#pragma clang diagnostic push #pragma ide diagnostic ignored "cert-err58-cpp" /* * ****************************************************************************** * * * * * * This program and the accompanying materials are made available under the * * terms of the Apache License, Version 2.0 which is available at * * https://www.apache.org/licenses/LICENSE-2.0. * * * * See the NOTICE file distributed with this work for additional * * information regarding copyright ownership. * * Unless required by applicable law or agreed to in writing, software * * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT * * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the * * License for the specific language governing permissions and limitations * * under the License. * * * * SPDX-License-Identifier: Apache-2.0 * ***************************************************************************** */ // // @author Yurii Shyrma (iuriish@yahoo.com), created on 24.11.2017 // @author Paul Dubs // #include #if NOT_EXCLUDED(OP_mean_pairwssqerr_loss) #include #include #include namespace sd { namespace ops { ////////////////////////////////////////////////////////////////////////// CUSTOM_OP_IMPL(mean_pairwssqerr_loss, 3, 1, false, 0, 1) { /* * Implementation of mean pairwise squared error loss * * For context on where this loss function may be useful see: * * Wei, Z., Zhang, J., Shen, X., Lin, Z., Mech, R., Hoai, M. and Samaras, D., 2018. * Good view hunting: learning photo composition from dense view pairs. In Proceedings of the IEEE Conference on * Computer Vision and Pattern Recognition (pp. 5437-5446). * * The paper defines the loss function as: * * L(y,q) = 1/((n*(n-1))/2) * (sum_(i,j=1..n,i!=j)((y_i - y_j) - (q_i - q_j))^2) * * with y: predictions, q: labels, n: length of y and q * * As creating those pairs is computationally expensive, we implement a mathematically equivalent function: * * L(y,q) = 4/(n*(n-1)) * (n * sum (y_i - q_i)^2 - (sum y_i - q_i)^2) * * This equivalency can be derived as: * * sum_(i,j=1..n,i!=j)((y_i - y_j) - (q_i - q_j))^2 = sum_(i,j=1..n,i!=j)((y_i - q_i) - (y_j - q_j))^2 * * To simplify the following equations we use * * sum_(i,j=1..n,i!=j)(d_i - d_j)^2 = sum_(i,j=1..n,i!=j)(d_i^2 + d_j^2 - 2*d_i*d_j) * * Due to the pairings each element will appear as both d_i and d_j exactly n-1 times. This allows us to split the * sum: * * sum_(i,j=1..n,i!=j)(d_i^2 + d_j^2 - 2*d_i*d_j) = 2*(n-1)*sum d_i^2 - 2 * sum_(i,j=1..n,i!=j) d_i * d_j * = 2*((n-1) * sum d_i^2 - sum_(i,j=1..n,i!=j) d_i * d_j) * * Now we use the following equivalency: * * (sum d_i)^2 = sum d_i^2 + sum_(i,j=1..n,i!=j) d_i * d_j * * This allows us to now use sum d_i^2 and (sum d_i)^2 as a quick way to calculate the sum: * * (n-1) * sum d_i^2 - sum_(i,j=1..n,i!=j) d_i * d_j = n * sum d_i^2 - (sum d_i)^2 * * And by substituting it into the original definition we get: * * 1/((n*(n-1))/2) * 2*(n * sum d_i^2 - (sum d_i)^2) * * Which can be again simplified to * * 4/(n*(n-1)) * (n * sum d_i^2 - (sum d_i)^2) * * After substituting d_i back to (y_i - q_i) this results in the function that we actually implement. * */ auto predictions = INPUT_VARIABLE(0); auto weights = INPUT_VARIABLE(1); auto labels = INPUT_VARIABLE(2); auto output = OUTPUT_VARIABLE(0); int reductionMode = INT_ARG(0); // 0 - "none"; 1 - "weighted_sum"; 2 - "weighted_mean"; 3 - "weighted_sum_by_nonzero_weights" // input validation REQUIRE_TRUE(labels->isSameShape(predictions), 0, "MEAN_PAIRWSSQERR_LOSS OP: labels and predictions arrays must have the same shapes, but got %s and %s " "correspondingly !", ShapeUtils::shapeAsString(labels).c_str(), ShapeUtils::shapeAsString(predictions).c_str()); // only 4 possible reduction modes exist REQUIRE_TRUE(reductionMode == 0 || reductionMode == 1 || reductionMode == 2 || reductionMode == 3, 0, "MEAN_PAIRWSSQERR_LOSS OP: reduction mode value is not acceptable, possible values are 0, 1, 2, 3, but " "got %i instead!", reductionMode); if (labels->rankOf() == 1) { // If labels and predictions are of rank 1, it means that all data entries are 0-tensor // (scalar) so that the result of becomes always zero. *output = 0.; return Status::OK; } std::vector zero; zero.push_back(0); std::vector *reductionIdx = ShapeUtils::evalDimsToExclude(labels->rankOf(),1,zero.data()); auto n = double(labels->sizeAt(1)); // Compute diffs = predictions - labels NDArray* diffs_ptr = (*predictions) - (*labels); NDArray diffs = *diffs_ptr; delete diffs_ptr; // Compute sumOfSquares = sum(diffs^2) NDArray* diffsSquared = diffs * diffs; NDArray* sumOfSquares_ptr = diffsSquared->reduceAlongDimension(reduce::Sum, reductionIdx, true); delete diffsSquared; NDArray sumOfSquares = *sumOfSquares_ptr; delete sumOfSquares_ptr; // Compute squareOfSum = (sum(diffs))^2 NDArray* squareOfSum_ptr = diffs.reduceAlongDimension(reduce::Sum, reductionIdx, true); NDArray squareOfSum = *squareOfSum_ptr; delete squareOfSum_ptr; squareOfSum.applyScalar(scalar::Pow, 2, &squareOfSum); delete reductionIdx; // Compute E = ((sumOfSquares * n) - squareOfSum) * (4 / (n * (n - 1))) NDArray* sumOfSquaresTimesN = sumOfSquares * n; NDArray* numerator = (*sumOfSquaresTimesN) - squareOfSum; delete sumOfSquaresTimesN; NDArray* E_ptr = (*numerator) * (4 / (n * (n - 1))); delete numerator; NDArray E = *E_ptr; delete E_ptr; // weights array can be single scalar or has the same rank as labels, and must be broadcastable to labels REQUIRE_TRUE(weights->isScalar() || weights->rankOf() == E.rankOf(), 0, "MEAN_PAIRWSSQERR_LOSS_GRAD OP: weights array should be scalar or have the same rank as results array, " "but got %i and %i correspondingly!", weights->rankOf(), E.rankOf()); // check whether broadcast operation is possible for weights array REQUIRE_TRUE(weights->isScalar() || ShapeUtils::areShapesBroadcastable(*weights, E), 0, "MEAN_PAIRWSSQERR_LOSS_GRAD OP: shapes of weights and labels arrays should be broadcastable, but got " "weights = %s and results = %s instead!", ShapeUtils::shapeAsString(weights).c_str(), ShapeUtils::shapeAsString(&E).c_str()); // perform weights broadcasting/tile to labels if needed auto weightsBroad = weights; if (!weights->isScalar() && !weights->isSameShape(E)) weightsBroad = new NDArray(weights->tileToShape(E.shapeInfo())); E *= *weightsBroad; switch (reductionMode) { case 0: // 0 - "none", un-reduced weighted losses with the same shape as labels. output->assign(&E); break; case 1: { // 1 - "weighted_sum", output is scalar and equal to sum of all elements of E array E.reduceNumber(reduce::Sum, output); break; } case 2: { // 2 - "weighted_mean", output is scalar and equal to sum of all elements of E array divided by sum of // all elements of weightsBroad array NDArray* sumPtr = nullptr; if (weights->isScalar()) { NDArray* weightTimesLen = (*weights) * E.lengthOf(); sumPtr = weightTimesLen; } else { sumPtr = weightsBroad->reduceNumber(reduce::Sum); } if (sumPtr->e(0) == 0.) { (*output) = 0.; } else { NDArray* eSum = E.reduceNumber(reduce::Sum); NDArray* result = (*eSum) / (*sumPtr); delete eSum; output->assign(result); delete result; } delete sumPtr; break; } case 3: { // 3 - "weighted_sum_by_nonzero_weights", output is scalar and equal to scalar sum of all elements of E // array divided by number of non-zero weights LongType numOfNonZeroWeights = 0; if (weights->isScalar()) { if (weights->e(0) != 0.) numOfNonZeroWeights = E.lengthOf(); } else { NDArray* countNonZero = weightsBroad->reduceNumber(reduce::CountNonZero); numOfNonZeroWeights = countNonZero->e(0); delete countNonZero; } if (numOfNonZeroWeights == 0) (*output) = 0.; else { NDArray* eSum = E.reduceNumber(reduce::Sum); NDArray* result = (*eSum) / double(numOfNonZeroWeights); delete eSum; output->assign(result); delete result; } break; } } if (weightsBroad != weights) delete weightsBroad; return Status::OK; } ////////////////////////////////////////////////////////////////////////// DECLARE_TYPES(mean_pairwssqerr_loss) { getOpDescriptor()->setAllowedInputTypes(ANY)->setAllowedOutputTypes({ALL_FLOATS}); } ////////////////////////////////////////////////////////////////////////// DECLARE_SHAPE_FN(mean_pairwssqerr_loss) { auto predictionsShapeInfo = inputShape->at(0); auto weightsShapeInfo = inputShape->at(1); auto labelsShapeInfo = inputShape->at(2); REQUIRE_TRUE(shape::shapeEquals(labelsShapeInfo, predictionsShapeInfo), 0, "MEAN_PAIRWSSQERR_LOSS OP: labels and predictions arrays must have the same shapes, but got %s and %s " "correspondingly !", ShapeUtils::shapeAsString(labelsShapeInfo).c_str(), ShapeUtils::shapeAsString(predictionsShapeInfo).c_str()); DataType outType = DataTypeUtils::pickFloatingType(ArrayOptions::dataType(predictionsShapeInfo)); LongType *outShapeInfo = nullptr; if (INT_ARG(0) != 0) // in this case output is scalar outShapeInfo = ConstantShapeHelper::getInstance().scalarShapeInfo(outType); else { // in this case output has the shape as labels and logits minus last dimension std::vector dimensions = {-1}; outShapeInfo = ShapeUtils::evalReduceShapeInfo(shape::order(predictionsShapeInfo), &dimensions, predictionsShapeInfo, false, true, block.getWorkspace()); // weights array can be single scalar or has the same rank as output, and must be broadcastable to output REQUIRE_TRUE(shape::isScalar(weightsShapeInfo) || shape::rank(weightsShapeInfo) == shape::rank(outShapeInfo), 0, "MEAN_PAIRWSSQERR_LOSS OP: weights array should be scalar or have the same rank as output array, but " "got %i and %i correspondingly!", shape::rank(weightsShapeInfo), shape::rank(outShapeInfo)); // check whether broadcast operation is possible for weights array REQUIRE_TRUE( shape::isScalar(weightsShapeInfo) || ShapeUtils::areShapesBroadcastable(weightsShapeInfo, outShapeInfo), 0, "MEAN_PAIRWSSQERR_LOSS OP: shapes of weights and output arrays should be broadcastable, but got weights = %s " "and output = %s instead!", ShapeUtils::shapeAsString(weightsShapeInfo).c_str(), ShapeUtils::shapeAsString(outShapeInfo).c_str()); } return SHAPELIST(outShapeInfo); } ////////////////////////////////////////////////////////////////////////// CUSTOM_OP_IMPL(mean_pairwssqerr_loss_grad, 3, 3, false, 0, 1) { auto predictions = INPUT_VARIABLE(0); auto weights = INPUT_VARIABLE(1); auto labels = INPUT_VARIABLE(2); auto dLdp = OUTPUT_VARIABLE(0); // dL/dpredictions auto dLdw = OUTPUT_VARIABLE(1); // dL/dweights auto dLdl = OUTPUT_VARIABLE(2); // dL/dlabels int reductionMode = INT_ARG(0); // 0 - "none"; 1 - "weighted_sum"; 2 - "weighted_mean"; 3 - "weighted_sum_by_nonzero_weights" // take into account Alex's proposition to treat "none" the same as "weighted_sum" mode when calculating gradients if (reductionMode == 0) reductionMode = 1; // inputs validation REQUIRE_TRUE(labels->isSameShape(predictions), 0, "MEAN_PAIRWSSQERR_LOSS_GRAD OP: labels and predictions arrays must have the same shapes, but got %s and " "%s correspondingly !", ShapeUtils::shapeAsString(labels).c_str(), ShapeUtils::shapeAsString(predictions).c_str()); // only 4 possible reduction modes exist REQUIRE_TRUE(reductionMode == 0 || reductionMode == 1 || reductionMode == 2 || reductionMode == 3, 0, "MEAN_PAIRWSSQERR_LOSS_GRAD OP: reduction mode value is not acceptable, possible values are 0, 1, 2, 3, " "but got %i instead!", reductionMode); auto n = double(labels->sizeAt(1)); // Compute diffs = predictions - labels NDArray* diffs_ptr = (*predictions) - (*labels); NDArray diffs = *diffs_ptr; delete diffs_ptr; std::vector dims2; dims2.push_back(0); std::vector *reductionIdx = ShapeUtils::evalDimsToExclude(labels->rankOf(), 1,dims2.data()); // Compute sumOfSquares NDArray* diffsSquared = diffs * diffs; NDArray* sumOfSquares_ptr = diffsSquared->reduceAlongDimension(reduce::Sum, reductionIdx, true); delete diffsSquared; NDArray sumOfSquares = *sumOfSquares_ptr; delete sumOfSquares_ptr; // Compute squareOfSum NDArray* squareOfSum_ptr = diffs.reduceAlongDimension(reduce::Sum, reductionIdx, true); NDArray squareOfSum = *squareOfSum_ptr; delete squareOfSum_ptr; squareOfSum.applyScalar(scalar::Pow, 2, &squareOfSum); // Compute E NDArray* sumOfSquaresTimesN = sumOfSquares * n; NDArray* eTerm1 = (*sumOfSquaresTimesN) - squareOfSum; delete sumOfSquaresTimesN; NDArray* E_ptr = (*eTerm1) * (4 / (n * (n - 1))); delete eTerm1; NDArray E = *E_ptr; delete E_ptr; // Compute gradients for predictions NDArray* sumPred_ptr = predictions->reduceAlongDimension(reduce::Sum, reductionIdx, true); NDArray sumPred = *sumPred_ptr; delete sumPred_ptr; NDArray* sumLabel_ptr = labels->reduceAlongDimension(reduce::Sum, reductionIdx, true); NDArray sumLabel = *sumLabel_ptr; delete sumLabel_ptr; delete reductionIdx; // Compute dLdp = ((diffs * n) - sumPred + sumLabel) * (8 / (n * (n - 1))) NDArray* diffsTimesN = diffs * n; NDArray* term1 = (*diffsTimesN) - sumPred; delete diffsTimesN; NDArray* term2 = (*term1) + sumLabel; delete term1; NDArray* dLdpTemp = (*term2) * (8 / (n * (n - 1))); delete term2; dLdp->assign(dLdpTemp); delete dLdpTemp; // weights array can be single scalar or has the same rank as labels, and must be broadcastable to labels REQUIRE_TRUE(weights->isScalar() || weights->rankOf() == E.rankOf(), 0, "MEAN_PAIRWSSQERR_LOSS_GRAD OP: weights array should be scalar or have the same rank as results array, " "but got %i and %i correspondingly!", weights->rankOf(), E.rankOf()); // check whether broadcast operation is possible for weights array REQUIRE_TRUE(weights->isScalar() || ShapeUtils::areShapesBroadcastable(*weights, E), 0, "MEAN_PAIRWSSQERR_LOSS_GRAD OP: shapes of weights and labels arrays should be broadcastable, but got " "weights = %s and results = %s instead!", ShapeUtils::shapeAsString(weights).c_str(), ShapeUtils::shapeAsString(&E).c_str()); // perform weights broadcasting/tile to labels if needed auto weightsBroad = weights; if (!weights->isScalar() && !weights->isSameShape(E)) weightsBroad = new NDArray(weights->tileToShape(E.shapeInfo())); switch (reductionMode) { case 1: { // 1 - "none" and "weighted_sum", output is scalar and equal to sum of all elements of E array *dLdp *= *weightsBroad; if (weights->isScalar()) { NDArray* eSum = E.reduceNumber(reduce::Sum); dLdw->assign(eSum); delete eSum; } else if (weights != weightsBroad) { std::vector axesToReduceAlong = ShapeUtils::evalBroadcastBackwardAxis(weights->shapeInfo(), weightsBroad->shapeInfo()); E.reduceAlongDimension(reduce::Sum, dLdw, &axesToReduceAlong, true); } else dLdw->assign(&E); break; } case 2: { // 2 - "weighted_mean", output is scalar and equal to sum of all elements of E array divided by sum of // all elements of weightsBroad array NDArray* sum = nullptr; if (weights->isScalar()) { NDArray* weightTimesLen = (*weights) * E.lengthOf(); sum = weightTimesLen; } else { sum = weightsBroad->reduceNumber(reduce::Sum); } if (sum->e(0) == 0.) { *dLdp = 0.; *dLdw = 0.; } else { NDArray* weightsDivSum = (*weightsBroad) / (*sum); *dLdp *= *weightsDivSum; delete weightsDivSum; if (weights->isScalar()) *dLdw = 0.; else if (weights != weightsBroad) { std::vector axesToReduceAlong = ShapeUtils::evalBroadcastBackwardAxis(weights->shapeInfo(), weightsBroad->shapeInfo()); // Compute (E * sum - (E * weightsBroad).reduceNumber(Sum)) / (sum * sum) NDArray* ETimesSum = E * (*sum); NDArray* ETimesWeights = E * (*weightsBroad); NDArray* ETimesWeightsSum = ETimesWeights->reduceNumber(reduce::Sum); delete ETimesWeights; NDArray* numerator = (*ETimesSum) - (*ETimesWeightsSum); delete ETimesSum; delete ETimesWeightsSum; NDArray* sumSquared = (*sum) * (*sum); NDArray* result = (*numerator) / (*sumSquared); delete numerator; delete sumSquared; result->reduceAlongDimension(reduce::Sum, dLdw, &axesToReduceAlong, true); delete result; } else { // Compute (E * sum - (E * weightsBroad).reduceNumber(Sum)) / (sum * sum) NDArray* ETimesSum = E * (*sum); NDArray* ETimesWeights = E * (*weightsBroad); NDArray* ETimesWeightsSum = ETimesWeights->reduceNumber(reduce::Sum); delete ETimesWeights; NDArray* numerator = (*ETimesSum) - (*ETimesWeightsSum); delete ETimesSum; delete ETimesWeightsSum; NDArray* sumSquared = (*sum) * (*sum); NDArray* result = (*numerator) / (*sumSquared); delete numerator; delete sumSquared; dLdw->assign(result); delete result; } } delete sum; break; } case 3: { // 3 - "weighted_sum_by_nonzero_weights", output is scalar and equal to scalar sum of all elements of E // array divided by number of non-zero weights LongType numOfNonZeroWeights = 0; if (weights->isScalar()) { if (weights->e(0) != 0.) numOfNonZeroWeights = E.lengthOf(); } else { NDArray* countNonZero = weightsBroad->reduceNumber(reduce::CountNonZero); numOfNonZeroWeights = countNonZero->e(0); delete countNonZero; } if (numOfNonZeroWeights == 0) { *dLdp = 0.; *dLdw = 0.; } else { auto* numOfNonZeroWeightsScalar = NDArrayFactory::create(dLdw->dataType(), numOfNonZeroWeights, block.launchContext()); if (weights->isScalar()) { NDArray* eSum = E.reduceNumber(reduce::Sum); NDArray* result = (*eSum) / double(numOfNonZeroWeights); delete eSum; dLdw->assign(result); delete result; } else if (weights != weightsBroad) { std::vector axesToReduceAlong = ShapeUtils::evalBroadcastBackwardAxis(weights->shapeInfo(), weightsBroad->shapeInfo()); E.reduceAlongDimension(reduce::Sum, dLdw, &axesToReduceAlong, true); *dLdw /= *numOfNonZeroWeightsScalar; } else { NDArray* eDivNum = E / (*numOfNonZeroWeightsScalar); dLdw->assign(eDivNum); delete eDivNum; } NDArray* weightsDivNum = (*weightsBroad) / (*numOfNonZeroWeightsScalar); NDArray temp = *weightsDivNum; delete weightsDivNum; *dLdp *= temp; delete numOfNonZeroWeightsScalar; } break; } } NDArray negDLdp = -(*dLdp); // unary negation returns value dLdl->assign(&negDLdp); if (weightsBroad != weights) delete weightsBroad; return Status::OK; } DECLARE_TYPES(mean_pairwssqerr_loss_grad) { getOpDescriptor()->setAllowedInputTypes(ANY)->setAllowedOutputTypes({ALL_FLOATS}); } DECLARE_SHAPE_FN(mean_pairwssqerr_loss_grad) { auto predictionsShapeInfo = inputShape->at(0); auto weightsShapeInfo = inputShape->at(1); auto labelsShapeInfo = inputShape->at(2); // labels and predictions must have the same shapes REQUIRE_TRUE(shape::shapeEquals(labelsShapeInfo, predictionsShapeInfo), 0, "MEAN_PAIRWSSQERR_LOSS_GRAD OP: labels and predictions arrays must have the same shapes, but got %s and " "%s correspondingly !", ShapeUtils::shapeAsString(labelsShapeInfo).c_str(), ShapeUtils::shapeAsString(predictionsShapeInfo).c_str()); // weights array can be single scalar or has the same rank as labels, and must be broadcastable to labels REQUIRE_TRUE(shape::isScalar(weightsShapeInfo) || shape::rank(weightsShapeInfo) == shape::rank(labelsShapeInfo), 0, "MEAN_PAIRWSSQERR_LOSS_GRAD OP: weights array should be scalar or have the same rank as labels array, " "but got %i and %i correspondingly!", shape::rank(weightsShapeInfo), shape::rank(labelsShapeInfo)); // check whether broadcast operation is possible for weights array REQUIRE_TRUE( shape::isScalar(weightsShapeInfo) || ShapeUtils::areShapesBroadcastable(weightsShapeInfo, labelsShapeInfo), 0, "MEAN_PAIRWSSQERR_LOSS_GRAD OP: shapes of weights and labels arrays should be broadcastable, but got weights = " "%s and labels = %s instead!", ShapeUtils::shapeAsString(weightsShapeInfo).c_str(), ShapeUtils::shapeAsString(labelsShapeInfo).c_str()); DataType outType = DataTypeUtils::pickFloatingType(ArrayOptions::dataType(predictionsShapeInfo)); LongType *dLdpShapeInfo = ShapeBuilders::copyShapeInfoAndType(predictionsShapeInfo, outType, false, block.getWorkspace()); LongType *dLdwShapeInfo = ShapeBuilders::copyShapeInfoAndType(weightsShapeInfo, outType, false, block.getWorkspace()); LongType *dLdlShapeInfo = ShapeBuilders::copyShapeInfoAndType(labelsShapeInfo, outType, false, block.getWorkspace()); return SHAPELIST(dLdpShapeInfo, dLdwShapeInfo, dLdlShapeInfo); } } // namespace ops } // namespace sd #endif #pragma clang diagnostic pop