;
    const float alpha = 0.0001f;
    const float beta = 0.75f;
    const float k = 1.0f;
    // create a lrn primitive descriptor
    auto lrn_pd = lrn_forward::primitive_desc(eng, prop_kind::forward,
            algorithm::lrn_across_channels, relu_pd.dst_desc(),
            relu_pd.dst_desc(), local_size, alpha, beta, k);
    // create lrn dst memory
    auto lrn_dst_memory = memory(lrn_pd.dst_desc(), eng);
    // create workspace only in training and only for forward primitive
    // query lrn_pd for workspace, this memory will be shared with forward lrn
    auto lrn_workspace_memory = memory(lrn_pd.workspace_desc(), eng);
    // finally create a lrn primitive
    net_fwd.push_back(lrn_forward(lrn_pd));
    net_fwd_args.push_back(
            {{DNNL_ARG_SRC, relu_dst_memory}, {DNNL_ARG_DST, lrn_dst_memory},
                    {DNNL_ARG_WORKSPACE, lrn_workspace_memory}});
    // AlexNet: pool
    // {batch, 96, 55, 55} -> {batch, 96, 27, 27}
    // kernel: {3, 3}
    // strides: {2, 2}
    memory::dims pool_dst_tz = {batch, 96, 27, 27};
    memory::dims pool_kernel = {3, 3};
    memory::dims pool_strides = {2, 2};
    memory::dims pool_dilation = {0, 0};
    memory::dims pool_padding = {0, 0};
    // create memory for pool dst data in user format
    auto pool_user_dst_memory
            = memory({{pool_dst_tz}, dt::f32, tag::nchw}, eng);
    // create pool dst memory descriptor in format any for bfloat16 data type
    auto pool_dst_md = memory::desc({pool_dst_tz}, dt::bf16, tag::any);
    // create a pooling primitive descriptor
    auto pool_pd = pooling_forward::primitive_desc(eng, prop_kind::forward,
            algorithm::pooling_max, lrn_dst_memory.get_desc(), pool_dst_md,
            pool_strides, pool_kernel, pool_dilation, pool_padding,
            pool_padding);
    // create pooling workspace memory if training
    auto pool_workspace_memory = memory(pool_pd.workspace_desc(), eng);
    // create a pooling primitive
    net_fwd.push_back(pooling_forward(pool_pd));
    // leave DST unknown for now (see the next reorder)
    net_fwd_args.push_back({{DNNL_ARG_SRC, lrn_dst_memory},
            // delay putting DST until reorder (if needed)
            {DNNL_ARG_WORKSPACE, pool_workspace_memory}});
    // create reorder primitive between pool dst and user dst format
    // if needed
    auto pool_dst_memory = pool_user_dst_memory;
    if (pool_pd.dst_desc() != pool_user_dst_memory.get_desc()) {
        pool_dst_memory = memory(pool_pd.dst_desc(), eng);
        net_fwd_args.back().insert({DNNL_ARG_DST, pool_dst_memory});
        net_fwd.push_back(reorder(pool_dst_memory, pool_user_dst_memory));
        net_fwd_args.push_back({{DNNL_ARG_FROM, pool_dst_memory},
                {DNNL_ARG_TO, pool_user_dst_memory}});
    } else {
        net_fwd_args.back().insert({DNNL_ARG_DST, pool_dst_memory});
    }
    //-----------------------------------------------------------------------
    //----------------- Backward Stream -------------------------------------
    // ... user diff_data in float data type ...
    std::vector<float> net_diff_dst(batch * 96 * 27 * 27);
    for (size_t i = 0; i < net_diff_dst.size(); ++i)
        net_diff_dst[i] = sinf((float)i);
    // create memory for user diff dst data stored in float data type
    auto pool_user_diff_dst_memory
            = memory({{pool_dst_tz}, dt::f32, tag::nchw}, eng);
    write_to_dnnl_memory(net_diff_dst.data(), pool_user_diff_dst_memory);
    // Backward pooling
    // create memory descriptors for pooling
    auto pool_diff_src_md = memory::desc({lrn_data_tz}, dt::bf16, tag::any);
    auto pool_diff_dst_md = memory::desc({pool_dst_tz}, dt::bf16, tag::any);
    // backward primitive descriptor needs to hint forward descriptor
    auto pool_bwd_pd = pooling_backward::primitive_desc(eng,
            algorithm::pooling_max, pool_diff_src_md, pool_diff_dst_md,
            pool_strides, pool_kernel, pool_dilation, pool_padding,
            pool_padding, pool_pd);
    // create reorder primitive between user diff dst and pool diff dst
    // if required
    auto pool_diff_dst_memory = pool_user_diff_dst_memory;
    if (pool_dst_memory.get_desc() != pool_user_diff_dst_memory.get_desc()) {
        pool_diff_dst_memory = memory(pool_dst_memory.get_desc(), eng);
        net_bwd.push_back(
                reorder(pool_user_diff_dst_memory, pool_diff_dst_memory));
        net_bwd_args.push_back({{DNNL_ARG_FROM, pool_user_diff_dst_memory},
                {DNNL_ARG_TO, pool_diff_dst_memory}});
    }
    // create memory for pool diff src
    auto pool_diff_src_memory = memory(pool_bwd_pd.diff_src_desc(), eng);
    // finally create backward pooling primitive
    net_bwd.push_back(pooling_backward(pool_bwd_pd));
    net_bwd_args.push_back({{DNNL_ARG_DIFF_DST, pool_diff_dst_memory},
            {DNNL_ARG_DIFF_SRC, pool_diff_src_memory},
            {DNNL_ARG_WORKSPACE, pool_workspace_memory}});
    // Backward lrn
    auto lrn_diff_dst_md = memory::desc({lrn_data_tz}, dt::bf16, tag::any);
    const auto &lrn_diff_src_md = lrn_diff_dst_md;
    // create backward lrn primitive descriptor
    auto lrn_bwd_pd = lrn_backward::primitive_desc(eng,
            algorithm::lrn_across_channels, lrn_diff_src_md, lrn_diff_dst_md,
            lrn_pd.src_desc(), local_size, alpha, beta, k, lrn_pd);
    // create reorder primitive between pool diff src and lrn diff dst
    // if required
    auto lrn_diff_dst_memory = pool_diff_src_memory;
    if (lrn_diff_dst_memory.get_desc() != lrn_bwd_pd.diff_dst_desc()) {
        lrn_diff_dst_memory = memory(lrn_bwd_pd.diff_dst_desc(), eng);
        net_bwd.push_back(reorder(pool_diff_src_memory, lrn_diff_dst_memory));
        net_bwd_args.push_back({{DNNL_ARG_FROM, pool_diff_src_memory},
                {DNNL_ARG_TO, lrn_diff_dst_memory}});
    }
    // create memory for lrn diff src
    auto lrn_diff_src_memory = memory(lrn_bwd_pd.diff_src_desc(), eng);
    // finally create a lrn backward primitive
    // backward lrn needs src: relu dst in this topology
    net_bwd.push_back(lrn_backward(lrn_bwd_pd));
    net_bwd_args.push_back({{DNNL_ARG_SRC, relu_dst_memory},
            {DNNL_ARG_DIFF_DST, lrn_diff_dst_memory},
            {DNNL_ARG_DIFF_SRC, lrn_diff_src_memory},
            {DNNL_ARG_WORKSPACE, lrn_workspace_memory}});
    // Backward relu
    auto relu_diff_src_md = memory::desc({relu_data_tz}, dt::bf16, tag::any);
    auto relu_diff_dst_md = memory::desc({relu_data_tz}, dt::bf16, tag::any);
    auto relu_src_md = conv_pd.dst_desc();
    // create backward relu primitive_descriptor
    auto relu_bwd_pd = eltwise_backward::primitive_desc(eng,
            algorithm::eltwise_relu, relu_diff_src_md, relu_diff_dst_md,
            relu_src_md, negative_slope, relu_pd);
    // create reorder primitive between lrn diff src and relu diff dst
    // if required
    auto relu_diff_dst_memory = lrn_diff_src_memory;
    if (relu_diff_dst_memory.get_desc() != relu_bwd_pd.diff_dst_desc()) {
        relu_diff_dst_memory = memory(relu_bwd_pd.diff_dst_desc(), eng);
        net_bwd.push_back(reorder(lrn_diff_src_memory, relu_diff_dst_memory));
        net_bwd_args.push_back({{DNNL_ARG_FROM, lrn_diff_src_memory},
                {DNNL_ARG_TO, relu_diff_dst_memory}});
    }
    // create memory for relu diff src
    auto relu_diff_src_memory = memory(relu_bwd_pd.diff_src_desc(), eng);
    // finally create a backward relu primitive
    net_bwd.push_back(eltwise_backward(relu_bwd_pd));
    net_bwd_args.push_back({{DNNL_ARG_SRC, conv_dst_memory},
            {DNNL_ARG_DIFF_DST, relu_diff_dst_memory},
            {DNNL_ARG_DIFF_SRC, relu_diff_src_memory}});
    // Backward convolution with respect to weights
    // create user format diff weights and diff bias memory for float data type
    auto conv_user_diff_weights_memory
            = memory({{conv_weights_tz}, dt::f32, tag::nchw}, eng);
    auto conv_diff_bias_memory = memory({{conv_bias_tz}, dt::f32, tag::x}, eng);
    // create memory descriptors for bfloat16 convolution data
    auto conv_bwd_src_md = memory::desc({conv_src_tz}, dt::bf16, tag::any);
    auto conv_diff_weights_md
            = memory::desc({conv_weights_tz}, dt::bf16, tag::any);
    auto conv_diff_dst_md = memory::desc({conv_dst_tz}, dt::bf16, tag::any);
    // use diff bias provided by the user
    auto conv_diff_bias_md = conv_diff_bias_memory.get_desc();
    // create backward convolution primitive descriptor
    auto conv_bwd_weights_pd = convolution_backward_weights::primitive_desc(eng,
            algorithm::convolution_direct, conv_bwd_src_md,
            conv_diff_weights_md, conv_diff_bias_md, conv_diff_dst_md,
            conv_strides, conv_padding, conv_padding, conv_pd);
    // for best performance convolution backward might chose
    // different memory format for src and diff_dst
    // than the memory formats preferred by forward convolution
    // for src and dst respectively
    // create reorder primitives for src from forward convolution to the
    // format chosen by backward convolution
    auto conv_bwd_src_memory = conv_src_memory;
    if (conv_bwd_weights_pd.src_desc() != conv_src_memory.get_desc()) {
        conv_bwd_src_memory = memory(conv_bwd_weights_pd.src_desc(), eng);
        net_bwd.push_back(reorder(conv_src_memory, conv_bwd_src_memory));
        net_bwd_args.push_back({{DNNL_ARG_FROM, conv_src_memory},
                {DNNL_ARG_TO, conv_bwd_src_memory}});
    }
    // create reorder primitives for diff_dst between diff_src from relu_bwd
    // and format preferred by conv_diff_weights
    auto conv_diff_dst_memory = relu_diff_src_memory;
    if (conv_bwd_weights_pd.diff_dst_desc()
            != relu_diff_src_memory.get_desc()) {
        conv_diff_dst_memory = memory(conv_bwd_weights_pd.diff_dst_desc(), eng);
        net_bwd.push_back(reorder(relu_diff_src_memory, conv_diff_dst_memory));
        net_bwd_args.push_back({{DNNL_ARG_FROM, relu_diff_src_memory},
                {DNNL_ARG_TO, conv_diff_dst_memory}});
    }
    // create backward convolution primitive
    net_bwd.push_back(convolution_backward_weights(conv_bwd_weights_pd));
    net_bwd_args.push_back({{DNNL_ARG_SRC, conv_bwd_src_memory},
            {DNNL_ARG_DIFF_DST, conv_diff_dst_memory},
            // delay putting DIFF_WEIGHTS until reorder (if needed)
            {DNNL_ARG_DIFF_BIAS, conv_diff_bias_memory}});
    // create reorder primitives between conv diff weights and user diff weights
    // if needed
    auto conv_diff_weights_memory = conv_user_diff_weights_memory;
    if (conv_bwd_weights_pd.diff_weights_desc()
            != conv_user_diff_weights_memory.get_desc()) {
        conv_diff_weights_memory
                = memory(conv_bwd_weights_pd.diff_weights_desc(), eng);
        net_bwd_args.back().insert(
                {DNNL_ARG_DIFF_WEIGHTS, conv_diff_weights_memory});
        net_bwd.push_back(reorder(
                conv_diff_weights_memory, conv_user_diff_weights_memory));
        net_bwd_args.push_back({{DNNL_ARG_FROM, conv_diff_weights_memory},
                {DNNL_ARG_TO, conv_user_diff_weights_memory}});
    } else {
        net_bwd_args.back().insert(
                {DNNL_ARG_DIFF_WEIGHTS, conv_diff_weights_memory});
    }
    // didn't we forget anything?
    assert(net_fwd.size() == net_fwd_args.size() && "something is missing");
    assert(net_bwd.size() == net_bwd_args.size() && "something is missing");
    int n_iter = 1; // number of iterations for training
    // execute
    while (n_iter) {
        // forward
        for (size_t i = 0; i < net_fwd.size(); ++i)
            net_fwd.at(i).execute(s, net_fwd_args.at(i));
        // update net_diff_dst
        // auto net_output = pool_user_dst_memory.get_data_handle();
        // ..user updates net_diff_dst using net_output...
        // some user defined func update_diff_dst(net_diff_dst.data(),
        // net_output)
        for (size_t i = 0; i < net_bwd.size(); ++i)
            net_bwd.at(i).execute(s, net_bwd_args.at(i));
        // update weights and bias using diff weights and bias
        //
        // auto net_diff_weights
        //     = conv_user_diff_weights_memory.get_data_handle();
        // auto net_diff_bias = conv_diff_bias_memory.get_data_handle();
        //
        // ...user updates weights and bias using diff weights and bias...
        //
        // some user defined func update_weights(conv_weights.data(),
        // conv_bias.data(), net_diff_weights, net_diff_bias);
        --n_iter;
    }
    s.wait();
}
int main(int argc, char **argv) {
    return handle_example_errors(simple_net, parse_engine_kind(argc, argv));
}