https://github.com/Microsoft/CNTK
Raw File
Tip revision: a7cfb7bce52880e55d8e8eb7a0ce60e31dddface authored by Vadim Mazalov on 01 October 2018, 18:27:25 UTC
Nan log
Tip revision: a7cfb7b
SGD.cpp
//
// Copyright (c) Microsoft. All rights reserved.
// Copyright (c) 2016-2017, NVIDIA CORPORATION. All rights reserved.
// Licensed under the MIT license. See LICENSE.md file in the project root for full license information.
//
// SGD.cpp -- implements SGD with all bells and whistles, parallelization, randomization, etc.
//

#define _CRT_SECURE_NO_WARNINGS // "secure" CRT not available on all platforms  --add this at the top of all CPP files that give "function or variable may be unsafe" warnings

#include "Basics.h"
#include "SGD.h"
#include "NonlinearityNodes.h"   // for DropoutNode
#include "SpecialPurposeNodes.h" // for SequenceWithSoftmaxNode
#include "DataReaderHelpers.h"
#include "MatrixQuantizerImpl.h"
#include "InputAndParamNodes.h"
#include "AccumulatorAggregation.h"

#ifdef CNTK_PARALLEL_TRAINING_SUPPORT
//static inline bool operator==(const std::pair<double,size_t>& a, double b) { assert(b==0); return a.first == b; }
// ^^ workaround until this line in AggregateGradientsImpl() gets updated: assert(headerCPU->evalErrors[i] == 0);
#include "AllReduceDistGradAggregator.h"

#include "BlockMomentumSGD.h"
#include "V2BlockMomentumSGD.h"

#include "V2AllReduceDistGradAggregator.h"
#endif

#include "ASGDHelper.h"

#include "CNTKLibraryInternals.h"
#include "SimpleDistGradAggregator.h"
#include "V2SimpleDistGradAggregator.h"
#include "ProgressTracing.h"
#include "PerformanceProfiler.h"

#include <map>
#include <set>

namespace Microsoft
{
namespace MSR
{
namespace CNTK
{

using namespace std;

// =======================================================================
// class SGD
// =======================================================================

template SGD<float>::SGD(const ConfigParameters&);
template SGD<double>::SGD(const ConfigParameters&);
template SGD<float>::SGD(const ScriptableObjects::IConfigRecord&);
template SGD<double>::SGD(const ScriptableObjects::IConfigRecord&);

// -----------------------------------------------------------------------
// Train() -- perform a multi-epoch training end-to-end with checkpointing
// -----------------------------------------------------------------------

template <class ElemType>
void SGD<ElemType>::Train(shared_ptr<ComputationNetwork> net, DEVICEID_TYPE deviceId,
                          IDataReader* trainSetDataReader,
                          IDataReader* validationSetDataReader, int startEpoch, bool loadNetworkFromCheckpoint)
{
    // log the device we are computing on
    LOGPRINTF(stderr, "\nModel has %d nodes. Using ", (int) net->GetTotalNumberOfNodes());
    if (net->GetDeviceId() < 0)
        fprintf(stderr, "CPU.\n");
    else
        fprintf(stderr, "GPU %d.\n", (int) net->GetDeviceId());

    // TODO: BUGBUG: if not starting from checkpoint, need to synchronize initial model
    // strategy should be to run the initializer above on mpiRank==0, and then broadcast parameters.

    startEpoch = max(startEpoch, 0);
    m_needAdaptRegularization = false;

    // set tracing flags
    net->EnableNodeTracing(m_traceNodeNamesReal, m_traceNodeNamesCategory, m_traceNodeNamesSparse);

    TrainOrAdaptModel(startEpoch, net, loadNetworkFromCheckpoint, net, nullptr, trainSetDataReader, validationSetDataReader);
}

// -----------------------------------------------------------------------
// Adapt() -- similar to Train(), but for purpose of adapting
// -----------------------------------------------------------------------

template <class ElemType>
void SGD<ElemType>::Adapt(wstring origModelFileName, wstring refNodeName,
                          IDataReader* trainSetDataReader,
                          IDataReader* validationSetDataReader,
                          const DEVICEID_TYPE deviceId, const bool makeMode)
{
    int startEpoch = DetermineStartEpoch(makeMode);
    if (startEpoch == m_maxEpochs)
    {
        LOGPRINTF(stderr, "No further training is necessary.\n");
        return;
    }

    ComputationNetworkPtr net;
    bool networkLoadedFromCheckpoint = false;
    if (startEpoch >= 0)
    {
        wstring modelFileName = GetModelNameForEpoch(int(startEpoch) - 1);
        LOGPRINTF(stderr, "Starting from checkpoint. Loading network from '%ls'.\n", modelFileName.c_str());
        net = ComputationNetwork::CreateFromFile<ElemType>(deviceId, modelFileName);
        networkLoadedFromCheckpoint = true;
    }
    else
    {
        LOGPRINTF(stderr, "Load Network From the original model file %ls.\n", origModelFileName.c_str());
        net = ComputationNetwork::CreateFromFile<ElemType>(deviceId, origModelFileName);
    }

    startEpoch = max(startEpoch, 0);

    ComputationNetworkPtr refNet;
    m_needAdaptRegularization = m_adaptationRegType != AdaptationRegType::None && m_adaptationRegWeight > 0;
    if (m_needAdaptRegularization)
    {
        LOGPRINTF(stderr, "Load reference Network From the original model file %ls.\n", origModelFileName.c_str());
        refNet = ComputationNetwork::CreateFromFile<ElemType>(deviceId, origModelFileName);
    }

    ComputationNodeBasePtr refNode;
    if (m_needAdaptRegularization && m_adaptationRegType == AdaptationRegType::KL)
    {
        LOGPRINTF(stderr, "Checking refNodeName %ls.\n", origModelFileName.c_str());
        if (refNodeName == L"")
            InvalidArgument("refNodeName does not exist and is needed when adaptationRegType is KL.");
        refNode = refNet->GetNodeFromName(refNodeName);
    }

    TrainOrAdaptModel(startEpoch, net, networkLoadedFromCheckpoint, refNet, refNode, trainSetDataReader, validationSetDataReader);
}

// -----------------------------------------------------------------------
// TrainOrAdaptModel() -- main training end-to-end, given a start model
// -----------------------------------------------------------------------

static double MomentumPerMB(double momentumPerSample, size_t minibatchSize);

// Loops through criteria (i.e. score) and updates the best one if smaller value is found.
static void UpdateBestEpochs(
    const vector<EpochCriterion>& vScore,
    const vector<wstring>& cvSetTrainAndEvalNodes,
    const int epoch,
    map<wstring, BestEpoch>& criteriaBestEpoch)
{
    for (size_t i = 0; i < vScore.size(); ++i)
    {
        BestEpoch& nodeBestEpoch = criteriaBestEpoch.at(cvSetTrainAndEvalNodes[i]);
        if (vScore[i].Average() < nodeBestEpoch.criterionMinValue)
        {
            nodeBestEpoch.criterionMinValue = vScore[i].Average();
            nodeBestEpoch.epochIndex = epoch;
        }
    }
    LOGPRINTF(stderr, "Best epoch per criterion so far: [Validate] ");
    for (size_t i = 0; i < cvSetTrainAndEvalNodes.size(); ++i)
    {
        const BestEpoch& bestEpoch = criteriaBestEpoch.at(cvSetTrainAndEvalNodes[i]);
        fprintf(
            stderr,
            "%ls = %f (Epoch %d)",
            cvSetTrainAndEvalNodes[i].c_str(),
            bestEpoch.criterionMinValue,
            bestEpoch.epochIndex + 1); // In actual loop epochs are 0 indexed but all outputs use 1 indexed.
        if (i + 1 < cvSetTrainAndEvalNodes.size())
            fprintf(stderr, "; ");
    }
    fprintf(stderr, "\n");
}

// For each criterion copies the best epoch to the new file with criterion name appended.
template <class ElemType>
static void CopyBestEpochs(
    const map<wstring, BestEpoch>& criteriaBestEpoch, const SGD<ElemType>& sgd, const int lastEpoch)
{
    const wstring& modelBaseName = sgd.GetModelNameForEpoch(lastEpoch);

    for (const auto& bestEpoch : criteriaBestEpoch)
    {
        const wstring modelCriterionName = modelBaseName + L"_" + bestEpoch.first;
        const wstring modelEpochName = sgd.GetModelNameForEpoch(bestEpoch.second.epochIndex);
        copyOrDie(modelEpochName, modelCriterionName);
        LOGPRINTF(
            stderr,
            "Best epoch for criterion '%ls' is %d and model %ls copied to %ls\n",
            bestEpoch.first.c_str(),
            bestEpoch.second.epochIndex + 1, // In actual loop epochs are 0 indexed but all outputs use 1 indexed.
            modelEpochName.c_str(),
            modelCriterionName.c_str());
    }
}

template <class ElemType>
void SGD<ElemType>::TrainOrAdaptModel(int startEpoch, ComputationNetworkPtr net,
                                      bool networkLoadedFromCheckpoint,
                                      ComputationNetworkPtr refNet,
                                      ComputationNodeBasePtr refNode,
                                      IDataReader* trainSetDataReader,
                                      IDataReader* validationSetDataReader)
{
    let& criterionNodes = GetTrainCriterionNodes(net);

    fprintf(stderr, "\n");
    if (criterionNodes.size() == 1)
    {
        LOGPRINTF(stderr, "Training criterion:   %ls = %ls\n", criterionNodes.front()->NodeName().c_str(), criterionNodes.front()->OperationName().c_str());
    }
    else
    {
        LOGPRINTF(stderr, "Training criteria:\n");
        for (const auto& node : criterionNodes)
        {
            LOGPRINTF(stderr, "\t%ls = %ls\n", node->NodeName().c_str(), node->OperationName().c_str());
        }
        if (criterionNodes.empty())
        {
            LOGPRINTF(stderr, "\t(none)\n");
            InvalidArgument("TrainOrAdaptModel: No criterion node was specified.");
        }
    }

    // This code is only relevant for the new (V2) readers. It exist because of
    // a shortcoming in DecimateMinibatchInPlace, which does not yet work when inputs
    // in the same minibatch have different layouts, which is something only V2 readers can
    // produce.
    if (m_enableDistributedMBReadingNotSpecified && m_mpi != nullptr && !trainSetDataReader->IsLegacyReader())
    {
        // we're running a parallel training with a v2 reader,
        // auto-enable distributed reading
        if (m_traceLevel > 0)
            LOGPRINTF(stderr, "\"distributedMBReading\" is not explicitly specified, defaulting to 'true'.\n");
        m_enableDistributedMBReading = true;
    }

    // determine evaluationNodes from GetEvalCriterionNodes(), ensuring each criterion is only logged once
    std::vector<ComputationNodeBasePtr> evaluationNodes;
    {
        auto originalEvaluationNodes = GetEvalCriterionNodes(net);
        set<ComputationNodeBasePtr> criteriaLogged; // set to make sure we don't double-log criteria
        for (const auto& node : criterionNodes)
            criteriaLogged.insert(node);

        for (const auto& node : originalEvaluationNodes)
            if (criteriaLogged.insert(node).second)
                evaluationNodes.push_back(node);

        if (evaluationNodes.size() == 1)
        {
            LOGPRINTF(stderr, "Evaluation criterion: %ls = %ls\n", evaluationNodes.front()->NodeName().c_str(), evaluationNodes.front()->OperationName().c_str());
        }
        else if (!evaluationNodes.empty())
        {
            fprintf(stderr, "\n");
            LOGPRINTF(stderr, "Evaluation criteria:\n");
            for (const auto& node : evaluationNodes)
            {
                LOGPRINTF(stderr, "\t%ls = %ls\n", node->NodeName().c_str(), node->OperationName().c_str());
            }
        }
    }

    std::vector<ComputationNodeBasePtr> additionalNodesToEvaluate;

    // Do not include the output nodes in the matrix sharing structure when using forward value matrix
    // sharing, since the output nodes are only used for AttemptUtteranceDerivativeFeatures functionality
    // which does not work properly with forward value matrix sharing.
    if (!Globals::ShouldEnableShareNodeValueMatrices())
    {
        auto& outputNodes = net->OutputNodes();
        additionalNodesToEvaluate.insert(additionalNodesToEvaluate.end(), outputNodes.cbegin(), outputNodes.cend());
    }

    auto preComputeNodesList = net->GetNodesRequiringPreComputation();
    additionalNodesToEvaluate.insert(additionalNodesToEvaluate.end(), preComputeNodesList.cbegin(), preComputeNodesList.cend());

    // allocate memory for forward and backward computation
    net->AllocateAllMatrices(evaluationNodes, additionalNodesToEvaluate, criterionNodes[0]); // TODO: use criterionNodes.front() throughout

    // get feature and label nodes into an array of matrices that will be passed to GetMinibatch()
    // TODO: instead, remember the nodes directly, to be able to handle both float and double nodes; current version will crash for mixed networks
    StreamMinibatchInputs* inputMatrices = new StreamMinibatchInputs();
    // TODO: ^^ change to shared_ptr or unique_ptr
    let& featureNodes = net->FeatureNodes();
    let& labelNodes = net->LabelNodes();
    // BUGBUG: ^^ should not get all feature/label nodes, but only the ones referenced in a criterion
    for (size_t pass = 0; pass < 2; pass++)
    {
        auto& nodes = (pass == 0) ? featureNodes : labelNodes;
        for (const auto& node : nodes)
            inputMatrices->AddInput(node->NodeName(), node->ValuePtr(), node->GetMBLayout(), node->GetSampleLayout());
    }

    // get hmm file for sequence training
    bool isSequenceTrainingCriterion = (criterionNodes[0]->OperationName() == L"SequenceWithSoftmax");
    if (isSequenceTrainingCriterion)
    {
        // SequenceWithSoftmaxNode<ElemType>* node = static_cast<SequenceWithSoftmaxNode<ElemType>*>(criterionNodes[0]);
        auto node = dynamic_pointer_cast<SequenceWithSoftmaxNode<ElemType>>(criterionNodes[0]);

        auto hmm = node->gethmm();
        trainSetDataReader->GetHmmData(hmm);
    }

    // used for KLD regularized adaptation. For all other adaptation techniques
    // use MEL to edit the model and using normal training algorithm
    // TODO: Should this be done in SGD::Adapt()?
    // TODO: Redo this leveraging that we now have shared_ptrs. It is probably even OK if both networks share feature nodes.
    // TODO: Then we can also share the MBLayout; which currently is copied by value.
    std::vector<ComputationNodeBasePtr> refFeatureNodes; // we keep the original network's features here
    if (m_needAdaptRegularization && m_adaptationRegType == AdaptationRegType::KL && refNode != nullptr)
    {
        refNet->InvalidateCompiledNetwork(); // prepare to re-compile
        // replace input nodes in ref network by input nodes of the main network
        refFeatureNodes.resize(featureNodes.size());
        for (size_t i = 0; i < featureNodes.size(); i++)
        {
            // we need to keep this info to undo this later
            // TODO: After the change to shared_ptrs, this may no longer be necessary.
            refFeatureNodes[i] = refNet->GetNodeFromName(featureNodes[i]->NodeName()); // remember so that we can restore them later
            refNet->ReplaceNode(featureNodes[i]->NodeName(), featureNodes[i]);
        }
        //const_cast<MBLayoutPtr&>(refNet->GetMBLayoutPtrOfNetwork()) = net->GetMBLayoutPtrOfNetwork(); // WORKAROUND
        refNet->CompileNetwork();

        // allocate memory for forward computation
        refNet->AllocateAllMatrices({refNode}, {}, nullptr);
    }

    // initializing weights and gradient holder
    // only one criterion so far TODO: support multiple ones?
    auto& learnableNodes = net->LearnableParameterNodes(criterionNodes[0]);
    list<Matrix<ElemType>> smoothedGradients;
    vector<double> smoothedCounts; // currently used by FSAdaGradUpdate()
    size_t numParameters = 0;

    vector<wstring> nodesToUpdateDescriptions; // for logging only
    for (auto nodeIter = learnableNodes.begin(); nodeIter != learnableNodes.end(); nodeIter++)
    {
        ComputationNodePtr node = dynamic_pointer_cast<ComputationNode<ElemType>>(*nodeIter);
        // Note: We don't actually need the smoothedGradients if !IsParameterUpdateRequired().
        // However, this is hard to fix since lots of code assumes smoothedGradients to be in the same order as learnableNodes.
        // V2 API fixes this.
        smoothedGradients.push_back(Matrix<ElemType>(node->Value().GetNumRows(),
                                                     node->Value().GetNumCols(),
                                                     net->GetDeviceId()));
        smoothedCounts.push_back(0);
        if (node->IsParameterUpdateRequired())
        {
            nodesToUpdateDescriptions.push_back(node->NodeDescription() + L" : [" + Microsoft::MSR::CNTK::ToFixedWStringFromMultiByte(string(node->GetSampleLayout())) + L"]");
            numParameters += node->GetSampleLayout().GetNumElements();
        }
    }
    size_t numNeedsGradient = 0;
    for (let node : net->GetEvalOrder(criterionNodes[0]))
    {
        if (node->NeedsGradient())
            numNeedsGradient++;
    }
    fprintf(stderr, "\n");
    LOGPRINTF(stderr, "Training %.0f parameters in %d ",
              (double) numParameters, (int) nodesToUpdateDescriptions.size());
    if (m_traceLevel == 0)
        fprintf(stderr, "parameter tensors.\n");
    else
    {
        fprintf(stderr, "out of %d parameter tensors and %d nodes with gradient:\n\n",
                (int) learnableNodes.size(), (int) numNeedsGradient);
        for (let nodeDescription : nodesToUpdateDescriptions)
        {
            LOGPRINTF(stderr, "\t%ls\n", nodeDescription.c_str());
        }
    }

    // one blank line before training progress log
    fprintf(stderr, "\n");

    double avgCriterion, lrControlCriterion;
    lrControlCriterion = avgCriterion = numeric_limits<double>::infinity();
    size_t epochsNotCountedInAvgCriterion = startEpoch % m_learnRateAdjustInterval;

    std::vector<wstring> evalNodeNames;
    for (size_t i = 0; i < evaluationNodes.size(); i++)
        evalNodeNames.push_back(evaluationNodes[i]->NodeName());

    double learnRatePerSample = 0.5f / m_mbSize[startEpoch];

    double learningRateAdjustmentFactor = 1.0f;
    vector<double> prevLearnRates;
    prevLearnRates.resize(m_numPrevLearnRates);
    for (int i = 0; i < m_numPrevLearnRates; i++)
        prevLearnRates[i] = -1.0;

    m_prevChosenMinibatchSize = m_mbSize[startEpoch];

    int currentNumGradientBits = 0; // this remembers the last #gradient bits we set for dataParallelSGD (init val 0 has no meaning, just keep compiler happy)
    if (GetParallelizationMethod() == ParallelizationMethod::dataParallelSGD)
    {
        currentNumGradientBits = m_numGradientBits[startEpoch]; // remember so that we can detect a change
        InitDistGradAgg(evaluationNodes.size(), currentNumGradientBits, net->GetDeviceId(), m_traceLevel);
    }
    else if (GetParallelizationMethod() == ParallelizationMethod::modelAveragingSGD ||
             GetParallelizationMethod() == ParallelizationMethod::blockMomentumSGD)
    {
        InitModelAggregationHandler(m_syncStatsTrace, net->GetDeviceId());
    }

    // precompute mean and invStdDev nodes and save initial model
    // When no precompute, only save if we did not load the model from a
    // checkpoint but instead built it from a network description
    if (PreCompute(net, trainSetDataReader, featureNodes, labelNodes, inputMatrices) || !networkLoadedFromCheckpoint)
    {
        // Synchronize all ranks before writing the model to ensure that
        // everyone is done loading the model
        if (m_mpi != nullptr)
        {
            m_mpi->WaitAll();
        }

        // In case of parallel training only the main node should we saving the model to prevent
        // the parallel training nodes from colliding to write the same file
        if ((m_mpi == nullptr) || m_mpi->IsMainNode())
            net->Save(GetModelNameForEpoch(int(startEpoch) - 1));
    }

    if (m_saveBestModelPerCriterion)
    {
        m_criteriaBestEpoch.clear();
        if (!criterionNodes.empty())
        {
            m_criteriaBestEpoch.emplace(criterionNodes[0]->NodeName(), BestEpoch());
        }
        for (const ComputationNodeBasePtr& node : evaluationNodes)
        {
            m_criteriaBestEpoch.emplace(node->NodeName(), BestEpoch());
        }
    }

    size_t totalTrainingSamplesSeen = 0; // aggregated over all epochs, for logging purposes only
    size_t totalMBsSeen = 0;

    bool learnRateInitialized = false;
    double prevCriterion = numeric_limits<double>::infinity();
    if (startEpoch > 0)
    {
        learnRateInitialized = TryLoadCheckPointInfo(startEpoch - 1,
                                                     /*out*/ totalTrainingSamplesSeen,
                                                     /*out*/ learnRatePerSample,
                                                     smoothedGradients,
                                                     smoothedCounts,
                                                     /*out*/ prevCriterion,
                                                     /*out*/ m_prevChosenMinibatchSize);
        if (learnRateInitialized)
            prevLearnRates[startEpoch % m_numPrevLearnRates] = learnRatePerSample;
    }

    if (m_autoLearnRateSearchType == LearningRateSearchAlgorithm::AdjustAfterEpoch &&
        !learnRateInitialized && m_learningRatesParam.size() <= startEpoch)
    {
        InvalidArgument(
            "When using \"AdjustAfterEpoch\", there must either exist a checkpoint file, "
            "or an explicit learning rate must be specified in config for the starting epoch.");
    }

    // TODO this assumes training is picked up with nodes with zero parameters
    double prevDropoutRate = 0;
    double prevNormalizationTimeConstant = 0;
    double prevNormalizationBlendTimeConstant = 0;

    bool learnRateReduced = false;

    // pass user config on memory allocation for convolution operations to the Network
    ComputationNetwork::SetMaxTempMemSizeForCNN(net, criterionNodes[0], m_maxTempMemSizeInSamplesForCNN);
    if (m_needAdaptRegularization && m_adaptationRegType == AdaptationRegType::KL && refNode)
    {
        ComputationNetwork::SetMaxTempMemSizeForCNN(refNet, refNode, m_maxTempMemSizeInSamplesForCNN);
    }

    // likewise for sequence training parameters
    if (isSequenceTrainingCriterion)
    {
        ComputationNetwork::SetSeqParam<ElemType>(net, criterionNodes[0], m_hSmoothingWeight, m_frameDropThresh, m_doReferenceAlign,
                                                  m_seqGammarCalcAMF, m_seqGammarCalcLMF, m_seqGammarCalcWP, m_seqGammarCalcbMMIFactor, m_seqGammarCalcUsesMBR);
    }

    // Multiverso Warpper for ASGD logic init
    if (m_parallelizationMethod == ParallelizationMethod::dataParallelASGD)
    {
        m_pASGDHelper.reset(NewASGDHelper<ElemType>(learnableNodes,
                                                    m_mpi->NumNodesInUse(),
                                                    m_isAsyncBufferEnabled,
                                                    m_isSimulateMA,
                                                    m_adjustLearningRateAtBeginning,
                                                    m_adjustCoefficient,
                                                    m_adjustPerMinibatches,
                                                    m_traceLevel,
                                                    m_syncStatsTrace));
        m_pASGDHelper->InitModel(learnableNodes);
    }

    // Create TensorBoard writer if needed. When using parallel training, make sure that only Rank 0 actually writes logs.
    ::CNTK::Internal::TensorBoardFileWriterPtr tensorBoardWriter;
    if (!m_tensorBoardLogDir.empty() && (m_mpi == nullptr || m_mpi->CurrentNodeRank() == 0))
    {
        tensorBoardWriter = make_shared<::CNTK::Internal::TensorBoardFileWriter>(m_tensorBoardLogDir, net);
    }

    // --- MAIN EPOCH LOOP
    for (int i = startEpoch; i < (int) m_maxEpochs; i++) // TODO: why is this an int, and not a size_t?
    {
        // Always skip the first epoch for profiling to avoid startup behavior.
        // This has effect only if the profiler is globally enabled (profilerEnabled="true" in the config).
        if (i > startEpoch)
        {
            ProfilerEnable(true);
        }

        // Synchronize all ranks before proceeding to ensure that
        // rank 0 has finished writing the previous model file
        SynchronizeWorkers();

        // (re-)initialize 1-bit SGD
        if (GetParallelizationMethod() == ParallelizationMethod::dataParallelSGD &&
            currentNumGradientBits != m_numGradientBits[i])
        {
            currentNumGradientBits = m_numGradientBits[i];
            InitDistGradAgg(evaluationNodes.size(), currentNumGradientBits, net->GetDeviceId(), m_traceLevel);
        }

        Timer timer;
        timer.Start();

        // set dropout rate for this epoch
        // We use the same seed across workers until parallel training kicks in to ensure that the workers have identical models
        size_t parallelWorkerIdx = ((m_mpi == nullptr) || !UsingParallelTrain(i)) ? 0 : m_mpi->CurrentNodeRank();
        size_t randSeedBase = (parallelWorkerIdx * m_maxEpochs) + i;
        ComputationNetwork::SetDropoutRate(net, criterionNodes[0], m_dropoutRates[i], prevDropoutRate);
        ComputationNetwork::SetIRngUserSeed(net, criterionNodes[0], randSeedBase);
        ComputationNetwork::SetBatchNormalizationTimeConstants<ElemType>(net, criterionNodes[0],
                                                                         m_batchNormalizationTimeConstant[i], prevNormalizationTimeConstant,
                                                                         m_batchNormalizationBlendTimeConstant[i], prevNormalizationBlendTimeConstant);

        // learning rate adjustment
        if (m_autoLearnRateSearchType == LearningRateSearchAlgorithm::None || i < m_learningRatesParam.size())
        {
            // BUGBUG: GetNumParallelSequences() returns 1 under certain situations; it seems when restarting from checkpoint
            learnRatePerSample = GetLearningRatePerSample(i /*BUGBUG workaround:*/, trainSetDataReader->GetNumParallelSequencesForFixingBPTTMode());
        }
        else if (m_autoLearnRateSearchType == LearningRateSearchAlgorithm::SearchBeforeEpoch)
        {
            double largestPrevLearnRatePerSample = prevLearnRates[0];
            for (int j = 1; j < m_numPrevLearnRates; j++)
            {
                largestPrevLearnRatePerSample = max(largestPrevLearnRatePerSample, prevLearnRates[j]);
            }

            // return a reasonable learning rate based on the initial minibatchSize
            double newLearningRatePerSample = SearchForBestLearnRate(net, refNet, refNode, i, learnRatePerSample,
                                                                     trainSetDataReader, featureNodes, labelNodes,
                                                                     criterionNodes, evaluationNodes, inputMatrices,
                                                                     learnableNodes, smoothedGradients, smoothedCounts,
                                                                     learnRateInitialized, largestPrevLearnRatePerSample);
            learningRateAdjustmentFactor = newLearningRatePerSample / learnRatePerSample;
            learnRatePerSample = newLearningRatePerSample;

            // save per sample learn rate to support changeable minibatchSize
            prevLearnRates[i % m_numPrevLearnRates] = learnRatePerSample;
        }

        learnRateInitialized = true;

        if (learnRatePerSample < m_minLearnRate)
        {
            LOGPRINTF(stderr, "Learn Rate Per Sample for Epoch[%d] = %.8g is less than minLearningRatePerSample %.8g. Training complete.\n",
                      i + 1, learnRatePerSample, m_minLearnRate);
            if (m_autoLearnRateSearchType != LearningRateSearchAlgorithm::None)
            {
                // In case of parallel training only the main node should we saving the model to prevent
                // the parallel training nodes from colliding to write the same file
                if ((m_mpi == nullptr) || m_mpi->IsMainNode())
                    net->Save(m_modelPath);
            }
            break;
        }

        size_t chosenMinibatchSize;
        size_t actualMinibatchSize;

        // Through the command line or config file the user can set minibatch sizes on a per epoch
        // basis for a set number of epochs.  For epochs after that point, m_mbSize.size(), either
        // we just keep using
        // the last minibatch size, or we use tuning to try and find a better one.
        if (m_autoAdjustMinibatch && i >= m_mbSize.size())
        {
            size_t numFramesToUseInSearch = m_numSamples4Search[i];
            if (m_epochSize != requestDataSize)
            {
                // ensure the numFramesToUseInSearch does not exceed the total number of frames in the epoch
                numFramesToUseInSearch = min(numFramesToUseInSearch, m_epochSize);
            }

            // Use tuning to try and find a better minibatch size
            chosenMinibatchSize = AdaptiveMinibatchSizing(net, refNet, refNode, i,
                                                          numFramesToUseInSearch,
                                                          trainSetDataReader, learnRatePerSample,
                                                          m_mbSize[i], featureNodes, labelNodes,
                                                          criterionNodes, evaluationNodes,
                                                          inputMatrices, learnableNodes,
                                                          smoothedGradients, smoothedCounts, learningRateAdjustmentFactor);
            if (m_traceLevel < 1 && chosenMinibatchSize != m_prevChosenMinibatchSize)
                LOGPRINTF(stderr, "Minibatch size adapted to %d.\n", (int) chosenMinibatchSize);
            m_prevChosenMinibatchSize = chosenMinibatchSize;
        }
        else
        {
            // use the explicitly set minibatch size
            chosenMinibatchSize = m_mbSize[i];
        }

        // For legacy readers, in BPTT mode the minibatch size was not the real minibatch size but truncation.
        // Because of that we have to fix up the real minibatch size multiplying the number of parallel sequences by the truncation length.
        // This is not require any more for the new readers.
        if (trainSetDataReader->IsLegacyReader())
            actualMinibatchSize = FixUpEffectiveMBSize(chosenMinibatchSize /*BUGBUG workaround:*/, trainSetDataReader->GetNumParallelSequencesForFixingBPTTMode());
        else
            actualMinibatchSize = chosenMinibatchSize;

        double momentumPerSample = GetMomentumPerSample(i /*BUGBUG workaround:*/, trainSetDataReader->GetNumParallelSequencesForFixingBPTTMode());
        // time constant = number of samples after which a contribution has been reduced to e^-1
        double momentumAsTimeConstant = momentumPerSample == 0.0
                                            ? 0.0
                                            : momentumPerSample >= 1.0
                                                  ? 0.0
                                                  : -1.0 / log(momentumPerSample);
        if (m_traceLevel > 0)
        {
            fprintf(stderr, "\n");
            LOGPRINTF(stderr, "Starting Epoch %d: learning rate per sample = %f  effective momentum = %f  momentum as time constant = %.1f samples\n",
                      i + 1, learnRatePerSample, MomentumPerMB(momentumPerSample, actualMinibatchSize), momentumAsTimeConstant);
        }

        EpochCriterion epochCriterion; // criterion values are returned in this
        std::vector<EpochCriterion> epochEvalErrors(evaluationNodes.size());
        totalMBsSeen += TrainOneEpoch(net,
                                      refNet,
                                      refNode,
                                      i,
                                      m_epochSize,
                                      trainSetDataReader,
                                      learnRatePerSample,
                                      chosenMinibatchSize,
                                      featureNodes,
                                      labelNodes,
                                      criterionNodes,
                                      evaluationNodes,
                                      inputMatrices,
                                      learnableNodes, smoothedGradients, smoothedCounts,
                                      epochCriterion, epochEvalErrors,
                                      "", SIZE_MAX, totalMBsSeen, tensorBoardWriter, startEpoch);
        totalTrainingSamplesSeen += epochCriterion.second; // aggregate #training samples, for logging purposes only

        timer.Stop();
        double epochTime = timer.ElapsedSeconds();

        if (m_useEvalCriterionControlLR && epochEvalErrors.size() > 0)
            lrControlCriterion = epochEvalErrors[0].Average();
        else
            lrControlCriterion = epochCriterion.Average();

        LOGPRINTF(stderr, "Finished Epoch[%2d of %d]: [Training] ", i + 1, (int) m_maxEpochs);
        epochCriterion.LogCriterion(criterionNodes[0]->NodeName());

        m_lastFinishedEpochTrainLoss = epochCriterion.Average();
        for (size_t j = 0; j < epochEvalErrors.size(); j++)
            epochEvalErrors[j].LogCriterion(evaluationNodes[j]->NodeName());
        fprintf(stderr, "totalSamplesSeen = %zu; learningRatePerSample = %.8g; epochTime=%.6gs\n", totalTrainingSamplesSeen, learnRatePerSample, epochTime);
#if 0
        // TODO: This was only printed if >1 eval criterion. Why? Needed?
        LOGPRINTF(stderr, "Finished Epoch[%2d of %d]:     Criterion Node [%ls] Per Sample = %.8g\n",
            i + 1, (int)m_maxEpochs, criterionNodes[0]->NodeName().c_str(), epochCriterion.Average());

        for (size_t j = 0; j < epochEvalErrors.size(); j++)
        {
            LOGPRINTF(stderr, "Finished Epoch[%2d of %d]:     Evaluation Node [%ls] Per Sample = %.8g\n",
                i + 1, (int) m_maxEpochs, evalNodeNames[j].c_str(), epochEvalErrors[j].Average());
        }
#endif

        if (tensorBoardWriter)
        {
            tensorBoardWriter->WriteValue(L"summary/" + criterionNodes[0]->NodeName(), (float) epochCriterion.Average(), i + 1);
            for (size_t j = 0; j < epochEvalErrors.size(); j++)
            {
                tensorBoardWriter->WriteValue(L"summary/" + evaluationNodes[0]->NodeName(), (float) epochEvalErrors[j].Average(), i + 1);
            }

            tensorBoardWriter->Flush();
        }

        if (validationSetDataReader != trainSetDataReader && validationSetDataReader != nullptr)
        {
            // TODO(dataASGD) making evaluator becoming nondistributed one when using ASGD, since Multiverso has another background thread using MPI.
            //                Making the evaluation serial (non-distributed) will slowdown training especially when validation set is large.
            SimpleEvaluator<ElemType> evalforvalidation(net, UsingAsyncGradientAggregation(i + 1) ? nullptr : m_mpi, m_enableDistributedMBReading);
            vector<wstring> cvSetTrainAndEvalNodes;
            if (criterionNodes.size() > 0)
            {
                cvSetTrainAndEvalNodes.push_back(criterionNodes[0]->NodeName());
            }
            for (let node : evaluationNodes)
            {
                cvSetTrainAndEvalNodes.push_back(node->NodeName());
            }

            // BUGBUG: We should not use the training MB size. The training MB size is constrained by both convergence and memory. Eval is only constrained by memory.
            let vScore = evalforvalidation.Evaluate(validationSetDataReader, cvSetTrainAndEvalNodes, UsingAsyncGradientAggregation(i + 1) ? m_mbSize[i] / m_mpi->NumNodesInUse() : m_mbSize[i]);
            LOGPRINTF(stderr, "Finished Epoch[%2d of %d]: [Validate] ", i + 1, (int) m_maxEpochs);
            for (size_t k = 0; k < vScore.size() /*&& k < 2*/; k++)
                vScore[k].LogCriterion(cvSetTrainAndEvalNodes[k], /*addSemicolon=*/k + 1 < vScore.size());
            //fprintf(stderr, "%s %ls = %.8f * %d", k ? ";" : "", cvSetTrainAndEvalNodes[k].c_str(), vScore[k].Average(), (int)vScore[k].second);
            fprintf(stderr, "\n");

            if (tensorBoardWriter)
            {
                for (size_t k = 0; k < vScore.size(); k++)
                {
                    tensorBoardWriter->WriteValue(L"summary/test_" + cvSetTrainAndEvalNodes[k], (float) vScore[k].Average(), i + 1);
                }

                tensorBoardWriter->Flush();
            }

            if (m_saveBestModelPerCriterion)
            {
                // Loops through criteria (i.e. score) and updates the best one if smaller value is found.
                UpdateBestEpochs(vScore, cvSetTrainAndEvalNodes, i, m_criteriaBestEpoch);
            }

            if (m_useCVSetControlLRIfCVExists)
            {
                if (m_useEvalCriterionControlLR && vScore.size() > 1)
                    lrControlCriterion = vScore[1].Average(); // use the first of possibly multiple eval criteria
                else
                    lrControlCriterion = vScore[0].Average(); // the first one is the training criterion
            }
        }

        // broadcast epochCriterion to make sure each processor will have the same learning rate schedule
        if ((GetParallelizationMethod() == ParallelizationMethod::modelAveragingSGD ||
             GetParallelizationMethod() == ParallelizationMethod::blockMomentumSGD) &&
            (m_mpi->NumNodesInUse() > 1))
        {
            m_mpi->Bcast(&epochCriterion.first, 1, m_mpi->MainNodeRank());
            m_mpi->Bcast(&epochCriterion.second, 1, m_mpi->MainNodeRank());
            m_mpi->Bcast(&lrControlCriterion, 1, m_mpi->MainNodeRank());
        }

        bool loadedPrevModel = false;
        size_t epochsSinceLastLearnRateAdjust = i % m_learnRateAdjustInterval + 1;
        if (avgCriterion == numeric_limits<double>::infinity())
        {
            avgCriterion = lrControlCriterion;
        }
        else
        {
            avgCriterion = ((epochsSinceLastLearnRateAdjust - 1 - epochsNotCountedInAvgCriterion) *
                                avgCriterion +
                            lrControlCriterion) /
                           (epochsSinceLastLearnRateAdjust - epochsNotCountedInAvgCriterion);
        }

        if (m_autoLearnRateSearchType == LearningRateSearchAlgorithm::AdjustAfterEpoch &&
            m_learningRatesParam.size() <= i && epochsSinceLastLearnRateAdjust == m_learnRateAdjustInterval)
        {
            if (std::isnan(avgCriterion) || (prevCriterion - avgCriterion < 0 && prevCriterion != numeric_limits<double>::infinity()))
            {
                if (m_loadBestModel)
                {
                    // roll back
                    auto bestModelPath = GetModelNameForEpoch(i - m_learnRateAdjustInterval);
                    LOGPRINTF(stderr, "Loading (rolling back to) previous model with best training-criterion value: %ls.\n", bestModelPath.c_str());
                    net->RereadPersistableParameters<ElemType>(bestModelPath);
                    LoadCheckPointInfo(i - m_learnRateAdjustInterval,
                                       /*out*/ totalTrainingSamplesSeen,
                                       /*out*/ learnRatePerSample,
                                       smoothedGradients,
                                       smoothedCounts,
                                       /*out*/ prevCriterion,
                                       /*out*/ m_prevChosenMinibatchSize);
                    loadedPrevModel = true;
                }
            }

            if (m_continueReduce)
            {
                if (std::isnan(avgCriterion) ||
                    (prevCriterion - avgCriterion <= m_reduceLearnRateIfImproveLessThan * prevCriterion &&
                     prevCriterion != numeric_limits<double>::infinity()))
                {
                    if (learnRateReduced == false)
                    {
                        learnRateReduced = true;
                    }
                    else
                    {
                        // In case of parallel training only the main node should we saving the model to prevent
                        // the parallel training nodes from colliding to write the same file
                        if ((m_mpi == nullptr) || m_mpi->IsMainNode())
                            net->Save(GetModelNameForEpoch(i, true));

                        LOGPRINTF(stderr, "Finished training and saved final model\n\n");
                        break;
                    }
                }

                if (learnRateReduced)
                {
                    learnRatePerSample *= m_learnRateDecreaseFactor;
                    LOGPRINTF(stderr, "learnRatePerSample reduced to %.8g\n", learnRatePerSample);
                }
            }
            else
            {
                if (std::isnan(avgCriterion) ||
                    (prevCriterion - avgCriterion <= m_reduceLearnRateIfImproveLessThan * prevCriterion &&
                     prevCriterion != numeric_limits<double>::infinity()))
                {

                    learnRatePerSample *= m_learnRateDecreaseFactor;
                    LOGPRINTF(stderr, "learnRatePerSample reduced to %.8g\n", learnRatePerSample);
                }
                else if (prevCriterion - avgCriterion > m_increaseLearnRateIfImproveMoreThan * prevCriterion &&
                         prevCriterion != numeric_limits<double>::infinity())
                {
                    learnRatePerSample *= m_learnRateIncreaseFactor;
                    LOGPRINTF(stderr, "learnRatePerSample increased to %.8g\n", learnRatePerSample);
                }
            }
        }
        else
        {
            if (std::isnan(avgCriterion))
            {
                wstring w = msra::strfun::wstrprintf(L"%ls.%ls", m_modelPath.c_str(), "debug");
                // m_modelPath = m_modelPath + L "debug"
                fprintf(stderr, "Saving model for debugging to:%ls", w.c_str());
                net->Save(w);
                RuntimeError("The2 training is not a number (NAN).");
            }

            // not loading previous values then set them
            if (!loadedPrevModel && epochsSinceLastLearnRateAdjust == m_learnRateAdjustInterval)
            {
                prevCriterion = avgCriterion;
                epochsNotCountedInAvgCriterion = 0;
            }

            // Synchronize all ranks before proceeding to ensure that
            // nobody tries reading the checkpoint file at the same time
            // as rank 0 deleting it below
            SynchronizeWorkers();

            // Persist model and check-point info
            if ((m_mpi == nullptr) || m_mpi->IsMainNode())
            {
                if (loadedPrevModel)
                {
                    // If previous best model is loaded, we will first remove epochs that lead to worse results
                    for (int j = 1; j < m_learnRateAdjustInterval; j++)
                    {
                        int epochToDelete = i - j;
                        LOGPRINTF(stderr, "SGD: removing model and checkpoint files for epoch %d after rollback to epoch %lu\n", epochToDelete + 1, (unsigned long) (i - m_learnRateAdjustInterval) + 1); // report 1 based epoch number
                        _wunlink(GetModelNameForEpoch(epochToDelete).c_str());
                        _wunlink(GetCheckPointFileNameForEpoch(epochToDelete).c_str());
                    }

                    // Set i back to the loaded model
                    i -= m_learnRateAdjustInterval;
                    LOGPRINTF(stderr, "SGD: revoke back to and update checkpoint file for epoch %d\n", i + 1); // report 1 based epoch number
                    SaveCheckPointInfo(
                        i,
                        totalTrainingSamplesSeen,
                        learnRatePerSample,
                        smoothedGradients,
                        smoothedCounts,
                        prevCriterion,
                        chosenMinibatchSize);
                }
                else
                {
                    SaveCheckPointInfo(
                        i,
                        totalTrainingSamplesSeen,
                        learnRatePerSample,
                        smoothedGradients,
                        smoothedCounts,
                        prevCriterion,
                        chosenMinibatchSize);
                    auto modelName = GetModelNameForEpoch(i);
                    if (m_traceLevel > 0)
                        LOGPRINTF(stderr, "SGD: Saving checkpoint model '%ls'\n", modelName.c_str());
                    net->Save(modelName);
                    if (!m_keepCheckPointFiles)
                    {
                        // delete previous checkpoint file to save space
                        if (m_autoLearnRateSearchType == LearningRateSearchAlgorithm::AdjustAfterEpoch && m_loadBestModel)
                        {
                            if (epochsSinceLastLearnRateAdjust != 1)
                            {
                                _wunlink(GetCheckPointFileNameForEpoch(i - 1).c_str());
                            }
                            if (epochsSinceLastLearnRateAdjust == m_learnRateAdjustInterval)
                            {
                                _wunlink(GetCheckPointFileNameForEpoch(i - m_learnRateAdjustInterval).c_str());
                            }
                        }
                        else
                        {
                            _wunlink(GetCheckPointFileNameForEpoch(i - 1).c_str());
                        }
                    }
                }
            }
            else
            {
                if (loadedPrevModel)
                {
                    // Set i back to the loaded model
                    i -= m_learnRateAdjustInterval;
                }
            }

            if (learnRatePerSample < 1e-12)
            {
                LOGPRINTF(stderr, "learnRate per sample is reduced to %.8g which is below 1e-12. stop training.\n",
                          learnRatePerSample);
            }
        }
        // --- END OF MAIN EPOCH LOOP

        // Check if we need to save best model per criterion and this is the main node as well.
        if (m_saveBestModelPerCriterion && ((m_mpi == nullptr) || m_mpi->IsMainNode()))
        {
            // For each criterion copies the best epoch to the new file with criterion name appended.
            CopyBestEpochs(m_criteriaBestEpoch, *this, m_maxEpochs - 1);
        }

        // Synchronize all ranks before proceeding to ensure that
        // rank 0 has finished writing the model file
        // TODO[DataASGD]: should othet other rank waiting in async-mode
        SynchronizeWorkers();

        // progress tracing for compute cluster management
        ProgressTracing::TraceProgressPercentage(m_maxEpochs, 0.0, true);
        ProgressTracing::TraceTrainLoss(m_lastFinishedEpochTrainLoss);

        // since we linked feature nodes. we need to remove it from the deletion
        if (m_needAdaptRegularization && m_adaptationRegType == AdaptationRegType::KL && refNode != nullptr)
        {
            for (size_t i = 0; i < refFeatureNodes.size(); i++)
            {
                // note we need to handle deletion carefully
                refNet->ReplaceNode(refFeatureNodes[i]->NodeName(), refFeatureNodes[i]);
            }
        }

        delete inputMatrices;
        if (m_parallelizationMethod == ParallelizationMethod::dataParallelASGD)
            m_pASGDHelper.reset();
    }

    // -----------------------------------------------------------------------
    // TrainOneEpoch() -- train one epoch
    // -----------------------------------------------------------------------

    template <class ElemType>
    size_t SGD<ElemType>::TrainOneEpoch(ComputationNetworkPtr net,
                                        ComputationNetworkPtr refNet,
                                        const ComputationNodeBasePtr& refNode,
                                        const int epochNumber,
                                        const size_t epochSize,
                                        IDataReader* trainSetDataReader,
                                        const double learnRatePerSample,
                                        size_t tunedMBSize,
                                        const std::vector<ComputationNodeBasePtr>& featureNodes,
                                        const std::vector<ComputationNodeBasePtr>& labelNodes,
                                        const std::vector<ComputationNodeBasePtr>& criterionNodes,
                                        const std::vector<ComputationNodeBasePtr>& evaluationNodes,
                                        StreamMinibatchInputs* inputMatrices, // TODO: why is this a pointer?
                                        const std::list<ComputationNodeBasePtr>& learnableNodes,
                                        std::list<Matrix<ElemType>>& smoothedGradients, vector<double>& smoothedCounts,
                                        /*out*/ EpochCriterion& epochCriterion,
                                        /*out*/ std::vector<EpochCriterion>& epochEvalErrors,
                                        const std::string& prefixMsg,
                                        const size_t maxNumberOfSamples,
                                        const size_t totalMBsSeenBefore,
                                        ::CNTK::Internal::TensorBoardFileWriterPtr tensorBoardWriter,
                                        const int startEpoch)
    {
        PROFILE_SCOPE(profilerEvtMainEpoch);

        ScopedNetworkOperationMode modeGuard(net, NetworkOperationMode::training);

        // bring our 'out' values into consistent state
        epochCriterion = EpochCriterion(0);
        epochEvalErrors.assign(epochEvalErrors.size(), EpochCriterion(0));

        double totalTimeInMBs = 0; // use double since timer has sub-microsecond time resolution

        // initialize statistics
        size_t totalEpochSamples = 0;

        int numMBsRun = 0;
        int numMBsRunSinceLastLogged = 0;

        bool useGradientAggregation = UsingGradientAggregation(epochNumber);
        bool useModelAggregation = UsingModelAggregation(epochNumber);
        bool useAsyncGradientAggregation = UsingAsyncGradientAggregation(epochNumber);
        bool useParallelTrain = UsingParallelTrain(epochNumber);

        // Find all evaluation nodes that accumulate error on their own.
        auto evaluationNodesWhichAccumulateResult = net->ExtractNodesWhichAccumulateResult(
            set<ComputationNodeBasePtr>(evaluationNodes.begin(), evaluationNodes.end()));
        auto ContainsAccumulatedResult = [&evaluationNodesWhichAccumulateResult](ComputationNodeBasePtr node) {
            return evaluationNodesWhichAccumulateResult.find(node) != evaluationNodesWhichAccumulateResult.end();
        };

        // MA-related variables
        size_t nSamplesSinceLastModelSync = 0;
        size_t blockSizePerWorker = 0;
        if (useParallelTrain && m_pMASGDHelper)
        {
            m_pMASGDHelper->OnEpochStart(learnableNodes);
            blockSizePerWorker = m_modelAggregationBlockSize / m_mpi->NumNodesInUse();
        }

        std::vector<Matrix<ElemType>*> learnParamsGradients;
        Profiler profiler(m_numMBsToCUDAProfile);

        // resetting this, so profiling is performed for one epoch only
        m_numMBsToCUDAProfile = 0;

        bool useDistributedMBReading = useParallelTrain &&
                                       m_enableDistributedMBReading &&
                                       trainSetDataReader->SupportsDistributedMBRead();
        if (useDistributedMBReading)
        {
            trainSetDataReader->StartDistributedMinibatchLoop(tunedMBSize, epochNumber, m_mpi->CurrentNodeRank(),
                                                              m_mpi->NumNodesInUse(), inputMatrices->GetStreamDescriptions(), epochSize);
        }
        else
        {
            trainSetDataReader->StartMinibatchLoop(tunedMBSize, epochNumber, inputMatrices->GetStreamDescriptions(), epochSize);
        }

        net->StartEvaluateMinibatchLoop(evaluationNodes);
        net->StartEvaluateMinibatchLoop(criterionNodes);
        if (m_needAdaptRegularization && m_adaptationRegType == AdaptationRegType::KL && refNode)
        {
            refNet->StartEvaluateMinibatchLoop(refNode);
        }

        // prepare for sub-minibatching
        // Sub-minibatching is used if a single minibatch is too large to fit into GPU RAM.
        DataReaderHelpers::SubminibatchDispatcher<ElemType> smbDispatcher;
        size_t numSubminibatchesNeeded = DataReaderHelpers::GetNumSubminibatchesNeeded<ElemType>(trainSetDataReader, m_maxSamplesInRAM, m_numSubminiBatches, tunedMBSize);

        // this is non-trivial, we need a manager object to handle this
        if (numSubminibatchesNeeded > 1)
            smbDispatcher.Init(net, learnableNodes, criterionNodes, evaluationNodes);

        // The following is a special feature only supported by the Kaldi2Reader for more efficient sequence training.
        // This attempts to compute the error signal for the whole utterance, which will
        // be fed to the neural network as features. Currently it is a workaround
        // for the two-forward-pass sequence and ctc training, which allows
        // processing more utterances at the same time.
        // TODO: move the two-forward-pass support out of the reader, make a first-class citizen.
        AttemptUtteranceDerivativeFeatures(net, trainSetDataReader, featureNodes, inputMatrices);

        if (m_traceLevel > 0)
        {
            fprintf(stderr, "\n");
            LOGPRINTF(stderr, "Starting minibatch loop");
            if (useGradientAggregation)
            {
                fprintf(stderr, ", DataParallelSGD training (myRank = %d, numNodes = %d, numGradientBits = %d)",
                        (int) m_mpi->CurrentNodeRank(), (int) m_mpi->NumNodesInUse(), (int) m_numGradientBits[epochNumber]);

                if (m_bufferedAsyncGradientAggregation)
                    fprintf(stderr, ", BufferedAsyncGradientAggregation is ENABLED");
            }

            if (useAsyncGradientAggregation)
            {
                fprintf(stderr, ", DataParallelASGD training (myRank = %d, numNodes = %d, SamplesSyncToServer = %d)",
                        (int) m_mpi->CurrentNodeRank(), (int) m_mpi->NumNodesInUse(), (int) m_nSyncSamplesPerWorker[epochNumber]);

                fprintf(stderr, ", Distributed Evaluation is DISABLED");

                if (m_isAsyncBufferEnabled)
                    fprintf(stderr, ", BufferedAsyncGradientAggregation is ENABLED");
            }

            if (useDistributedMBReading)
                fprintf(stderr, ", distributed reading is ENABLED");

            if (numSubminibatchesNeeded > 1)
            {
                if (m_maxSamplesInRAM < SIZE_MAX)
                    fprintf(stderr, ", with maximum %d samples in RAM", (int) m_maxSamplesInRAM);
                else
                    fprintf(stderr, ", with %d subminibatch", (int) numSubminibatchesNeeded);
            }
            fprintf(stderr, ".\n");
        }

        Timer timer;
        timer.Start();

        // NOTE: the following two local matrices are not used in distGradAgg path
        // assume only one training criterion node for each epoch.
        // The criterion values are accumulated here over the minibatches (without having to pull them off the GPU).
        CriterionAccumulator<ElemType> localEpochCriterion(criterionNodes, net->GetDeviceId());
        CriterionAccumulator<ElemType> localEpochEvalErrors(
            evaluationNodes, net->GetDeviceId(),
            {evaluationNodesWhichAccumulateResult.begin(), evaluationNodesWhichAccumulateResult.end()});

        // --- MAIN MINIBATCH LOOP

        // for differential logging, we keep the previous criterion values around
        EpochCriterion epochCriterionLastLogged = epochCriterion;
        vector<EpochCriterion> epochEvalErrorsLastLogged = epochEvalErrors;

        EpochCriterion tensorBoardEpochCriterionLastLogged = epochCriterion;
        vector<EpochCriterion> tensorBoardEpochEvalErrorsLastLogged = epochEvalErrors;

        // NOTE: For ResNet, the regularization in BatchNormalization should be disabled.
        if (m_disableRegInBatchNormalization)
        {
            let bnNodes = net->GetNodesWithType(L"BatchNormalization");
            for (auto& node : bnNodes)
            {
                let bnNode = dynamic_pointer_cast<BatchNormalizationNode<ElemType>>(node);
                bnNode->DisableRegInBatchNormalization();
            }
        }

        // In case adaptive minibatch/learning rates are used, the training can be limited by the maxNumberOfSamples.
        bool maxNumSamplesExceeded = false;
        size_t epochStartSample = 0;
        bool shouldCheckEarlyExit = (maxNumberOfSamples != SIZE_MAX);
        if (shouldCheckEarlyExit)
        {
            // SparsePC, LibSCV and DSS readers do not implement GetCurrentSamplePosition()
            // for those adaptive minibatch size is not supported, thus specifying adaptive
            // minibatch for them will cause an error message.
            epochStartSample = trainSetDataReader->GetCurrentSamplePosition();
        }

        auto forwardPropRoots = evaluationNodes;
        forwardPropRoots.push_back(criterionNodes[0]);

        bool noMoreSamplesToProcess = false;
        bool isFirstMinibatch = true;
        for (;;)
        {
            auto profMinibatch = ProfilerTimeBegin();

            // get minibatch
            // TODO: is it guaranteed that the GPU is already completed at this point, is it safe to overwrite the buffers?
            size_t actualMBSize = 0;

            auto profGetMinibatch = ProfilerTimeBegin();
            bool wasDataRead = DataReaderHelpers::GetMinibatchIntoNetwork<ElemType>(*trainSetDataReader, net, criterionNodes[0],
                                                                                    useDistributedMBReading, useParallelTrain, *inputMatrices, actualMBSize, m_mpi);

            if (maxNumSamplesExceeded) // Dropping data.
                wasDataRead = false;

            if (!wasDataRead && (!useDistributedMBReading || noMoreSamplesToProcess)) // in case of distributed reading, we do a few more loops until all ranks have completed
                break;                                                                // end of epoch

            // Note: If !wasDataRead then the data that GetMinibatchIntoNetwork() was supposed to fill in are undefined.
            // Must not touch them.

            if (!wasDataRead)
            {
                actualMBSize = 0;      // (undefined if !wasDataRead)
                ProfilerEnable(false); // Profiler will be enabled at the beginning of the next epoch.
            }

            ProfilerTimeEnd(profGetMinibatch, profilerEvtMainGetMinibatch);
            auto profForwardBackward = ProfilerTimeBegin();

            nSamplesSinceLastModelSync += actualMBSize;

            // Dropout nodes have an implicit input in the form of the random mask that is applied to its explicit input
            // This mask is regerated every minibatch and hence dropout nodes with a non-zero dropout rate must me marked outdated
            // w.r.t. inputs to force evaluation in each minibatch
            MarkDropoutNodesEvalTimeStampAsOutdated(net, criterionNodes[0]);

            // node data was changed
            // TODO: move this to that function as well--just tired to pass everything as arguments
            // TODO: We should do this right after the GetMinibatch() call, since that's where these changed.
            //       Need to check whether that would cause unintended side effects.
            // TODO: original code did not call this for actualMBSize == 0
            ComputationNetwork::BumpEvalTimeStamp(featureNodes);
            ComputationNetwork::BumpEvalTimeStamp(labelNodes);

            if (actualMBSize > 0)
            {
                assert(wasDataRead);
#ifndef EVALDLL
                if (m_doGradientCheck && GradientCheck(net, criterionNodes, learnableNodes, 0) == false)
                    LogicError("cannot pass gradient checker");
#endif
                // TODO: currently we only support one node for regularization
                if (m_needAdaptRegularization && m_adaptationRegType == AdaptationRegType::KL && refNode)
                {
                    size_t actualMBSize2 = refNet->DetermineActualMBSizeFromFeatures();
                    refNet->GetMBLayoutPtrOfNetwork()->CopyFrom(net->GetMBLayoutPtrOfNetwork()); // TODO: This is UNTESTED (before this was missing, seemingly inconsistently)

                    if (actualMBSize2 != actualMBSize)
                        LogicError("TrainOneEpoch: refNet has different MB size than main net??");

                    refNet->ForwardProp(refNode);
                    Matrix<ElemType>::ScaleAndAdd((ElemType) m_adaptationRegWeight,
                                                  dynamic_pointer_cast<ComputationNode<ElemType>>(refNode)->Value(),
                                                  (ElemType)(1.0 - m_adaptationRegWeight),
                                                  dynamic_pointer_cast<ComputationNode<ElemType>>(labelNodes[0])->Value());
                }

                // do forward and back propagation

                // We optionally break the minibatch into sub-minibatches.
                // This, when enabled, is used when a full minibatch does not fit into GPU RAM.
                size_t actualNumSubminibatches = numSubminibatchesNeeded <= 1 ? 1 : smbDispatcher.GetMinibatchIntoCache(*trainSetDataReader, *net, *inputMatrices, numSubminibatchesNeeded);
                for (size_t ismb = 0; ismb < actualNumSubminibatches; ismb++)
                {
                    if (actualNumSubminibatches > 1)
                    {
                        smbDispatcher.GetSubMinibatchToNet(ismb); // get sub-minibatch from full-size one
                        ComputationNetwork::BumpEvalTimeStamp(featureNodes);
                        ComputationNetwork::BumpEvalTimeStamp(labelNodes);
                    }

                    // ===========================================================
                    // forward prop for evaluate eval nodes
                    // ===========================================================

                    // compute eval node first since when gradient is computed the forward function values
                    // may be changed and need to be recomputed when gradient and function value share the same matrix
                    net->ForwardProp(forwardPropRoots); // the bulk of this evaluation is reused in ComputeGradient() below

                    // ===========================================================
                    // backprop
                    // ===========================================================

                    if (learnRatePerSample > 0.01 * m_minLearnRate) // only compute gradient when learning rate is large enough
                        net->Backprop(criterionNodes[0]);

                    // house-keeping for sub-minibatching
                    if (actualNumSubminibatches > 1)
                        smbDispatcher.DoneWithCurrentSubMinibatch(ismb); // page state out
                }                                                        // end sub-minibatch loop
                if (actualNumSubminibatches > 1)
                    smbDispatcher.DoneWithCurrentMinibatch();
            } // if (actualMBSize > 0)
            // WARNING: If actualMBSize == 0, then criterion nodes have NOT been updated, and contain garbage (last MB's) values.

            // In case of mini epochs (used for adaptive minibatch size and learning rate),
            // no more data should be processed by this worker.
            if (shouldCheckEarlyExit)
            {
                if (epochStartSample + maxNumberOfSamples < trainSetDataReader->GetCurrentSamplePosition())
                    maxNumSamplesExceeded = true;
            }

            ProfilerTimeEnd(profForwardBackward, profilerEvtMainFB);
            auto profGradientAgg = ProfilerTimeBegin();

            // for momentum/clipping/regularization/etc., as well as for progress and statistics, we should only count frames that are not gaps
            // #samples according to the default dynamic axis, for use with criterion nodes that do not have an MBLayout
            size_t numSamplesWithLabelOfNetwork = wasDataRead ? net->GetNumSamplesWithLabelOfNetwork(actualMBSize) : 0; // (0 for empty MB)
            // Note: All accumulation into an EpochCriterion uses 'numSamplesWithLabelOfNetwork' as the generic,
            // fallback minibatch size. If that is 0, then nodes are considered containing zero samples,
            // independent of their actual content (which is considered outdated).

            // Sum of actualMBSize across all nodes when using parallel training
            // 'aggregate' here means across-worker aggregate for this one minibatch.
            size_t aggregateNumSamples = actualMBSize;                                                                                            // (0 for empty MB)
            size_t aggregateNumSamplesWithLabel = CriterionAccumulator<ElemType>::GetNumSamples(criterionNodes[0], numSamplesWithLabelOfNetwork); // (0 for empty MB)

            if (!useGradientAggregation)
            {
                // accumulate criterion values (objective, eval)
                assert(wasDataRead || numSamplesWithLabelOfNetwork == 0);
                // criteria are in Value()(0,0), we accumulate into another 1x1 Matrix (to avoid having to pull the values off the GPU)
                localEpochCriterion.Add(0, numSamplesWithLabelOfNetwork);
                for (size_t i = 0; i < evaluationNodes.size(); i++)
                    localEpochEvalErrors.Add(i, numSamplesWithLabelOfNetwork);
            }
            else
            {
                // distributed gradient aggregation
                if (learnParamsGradients.size() == 0)
                {
                    // lazily form the list of smoothedGradients to exchange
                    learnParamsGradients.reserve(learnableNodes.size());
                    for (auto nodeIter = learnableNodes.begin(); nodeIter != learnableNodes.end(); nodeIter++)
                    {
                        ComputationNodePtr node = dynamic_pointer_cast<ComputationNode<ElemType>>(*nodeIter);
                        if (node->IsParameterUpdateRequired())
                        {
                            Matrix<ElemType>* currParamsGradient = &(node->Gradient()); // TODO: we can use shared_ptrs now

                            // Sometimes, in parallel training, the current node may not get any samples to process
                            // In this case, the gradient matrix may not have been sized yet. If so, lets size it.
                            if (currParamsGradient->GetNumCols() == 0)
                            {
                                Matrix<ElemType>* currParamsValues = &(node->Value());
                                currParamsGradient->Resize(currParamsValues->GetNumRows(), currParamsValues->GetNumCols());
                            }

                            learnParamsGradients.push_back(currParamsGradient);
                        }
                    }
                }

                // hoist the criterion into CPU space for all-reduce
                localEpochCriterion.Assign(0, numSamplesWithLabelOfNetwork);
                for (size_t i = 0; i < evaluationNodes.size(); i++)
                    localEpochEvalErrors.Assign(i, numSamplesWithLabelOfNetwork);

                // copy all values to be aggregated into the header
                m_gradHeader->numSamples = aggregateNumSamples;
                m_gradHeader->criterion = localEpochCriterion.GetCriterion(0).first;
                m_gradHeader->numSamplesWithLabel = localEpochCriterion.GetCriterion(0).second; // same as aggregateNumSamplesWithLabel
                assert(m_gradHeader->numSamplesWithLabel == aggregateNumSamplesWithLabel);
                for (size_t i = 0; i < evaluationNodes.size(); i++)
                    m_gradHeader->evalErrors[i] = localEpochEvalErrors.GetCriterion(i);

                // aggregate
                m_gradHeader->numEvalNode = evaluationNodes.size(); // TODO: rename numEvalNode (plural)
                bool samplesProcessed = m_distGradAgg->AggregateGradients(learnParamsGradients, m_gradHeader.get(), isFirstMinibatch);
                noMoreSamplesToProcess = !samplesProcessed;

                // read out the header--now everything is aggregated
                aggregateNumSamples = m_gradHeader->numSamples;
                aggregateNumSamplesWithLabel = m_gradHeader->numSamplesWithLabel;
                epochCriterion += EpochCriterion(m_gradHeader->criterion, m_gradHeader->numSamplesWithLabel);
                for (size_t i = 0; i < epochEvalErrors.size(); i++)
                {
                    if (ContainsAccumulatedResult(evaluationNodes[i]))
                    {
                        // We don't accumulate error in epoch criterion as this node has already accumulated error for
                        // all samples that passed through network in forward pass.
                        if (samplesProcessed)
                        {
                            epochEvalErrors[i] = m_gradHeader->evalErrors[i];
                        }
                        // else: no samples processed, no aggregation happened -> we do not want to override current value
                        // with 0.
                    }
                    else
                        epochEvalErrors[i] += m_gradHeader->evalErrors[i];
                }
            }

            ProfilerTimeEnd(profGradientAgg, profilerEvtMainGradient);
            auto profWeights = ProfilerTimeBegin();

            // update model parameters
            if ((aggregateNumSamples > 0) && (learnRatePerSample > m_minLearnRate * 0.01))
            {
#if 1 // BUGBUG: We must skip gaps in our momentum, clipping, regularization etc. criteria. \
    // This will break test cases. So for now, we will only enable this for per-sample criteria.
                size_t numSamplesInMinibatch = aggregateNumSamples;
                if (criterionNodes[0]->HasMBLayout())
#endif
                    numSamplesInMinibatch = aggregateNumSamplesWithLabel;
#if 0
            if (numSamplesInMinibatch != aggregateNumSamples)
                fprintf(stderr, "SGD: using true #samples %d instead of MB size %d\n", (int)numSamplesInMinibatch, (int)aggregateNumSamples);
#endif
                auto smoothedGradientIter = smoothedGradients.begin();
                auto smoothedCountIter = smoothedCounts.begin();
                for (auto nodeIter = learnableNodes.begin(); nodeIter != learnableNodes.end(); nodeIter++, smoothedGradientIter++, smoothedCountIter++)
                {
                    ComputationNodeBasePtr node = *nodeIter;
                    if (node->IsParameterUpdateRequired())
                    {
#ifdef _DEBUG
                        if (smoothedGradientIter->HasNan("TrainOneEpoch/UpdateWeights(): "))
                            LogicError("%ls %ls operation has NaNs in smoothedGradient.", node->NodeName().c_str(), node->OperationName().c_str());
#endif
                        double nodeDependentLearningRatePerSample = learnRatePerSample * node->GetLearningRateMultiplier();
                        double nodeDependentRegMultiplier = dynamic_pointer_cast<LearnableParameter<ElemType>>(node)->GetRegMultiplier();
                        double momentumPerSample = GetMomentumPerSample(epochNumber /*BUGBUG workaround:*/, net->GetMBLayoutPtrOfNetwork()->GetNumParallelSequences());
                        // TODO: Check why l2Factor is not applied to L1. Bug?
                        // BUGBUG (Issue #95): Access to net MBLayout can no longer be done if we have multiple input layouts
                        UpdateWeights(dynamic_pointer_cast<ComputationNode<ElemType>>(node)->Value(),
                                      dynamic_pointer_cast<ComputationNode<ElemType>>(node)->Gradient(),
                                      *smoothedGradientIter, *smoothedCountIter,
                                      nodeDependentLearningRatePerSample, momentumPerSample,
                                      numSamplesInMinibatch,
                                      m_L2RegWeight * nodeDependentRegMultiplier, m_L1RegWeight * nodeDependentRegMultiplier,
                                      m_needAveMultiplier, m_useNesterovMomentum);
                        node->BumpEvalTimeStamp();
#ifdef _DEBUG
                        if (dynamic_pointer_cast<ComputationNode<ElemType>>(node)->Value().HasNan("TrainOneEpoch/UpdateWeights(): "))
                            LogicError("%ls %ls operation has NaNs in functionValues after parameter update.", node->NodeName().c_str(), node->OperationName().c_str());
#endif
                    }
                }
            }

            // aggregation by model averaging or block momentum
            if (useModelAggregation)
            {
                if (nSamplesSinceLastModelSync >= blockSizePerWorker)
                {
                    bool synced = m_pMASGDHelper->OnArrivingAtSyncPoint(learnableNodes, smoothedGradients, nSamplesSinceLastModelSync);
                    if (synced)
                    {
                        nSamplesSinceLastModelSync = 0;
                    }
                }
                // prepare break condition
                if (useDistributedMBReading)
                {
                    noMoreSamplesToProcess = !wasDataRead;
                }
            }

            // using parameter server for parameter update
            if (useAsyncGradientAggregation && m_mpi->NumNodesInUse() > 1)
            {
                // Determine if any samples were processed across any of the ranks
                if (useDistributedMBReading)
                {
                    noMoreSamplesToProcess = !wasDataRead;
                }

                if (nSamplesSinceLastModelSync >= m_nSyncSamplesPerWorker[epochNumber])
                {
                    m_pASGDHelper->PushAndPullModel(learnableNodes, nSamplesSinceLastModelSync);
                    nSamplesSinceLastModelSync = 0;
                }
            }

            ProfilerTimeEnd(profWeights, profilerEvtMainWeights);
            auto profPost = ProfilerTimeBegin();

            timer.Stop();

            numMBsRun++;
            totalTimeInMBs += timer.ElapsedSeconds();

            bool progressPrintNeeded = numMBsRun <= m_firstMBsToShowResult || (m_numMBsToShowResult && (numMBsRun % m_numMBsToShowResult == 0));
            bool tensorBoardWriteNeeded = tensorBoardWriter && m_tensorBoardNumMBsToLogResult &&
                                          ((totalMBsSeenBefore + numMBsRun) % m_tensorBoardNumMBsToLogResult == 0);

            // Get the epoch Values updated. Take care to fetch values from GPU only when this is really needed.
            if ((progressPrintNeeded || tensorBoardWriteNeeded) && !useGradientAggregation)
            {
                // if no aggregation, we directly get the values from the minibatch accumulators
                timer.Restart();
                epochCriterion = localEpochCriterion.GetCriterion(0);
                for (size_t i = 0; i < epochEvalErrors.size(); i++)
                    epochEvalErrors[i] = localEpochEvalErrors.GetCriterion(i);
                timer.Stop();

                // Add the last trailing compute
                totalTimeInMBs += timer.ElapsedSeconds();
            }

            // log
            // This shows the criterion since last logged.
            if (progressPrintNeeded)
            {
                // epochCriterion aggregates over entire epoch, but we only show difference to last time we logged
                EpochCriterion epochCriterionSinceLastLogged = epochCriterion - epochCriterionLastLogged;
                let trainLossSinceLastLogged = epochCriterionSinceLastLogged.Average(); // TODO: Check whether old trainSamplesSinceLastLogged matches this ^^ difference
                let trainSamplesSinceLastLogged = (int) epochCriterionSinceLastLogged.second;

                // determine progress in percent
                int mbProgNumPrecision = 2;
                double mbProg = 0.0;

                // Skip epoch size computation if we aren't asked to and epoch is not the starting epoch
                bool skipComputeEpochSize = epochNumber > startEpoch || epochSize != requestDataSize;

                if (skipComputeEpochSize)
                {
                    if (m_maxComputedEpochSize != 0)
                    {
                        double numMBPerEpoch = (double) m_maxComputedEpochSize / (double) tunedMBSize;
                        mbProg = (double) numMBsRun / numMBPerEpoch;
                        mbProgNumPrecision = (int) ceil(log10(numMBPerEpoch / (double) (numMBsRun - numMBsRunSinceLastLogged)));
                        mbProgNumPrecision = max(mbProgNumPrecision - 2, 2);
                    }
                }
                else // estimate epoch size
                    m_maxComputedEpochSize = numMBsRun * trainSamplesSinceLastLogged / (numMBsRun - numMBsRunSinceLastLogged);

                // progress tracing for compute cluster management
                let wasProgressPrinted = ProgressTracing::TraceProgressPercentage(epochNumber, mbProg, false);

                // progress tracing for regular log
                if (m_traceLevel > 0)
                {
                    PREPENDTS(stderr);
                    fprintf(stderr, "%s Epoch[%2d of %d]-Minibatch[%4d-%4d",
                            prefixMsg.c_str(), epochNumber + 1, (int) m_maxEpochs,
                            (int) (numMBsRunSinceLastLogged + 1), numMBsRun);
                    if (skipComputeEpochSize)
                        fprintf(stderr, (", %2." + to_string(mbProgNumPrecision) + "f%%").c_str(), mbProg * 100); // --TODO: use a * format?
                    fprintf(stderr, "]: ");
                    epochCriterionSinceLastLogged.LogCriterion(criterionNodes[0]->NodeName());
                    for (size_t i = 0; i < epochEvalErrors.size(); i++)
                    {
                        const std::wstring& nodeName = evaluationNodes[i]->NodeName();
                        if (ContainsAccumulatedResult(evaluationNodes[i]))
                        {
                            // For aggregation nodes, we don't report per minibatch error. These nodes calculate
                            // aggregated error for all samples that passed through network, instead of calculating per
                            // sample error. Aggregated error for all samples will be reported for these nodes.
                            epochEvalErrors[i].LogCriterion(nodeName);
                        }
                        else
                        {
                            // Report per minibatch error.
                            (epochEvalErrors[i] - epochEvalErrorsLastLogged[i]).LogCriterion(nodeName);
                        }
                    }

                    fprintf(stderr, ("time = " + GeneratePaddedFloatOrExpFormat(0, 4, totalTimeInMBs) + "s; samplesPerSecond = %.1f\n").c_str(),
                            totalTimeInMBs, trainSamplesSinceLastLogged / totalTimeInMBs);
                }

                // progress tracing for compute cluster management
                if (wasProgressPrinted)
                    ProgressTracing::TraceTrainLoss(trainLossSinceLastLogged);

                if (m_traceLevel > 0)
                    fflush(stderr);

                if (epochCriterion.IsNan())
                {
                    wstring w = msra::strfun::wstrprintf(L"%ls.%ls", m_modelPath.c_str(), "debug");
                    // m_modelPath = m_modelPath + L "debug"
                    fprintf(stderr, "Saving model for debugging to:%ls", w.c_str());
                    net->Save(w);
                    RuntimeError("The1 training is not a number (NAN).");
                }

                // reset statistics for differential logging
                epochCriterionLastLogged = epochCriterion;
                epochEvalErrorsLastLogged = epochEvalErrors;
                numMBsRunSinceLastLogged = numMBsRun;
                for (size_t i = 0; i < epochEvalErrors.size(); i++)
                {
                    if (ContainsAccumulatedResult(evaluationNodes[i]))
                    {
                        // For nodes that accumulate result we report accumulated error for all samples that passed through
                        // network so far, instead of per minibatch error. So, we reset last logged error here.
                        epochEvalErrorsLastLogged[i] = EpochCriterion(0);
                    }
                }

                totalTimeInMBs = 0;
            }

            // Log progress to TensorBoard.
            // Only do this if TensorBoard logging is enabled, the current worker has rank 0, and it is time to write
            // the log (as controlled by tensorBoardNumMBsToLogResult).
            if (tensorBoardWriteNeeded)
            {
                // epochCriterion aggregates over entire epoch, but we only show difference to last time we logged
                EpochCriterion epochCriterionSinceLastLogged = epochCriterion - tensorBoardEpochCriterionLastLogged;
                double trainLossSinceLastLogged = epochCriterionSinceLastLogged.Average();

                // numMBsRun is specific to the current epoch and is reset for each epoch.
                // We cannot use it if we want to view progress of loss/eval since the start of training.
                // Instead, we use a total number of minibatches run from the start of training as a step.
                const size_t step = totalMBsSeenBefore + (size_t) numMBsRun;
                tensorBoardWriter->WriteValue(L"minibatch/" + criterionNodes[0]->NodeName(), (float) trainLossSinceLastLogged, step);
                for (size_t i = 0; i < epochEvalErrors.size(); i++)
                {
                    const std::wstring& nodeName = evaluationNodes[i]->NodeName();
                    // For aggregation nodes, we don't report per minibatch error. These nodes calculate
                    // aggregated error for all samples that passed through network, instead of calculating per
                    // sample error. Aggregated error for all samples will be reported for these nodes.
                    const EpochCriterion& evalErrorSinceLastLogged = ContainsAccumulatedResult(evaluationNodes[i])
                                                                         ? epochEvalErrors[i]
                                                                         : epochEvalErrors[i] - tensorBoardEpochEvalErrorsLastLogged[i];
                    tensorBoardWriter->WriteValue(L"minibatch/" + nodeName, (float) evalErrorSinceLastLogged.Average(), step);
                }

                tensorBoardWriter->Flush();

                // reset statistics for differential logging
                tensorBoardEpochCriterionLastLogged = epochCriterion;
                tensorBoardEpochEvalErrorsLastLogged = epochEvalErrors;
                for (size_t i = 0; i < epochEvalErrors.size(); i++)
                {
                    if (ContainsAccumulatedResult(evaluationNodes[i]))
                    {
                        // For nodes that accumulate result we report accumulated error for all samples that passed through
                        // network so far, instead of per minibatch error. So, we reset last logged error here.
                        tensorBoardEpochEvalErrorsLastLogged[i] = EpochCriterion(0);
                    }
                }
            }

            timer.Restart();
            totalEpochSamples += aggregateNumSamplesWithLabel;

            // call DataEnd function
            // This signals something from SGD to the reader.
            // DataEnd does reader specific process if sentence ending is reached
            trainSetDataReader->DataEnd();

            // Attempts to compute the error signal for the whole utterance, which will
            // be fed to the neural network as features. Currently it is a workaround
            // for the two-forward-pass sequence and ctc training, which allows
            // processing more utterances at the same time. Only used in Kaldi2Reader.
            // TODO: move the two-forward-pass support out of the reader.
            AttemptUtteranceDerivativeFeatures(net, trainSetDataReader, featureNodes, inputMatrices);

            profiler.NextSample();
            isFirstMinibatch = false;

            ProfilerTimeEnd(profPost, profilerEvtMainPost);
            ProfilerTimeEnd(profMinibatch, profilerEvtMainMinibatch);
        }

        // --- END MAIN MINIBATCH LOOP

        if (useModelAggregation)
        {
            m_pMASGDHelper->OnEpochEnd(learnableNodes, smoothedGradients, nSamplesSinceLastModelSync);
            nSamplesSinceLastModelSync = 0;
        }

        if (useAsyncGradientAggregation && (m_mpi->NumNodesInUse() > 1))
        {
            m_pASGDHelper->PushAndPullModel(learnableNodes, nSamplesSinceLastModelSync);
            nSamplesSinceLastModelSync = 0;
        }

        // hoist the accumulated criterion value from GPU side to our 'out'  variables
        // (unless we useGradientAggregation, in which case they are accumulated in the 'out' variables directly)
        if (!useGradientAggregation)
        {
            epochCriterion = localEpochCriterion.GetCriterion(0);
            for (size_t i = 0; i < epochEvalErrors.size(); i++)
                epochEvalErrors[i] = localEpochEvalErrors.GetCriterion(i);
        }

        // in case of model averaging, do one more final aggregation of criteria
        if (useModelAggregation && (m_mpi->NumNodesInUse() > 1))
        {
            // 1. total epoch samples processed by all workers
            size_t totalEpochSamplesOfAllWorkers = totalEpochSamples;
            m_mpi->AllReduce(&totalEpochSamplesOfAllWorkers, 1);

            // get criteria for this worker
            assert(!useGradientAggregation); // (otherwise the data would not be in localEpochCriterion)
            epochCriterion = localEpochCriterion.GetCriterion(0);
            for (size_t i = 0; i < epochEvalErrors.size(); i++)
                epochEvalErrors[i] = localEpochEvalErrors.GetCriterion(i);

            // all-reduce epochCriterion and epochEvalErrors over nodes
            m_mpi->AllReduce(&epochCriterion.first, 1);
            m_mpi->AllReduce(&epochCriterion.second, 1);
            // to transfer the eval vectors, we must pull them apart into STL objects and exchange them separately
            // TODO: merge with training criteria
            vector<double> numer(epochEvalErrors.size());
            vector<size_t> denom(epochEvalErrors.size());
            for (size_t i = 0; i < epochEvalErrors.size(); i++)
            {
                numer[i] = epochEvalErrors[i].first;
                denom[i] = epochEvalErrors[i].second;
            }
            m_mpi->AllReduce(numer);
            m_mpi->AllReduce(denom);
            for (size_t i = 0; i < epochEvalErrors.size(); i++)
                epochEvalErrors[i] = EpochCriterion(numer[i], denom[i]);

            totalEpochSamples = totalEpochSamplesOfAllWorkers;
        }

        if (useGradientAggregation && !evaluationNodesWhichAccumulateResult.empty())
        {
            // Each worker contains accumulated values for part of the data set, we have to aggregate accumulated values
            // and recalculate evaluation errors based on accumulators.
            AggregateAccumulatorValuesAndUpdateEpochEvaluation<ElemType>(
                net, evaluationNodesWhichAccumulateResult, m_gradHeader, m_mpi, epochEvalErrors, evaluationNodes,
                localEpochEvalErrors, ContainsAccumulatedResult, m_packThresholdSizeInBytes);
        }

        return numMBsRun;
    }

    // -----------------------------------------------------------------------
    // subroutines and helpers follow below
    // -----------------------------------------------------------------------

    static double MomentumPerMB(double momentumPerSample, size_t minibatchSize)
    {
        return pow(momentumPerSample, minibatchSize);
    }

    template <class ElemType>
    const std::vector<ComputationNodeBasePtr>& SGD<ElemType>::GetTrainCriterionNodes(ComputationNetworkPtr net)
    {
        if (!m_trainCriterionNodeName.empty())
        {
            return net->CriterionNodesFrom(m_trainCriterionNodeName);
        }
        else
            return net->FinalCriterionNodes();
    }

    template <class ElemType>
    const std::vector<ComputationNodeBasePtr>& SGD<ElemType>::GetEvalCriterionNodes(ComputationNetworkPtr net)
    {
        if (!m_evalCriterionNodeName.empty())
        {
            return net->CriterionNodesFrom(m_evalCriterionNodeName);
        }
        else
            return net->EvaluationNodes();
    }

    // execute PreComputeNodes
    // Returns true if precomputation was executed.
    template <class ElemType>
    bool SGD<ElemType>::PreCompute(ComputationNetworkPtr net,
                                   IDataReader * trainSetDataReader,
                                   const std::vector<ComputationNodeBasePtr>& featureNodes,
                                   const std::vector<ComputationNodeBasePtr>& labelNodes,
                                   StreamMinibatchInputs* inputMatrices)
    {
        std::list<ComputationNodeBasePtr> nodes = net->GetNodesRequiringPreComputation(); // this tests all HasComputed() flags

        if (nodes.size() == 0)
        {
            if (m_traceLevel > 0)
                LOGPRINTF(stderr, "No PreCompute nodes found, or all already computed. Skipping pre-computation step.\n");
            return false;
        }

        fprintf(stderr, "\n");
        LOGPRINTF(stderr, "Precomputing --> %lu PreCompute nodes found.\n\n", (unsigned long) nodes.size());
        if (m_traceLevel > 0)
        {
            for (const auto& node : nodes)
            {
                LOGPRINTF(stderr, "\t%ls = %ls()\n", node->NodeName().c_str(), node->OperationName().c_str());
            }
        }

        // compute
        ScopedNetworkOperationMode modeGuard(net, NetworkOperationMode::preComputing);

        // trainSetDataReader->StartMinibatchLoop(m_mbSize[0],  0 , requestDataSize);
        // trainSetDataReader->StartMinibatchLoop(m_mbSize[0],  0 , m_epochSize); // only based on one epoch
        // To support large dataset, we usually partition whole dataset into several epoch's,
        // so we need to use all the data to do precomputing
        if (m_useAllDataForPreComputedNode) // using all the data
            trainSetDataReader->StartMinibatchLoop(m_mbSize[0], 0, inputMatrices->GetStreamDescriptions());
        else // using only one epoch. Note: One epoch is often enough for feature mean/stddev, but not for estimating priors.
            trainSetDataReader->StartMinibatchLoop(m_mbSize[0], 0, inputMatrices->GetStreamDescriptions(), m_epochSize);
        net->StartEvaluateMinibatchLoop(nodes);

        // initialize
        for (auto& node : nodes)
            dynamic_pointer_cast<IPreComputeNode>(node)->MarkComputed(false /*begin accumulating*/);

        const size_t numIterationsBeforePrintingProgress = 100;
        size_t numItersSinceLastPrintOfProgress = 0;
        size_t actualMBSizeDummy;
        while (DataReaderHelpers::GetMinibatchIntoNetwork<ElemType>(*trainSetDataReader, net, nullptr, false, false, *inputMatrices, actualMBSizeDummy, m_mpi))
        {
            // TODO: move these into GetMinibatchIntoNetwork()  --but those are passed around; necessary? Can't we get them from 'net'?
            ComputationNetwork::BumpEvalTimeStamp(featureNodes);
            ComputationNetwork::BumpEvalTimeStamp(labelNodes);

            net->ForwardProp(nodes);

            numItersSinceLastPrintOfProgress = ProgressTracing::TraceFakeProgress(numIterationsBeforePrintingProgress, numItersSinceLastPrintOfProgress);
        }

        // finalize
        for (auto& node : nodes)
            dynamic_pointer_cast<IPreComputeNode>(node)->MarkComputed(true /*done accumulating*/);

        fprintf(stderr, "\n");
        LOGPRINTF(stderr, "Precomputing --> Completed.\n\n");

        return true;
    }

    // return a reasonable initial learning rate based on the initial mbsize
    template <class ElemType>
    double SGD<ElemType>::SearchForBestLearnRate(ComputationNetworkPtr net,
                                                 ComputationNetworkPtr refNet,
                                                 const ComputationNodeBasePtr& refNode, const int epochNumber,
                                                 const double curLearnRate,
                                                 IDataReader* trainSetDataReader,
                                                 const std::vector<ComputationNodeBasePtr>& featureNodes,
                                                 const std::vector<ComputationNodeBasePtr>& labelNodes,
                                                 const std::vector<ComputationNodeBasePtr>& criterionNodes,
                                                 const std::vector<ComputationNodeBasePtr>& evaluationNodes,
                                                 StreamMinibatchInputs* inputMatrices,
                                                 const std::list<ComputationNodeBasePtr>& learnableNodes,
                                                 std::list<Matrix<ElemType>>& smoothedGradients, vector<double> smoothedCounts,
                                                 const bool learnRateInitialized,
                                                 const double largestPrevLearnRatePerSample)
    {
        double bestLearnRatePerSample = curLearnRate;

        size_t numFramesToUseInSearch = m_numSamples4Search[epochNumber];
        if (m_epochSize != requestDataSize)
        {
            // ensure the numFramesToUseInSearch does not exceed the total number of frames in the epoch
            numFramesToUseInSearch = min(numFramesToUseInSearch, m_epochSize);
        }

        double minLearnRate = m_minLearnRate * 0.3f;
        double learnRatePerSample = 1.0f / 8.0f / 0.618f / sqrt((double) m_mbSize[epochNumber]); // TODO: comment on these magic constants

        if (learnRateInitialized && largestPrevLearnRatePerSample > 0)
        {
            // largestPrevLearnRatePerSample is per sample, first 0.618f is for compensation, second one is for safety
            learnRatePerSample = largestPrevLearnRatePerSample / 0.618f / 0.618f;
        }

        int baseModelEpoch = epochNumber - 1;
        net->RereadPersistableParameters<ElemType>(GetModelNameForEpoch(baseModelEpoch));

        double learnRate = learnRatePerSample;
        size_t dummyMinibatchSize;            // (not used)
        size_t dummyTotalTrainingSamplesSeen; // (not used)
        double prevCriterion = numeric_limits<double>::infinity();
        LoadCheckPointInfo(baseModelEpoch,
                           /*out*/ dummyTotalTrainingSamplesSeen,
                           /*out*/ learnRate,
                           smoothedGradients,
                           smoothedCounts,
                           /*out*/ prevCriterion,
                           /*out*/ dummyMinibatchSize);

        // if model is not changed this is what we will get
        EpochCriterion baseCriterion;
        vector<EpochCriterion> epochEvalErrors(evaluationNodes.size(), EpochCriterion::Infinity()); // these are ignored in this entire method
        TrainOneMiniEpochAndReloadModel(net, refNet, refNode, epochNumber,
                                        m_epochSize, trainSetDataReader, 0, m_mbSize[epochNumber],
                                        featureNodes, labelNodes,
                                        criterionNodes, evaluationNodes,
                                        inputMatrices, learnableNodes,
                                        smoothedGradients, smoothedCounts,
                                        /*out*/ baseCriterion, /*out*/ epochEvalErrors,
                                        "BaseAdaptiveLearnRateSearch:",
                                        numFramesToUseInSearch);

        if (m_autoLearnRateSearchType == LearningRateSearchAlgorithm::SearchBeforeEpoch)
        {
            if (prevCriterion == numeric_limits<double>::infinity())
                prevCriterion = baseCriterion.Average();

            double ratio = 0.3;

            if (m_epochSize != requestDataSize)
                ratio = pow(((double) numFramesToUseInSearch) / m_epochSize, 1.0f / 2);

            // interpolate prevCriterion into 'baseCriterion'
            baseCriterion.first = baseCriterion.second * max(ratio * prevCriterion + (1 - ratio) * baseCriterion.Average(), baseCriterion.Average());
        }

        EpochCriterion epochCriterion(EpochCriterion::Infinity());
        do
        {
            learnRatePerSample *= 0.618;
            TrainOneMiniEpochAndReloadModel(net, refNet, refNode, epochNumber,
                                            m_epochSize, trainSetDataReader,
                                            learnRatePerSample, m_mbSize[epochNumber], featureNodes,
                                            labelNodes, criterionNodes,
                                            evaluationNodes, inputMatrices,
                                            learnableNodes, smoothedGradients, smoothedCounts,
                                            /*out*/ epochCriterion, /*out*/ epochEvalErrors,
                                            "AdaptiveLearnRateSearch:",
                                            numFramesToUseInSearch);
        } while (epochCriterion.IsNan() || (epochCriterion.Average() > baseCriterion.Average() && learnRatePerSample > minLearnRate));

        bestLearnRatePerSample = learnRatePerSample;

        // grid search for the first m_numBestSearchEpoch  epochs
        if (epochNumber < m_numBestSearchEpoch)
        {
            double leftLearnRatePerSample = 0.01 / m_mbSize[epochNumber];
            double rightLearnRatePerSample = learnRatePerSample;
            EpochCriterion rightCriterion = epochCriterion;
            EpochCriterion leftCriterion; // we compute this from the mini epoch

            TrainOneMiniEpochAndReloadModel(net, refNet, refNode, epochNumber,
                                            m_epochSize, trainSetDataReader,
                                            leftLearnRatePerSample, m_mbSize[epochNumber],
                                            featureNodes, labelNodes,
                                            criterionNodes, evaluationNodes,
                                            inputMatrices, learnableNodes,
                                            smoothedGradients, smoothedCounts,
                                            /*out*/ leftCriterion, /*out*/ epochEvalErrors,
                                            "DetailBaseAdaptiveLearnRateSearch:",
                                            numFramesToUseInSearch);

            while (rightLearnRatePerSample > leftLearnRatePerSample * 1.2)
            {
                if (rightCriterion.Average() > leftCriterion.Average())
                {
                    rightLearnRatePerSample *= 0.618;

                    TrainOneMiniEpochAndReloadModel(net, refNet, refNode,
                                                    epochNumber,
                                                    m_epochSize,
                                                    trainSetDataReader,
                                                    rightLearnRatePerSample, m_mbSize[epochNumber],
                                                    featureNodes, labelNodes,
                                                    criterionNodes,
                                                    evaluationNodes,
                                                    inputMatrices,
                                                    learnableNodes,
                                                    smoothedGradients, smoothedCounts,
                                                    /*out*/ rightCriterion,
                                                    /*out*/ epochEvalErrors,
                                                    "DetailRightAdaptiveLearnRateSearch:",
                                                    numFramesToUseInSearch);
                }
                else
                {
                    leftLearnRatePerSample /= 0.618;

                    TrainOneMiniEpochAndReloadModel(net, refNet, refNode,
                                                    epochNumber,
                                                    m_epochSize,
                                                    trainSetDataReader,
                                                    leftLearnRatePerSample, m_mbSize[epochNumber],
                                                    featureNodes, labelNodes,
                                                    criterionNodes,
                                                    evaluationNodes,
                                                    inputMatrices,
                                                    learnableNodes,
                                                    smoothedGradients, smoothedCounts,
                                                    /*out*/ leftCriterion,
                                                    /*out*/ epochEvalErrors,
                                                    "DetailLeftAdaptiveLearnRateSearch:",
                                                    numFramesToUseInSearch);
                }
            }

            bestLearnRatePerSample = (leftCriterion.Average() < rightCriterion.Average()) ? leftLearnRatePerSample : rightLearnRatePerSample;
        }

        LOGPRINTF(stderr, " SearchForBestLearnRate Epoch[%d]: Best learningRatePerSample = %.10g, baseCriterion=%.10g\n",
                  (int) epochNumber + 1, bestLearnRatePerSample, baseCriterion.Average());

        return bestLearnRatePerSample;
    }

    // AdaptiveMinibatchSizing() -- choose the largest feasible minibatch size
    // This is necessary for data-parallel operation. The aim is to minimize model updates, and hence bandwidth
    // This implements
    //    F. Seide, H. Fu, J. Droppo, G. Li, and D. Yu:
    //    "On Parallelizability of Stochastic Gradient Descent for Speech DNNs"
    //    In Proc. ICASSP 2014.
    template <class ElemType>
    size_t SGD<ElemType>::AdaptiveMinibatchSizing(ComputationNetworkPtr net,
                                                  ComputationNetworkPtr refNet,
                                                  const ComputationNodeBasePtr& refNode,
                                                  const int epochNumber,
                                                  const size_t numFramesToUseInSearch,
                                                  IDataReader* trainSetDataReader,
                                                  const double learnRatePerSample,
                                                  const size_t initialMinibatchSize,
                                                  const std::vector<ComputationNodeBasePtr>& featureNodes,
                                                  const std::vector<ComputationNodeBasePtr>& labelNodes,
                                                  const std::vector<ComputationNodeBasePtr>& criterionNodes,
                                                  const std::vector<ComputationNodeBasePtr>& evaluationNodes,
                                                  StreamMinibatchInputs* inputMatrices,
                                                  const std::list<ComputationNodeBasePtr>& learnableNodes,
                                                  std::list<Matrix<ElemType>>& smoothedGradients, vector<double> smoothedCounts,
                                                  const double learningRateAdjustmentFactor)
    {
        size_t minMinibatchSize = initialMinibatchSize;
        size_t chosenMinibatchSize = initialMinibatchSize;

        // do some pre-adjustment based on LR
        // Basically we assume that the LR for epoch 1 is safe for mbsize.
        // If LR control led to a smaller LR, then we can safely increase the lower bound of the MB size.
        double learningRateChangeSoFar = GetLearningRatePerSample(epochNumber /*BUGBUG workaround:*/, trainSetDataReader->GetNumParallelSequencesForFixingBPTTMode()) / GetLearningRatePerSample(0 /*BUGBUG workaround:*/, trainSetDataReader->GetNumParallelSequencesForFixingBPTTMode());
        learningRateChangeSoFar *= learningRateAdjustmentFactor;

        // increasing by the full factor is found to be too aggressive; sqrt() seems more robust
        learningRateChangeSoFar = sqrt(learningRateChangeSoFar);

        // LR was indeed reduced
        if (learningRateChangeSoFar < 1.0f)
        {
            // we can safely increase MB size (note: this may be bigger than our max)
            minMinibatchSize = (size_t)(minMinibatchSize / learningRateChangeSoFar);
        }

        if (epochNumber < 2 && m_prevChosenMinibatchSize != 0)
        {
            // newly started training: any previous MB size stored in the model is to be ignored
            LOGPRINTF(stderr, " Before Epoch[2], previous minibatchSize %d is considered invalid -> resetting.\n",
                      (int) m_prevChosenMinibatchSize);
            m_prevChosenMinibatchSize = 0;
        }

        // check if we need to skip
        if (m_prevChosenMinibatchSize != 0 &&
            (epochNumber + 1) > m_minibatchSizeTuningFrequency &&
            (epochNumber + 1) % m_minibatchSizeTuningFrequency != 0)
        {
            LOGPRINTF(stderr, " AdaptiveMinibatchSearch: Search for a better minibatchSize in epoch %d skipped, keeping minibatchSize of %d\n",
                      (int) epochNumber + 1, (int) m_prevChosenMinibatchSize);
            chosenMinibatchSize = m_prevChosenMinibatchSize;
        }
        else
        {
            if (m_prevChosenMinibatchSize != 0)
            {
                // if m_prevChosenMinibatchSize (the chosen minibatch size for the previous epoch) div 2
                // is higher than initialMinibatchSize (the minibatch size we start with for this epoch),
                // then start the search with m_prevChosenMinibatchSize/2 instead of initialMinibatchSize.
                //LOGPRINTF(stderr, " AdaptiveMinibatchSearch: Limiting minMinibatchSize to largest of previous minibatchSize = (%d / 2) or %d\n",
                //          (int) m_prevChosenMinibatchSize, (int) minMinibatchSize);
                minMinibatchSize = max(minMinibatchSize, m_prevChosenMinibatchSize / 2);
            }

            size_t maxMinibatchSize = m_minibatchSizeTuningMax;

            // only grow at most 2 x compared to previous step
            if (m_prevChosenMinibatchSize != 0.0f)
            {
                assert(m_prevChosenMinibatchSize >= chosenMinibatchSize);

                //LOGPRINTF(stderr, " AdaptiveMinibatchSearch: Limiting maxMinibatchSize to previous minibatchSize %d*2\n",
                //          (int) m_prevChosenMinibatchSize);
                maxMinibatchSize = min(maxMinibatchSize, m_prevChosenMinibatchSize * 2);
            }

            chosenMinibatchSize = SearchForBestMinibatchSize(net, refNet, refNode, epochNumber,
                                                             numFramesToUseInSearch, trainSetDataReader,
                                                             learnRatePerSample, featureNodes,
                                                             labelNodes, criterionNodes,
                                                             evaluationNodes, inputMatrices,
                                                             learnableNodes, smoothedGradients, smoothedCounts,
                                                             minMinibatchSize, maxMinibatchSize);
        }

        return chosenMinibatchSize;
    }

    static size_t RoundToMultipleOf64(float val)
    {
        return 64 * (size_t)((val + 32) / 64);
    }

    static size_t RoundToMultipleOf64(size_t val)
    {
        return 64 * ((val + 32) / 64);
    }

    // uses a small percentage of training data of minibatch to
    // speculatively train with various MB sizes; then picks the best
    template <class ElemType>
    size_t SGD<ElemType>::SearchForBestMinibatchSize(ComputationNetworkPtr net,
                                                     ComputationNetworkPtr refNet,
                                                     const ComputationNodeBasePtr& refNode,
                                                     const int epochNumber,
                                                     const size_t numFramesToUseInSearch,
                                                     IDataReader* trainSetDataReader,
                                                     const double learnRatePerSample,
                                                     const std::vector<ComputationNodeBasePtr>& featureNodes,
                                                     const std::vector<ComputationNodeBasePtr>& labelNodes,
                                                     const std::vector<ComputationNodeBasePtr>& criterionNodes,
                                                     const std::vector<ComputationNodeBasePtr>& evaluationNodes,
                                                     StreamMinibatchInputs* inputMatrices,
                                                     const std::list<ComputationNodeBasePtr>& learnableNodes,
                                                     std::list<Matrix<ElemType>>& smoothedGradients, std::vector<double> smoothedCounts,
                                                     const size_t minMinibatchSize, const size_t maxMinibatchSize)
    {
        // may happen for automatically reduced learning rates
        if (minMinibatchSize > maxMinibatchSize)
        {
            return maxMinibatchSize;
        }

        size_t trialMinibatchSize = 0;
        bool isFirstIteration = true;
        EpochCriterion baseCriterion(0);

        // increase the minibatch size by a factor of sqrt(2) in each step.
        const float minibatchSizeTuningFactor = sqrtf(2.0f);

        LOGPRINTF(stderr, " AdaptiveMinibatchSearch Epoch[%d]: Evaluating minibatchSizes %d..%d\n",
                  (int) epochNumber + 1, (int) RoundToMultipleOf64(minMinibatchSize), (int) RoundToMultipleOf64(maxMinibatchSize));

        size_t lastGoodMinibatchSize = 0;
        EpochCriterion lastGoodEpochCriterion(0);
        for (float trialMinibatchSizeFloat = (float) minMinibatchSize;
             trialMinibatchSizeFloat <= maxMinibatchSize;
             trialMinibatchSizeFloat *= minibatchSizeTuningFactor)
        {
            // round mbsize to something meaningful
            trialMinibatchSize = RoundToMultipleOf64(trialMinibatchSizeFloat);
            if (m_traceLevel > 0)
            {
                LOGPRINTF(stderr, " AdaptiveMinibatchSearch Epoch[%d]: Evaluating trial minibatchSize=%d (search range: %d..%d)...\n",
                          (int) epochNumber + 1, (int) trialMinibatchSize, (int) RoundToMultipleOf64(minMinibatchSize), (int) RoundToMultipleOf64(maxMinibatchSize));
            }
            std::vector<EpochCriterion> epochEvalErrors(evaluationNodes.size(), EpochCriterion::Infinity());
            EpochCriterion epochCriterion(EpochCriterion::Infinity());

            // Train on a few minibatches and so we can observe the epochCriterion as we try increasing
            // minibatches with iteration of this loop.
            TrainOneMiniEpochAndReloadModel(net, refNet, refNode, epochNumber,
                                            m_epochSize, trainSetDataReader,
                                            learnRatePerSample, trialMinibatchSize, featureNodes,
                                            labelNodes, criterionNodes,
                                            evaluationNodes, inputMatrices,
                                            learnableNodes, smoothedGradients, smoothedCounts,
                                            /*out*/ epochCriterion, /*out*/ epochEvalErrors,
                                            isFirstIteration ? "BaseAdaptiveMinibatchSearch:" : "AdaptiveMinibatchSearch:",
                                            numFramesToUseInSearch);

            if (isFirstIteration)
            {
                // for the first iteration of the loop only, set baseCriterion
                // to the result we got from TrainOneMiniEpochAndReloadModel().
                baseCriterion = epochCriterion;
                lastGoodMinibatchSize = trialMinibatchSize;
                lastGoodEpochCriterion = baseCriterion;
                isFirstIteration = false;

                if (m_traceLevel > 0)
                {
                    LOGPRINTF(stderr, " AdaptiveMinibatchSearch Epoch[%d]: Computed baseCriterion %.8f for minibatchSize=%d\n",
                              (int) epochNumber + 1, baseCriterion.Average(), (int) trialMinibatchSize);
                }
            }
            else if (!epochCriterion.IsNan() &&
                     epochCriterion.Average() > (baseCriterion.Average() * (1.0 + (m_minibatchSearchCriterionErrorMargin / 100.0))))
            {
                // As soon as we see the Criterion (a measure of error) start to get larger than the
                // Criterion we started with, we stop.
                // TODO: if this is too sensitive, we can add a margin on the bases of percentage of
                // baseCriterion.
                break;
            }
            else
            {
                lastGoodMinibatchSize = trialMinibatchSize;
                lastGoodEpochCriterion = epochCriterion;
                if (m_traceLevel > 0 && trialMinibatchSizeFloat * minibatchSizeTuningFactor <= maxMinibatchSize)
                {
                    LOGPRINTF(stderr, " AdaptiveMinibatchSearch Epoch[%d]: Keep searching... epochCriterion = %.8f vs. baseCriterion = %.8f\n",
                              (int) epochNumber + 1, epochCriterion.Average(), baseCriterion.Average());
                }
            }
        }
        if (m_traceLevel > 0)
        {
            LOGPRINTF(stderr, " AdaptiveMinibatchSearch Epoch[%d]: Search successful. New minibatchSize is %d. epochCriterion = %.8f vs baseCriterion = %.8f\n",
                      (int) epochNumber + 1, (int) lastGoodMinibatchSize, lastGoodEpochCriterion.Average(), baseCriterion.Average());
        }
        return lastGoodMinibatchSize;
    }

    // run training over a small subset of an epoch, used by automatic LR and MB-size tuning
    template <class ElemType>
    void SGD<ElemType>::TrainOneMiniEpochAndReloadModel(ComputationNetworkPtr net,
                                                        ComputationNetworkPtr refNet,
                                                        const ComputationNodeBasePtr& refNode, const int epochNumber,
                                                        const size_t epochSize, IDataReader* trainSetDataReader,
                                                        const double learnRatePerSample,
                                                        const size_t minibatchSize,
                                                        const std::vector<ComputationNodeBasePtr>& featureNodes,
                                                        const std::vector<ComputationNodeBasePtr>& labelNodes,
                                                        const std::vector<ComputationNodeBasePtr>& criterionNodes,
                                                        const std::vector<ComputationNodeBasePtr>& evaluationNodes,
                                                        StreamMinibatchInputs* inputMatrices,
                                                        const std::list<ComputationNodeBasePtr>& learnableNodes,
                                                        std::list<Matrix<ElemType>>& smoothedGradients, vector<double> smoothedCounts,
                                                        /*out*/ EpochCriterion& epochCriterion,
                                                        /*out*/ std::vector<EpochCriterion>& epochEvalErrors,
                                                        std::string prefixMsg,
                                                        const size_t maxNumOfSamples)
    {
        TrainOneEpoch(net, refNet, refNode, epochNumber, epochSize,
                      trainSetDataReader, learnRatePerSample, minibatchSize, featureNodes,
                      labelNodes, criterionNodes, evaluationNodes,
                      inputMatrices, learnableNodes, smoothedGradients, smoothedCounts,
                      /*out*/ epochCriterion, /*out*/ epochEvalErrors,
                      "  " + prefixMsg, maxNumOfSamples); // indent log msg by 2 (that is 1 more than the Finished message below)

        LOGPRINTF(stderr, " Finished Mini-Epoch[%d]: ", (int) epochNumber + 1);
        epochCriterion.LogCriterion(criterionNodes[0]->NodeName());
        for (size_t j = 0; j < epochEvalErrors.size(); j++)
            epochEvalErrors[j].LogCriterion(evaluationNodes[j]->NodeName());
        fprintf(stderr, "learningRatePerSample = %.8g; minibatchSize = %d\n", learnRatePerSample, (int) minibatchSize);

        // go back to where we came from
        int baseModelEpoch = epochNumber - 1;
        let path = GetModelNameForEpoch(baseModelEpoch);
        //fprintf(stderr, "Reverting parameters back to %ls\n", path.c_str());
        net->RereadPersistableParameters<ElemType>(path);

        double dummyLearnRate;
        double dummyPrevCriterion;
        size_t dummyTotalTrainingSamplesSeen; // (not used)
        size_t dummyMinibatchSize;
        LoadCheckPointInfo(baseModelEpoch,
                           /*out*/ dummyTotalTrainingSamplesSeen,
                           /*out*/ dummyLearnRate,
                           smoothedGradients,
                           smoothedCounts,
                           /*out*/ dummyPrevCriterion,
                           /*out*/ dummyMinibatchSize);
    }

    // Attempts to compute the error signal for the whole utterance, which will
    // be fed to the neural network as features. Currently it is a workaround
    // for the two-forward-pass sequence and ctc training, which allows
    // processing more utterances at the same time. Only used in Kaldi2Reader.
    // TODO: move the two-forward-pass support out of the reader.
    template <class ElemType>
    void SGD<ElemType>::AttemptUtteranceDerivativeFeatures(ComputationNetworkPtr net,
                                                           IDataReader * trainSetDataReader,
                                                           const std::vector<ComputationNodeBasePtr>& featureNodes,
                                                           StreamMinibatchInputs* inputMatrices)
    {
        assert(trainSetDataReader != NULL);
        std::vector<std::vector<std::pair<wstring, size_t>>> uttInfo;
        auto pMBLayout = make_shared<MBLayout>();
        // TODO: use GetMinibatchIntoNetwork().
        while (trainSetDataReader->GetMinibatchCopy(uttInfo, *inputMatrices, pMBLayout))
        {
            ComputationNetwork::BumpEvalTimeStamp(featureNodes);

            auto& outputNodes = net->OutputNodes();
            if (outputNodes.empty())
                LogicError("no output node was found.");

            if (Globals::ShouldEnableShareNodeValueMatrices())
                InvalidArgument("AttemptUtteranceDerivativeFeatures cannot be used together with forward value memory sharing. "
                                "Set 'shareNodeValueMatrices=false' at the top level of your CNTK config file to get around this error");

            // BUGBUG (Issue #95): This is no longer correct once we have multiple input layouts.
            trainSetDataReader->CopyMBLayoutTo(net->GetMBLayoutPtrOfNetwork());
            net->ForwardProp(outputNodes[0]); // only evaluate the first output
            trainSetDataReader->SetNetOutput(uttInfo,
                                             dynamic_pointer_cast<ComputationNode<ElemType>>(outputNodes[0])->Value(),
                                             pMBLayout);
        }
    }

    template <class ElemType>
    void SGD<ElemType>::InitDistGradAgg(int numEvalNodes, int numGradientBits, int deviceId, int traceLevel)
    {
        assert(GetParallelizationMethod() == ParallelizationMethod::dataParallelSGD);

        if (numGradientBits != (8 * sizeof(ElemType)))
        {
            if (traceLevel > 0)
                fprintf(stderr, "Initializing dataParallelSGD for %d-bit quantization.\n", numGradientBits);
#ifdef CNTK_PARALLEL_TRAINING_SUPPORT
            if (Globals::UseV2Aggregator())
            {
                auto communicator = ::CNTK::QuantizedMPICommunicator(m_zeroThresholdFor1Bit, true, numGradientBits);
                m_distGradAgg = std::make_shared<V2AllReduceDistGradAggregator<ElemType>>(communicator, m_bufferedAsyncGradientAggregation, traceLevel, m_syncStatsTrace);
            }
            else
                m_distGradAgg = std::make_shared<AllReduceDistGradAggregator<ElemType>>(m_mpi, numGradientBits, m_zeroThresholdFor1Bit, true /*useQuantizationForSelfStripe*/, m_bufferedAsyncGradientAggregation, traceLevel, m_syncStatsTrace);
#else
            RuntimeError("Gradient quantization is unsupported in CNTK binaries built without quantized gradient aggregation support!");
#endif // !CNTK_PARALLEL_TRAINING_SUPPORT
        }
        else
        {
            if (traceLevel > 0)
                fprintf(stderr, "Initializing dataParallelSGD with FP%d aggregation.\n", numGradientBits);
            if (Globals::UseV2Aggregator()) // Currently used to check V2 against baselines.
                m_distGradAgg = std::make_shared<V2SimpleDistGradAggregator<ElemType>>(m_mpi, m_bufferedAsyncGradientAggregation, deviceId, m_syncStatsTrace, ::CNTK::MPICommunicator(m_packThresholdSizeInBytes));
            else
                m_distGradAgg = std::make_shared<SimpleDistGradAggregator<ElemType>>(m_mpi, m_bufferedAsyncGradientAggregation, deviceId, m_syncStatsTrace, m_packThresholdSizeInBytes);
        }

        m_gradHeader.reset(DistGradHeader::Create(numEvalNodes), [](DistGradHeader* ptr) { DistGradHeader::Destroy(ptr); });
    }

    template <class ElemType>
    void SGD<ElemType>::InitModelAggregationHandler(int traceLevel, DEVICEID_TYPE devID)
    {
        if (m_pMASGDHelper)
        {
            return; // no need to do anything if already initialized. TODO: make it singleton
        }
        if (GetParallelizationMethod() == ParallelizationMethod::modelAveragingSGD)
        {
            m_pMASGDHelper = make_shared<BasicModelAveragingSGD<ElemType>>(m_mpi, traceLevel, devID);
        }
        else if (GetParallelizationMethod() == ParallelizationMethod::blockMomentumSGD)
        {
#ifndef CNTK_PARALLEL_TRAINING_SUPPORT
            RuntimeError("Block Momentum is not supported in the main CNTK repo. You need to enable 1bit submodule.");
#else
            if (Globals::UseV2Aggregator())
            {
                auto communicator = ::CNTK::MPICommunicator();
                m_pMASGDHelper = make_shared<V2BlockMomentumSGD<ElemType>>(
                    m_mpi,
                    communicator,
                    traceLevel,
                    devID,
                    m_useNesterovBlockMomentum,
                    m_resetSGDMomentum,
                    m_blockLearningRate,
                    m_blockMomentumAsTimeConstant,
                    m_modelAggregationBlockSize);
            }
            else
                m_pMASGDHelper = make_shared<BlockMomentumSGD<ElemType>>(m_mpi, traceLevel, devID,
                                                                         m_useNesterovBlockMomentum, m_resetSGDMomentum,
                                                                         m_blockLearningRate, m_blockMomentumAsTimeConstant,
                                                                         m_modelAggregationBlockSize);
#endif
        }
    }

    // public:
    // UpdateWeights() - actual weight update, implementing various update rules
    template <class ElemType>
    void SGD<ElemType>::UpdateWeights(Matrix<ElemType> & functionValues, Matrix<ElemType> & gradientValues,
                                      Matrix<ElemType> & smoothedGradientValues, double& smoothedCount,
                                      const double learnRatePerSample, const double momentumPerSample,
                                      size_t actualMBSize,
                                      const double L2RegWeight, const double L1RegWeight,
                                      const bool needAveMultiplier,
                                      const bool useNesterovMomentum) const
    {
        // we use simple linear (instead of log linear) exponentiation here
        const double momentum = MomentumPerMB(momentumPerSample, actualMBSize);
#if DUMPOUTPUT
        LOGPRINTF(stderr, "learnRatePerSample=%0.8f, momentum=%0.8f, actualMBSize=%ld\n",
                  learnRatePerSample, momentum, actualMBSize);
        LOGPRINTF(stderr, "GradUpdateType()=%d, GradientUpdateNoiseStd()=%0.8f\n",
                  GradUpdateType(), GradientUpdateNoiseStd());
        gradientValues.Print("Gradient Input");
        smoothedGradientValues.Print("Smoothed Gradient Input");
#endif

        // make actualMBSize is a valid value
        assert(actualMBSize > 0);

        // clipping gradients to prevent outliers
        ClipGradient(gradientValues, actualMBSize);

        GradientsUpdateType adpType = GradUpdateType();
        double noiseStd = GradientUpdateNoiseStd();
        Matrix<ElemType> sgdUpdateNoise((DEVICEID_TYPE) functionValues.GetDeviceId());
        if (noiseStd > 0)
        {
            // get the gradient structure since gradient is sparse
            sgdUpdateNoise.SetValue(gradientValues);

            // reset its value to random
            sgdUpdateNoise.SetGaussianRandomValue(0, (ElemType) noiseStd);
        }

        // L2 regularizer
        if (L2RegWeight > 0)
        {
            // multiply by actualMBSize so that it's invariant to minibatch size since learning rate is per sample
            Matrix<ElemType>::ScaleAndAdd((ElemType)(L2RegWeight * actualMBSize), functionValues, gradientValues);
        }

        if (adpType == GradientsUpdateType::None)
        {
            // even if momentum is 0.0, still need to call a momentum-based update to store
            // [learning rate * current gradient values] in the smoothed gradients, in case
            // the momentum value for the next epoch is non-zero. Note that the unit gain factor
            // can not be computed from the momentum scaled for per sample update; it should be
            // based on the original momentum rate.
            if (!useNesterovMomentum)
            {
                functionValues.MomentumSGDUpdate(gradientValues, smoothedGradientValues,
                                                 ElemType(learnRatePerSample),
                                                 //By defualt, V1 uses UnitGain momentum. TODO: Do we need to enable V1 with non unit gain update?
                                                 ElemType(momentum), ElemType(1.0) - ElemType(momentum));
            }
            else
            {
                functionValues.NesterovAcceleratedMomentumSGDUpdate(gradientValues, smoothedGradientValues,
                                                                    ElemType(learnRatePerSample), ElemType(momentum), ElemType(1.0) - ElemType(momentum));
            }
        }
        else if (adpType == GradientsUpdateType::AdaGrad)
        {
            double aveMultiplier = smoothedGradientValues.Adagrad(gradientValues, needAveMultiplier);
            Matrix<ElemType>::ScaleAndAdd((ElemType)(-learnRatePerSample / aveMultiplier), gradientValues, functionValues);
        }
        else if (adpType == GradientsUpdateType::FSAdaGrad)
        {
            const double varMomentum = (exp(-1.0 * actualMBSize / m_gradType.varianceTimeConstant));
#if 0 // BUGBUG!!! This replicates a bug carried over from Alexey's original implementation.
        static double smoothedCount = 0;
#endif
            smoothedCount = varMomentum * smoothedCount + (1.0 - varMomentum) * actualMBSize;
            double targetAdagradAvDenom_x_sqrtAdagradSqrFrames = m_gradType.targetAdagradAvDenom * sqrt(smoothedCount);

            smoothedGradientValues.FSAdagradUpdate(
                gradientValues, functionValues, targetAdagradAvDenom_x_sqrtAdagradSqrFrames,
                learnRatePerSample, momentum, varMomentum, ElemType(1.0) - ElemType(momentum));
        }
        else if (adpType == GradientsUpdateType::RmsProp)
        {
            double aveMultiplier = smoothedGradientValues.RmsProp(gradientValues, (ElemType) m_rpi.gamma,
                                                                  (ElemType) m_rpi.inc, (ElemType) m_rpi.max,
                                                                  (ElemType) m_rpi.dec, (ElemType) m_rpi.min, needAveMultiplier, true);
            Matrix<ElemType>::ScaleAndAdd((ElemType)(-learnRatePerSample / aveMultiplier), gradientValues, functionValues);
        }

        if (noiseStd > 0)
        {
            Matrix<ElemType>::ScaleAndAdd(1.0, sgdUpdateNoise, functionValues);
        }

        // L1 regularizer with proximal gradient descent method
        if (L1RegWeight > 0)
        {
            // multiply by actualMBSize so that it's invariant to minibatch size since learning rate is per sample
            functionValues.InplaceSoftThreshold((ElemType)(learnRatePerSample * L1RegWeight * actualMBSize));
        }

#if DUMPOUTPUT
        functionValues.Print("Parameter Update");
#endif
    }

    // protected:
    template <class ElemType>
    void SGD<ElemType>::ClipGradient(Matrix<ElemType> & gradient, const size_t actualMBSize) const
    {
        if (m_clippingThresholdPerSample != std::numeric_limits<double>::infinity())
        {
            double maxGradientPerMB = m_clippingThresholdPerSample * actualMBSize;
            if (m_gradientClippingWithTruncation)
                gradient.InplaceTruncate((ElemType)(maxGradientPerMB));
            else
            {
                // norm2 normalized
                double gradientNorm = gradient.FrobeniusNorm();
                if (gradientNorm > maxGradientPerMB)
                {
                    double normFactor = maxGradientPerMB / gradientNorm;
                    gradient *= (ElemType) normFactor;
                }
            }
        }
    }

    template <class ElemType>
    void SGD<ElemType>::SaveCheckPointInfo(const size_t epoch, const size_t totalSamplesSeen,
                                           const double learnRatePerSample,
                                           const std::list<Matrix<ElemType>>& smoothedGradients,
                                           const std::vector<double>& smoothedCounts,
                                           const double prevCriterion,
                                           const size_t minibatchSize)
    {
        // In case of parallel training only the main node should we saving the checkpoint to prevent
        // the parallel training nodes from colliding to write the same file
        if ((m_mpi == nullptr) || m_mpi->IsMainNode())
        {
            wstring checkPointFileName = GetCheckPointFileNameForEpoch(int(epoch));
            // Saving into temporary file and then renaming it to the checkPointFileName
            // This is a standard trick to avoid havign corrupted checkpoints files if process dies during writing
            wstring tempFileName = checkPointFileName + L".tmp";

            {
                File fstream(tempFileName, FileOptions::fileOptionsBinary | FileOptions::fileOptionsWrite);
                // Buffer writes in memory then flush to filesystem, which reduces number of small writes
                fstream.Setvbuf();
                fstream.PutMarker(FileMarker::fileMarkerBeginSection, L"BVersion");
                fstream << (size_t) CURRENT_CNTK_CHECKPOINT_VERSION;
                fstream.PutMarker(FileMarker::fileMarkerEndSection, L"EVersion");

                fstream.PutMarker(FileMarker::fileMarkerBeginSection, L"BCKP");
                fstream.PutMarker(FileMarker::fileMarkerBeginSection, L"BLearnRate");
                fstream << totalSamplesSeen << learnRatePerSample << prevCriterion;
                fstream.PutMarker(FileMarker::fileMarkerEndSection, L"ELearnRate");

                fstream.PutMarker(FileMarker::fileMarkerBeginSection, L"BMinibatchSize");
                fstream << minibatchSize;
                fstream.PutMarker(FileMarker::fileMarkerEndSection, L"EMinibatchSize");

                fstream.PutMarker(FileMarker::fileMarkerBeginSection, L"BGradient");

                for (auto smoothedGradientIter = smoothedGradients.begin(); smoothedGradientIter != smoothedGradients.end(); smoothedGradientIter++)
                {
                    const Matrix<ElemType>& smoothedGradientValues = *smoothedGradientIter;
                    fstream << smoothedGradientValues;
                }

                fstream.PutMarker(FileMarker::fileMarkerEndSection, L"EGradient");

                fstream.PutMarker(FileMarker::fileMarkerEndSection, L"BCount");

                for (auto sc : smoothedCounts)
                    fstream << sc;

                fstream.PutMarker(FileMarker::fileMarkerEndSection, L"ECount");

                if (m_saveBestModelPerCriterion)
                {
                    fstream.PutMarker(FileMarker::fileMarkerBeginSection, L"BCriteria");
                    const int32_t criteriaSize = static_cast<int32_t>(m_criteriaBestEpoch.size());
                    fstream << criteriaSize;
                    for (const auto& criterion : m_criteriaBestEpoch)
                    {
                        fstream << criterion.second.criterionMinValue << criterion.second.epochIndex;
                    }
                    fstream.PutMarker(FileMarker::fileMarkerEndSection, L"ECriteria");
                }

                fstream.PutMarker(FileMarker::fileMarkerEndSection, L"ECKP");
                if (m_pMASGDHelper)
                    m_pMASGDHelper->SaveToCheckPoint(fstream);
                // Ensuring that data is written
                fstream.Flush();
            }

            _wunlink(checkPointFileName.c_str());
            renameOrDie(tempFileName, checkPointFileName);
        }
    }

    template <class ElemType>
    bool SGD<ElemType>::TryLoadCheckPointInfo(const size_t epochNumber,
                                              /*out*/ size_t& totalSamplesSeen,
                                              /*out*/ double& learnRatePerSample,
                                              std::list<Matrix<ElemType>>& smoothedGradients,
                                              std::vector<double>& smoothedCounts,
                                              /*out*/ double& prevCriterion,
                                              /*out*/ size_t& minibatchSize)
    {
        // gracefully handle if a checkpoint file is missing
        // This means a user wanted to continue training from an older model, but that model had no checkpoint info anymore.
        // This is valid, we just don't get the features that require previous models, such as LR or MBSize control.
        let checkPointFileName = GetCheckPointFileNameForEpoch(int(epochNumber));
        if (!fexists(checkPointFileName.c_str()))
        {
            // initialize as if nothing
            totalSamplesSeen = 0;
            learnRatePerSample = numeric_limits<double>::quiet_NaN(); // must be overwritten
            prevCriterion = 0;
            minibatchSize = m_mbSize[epochNumber];

            LOGPRINTF(stderr, "Warning: Checkpoint file is missing. Parameter-learning state (such as momentum) will be reset.\n");
            return false;
        }

        LoadCheckPointInfo(epochNumber, totalSamplesSeen, learnRatePerSample, smoothedGradients, smoothedCounts, prevCriterion, minibatchSize);
        return true;
    }

    template <class ElemType>
    void SGD<ElemType>::LoadCheckPointInfo(const size_t epochNumber,
                                           /*out*/ size_t& totalSamplesSeen,
                                           /*out*/ double& learnRatePerSample,
                                           std::list<Matrix<ElemType>>& smoothedGradients,
                                           std::vector<double>& smoothedCounts,
                                           /*out*/ double& prevCriterion,
                                           /*out*/ size_t& minibatchSize)
    {
        let checkPointFileName = GetCheckPointFileNameForEpoch(int(epochNumber));
        //fprintf(stderr, "Loading checkpoint info from %ls\n", checkPointFileName.c_str());
        File fstream(checkPointFileName,
                     FileOptions::fileOptionsBinary | FileOptions::fileOptionsRead);

        // version info
        size_t ckpVersion = CNTK_CHECKPOINT_VERSION_1; // if no version info is found -> version 1
        if (fstream.TryGetMarker(FileMarker::fileMarkerBeginSection, L"BVersion"))
        {
            fstream >> ckpVersion;
            fstream.GetMarker(FileMarker::fileMarkerEndSection, L"EVersion");
        }

        fstream.GetMarker(FileMarker::fileMarkerBeginSection, L"BCKP");

        fstream.GetMarker(FileMarker::fileMarkerBeginSection, L"BLearnRate");
        fstream >> totalSamplesSeen >> learnRatePerSample >> prevCriterion;
        fstream.GetMarker(FileMarker::fileMarkerEndSection, L"ELearnRate");

        if (fstream.TryGetMarker(FileMarker::fileMarkerBeginSection, L"BMinibatchSize"))
        {
            fstream >> minibatchSize;
            fstream.GetMarker(FileMarker::fileMarkerEndSection, L"EMinibatchSize");
        }
        else // some legacy files do not have this
        {
            minibatchSize = m_mbSize[epochNumber];
        }

        fstream.GetMarker(FileMarker::fileMarkerBeginSection, L"BGradient");

        for (auto smoothedGradientIter = smoothedGradients.begin(); smoothedGradientIter != smoothedGradients.end(); smoothedGradientIter++)
        {
            Matrix<ElemType>& smoothedGradientValues = *smoothedGradientIter;
            fstream >> smoothedGradientValues;
        }
        fstream.GetMarker(FileMarker::fileMarkerEndSection, L"EGradient");

        if (fstream.TryGetMarker(FileMarker::fileMarkerBeginSection, L"BCount"))
        {
            for (auto& sc : smoothedCounts)
                fstream >> sc;
            fstream.GetMarker(FileMarker::fileMarkerEndSection, L"ECount");
        }
        else // deal with legacy checkpoints
            std::fill(smoothedCounts.begin(), smoothedCounts.end(), static_cast<double>(minibatchSize));

        if (fstream.TryGetMarker(FileMarker::fileMarkerBeginSection, L"BCriteria"))
        {
            int32_t criteriaSize = 0;
            fstream >> criteriaSize;
            // Sanity check: criteria size in checkpoint must be the same as preallocated one we shall fill in.
            if (criteriaSize != static_cast<int32_t>(m_criteriaBestEpoch.size()))
            {
                RuntimeError(
                    "Criteria size mismatch: checkpoint size %d but input size %d",
                    criteriaSize,
                    static_cast<int32_t>(m_criteriaBestEpoch.size()));
            }
            for (auto& criterion : m_criteriaBestEpoch)
                fstream >> criterion.second.criterionMinValue >> criterion.second.epochIndex;
            fstream.GetMarker(FileMarker::fileMarkerBeginSection, L"ECriteria");
        }

        fstream.GetMarker(FileMarker::fileMarkerEndSection, L"ECKP");

        if (m_pMASGDHelper)
        {
            m_pMASGDHelper->LoadFromCheckPoint(fstream);
        }

        return;
    }

    template <class ElemType>
    wstring SGD<ElemType>::GetCheckPointFileNameForEpoch(const int epoch)
    {
        return GetModelNameForEpoch(epoch) + L".ckp";
    }

    template <class ElemType>
    wstring SGD<ElemType>::GetModelNameForEpoch(const int epoch, bool bLastModel) const
    {
        int epoch1Base = epoch + 1;
        if (epoch1Base == m_maxEpochs || bLastModel)
        {
            return m_modelPath;
        }
        else
        {
            wstring w = msra::strfun::wstrprintf(L"%ls.%d", m_modelPath.c_str(), (int) epoch1Base);
            return w;
        }
    }

    // return -1 if nothing exists
    template <class ElemType> // TODO: needed?
    int SGD<ElemType>::DetermineStartEpoch(const bool makeMode)
    {
        if (!makeMode)
        {
            // always start from scratch
            return -1;
        }

        int firstEpoch = -1;

        wstring curEpochFile = GetModelNameForEpoch(int(m_maxEpochs) - 1);
        for (int e = int(m_maxEpochs) - 1; e >= -1; e--)
        {
            const wstring prevEpochFile = GetModelNameForEpoch(e - 1);

            if (msra::files::fuptodate(curEpochFile, prevEpochFile, false))
            {
                firstEpoch = e + 1;
                break;
            }
            else
            {
                curEpochFile = prevEpochFile;
            }
        }
        if (firstEpoch == m_maxEpochs)
            LOGPRINTF(stderr, "Final model exists: %ls\n", GetModelNameForEpoch(firstEpoch - 1).c_str());

        return firstEpoch;
    }

#define EPSILON 1e-5

    // this probes the automatic gradient computation with random inputs
    template <class ElemType>
    bool SGD<ElemType>::GradientCheck(ComputationNetworkPtr net,
                                      const std::vector<ComputationNodeBasePtr>& criterionNodes,
                                      const std::list<ComputationNodeBasePtr>& learnableNodes,
                                      int npos2)
    {
        ScopedNetworkOperationMode modeGuard(net, NetworkOperationMode::training);

        net->StartEvaluateMinibatchLoop(criterionNodes[npos2]);

        vector<string> errMsgs; // TODO: These are created but actually not returned, only their count is checked.

        // gradient checking
        for (auto nodeIter = learnableNodes.begin(); nodeIter != learnableNodes.end(); nodeIter++)
        {
            ComputationNodePtr node = dynamic_pointer_cast<ComputationNode<ElemType>>(*nodeIter);
            char wstrtmp[2048];

            for (size_t itry = 0; itry < min((size_t) 50, node->Value().GetNumElements()); itry++)
            {
                // no support to sparse matrix yet
                int irow = (int) fmod(rand(), node->Value().GetNumRows() - 1);
                int icol = (int) fmod(rand(), node->Value().GetNumCols() - 1);
                irow = max(0, irow);
                icol = max(0, icol);

                fprintf(stderr, "\n");
                LOGPRINTF(stderr, "###### d%ls######\n", node->NodeName().c_str());

                double eOrg = node->Value()(irow, icol);
                node->Value().TransferToDeviceIfNotThere(net->GetDeviceId(), true);

                node->BumpEvalTimeStamp();

                net->ForwardProp(criterionNodes[npos2]);
                net->Backprop(criterionNodes[npos2]);

                if (node->Gradient().GetMatrixType() == MatrixType::SPARSE)
                {
                    break;
                }

                // double mbEvalCri =
                // criterionNode should be a scalar
                // TODO: why is this value not used?
                criterionNodes[npos2]->Get00Element();
                double eGradErr = node->Gradient()(irow, icol);
                node->Gradient().TransferToDeviceIfNotThere(net->GetDeviceId(), true);

                double ePos = eOrg + EPSILON;
                double eNeg = eOrg - EPSILON;

                node->Value()(irow, icol) = (ElemType) ePos;
                node->Value().TransferToDeviceIfNotThere(net->GetDeviceId(), true);

                node->BumpEvalTimeStamp();
                net->ForwardProp(criterionNodes[npos2]);
                // criterionNode should be a scalar

                double mbEvalCriPos = criterionNodes[npos2]->Get00Element(); // TODO: make Get00Element() a function of ComputationNodeBase

                node->Value()(irow, icol) = (ElemType) eNeg;
                node->Value().TransferToDeviceIfNotThere(net->GetDeviceId(), true);

                node->BumpEvalTimeStamp();
                net->ForwardProp(criterionNodes[npos2]);

                // criterionNode should be a scalar
                double mbEvalCriNeg = criterionNodes[npos2]->Get00Element();

                // back to its original parameter value
                node->Value()(irow, icol) = (ElemType) eOrg;
                node->Value().TransferToDeviceIfNotThere(net->GetDeviceId(), true);

                // check if they are consistent
                double eGradNum = ((mbEvalCriPos - mbEvalCriNeg) / (ePos - eNeg));
                double threshold = pow(10.0,
                                       max(0.0,
                                           ceil(log10(min(fabs(eGradErr),
                                                          fabs(eGradNum))))) -
                                           (int) m_gradientCheckSigDigit);
                double diff = fabs(eGradErr - eGradNum);
                bool wrong = (std::isnan(diff) || diff > threshold);
                if (wrong)
                {
                    fprintf(stderr, "\n");
                    LOGPRINTF(stderr, "d%ls Numeric gradient = %e, Error BP gradient = %e\n",
                              node->NodeName().c_str(), eGradNum, eGradErr);
                    sprintf(wstrtmp, "\nd%ls Numeric gradient = %e, Error BP gradient = %e\n",
                            node->NodeName().c_str(), eGradNum, eGradErr);
                    errMsgs.push_back(wstrtmp);
                }
            }
        }

        return errMsgs.empty();
    }

    template <class ElemType>
    void SGD<ElemType>::MarkDropoutNodesEvalTimeStampAsOutdated(const ComputationNetworkPtr& net, const ComputationNodeBasePtr& criterionNode)
    {
        list<ComputationNodeBasePtr> dropoutNodes = net->GetNodesWithType(OperationNameOf(DropoutNode), criterionNode);
        for (auto& nodeIter : dropoutNodes)
            nodeIter->SetEvalTimeStampOutdatedWrtAll();
    }

    template class SGD<float>;
    template class SGD<double>;

    // =======================================================================
    // class SGDParams
    // =======================================================================

    static AdaptationRegType ParseAdaptationRegType(const wstring& s)
    {
        if (EqualCI(s, L"") || EqualCI(s, L"none"))
            return AdaptationRegType::None;
        else if (EqualCI(s, L"kl") || EqualCI(s, L"klReg"))
            return AdaptationRegType::KL;
        else
            InvalidArgument("ParseAdaptationRegType: Invalid Adaptation Regularization Type. Valid values are (none | kl)");
    }

    static GradientsUpdateType ParseGradUpdateType(const wstring& s)
    {
        if (EqualCI(s, L"") || EqualCI(s, L"none"))
            return GradientsUpdateType::None;
        else if (EqualCI(s, L"adagrad"))
            return GradientsUpdateType::AdaGrad;
        else if (EqualCI(s, L"rmsProp"))
            return GradientsUpdateType::RmsProp;
        else if (EqualCI(s, L"fsAdagrad"))
            return GradientsUpdateType::FSAdaGrad;
        // legacy, deprecated
        else if (EqualCI(s, L"normal") || EqualCI(s, L"simple"))
            return GradientsUpdateType::None;
        else
            InvalidArgument("ParseGradUpdateType: Invalid Gradient Updating Type. Valid values are (none | adagrad | rmsProp | fsAdagrad )");
    }

    static ParallelizationMethod ParseParallelizationMethod(const wstring& s)
    {
        if (EqualCI(s, L"") || EqualCI(s, L"none"))
            return ParallelizationMethod::none;
        else if (EqualCI(s, L"DataParallelSGD"))
            return ParallelizationMethod::dataParallelSGD;
        else if (EqualCI(s, L"ModelAveragingSGD"))
            return ParallelizationMethod::modelAveragingSGD;
        else if (EqualCI(s, L"BlockMomentumSGD"))
            return ParallelizationMethod::blockMomentumSGD;
        else if (EqualCI(s, L"dataParallelASGD"))
            return ParallelizationMethod::dataParallelASGD;
        else
            InvalidArgument("ParseParallelizationMethod: Invalid Parallelization Method. Valid values are (none | DataParallelSGD | ModelAveragingSGD | BlockMomentumSGD | dataParallelASGD)");
    }

    static LearningRateSearchAlgorithm ParseLearningRateSearchType(const wstring& s)
    {
        if (EqualCI(s, L"false") || EqualCI(s, L"none"))
            return LearningRateSearchAlgorithm::None;
        else if (EqualCI(s, L"searchBeforeEpoch"))
            return LearningRateSearchAlgorithm::SearchBeforeEpoch;
        else if (EqualCI(s, L"adjustAfterEpoch"))
            return LearningRateSearchAlgorithm::AdjustAfterEpoch;
        // legacy, deprecated
        else if (EqualCI(s, L"beforeEpoch") || EqualCI(s, L"before"))
            return LearningRateSearchAlgorithm::SearchBeforeEpoch;
        else if (EqualCI(s, L"afterEpoch") || EqualCI(s, L"after"))
            return LearningRateSearchAlgorithm::AdjustAfterEpoch;
        else
            InvalidArgument("autoAdjustLR: Invalid learning rate search type. Valid values are (none | searchBeforeEpoch | adjustAfterEpoch)");
    }

#ifdef ASGD_PARALLEL_SUPPORT
    static AdjustLearningRateAtBeginning AdjustLearningRateAtBeginningType(const wstring& s)
    {
        if (EqualCI(s.c_str(), L"") || EqualCI(s.c_str(), L"none"))
            return AdjustLearningRateAtBeginning::None;
        else if (EqualCI(s.c_str(), L"linearly"))
            return AdjustLearningRateAtBeginning::Linearly;
        else if (EqualCI(s.c_str(), L"staircase"))
            return AdjustLearningRateAtBeginning::Staircase;
        else
            InvalidArgument("AdjustLearningRateatBeginningType: Invalid Type. Valid values are (None | Linearly | Staircase)");
    }
#endif

    template <class ConfigRecordType>
    SGDParams::SGDParams(const ConfigRecordType& configSGD, size_t sizeofElemType)
    {
        floatargvector learningRatesPerMB = configSGD(L"learningRatesPerMB", ConfigRecordType::Array(floatargvector()));

        floatargvector learningRatesPerSample = configSGD(L"learningRatesPerSample", ConfigRecordType::Array(floatargvector()));

        string executionEngineValue = configSGD(L"executionEngine", "synchronous");

        // AutoAdjust Parameters
        const ConfigRecordType& configAALR(configSGD(L"AutoAdjust", ConfigRecordType::Record()));
        m_autoLearnRateSearchType = ParseLearningRateSearchType(configAALR(L"autoAdjustLR", L"None"));
        m_reduceLearnRateIfImproveLessThan = configAALR(L"reduceLearnRateIfImproveLessThan", 0.0);
        m_continueReduce = configAALR(L"continueReduce", false);
        m_learnRateAdjustInterval = configAALR(L"learnRateAdjustInterval", (size_t) 1);
        m_learnRateAdjustInterval = max((size_t) 1, m_learnRateAdjustInterval); // minimum interval is 1 epoch
        m_learnRateDecreaseFactor = configAALR(L"learnRateDecreaseFactor", 0.618);
        m_increaseLearnRateIfImproveMoreThan = configAALR(L"increaseLearnRateIfImproveMoreThan", numeric_limits<double>::infinity());
        m_learnRateIncreaseFactor = configAALR(L"learnRateIncreaseFactor", 1.382);

        // AutoAdjust Auto Adjust Minibatch Parameters
        m_autoAdjustMinibatch = configAALR(L"autoAdjustMinibatch", false);
        m_minibatchSizeTuningFrequency = configAALR(L"minibatchSizeTuningFrequency", (size_t) 1);
        m_minibatchSizeTuningMax = configAALR(L"minibatchSizeTuningMax", (size_t) 1048576);
        m_minibatchSearchCriterionErrorMargin = configAALR(L"minibatchSearchCriterionErrorMargin", (size_t) 1);

        m_numPrevLearnRates = configAALR(L"numPrevLearnRates", (size_t) 5);
        m_numBestSearchEpoch = configAALR(L"numBestSearchEpoch", (size_t) 1);
        m_loadBestModel = configAALR(L"loadBestModel", true);
        m_useCVSetControlLRIfCVExists = configAALR(L"UseCVSetControlLRIfCVExists", true);
        m_useEvalCriterionControlLR = configAALR(L"UseEvalCriterionControlLR", false);

        // TODO: mbSize and truncated should be specified differently for truncated BPTT:
        //       mbSize = total number of samples after which a model update should happen
        //       truncated = truncation length
        m_mbSize = configSGD(L"minibatchSize", ConfigRecordType::Array(intargvector(vector<int>{256})));
        m_truncated = configSGD(L"truncated", false);
        m_maxSamplesInRAM = configSGD(L"maxSamplesInRAM", (size_t) SIZE_MAX);
        m_numSubminiBatches = configSGD(L"numSubminibatches", (size_t) 1);

        m_packThresholdSizeInBytes = configSGD(L"packThresholdSizeInKB", DEFAULT_PACK_THRESHOLD_SIZE_IN_KB) * 1024;

        if (configAALR.Exists(L"numMiniBatch4LRSearch"))
        {
            LOGPRINTF(stderr, "WARNING: 'numMiniBatch4LRSearch' is deprecated, please remove it and use 'numSamples4Search' instead.\n");
            // the number of minibatches used to search
            // the learning rate. It's typically set to 10-20% of
            // the total minibatches in an epoch.
            auto numMiniBatch4LRSearch = configAALR(L"numMiniBatch4LRSearch", ConfigRecordType::Array(intargvector(vector<int>{500})));
            m_numSamples4Search.resize(numMiniBatch4LRSearch.size());
            for (size_t i = 0; i < numMiniBatch4LRSearch.size(); ++i)
                m_numSamples4Search[i] = numMiniBatch4LRSearch[i] * m_mbSize[i];
        }
        else
        {
            // Default is default mbSize * 500, same as above.
            intargvector defaultValues;
            defaultValues.resize(m_mbSize.size());
            std::transform(m_mbSize.begin(), m_mbSize.end(), defaultValues.begin(), [](int v) { return v * 500; });
            m_numSamples4Search = configAALR(L"numSamples4Search", ConfigRecordType::Array(defaultValues));
        }

        // the number of samples in each epoch (0 means, use all the samples in each epoch).
        m_epochSize = configSGD(L"epochSize", (size_t) 0);
        // the number of samples in each epoch (0 means, use all the samples in each epoch).
        if (m_epochSize == 0)
            m_epochSize = requestDataSize;
        m_maxComputedEpochSize = m_epochSize;

        // the total number of epochs to run.
        m_maxEpochs = configSGD(L"maxEpochs");

        // Note: Momentum is best specified as a MB-size agnostic fashion.
        // Because momentum per sample is a number very close to 1, it is more handy to use a logarithmic specification.
        // We use 'momentumAsTimeConstant' to specify the time constant of the low-pass filter that momentum really is.
        // To convert a typical per-MB momentum value of 'm' used with a MB size of 'N', use momentumAsTimeConstant = -N/ln(m).
        // For the common configuration of momentum 0.9 at MB size of 256, that is momentumAsTimeConstant = 2429.8.
        floatargvector momentumPerMB = configSGD(L"momentumPerMB", ConfigRecordType::Array(floatargvector()));
        floatargvector momentumPerSample = configSGD(L"momentumPerSample", ConfigRecordType::Array(floatargvector()));
        floatargvector momentumAsTimeConstant = configSGD(L"momentumAsTimeConstant", ConfigRecordType::Array(floatargvector()));
        bool useNesterovMomentum = configSGD(L"useNAG", false);

        m_maxTempMemSizeInSamplesForCNN = configSGD(L"maxTempMemSizeInSamplesForCNN", (size_t) 0);

        m_traceLevel = configSGD(L"traceLevel", 0);
        m_numMBsToShowResult = configSGD(L"numMBsToShowResult", (size_t) 10);
        m_firstMBsToShowResult = configSGD(L"firstMBsToShowResult", (size_t) 0);
        m_numMBsToCUDAProfile = configSGD(L"numMBsToCUDAProfile", (size_t) 0);

        // Parameters that control logging of training progress in TensorBoard.
        // Directory to create TensorBoard event files in. If empty (default), the progress is not logged as event files.
        m_tensorBoardLogDir = static_cast<std::wstring>(configSGD(L"tensorBoardLogDir", L""));
        // Frequency at which to log intermediate training progress results. Used only when tensorBoardLogDir is not empty.
        // Setting this to 0 disables intermediate progress logging (only per-epoch loss/eval metric are logged).
        // Setting this to any other value (n) will log average loss/eval metric for each n minibatches.
        m_tensorBoardNumMBsToLogResult = configSGD(L"tensorBoardNumMBsToLogResult", m_numMBsToShowResult);

        m_gradientClippingWithTruncation = configSGD(L"gradientClippingWithTruncation", true);
        m_clippingThresholdPerSample = configSGD(L"clippingThresholdPerSample", numeric_limits<double>::infinity());

        // sequence-training parameters
        m_hSmoothingWeight = configSGD(L"hSmoothingWeight", 0.95);
        m_frameDropThresh = configSGD(L"frameDropThresh", 1e-10);
        m_doReferenceAlign = configSGD(L"doReferenceAlign", false);
        m_seqGammarCalcUsesMBR = configSGD(L"seqGammarUsesMBR", false);
        m_seqGammarCalcAMF = configSGD(L"seqGammarAMF", 14.0);
        m_seqGammarCalcLMF = configSGD(L"seqGammarLMF", 14.0);
        m_seqGammarCalcbMMIFactor = configSGD(L"seqGammarBMMIFactor", 0.0);
        m_seqGammarCalcWP = configSGD(L"seqGammarWordPen", 0.0);
        m_disableRegInBatchNormalization = configSGD(L"disableRegInBatchNormalization", false);

        m_dropoutRates = configSGD(L"dropoutRate", ConfigRecordType::Array(doubleargvector(vector<double>{0.0})));
        m_batchNormalizationTimeConstant = configSGD(L"batchNormalizationTimeConstant", ConfigRecordType::Array(doubleargvector(vector<double>{0})));
        m_batchNormalizationBlendTimeConstant = configSGD(L"batchNormalizationBlendTimeConstant", ConfigRecordType::Array(doubleargvector(vector<double>{0})));

        GradientsUpdateType gradUpdateType = ParseGradUpdateType(configSGD(L"gradUpdateType", L"None"));
        m_gradType.type = gradUpdateType;
        m_gradType.gaussianNoiseInjectStd = (float) configSGD(L"gaussianNoiseInjectStd", 0.0);

        // parameters for FSAdaGrad
        m_gradType.varianceTimeConstant = configSGD(L"varianceTimeConstant", 2 * 3600 * 100); // default originates from 2h of speech
        m_gradType.targetAdagradAvDenom = configSGD(L"fsAdagradTargetAvDenom", 1.0);          // TODO: deprecated parameter kept for back compat (set to 0.0025 inconjunction with reenabling the static bug)

        // extract RMSProp parameters from config, if they exist. Default to reasonable values.
        m_rpi.dec = configSGD(L"rms_wgt_dec", 0.75);
        m_rpi.inc = configSGD(L"rms_wgt_inc", 1.2);
        m_rpi.min = configSGD(L"rms_wgt_min", 0.1);
        m_rpi.max = configSGD(L"rms_wgt_max", 10.0);
        m_rpi.gamma = configSGD(L"rms_gamma", 0.99);

        m_needAveMultiplier = configSGD(L"normWithAveMultiplier", true);
        m_L2RegWeight = configSGD(L"L2RegWeight", 0.0);
        m_L1RegWeight = configSGD(L"L1RegWeight", 0.0);

        // for backward support. future setups should use gradUpdateType='AdaGrad', instead of useAdagrad=true
        if (configSGD(L"useAdagrad", false))
            m_gradType.type = GradientsUpdateType::AdaGrad;

        m_adaptationRegType = ParseAdaptationRegType(configSGD(L"adaptationRegType", L"None"));
        m_adaptationRegWeight = configSGD(L"adaptationRegWeight", 0.0);

        // gradient check setup
        m_doGradientCheck = configSGD(L"gradientcheck", false);
        m_gradientCheckSigDigit = configSGD(L"sigFigs", 6.0); // TODO: why is this a double?

        if (m_doGradientCheck && sizeofElemType != sizeof(double))
        {
            LogicError("Gradient check needs to use precision = 'double'.");
        }

        m_useAllDataForPreComputedNode = configSGD(L"UseAllDataForPreComputedNode", true);

        // consistency checks
        for (size_t i = 0; i < m_mbSize.size(); i++)
        {
            if (m_epochSize != requestDataSize && m_epochSize < m_mbSize[i])
            {
                InvalidArgument("epoch size must be larger than mbsize.");
            }
        }

        if (m_autoLearnRateSearchType == LearningRateSearchAlgorithm::None &&
            (learningRatesPerSample.size() == 0 && learningRatesPerMB.size() == 0))
        {
            InvalidArgument("If autoLearnRateSearchType is false you must specify the learningRatesPerSample or learningRatesPerMB parameter.");
        }

        if (learningRatesPerSample.size() > 0 && learningRatesPerMB.size() > 0)
        {
            InvalidArgument("You specified both learningRatesPerSample and learningRatesPerMB. Please comment out one of them.");
        }

        if (learningRatesPerSample.size() > 0)
        {
            m_learningRatesParam = learningRatesPerSample;
            m_learningRatesSpecifiedForMBSize = intargvector(L"1");
        }
        else if (learningRatesPerMB.size() > 0) // this actually means per specified minibatch size
        {
            m_learningRatesParam = learningRatesPerMB;
            m_learningRatesSpecifiedForMBSize = m_mbSize;
        }

        if ((int) (momentumPerSample.size() > 0) + (int) (momentumPerMB.size() > 0) + (int) (momentumAsTimeConstant.size() > 0) > 1)
        {
            InvalidArgument("You specified more than one of momentumPerSample, momentumPerMB, and momentumAsTimeConstant. Please only specify one.");
        }

        if (momentumPerSample.size() > 0) // note: noone would ever use this; use momentumAsTimeConstant instead
        {
            m_momentumParam = momentumPerSample;
            m_momentumSpecifiedForMBSize = intargvector(L"1");
        }
        else if (momentumAsTimeConstant.size() > 0)
        {
            vector<float> momentumPerSampleVec;
            for (int i = 0; i < momentumAsTimeConstant.size(); i++)
            {
                double momTC = momentumAsTimeConstant[i];
                double momPS = momTC == 0.0 ? 0 : exp(-1.0 / momTC);
                momentumPerSampleVec.push_back((float) momPS);
            }
            m_momentumParam = momentumPerSampleVec;
            m_momentumSpecifiedForMBSize = intargvector(L"1");
        }
        else if (momentumPerMB.size() > 0)
        {
            m_momentumParam = momentumPerMB;
            m_momentumSpecifiedForMBSize = m_mbSize;
        }
        else // default: momentumPerMB = 0.9 per MB
        {
            m_momentumParam = floatargvector(L"0.9");
            m_momentumSpecifiedForMBSize = m_mbSize;
        }
        m_useNesterovMomentum = useNesterovMomentum;

        for (int i = 0; i < m_momentumParam.size(); i++)
        {
            if (m_momentumParam[i] >= 1.0 || m_momentumParam[i] < 0.0)
            {
                InvalidArgument("Momentum parameter must be in [0, 1).");
            }
        }

        if (m_learnRateDecreaseFactor > 1 || m_learnRateIncreaseFactor < 1)
        {
            InvalidArgument("learnRateIncreaseFactor must be >= 1 and learnRateDecreaseFactor must be <= 1.");
        }

        for (size_t i = 0; i < m_dropoutRates.size(); i++)
        {
            if (m_dropoutRates[i] >= 1 || m_dropoutRates[i] < 0)
            {
                InvalidArgument("dropoutRate must be >= 0 and < 1.");
            }
        }

        if (m_adaptationRegWeight > 1 || m_adaptationRegWeight < 0)
            InvalidArgument("adaptationRegWeight must be in [0 1]");

        m_minLearnRate = configSGD(L"minLearningRatePerSample", 1e-9f);

        m_needAdaptRegularization = false;

        // BUGBUG: these are not passed to Init()
        m_doUnitTest = configSGD(L"unitTest", false);

        // parallel training
        m_parallelizationMethod = ParallelizationMethod::none;
        m_numGradientBits = vector<int>{8 * (int) sizeofElemType}; // means no quantization
        m_zeroThresholdFor1Bit = true;
        m_bufferedAsyncGradientAggregation = false;
        m_enableDistributedMBReading = false;
        m_parallelizationStartEpochNum = 0;
        m_modelAggregationBlockSize = 0;

        if (configSGD.Exists(L"ParallelTrain"))
        {
            MPIWrapperPtr pMPI = MPIWrapper::GetInstance();
            if (!pMPI)
            {
                // some users may forget to specify parallelTrain option
                // in this case, falling back to normal SGD
                fprintf(stderr, "parallelTrain option is not enabled. ParallelTrain config will be ignored.\n");
            }
            else
            {
                size_t numMPIWorkers = pMPI->NumNodesInUse();
                const ConfigRecordType& configParallelTrain(configSGD(L"ParallelTrain", ConfigRecordType::Record()));
                m_parallelizationMethod = ParseParallelizationMethod(configParallelTrain(L"parallelizationMethod", L"none"));
                m_parallelizationStartEpochNum = configParallelTrain(L"parallelizationStartEpoch", (int) 1) - 1; // Internally, epoch numbers are 0-based
                if (m_parallelizationStartEpochNum < 0 /* sic */)
                    // Be explicit that user-facing epoch numbers are 1-based
                    InvalidArgument("parallelizationStartEpoch must be greater or equal to 1");
                m_enableDistributedMBReadingNotSpecified = !configParallelTrain.Exists(L"distributedMBReading");
                m_enableDistributedMBReading = configParallelTrain(L"distributedMBReading", false);
                m_syncStatsTrace = configParallelTrain(L"syncPerfStats", (int) 0);

                if (configParallelTrain.Exists(L"DataParallelSGD"))
                {
                    const ConfigRecordType& configDataParallelSGD(configParallelTrain(L"DataParallelSGD", ConfigRecordType::Record()));
                    let defaultGradientBits = 8 * (int) sizeofElemType;
                    m_numGradientBits = configDataParallelSGD(L"gradientBits", ConfigRecordType::Array(intargvector(vector<int>{defaultGradientBits})));
                    m_zeroThresholdFor1Bit = configDataParallelSGD(L"useZeroThresholdFor1BitQuantization", true);
                    m_bufferedAsyncGradientAggregation = configDataParallelSGD(L"useBufferedAsyncGradientAggregation", false);
                    for (size_t i = 0; i < m_numGradientBits.size(); i++)
                    {
                        if (m_numGradientBits[i] < 1 || m_numGradientBits[i] > defaultGradientBits)
                            InvalidArgument("gradientBits values must be in the range [1, 32] when using precision=float and in range [1, 64] when using precision=double.");
                    }
                }
                if (configParallelTrain.Exists(L"ModelAveragingSGD"))
                {
                    const ConfigRecordType& configMASGD(configParallelTrain(L"ModelAveragingSGD", ConfigRecordType::Record()));
                    if (configMASGD.Exists(L"blockSizePerWorker") && configMASGD.Exists(L"blockSize"))
                        InvalidArgument("It is only allowed to set blockSizePerWorker or blockSize, not both of them");
                    else if (configMASGD.Exists(L"blockSize"))
                        m_modelAggregationBlockSize = configMASGD(L"blockSize");
                    else if (configMASGD.Exists(L"blockSizePerWorker"))
                    {
                        m_modelAggregationBlockSize = configMASGD(L"blockSizePerWorker");
                        m_modelAggregationBlockSize *= numMPIWorkers;
                    }
                    else
                        m_modelAggregationBlockSize = 40000 * numMPIWorkers; // default value
#if 1                                                                        // legacy option
                    if (configMASGD.Exists(L"syncFrequencyInFrames"))
                    {
                        if (configMASGD.Exists(L"blockSizePerWorker") || configMASGD.Exists(L"blockSize"))
                            InvalidArgument("syncFrequencyInFrames is a deprecated alias of blockSizePerWorker. It is not allowed to specify both of them");
                        m_modelAggregationBlockSize = configMASGD(L"syncFrequencyInFrames");
                        m_modelAggregationBlockSize *= numMPIWorkers;
                        fprintf(stderr, "WARNING: option syncFrequencyInFrames in ModelAveragingSGD is going to be deprecated. Please use blockSizePerWorker instead\n");
                    }
                    if (configMASGD.Exists(L"syncPeroid"))
                    {
                        if (configMASGD.Exists(L"blockSizePerWorker") || configMASGD.Exists(L"blockSize"))
                            InvalidArgument("syncPeriod is a deprecated alias of blockSizePerWorker. It is not allowed to specify both of them");
                        m_modelAggregationBlockSize = configMASGD(L"syncPeriod");
                        m_modelAggregationBlockSize *= numMPIWorkers;
                        fprintf(stderr, "WARNING: option syncPeroid in ModelAveragingSGD is going to be deprecated. Please use blockSizePerWorker instead in the future.\n");
                    }
#endif
                }
                if (configParallelTrain.Exists(L"BlockMomentumSGD"))
                {
#ifndef CNTK_PARALLEL_TRAINING_SUPPORT
                    InvalidArgument("BlockMomentumSGD is not enabled in this version.\n");
#else
                    const ConfigRecordType& configBMSGD(configParallelTrain(L"BlockMomentumSGD", ConfigRecordType::Record()));
                    if (configBMSGD.Exists(L"blockSize") && configBMSGD.Exists(L"blockSizePerWorker"))
                        InvalidArgument("It is only allowed to set blockSizePerWorker or blockSize, not both of them");
                    else if (configBMSGD.Exists(L"blockSizePerWorker"))
                    {
                        m_modelAggregationBlockSize = configBMSGD(L"blockSizePerWorker");
                        m_modelAggregationBlockSize *= numMPIWorkers;
                    }
                    else if (configBMSGD.Exists(L"blockSize"))
                        m_modelAggregationBlockSize = configBMSGD(L"blockSize");
                    else
                        m_modelAggregationBlockSize = 120000 * numMPIWorkers; // default value
#if 1 // legacy option
                    if (configBMSGD.Exists(L"syncPeriod"))
                    {
                        if (configBMSGD.Exists(L"blockSizePerWorker") || configBMSGD.Exists(L"blockSize"))
                            InvalidArgument("syncPeriod is a deprecated alias of blockSizePerWorker. It is not allowed to specify both of them");
                        m_modelAggregationBlockSize = configBMSGD(L"syncPeriod");
                        m_modelAggregationBlockSize *= numMPIWorkers;
                        fprintf(stderr, "WARNING: option syncPeroid in BlockMomentumSGD is going to be deprecated. Please use blockSizePerWorker instead in the future.\n");
                    }
#endif
                    m_resetSGDMomentum = configBMSGD(L"resetSGDMomentum", true);
                    m_useNesterovBlockMomentum = configBMSGD(L"useNesterovMomentum", true);
                    m_blockLearningRate = configBMSGD(L"blockLearningRate", 1.0);

                    if (configBMSGD.Exists(L"blockMomentumPerSync") && configBMSGD.Exists(L"blockMomentumAsTimeConstant"))
                    {
                        InvalidArgument("It is only allowed to set either blockMomentumPerSync or blockMomentumAsTimeConstant, not both of them");
                    }
                    else if (configBMSGD.Exists(L"blockMomentumAsTimeConstant"))
                    {
                        m_blockMomentumAsTimeConstant = configBMSGD(L"blockMomentumAsTimeConstant");
                    }
#if 1 // This option "blockMomentumPerSync" is going to be deprecated in the future
                    else if (configBMSGD.Exists(L"blockMomentumPerSync"))
                    {
                        double blockMomentum = configBMSGD(L"blockMomentumPerSync");
                        m_blockMomentumAsTimeConstant = BlockMomentumSGD<double>::Momentum2TimeConstant(blockMomentum, m_modelAggregationBlockSize);
                    }
#endif
                    else /*if (!configBMSGD.Exists(L"blockMomentumPerSync") && !configBMSGD.Exists(L"blockMomentumAsTimeConstant"))*/
                    {
                        double blockMomentum = 1.0 - 1.0 / (double) numMPIWorkers; // this is a default value which ensures each block update contributes equally
                        m_blockMomentumAsTimeConstant = BlockMomentumSGD<double>::Momentum2TimeConstant(blockMomentum, m_modelAggregationBlockSize);
                    }
#endif
                }

                if (configParallelTrain.Exists(L"DataParallelASGD"))
                {
#ifndef ASGD_PARALLEL_SUPPORT
                    InvalidArgument("DataParallelASGD is not enabled in this version.\n");
#else
                    const ConfigRecordType& configDataParallelASGD(configParallelTrain(L"DataParallelASGD", ConfigRecordType::Record()));
                    m_nSyncSamplesPerWorker = configDataParallelASGD(L"syncPeriodPerWorker", ConfigRecordType::Array(intargvector(vector<int>{256})));
#if 1 // legacy option
                    if (configDataParallelASGD.Exists(L"syncPeriod"))
                    {
                        if (configDataParallelASGD.Exists(L"syncPeriodPerWorker"))
                            InvalidArgument("syncPeriod is a deprecated alias of syncPeriodPerWorker. It is not allowed to specify both of them");
                        m_nSyncSamplesPerWorker = configDataParallelASGD(L"syncPeriod", ConfigRecordType::Array(intargvector(vector<int>{256})));
                    }
#endif
                    m_isAsyncBufferEnabled = configDataParallelASGD(L"UsePipeline", false);
                    m_isSimulateMA = configDataParallelASGD(L"SimModelAverage", false);  // using parameter server-based version of ModelAveragingSGD
                    if (configDataParallelASGD.Exists(L"AdjustLearningRateAtBeginning")) // adjust learning rate per m_adjustNumInBatch minibatches until to original one,
                                                                                         // this option could be used to takcle the unstableness of DataParallelASGD if you get a chance
                    {
                        const ConfigRecordType& configAdjustLearningRateAtBeginning(configDataParallelASGD(L"AdjustLearningRateAtBeginning", ConfigRecordType::Record()));
                        m_adjustLearningRateAtBeginning = AdjustLearningRateAtBeginningType(configAdjustLearningRateAtBeginning(L"adjustType", L"staircase"));
                        m_adjustCoefficient = configAdjustLearningRateAtBeginning(L"adjustCoefficient", (double) 0.1);
                        m_adjustPerMinibatches = configAdjustLearningRateAtBeginning(L"adjustPerMinibatches", (size_t) 256);
                    }
#endif
                }
            } // if (!pMPI)
        }     // if (configSGD.Exists(L"ParallelTrain"))
    }

    static size_t GetSizeOfPrecision(const ScriptableObjects::IConfigRecordPtr configp)
    {
        wstring precision = configp->Get(L"precision");
        if (precision == L"float")
            return sizeof(float);
        else if (precision == L"double")
            return sizeof(double);
        else
            RuntimeError("invalid value '%ls' for 'precision', must be 'float' or 'double'", precision.c_str());
    }

    SGDParams::SGDParams(const ScriptableObjects::IConfigRecordPtr configp)
        : SGDParams(*configp, GetSizeOfPrecision(configp))
    {
    }

    void SGDParams::InitializeAndCheckBlockMomentumSGDParameters()
    {
#ifdef CNTK_PARALLEL_TRAINING_SUPPORT
        // final argument checking in case of user specifying a bad parameter
        size_t numMPIWorker = MPIWrapper::GetInstance()->NumNodesInUse();
        double blockMomentum = BlockMomentumSGD<double>::TimeConstant2Momentum(m_blockMomentumAsTimeConstant, m_modelAggregationBlockSize);
        if ((1 - blockMomentum) * m_blockLearningRate * numMPIWorker >= 2.0)
        {
            fprintf(stderr, "WARNING: (1-blockMomentumPerSync)*blockLearningRate is larger than 2*numWorkers; it is possible to overshoot.");
        }
        if (blockMomentum == 0.0)
        {
            fprintf(stderr, "WARNING: blockMomentum equals to zero. \n");
        }
#else
        // don't need do anything here
        m_blockMomentumAsTimeConstant = 0.0;
        m_blockLearningRate = 1.0;
#endif
    }

    // register SGD<> with the ScriptableObject system
    ScriptableObjects::ConfigurableRuntimeTypeRegister::AddFloatDouble<SGD<float>, SGD<double>> registerSGDOptimizer(L"SGDOptimizer");
}
} // namespace CNTK
} // namespace MSR
back to top