haojin2 commented on a change in pull request #14617: PDF operators for the random samplers, and also the Dirichlet URL: https://github.com/apache/incubator-mxnet/pull/14617#discussion_r280231870
########## File path: src/operator/random/pdf_op.h ########## @@ -0,0 +1,613 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one + * or more contributor license agreements. See the NOTICE file + * distributed with this work for additional information + * regarding copyright ownership. The ASF licenses this file + * to you under the Apache License, Version 2.0 (the + * "License"); you may not use this file except in compliance + * with the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, + * software distributed under the License is distributed on an + * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY + * KIND, either express or implied. See the License for the + * specific language governing permissions and limitations + * under the License. + */ + +/*! + * Copyright (c) 2018 by Contributors + * \file pdf_op.h + * \brief Operators for computing the pdf of random distributions. + */ +#ifndef MXNET_OPERATOR_RANDOM_PDF_OP_H_ +#define MXNET_OPERATOR_RANDOM_PDF_OP_H_ + +#include <mxnet/operator_util.h> +#include <vector> +#include <algorithm> +#include "../mshadow_op.h" +#include "../mxnet_op.h" +#include "../operator_common.h" +#include "../elemwise_op_common.h" +#include "../special_functions-inl.h" +#include "../tensor/broadcast_reduce_op.h" + +namespace mxnet { +namespace op { + +template<typename DType> +MSHADOW_XINLINE static DType ceph_psi(DType val) { return special_functions::cephes::psi(val); } +template<> +MSHADOW_XINLINE mshadow::half::half_t ceph_psi(mshadow::half::half_t val) { + return special_functions::cephes::psi<float>(val); +} + +template<bool logpdf> +struct PDF_Uniform { + template<typename DType, typename IType1, typename IType2> + MSHADOW_XINLINE static void Map(int start, int length, int sample_size, + DType *out, IType1 *sample, IType2 *lower, IType2 *upper) { + const int index(start / sample_size); + const DType l(lower[index]), h(upper[index]); + const int end = start + length; + for (int i = start; i < end; ++i) { + // No check whether sample is in the support. + out[i] = logpdf ? -DType(log(h-l)) : DType(1.0)/(h-l); + } + } +}; + +template<bool logpdf> +struct PDF_Uniform_Grad { + template<typename DType, typename IType1, typename IType2> + MSHADOW_XINLINE static void Map(int start, int length, int sample_size, OpReqType req, + DType *out, IType1 *sample, IType2 *lower, IType2 *upper, + DType *grad_out, IType1 *grad_sample, IType2 *grad_lower, IType2 *grad_upper) { + const int index(start / sample_size); + const DType l(lower[index]), h(upper[index]); + + const int end = start + length; + for (int i = start; i < end; ++i) { + const DType scaling(grad_out[i]*(logpdf ? DType(1) : out[i])); + grad_lower[i] = scaling/(h-l); + grad_upper[i] = scaling/(l-h); + KERNEL_ASSIGN(grad_sample[i], req, 0); + } + } +}; + +template<bool logpdf> +struct PDF_Normal { + template<typename DType, typename IType1, typename IType2> + MSHADOW_XINLINE static void Map(int start, int length, int sample_size, + DType *out, IType1 *sample, IType2 *loc, IType2 *scale) { + const int index(start / sample_size); + const DType u(loc[index]), s(scale[index]), sq(s*s); + const DType normalizer(sqrt(2.0*mxnet_op::PI)*s); + + const int end = start + length; + for (int i = start; i < end; ++i) { + const DType x(sample[i]); + const DType exponent((DType(-0.5)*(x-u)*(x-u))/(sq)); + out[i] = logpdf ? exponent-log(normalizer) : exp(exponent)/normalizer; + } + } +}; + +template<bool logpdf> +struct PDF_Normal_Grad { + template<typename DType, typename IType1, typename IType2> + MSHADOW_XINLINE static void Map(int start, int length, int sample_size, OpReqType req, + DType *out, IType1 *sample, IType2 *loc, IType2 *scale, + DType *grad_out, IType1 *grad_sample, IType2 *grad_loc, IType2 *grad_scale) { + const int index(start / sample_size); + const DType u(loc[index]), s(scale[index]), s_squared(s*s), s_cubed(s_squared*s); + + const int end = start + length; + for (int i = start; i < end; ++i) { + const DType x(sample[i]); + const DType scaling(grad_out[i]*(logpdf ? DType(1) : out[i])); + grad_loc[i] = scaling*(x-u)/s_squared; + grad_scale[i] = scaling*((x-u)*(x-u)-s_squared)/s_cubed; + KERNEL_ASSIGN(grad_sample[i], req, scaling*(u-x)/s_squared); + } + } +}; + +template<bool logpdf> +struct PDF_Gamma { + template<typename DType, typename IType1, typename IType2> + MSHADOW_XINLINE static void Map(int start, int length, int sample_size, + DType *out, IType1 *sample, IType2 *alpha, IType2 *beta) { + const int index(start / sample_size); + const DType a(alpha[index]), b(beta[index]), lgamma_a(lgamma(a)), a_log_b(a*log(b)); + + const int end = start + length; + for (int i = start; i < end; ++i) { + const DType x(sample[i]); + const DType lpdf(a_log_b+(a-1)*log(x)-b*x-lgamma_a); + out[i] = logpdf ? lpdf : DType(exp(lpdf)); + } + } +}; + +template<bool logpdf> +struct PDF_Gamma_Grad { + template<typename DType, typename IType1, typename IType2> + MSHADOW_XINLINE static void Map(int start, int length, int sample_size, OpReqType req, + DType *out, IType1 *sample, IType2 *alpha, IType2 *beta, + DType *grad_out, IType1 *grad_sample, IType2 *grad_alpha, IType2 *grad_beta) { + const int index(start / sample_size); + const DType a(alpha[index]), b(beta[index]), log_b(log(b)), ceph_psi_a(ceph_psi(a)); + + const int end = start + length; + for (int i = start; i < end; ++i) { + const DType x(sample[i]); + const DType scaling(grad_out[i]*(logpdf ? DType(1) : out[i])); + grad_alpha[i] = scaling*(log_b+log(x)-ceph_psi_a); + grad_beta[i] = scaling*(a/b-x); + KERNEL_ASSIGN(grad_sample[i], req, scaling*((a-1)/x-b)); + } + } +}; + +template<bool logpdf> +struct PDF_Exponential { + template<typename DType, typename IType1, typename IType2> + MSHADOW_XINLINE static void Map(int start, int length, int sample_size, + DType *out, IType1 *sample, IType2 *lambda) { + const int index(start / sample_size); + const DType l(lambda[index]), log_l(log(l)); + + const int end = start + length; + for (int i = start; i < end; ++i) { + const DType x(sample[i]); + out[i] = logpdf ? log_l-l*x : l*exp(-l*x); + } + } +}; + +template<bool logpdf> +struct PDF_Exponential_Grad { + template<typename DType, typename IType1, typename IType2> + MSHADOW_XINLINE static void Map(int start, int length, int sample_size, OpReqType req, + DType *out, IType1 *sample, IType2 *lambda, + DType *grad_out, IType1 *grad_sample, IType2 *grad_lambda) { + const int index(start / sample_size); + const DType l(lambda[index]); + + const int end = start + length; + for (int i = start; i < end; ++i) { + const DType x(sample[i]); + const DType scaling(grad_out[i]*(logpdf ? DType(1) : out[i])); + grad_lambda[i] = scaling*(DType(1)/l-x); + KERNEL_ASSIGN(grad_sample[i], req, -scaling*l); + } + } +}; + +template<bool logpdf> +struct PDF_Poisson { + template<typename DType, typename IType1, typename IType2> + MSHADOW_XINLINE static void Map(int start, int length, int sample_size, + DType *out, IType1 *sample, IType2 *lambda) { + const int index(start / sample_size); + const DType l(lambda[index]), log_l(log(l)); + + const int end = start + length; + for (int i = start; i < end; ++i) { + const DType x(sample[i]); + const DType lpdf((x*log_l-lgamma(x+1))-l); + out[i] = logpdf ? lpdf : DType(exp(lpdf)); + } + } +}; + +template<bool logpdf> +struct PDF_Poisson_Grad { + template<typename DType, typename IType1, typename IType2> + MSHADOW_XINLINE static void Map(int start, int length, int sample_size, OpReqType req, + DType *out, IType1 *sample, IType2 *lambda, + DType *grad_out, IType1 *grad_sample, IType2 *grad_lambda) { + const int index(start / sample_size); + const DType l(lambda[index]); + + const int end = start + length; + for (int i = start; i < end; ++i) { + const DType x(sample[i]); + const DType scaling(grad_out[i]*(logpdf ? DType(1) : out[i])); + grad_lambda[i] = scaling*(x/l-DType(1)); + KERNEL_ASSIGN(grad_sample[i], req, 0); + } + } +}; + + +template<bool logpdf> +struct PDF_NegativeBinomial { + template<typename DType, typename IType1, typename IType2> + MSHADOW_XINLINE static void Map(int start, int length, int sample_size, + DType *out, IType1 *sample, IType2 *limit, IType2 *prob) { + const int index(start / sample_size); + const DType l(limit[index]), p(prob[index]), lgamma_l(lgamma(l)); + + const int end = start + length; + for (int i = start; i < end; ++i) { + const DType x(sample[i]); + const DType lpdf((lgamma(x+l)-lgamma(x+1)-lgamma_l)+l*log(p)+x*log(1-p)); + out[i] = logpdf ? lpdf : DType(exp(lpdf)); + } + } + + template<typename DType> + MSHADOW_XINLINE static DType LPDF(DType l, DType p, DType x) { + // Note that "p" is the failure and not the success probability. + return (lgamma(x+l)-lgamma(x+1)-lgamma(l))+l*log(p)+x*log(1-p); + } +}; + +template<bool logpdf> +struct PDF_NegativeBinomial_Grad { + template<typename DType, typename IType1, typename IType2> + MSHADOW_XINLINE static void Map(int start, int length, int sample_size, OpReqType req, + DType *out, IType1 *sample, IType2 *limit, IType2 *prob, + DType *grad_out, IType1 *grad_sample, IType2 *grad_limit, IType2 *grad_prob) { + const int index(start / sample_size); + const int end = start + length; + for (int i = start; i < end; ++i) { + DType grad_l(0), grad_p(0); + LPDF_GRAD(DType(limit[index]), DType(prob[index]), + DType(sample[i]), out[i], + grad_out[i], &grad_l, &grad_p); + grad_limit[i] = grad_l; + grad_prob[i] = grad_p; + KERNEL_ASSIGN(grad_sample[i], req, 0); + } + } + + template<typename DType> + MSHADOW_XINLINE static void LPDF_GRAD(DType l, DType p, DType x, DType o, DType grad_o, + DType* grad_l, DType* grad_p) { + const DType scaling(grad_o*(logpdf ? DType(1) : o)); + *grad_l = scaling*((ceph_psi(x+l)-ceph_psi(l))+log(p)); + *grad_p = scaling*(l/p-x/(1-p)); + } +}; + +template<bool logpdf> +struct PDF_GeneralizedNegativeBinomial { + template<typename DType, typename IType1, typename IType2> + MSHADOW_XINLINE static void Map(int start, int length, int sample_size, + DType *out, IType1 *sample, IType2 *mu, IType2 *alpha) { + const int index(start / sample_size); + + // Reparameterize with limit = 1/alpha, prob = 1/(mu*alpha+1) + const DType limit(1.0/alpha[index]), prob(1.0/(mu[index]*alpha[index]+1.0)); + + const int end = start + length; + for (int i = start; i < end; ++i) { + const DType lpdf(PDF_NegativeBinomial<logpdf>::LPDF(limit, prob, DType(sample[i]))); + out[i] = logpdf ? lpdf : DType(exp(lpdf)); + } + } +}; + +template<bool logpdf> +struct PDF_GeneralizedNegativeBinomial_Grad { + template<typename DType, typename IType1, typename IType2> + MSHADOW_XINLINE static void Map(int start, int length, int sample_size, OpReqType req, + DType *out, IType1 *sample, IType2 *mu, IType2 *alpha, + DType *grad_out, IType1 *grad_sample, IType2 *grad_mu, IType2 *grad_alpha) { + const int index(start / sample_size); + const DType fmu(mu[index]), falpha(alpha[index]), den(fmu*falpha+1.0); + + // Reparameterize with limit = 1/alpha, prob = 1/(mu*alpha+1) + const DType limit(1.0/falpha), prob(1.0/(fmu*falpha+1.0)); + + const int end = start + length; + for (int i = start; i < end; ++i) { + // Grad returned as d_limit, d_prob + DType grad_l(0), grad_p(0); + PDF_NegativeBinomial_Grad<logpdf>::LPDF_GRAD(limit, prob, + DType(sample[i]), out[i], + grad_out[i], &grad_l, &grad_p); + grad_mu[i] = -grad_p*falpha/(den*den); + grad_alpha[i] = -grad_l/(falpha*falpha)-grad_p*fmu/(den*den); + KERNEL_ASSIGN(grad_sample[i], req, 0); + } + } +}; + +template<bool logpdf> +struct PDF_Dirichlet { + template<typename DType, typename IType1, typename IType2> + MSHADOW_XINLINE static void Map(int start, int length, int sample_size, int k, + DType *out, IType1 *sample, IType2 *alpha) { + const int index(start / sample_size); + const int end = start + length; + for (int i = start; i < end; ++i) { + const IType1 *cur_sample = sample+i*k; + const IType2 *cur_alpha = alpha+index*k; + DType sum_alpha(0), sum_lgamma(0), sum_sample(0); + for ( int j = 0; j < k; ++j ) { + sum_alpha += cur_alpha[j]; + sum_lgamma += lgamma(cur_alpha[j]); + sum_sample += (cur_alpha[j]-1)*log(cur_sample[j]); + } + DType lpdf(sum_sample+(lgamma(sum_alpha)-sum_lgamma)); + out[i] = logpdf ? lpdf : DType(exp(lpdf)); + } + } +}; + + +template<bool logpdf> +struct PDF_Dirichlet_Grad { + template<typename DType, typename IType1, typename IType2> + MSHADOW_XINLINE static void Map(int start, int length, int sample_size, + OpReqType req, int k, + DType *out, IType1 *sample, IType2 *alpha, + DType *grad_out, IType1 *grad_sample, IType2 *grad_alpha) { + const int index(start / sample_size); + const int end = start + length; + for (int i = start; i < end; ++i) { + // Digamma function + const IType1 *cur_sample = sample+i*k; + const IType2 *cur_alpha = alpha+index*k; + const DType scaling(grad_out[i]*(logpdf ? DType(1) : out[i])); + DType sum_alpha(0); + for ( int j = 0; j < k; ++j ) { + sum_alpha += cur_alpha[j]; + } + const DType psi_sum(ceph_psi(sum_alpha)); + for ( int j = 0; j < k; ++j ) { + // order grad_alpha differently to allow efficient reduction at the end. + grad_alpha[i%sample_size+sample_size*(j+k*index)] = + scaling * (log(cur_sample[j])+(psi_sum-ceph_psi(cur_alpha[j]))); + KERNEL_ASSIGN(grad_sample[i*k+j], req, scaling*(cur_alpha[j]-1)/cur_sample[j]); + } + } + } +}; + +struct PdfParam : public dmlc::Parameter<PdfParam> { + bool is_log; + DMLC_DECLARE_PARAMETER(PdfParam) { + DMLC_DECLARE_FIELD(is_log).set_default(false) + .describe("If set, compute the density of the log-probability instead of the probability."); + } +}; + +template<bool vparm = false> +inline bool PdfOpShape(const nnvm::NodeAttrs& attrs, + std::vector<TShape>* in_attrs, + std::vector<TShape>* out_attrs) { + CHECK_GT(in_attrs->size(), 1) + << "pdf operator takes at least 2 arguments (" << in_attrs->size() << " given)"; + CHECK_EQ(out_attrs->size(), 1); + // All inputs must be defined in order to infer output shape. + if ( std::all_of((*in_attrs).begin(), + (*in_attrs).end(), + [](const TShape& s){ return s.ndim() > 0; }) ) { + // Tensors of distribution parameters must have same shape. + for (size_t i = 2; i < in_attrs->size(); ++i) { + SHAPE_ASSIGN_CHECK(*in_attrs, i, (*in_attrs)[i-1]); + } + // Tensors of distribution parameters must match leftmost subshape of samples. + CHECK_LE((*in_attrs)[1].ndim(), (*in_attrs)[0].ndim()) + << "dimension of input samples (" << (*in_attrs)[0].ndim() + << ") must be at least dimension of distribution parameters ("<< (*in_attrs)[1].ndim() << ")"; + TShape tshape((*in_attrs)[0].begin(), (*in_attrs)[0].begin()+(*in_attrs)[1].ndim()); + if (vparm) { + *(tshape.end()-1) = *((*in_attrs)[0].end()-1); + } + for (size_t i = 1; i < in_attrs->size(); ++i) { + SHAPE_ASSIGN_CHECK(*in_attrs, i, tshape); + } + // Output shape must equal input tensor of samples except for last dimension if we are + // dealing with samples that are itself vectors. Be aware of the special case where we + // are dealing with a single vector sample. + if (vparm && ((*in_attrs)[0].ndim() == 1)) { + // Special case where we are dealing with a single vector sample. + SHAPE_ASSIGN_CHECK(*out_attrs, 0, mshadow::Shape1(1)); + } else { + TShape oshape((*in_attrs)[0].begin(), (*in_attrs)[0].end()-(vparm ? 1 : 0)); + SHAPE_ASSIGN_CHECK(*out_attrs, 0, oshape); + } + return true; + } + return false; +} + +template<typename OP> +struct LaunchExWrapper { + template<typename ...Args> + MSHADOW_XINLINE static void Map(const int start, const int length, const int sample_size, + Args... args) { + // Apply the operator to the sample in strides of sample_size, so that + // the operators can assume that their distribution parameters are constant. + int i = start; + + // Get aligned + const int align_step = sample_size - (i % sample_size); + const int first_stride = length > align_step ? align_step : length; + OP::Map(i, first_stride, sample_size, args...); + i += first_stride; + + const int end = start + length - sample_size; + for (; i < end; i += sample_size) { + OP::Map(i, sample_size, sample_size, args...); + } + + // Last stride might not be aligned either + const int last_stride = start + length - i; + if (last_stride > 0) { // Don't overstep even if length <= sample_size + OP::Map(i, last_stride, sample_size, args...); + } + } +}; + +template<typename xpu, typename DType, typename pdf, int pnum, bool vparm = false> +struct PdfCaller; + +template<typename xpu, typename DType, typename pdf> +struct PdfCaller<xpu, DType, pdf, 1, false> { + static void op(const std::vector<TBlob>& inputs, + const std::vector<TBlob>& outputs, + mshadow::Stream<xpu> *s) { + CHECK_EQ(inputs[0].Size()%inputs[1].Size(), 0); + CHECK_EQ(inputs[0].Size()%outputs[0].Size(), 0); + index_t num_samples(inputs[0].Size()/inputs[1].Size()); + mxnet_op::Kernel<LaunchExWrapper<pdf>, xpu>::LaunchEx(s, outputs[0].Size(), num_samples, + outputs[0].dptr<DType>(), inputs[0].dptr<DType>(), inputs[1].dptr<DType>()); + } +}; + +template<typename xpu, typename DType, typename pdf> +struct PdfCaller<xpu, DType, pdf, 1, true> { + static void op(const std::vector<TBlob>& inputs, + const std::vector<TBlob>& outputs, + mshadow::Stream<xpu> *s) { + CHECK_EQ(inputs[0].Size()%inputs[1].Size(), 0); + CHECK_EQ(inputs[0].Size()%outputs[0].Size(), 0); + index_t num_samples(inputs[0].Size()/inputs[1].Size()); + index_t sample_size(inputs[0].Size()/outputs[0].Size()); + // Covers distributions parametrized by a vector of parameters (Dirichlet distribution). + mxnet_op::Kernel<LaunchExWrapper<pdf>, xpu>::LaunchEx(s, outputs[0].Size(), + num_samples, sample_size, + outputs[0].dptr<DType>(), inputs[0].dptr<DType>(), inputs[1].dptr<DType>()); + } +}; + +template<typename xpu, typename DType, typename pdf> +struct PdfCaller<xpu, DType, pdf, 2, false> { + static void op(const std::vector<TBlob>& inputs, + const std::vector<TBlob>& outputs, + mshadow::Stream<xpu> *s) { + CHECK_EQ(inputs[0].Size()%inputs[1].Size(), 0); + CHECK_EQ(inputs[0].Size(), outputs[0].Size()); + index_t num_samples(inputs[0].Size()/inputs[1].Size()); + mxnet_op::Kernel<LaunchExWrapper<pdf>, xpu>::LaunchEx(s, outputs[0].Size(), num_samples, + outputs[0].dptr<DType>(), inputs[0].dptr<DType>(), + inputs[1].dptr<DType>(), inputs[2].dptr<DType>()); + } +}; + +template<typename xpu, template<bool> class pdf, int pnum, bool vparm> +void PdfOpForward(const nnvm::NodeAttrs& attrs, + const OpContext& ctx, + const std::vector<TBlob>& inputs, + const std::vector<OpReqType>& req, + const std::vector<TBlob>& outputs) { + CHECK_NE(req[0], kAddTo); + CHECK_EQ(inputs.size(), pnum+1); + CHECK_EQ(outputs.size(), 1); + mshadow::Stream<xpu> *s = ctx.get_stream<xpu>(); + const PdfParam& param = nnvm::get<PdfParam>(attrs.parsed); + MSHADOW_REAL_TYPE_SWITCH(outputs[0].type_flag_, DType, { + if ( param.is_log ) { + PdfCaller<xpu, DType, pdf<true>, pnum, vparm>::op(inputs, outputs, s); + } else { + PdfCaller<xpu, DType, pdf<false>, pnum, vparm>::op(inputs, outputs, s); + } + }); +} + + +template<typename xpu, typename DType, typename pdfgrad, int pnum, int vparm = false> +struct PdfGradCaller; + +template<typename xpu, typename DType, typename pdfgrad> +struct PdfGradCaller<xpu, DType, pdfgrad, 1, false> { + static void op(const std::vector<TBlob>& inputs, + const std::vector<OpReqType>& req, + const std::vector<TBlob>& grads, + mshadow::Stream<xpu> *s) { + index_t num_samples(inputs[1].Size()/inputs[2].Size()); + mxnet_op::Kernel<LaunchExWrapper<pdfgrad>, xpu>::LaunchEx(s, inputs[0].Size(), + num_samples, req[0], + inputs[3].dptr<DType>(), inputs[1].dptr<DType>(), inputs[2].dptr<DType>(), + inputs[0].dptr<DType>(), grads[0].dptr<DType>(), grads[1].dptr<DType>()); + } +}; + +template<typename xpu, typename DType, typename pdfgrad> +struct PdfGradCaller<xpu, DType, pdfgrad, 1, true> { + static void op(const std::vector<TBlob>& inputs, + const std::vector<OpReqType>& req, + const std::vector<TBlob>& grads, + mshadow::Stream<xpu> *s) { + index_t num_samples(inputs[1].Size()/inputs[2].Size()); + index_t sample_size(inputs[1].Size()/inputs[0].Size()); + mxnet_op::Kernel<LaunchExWrapper<pdfgrad>, xpu>::LaunchEx(s, inputs[0].Size(), num_samples, + req[0], sample_size, + inputs[3].dptr<DType>(), inputs[1].dptr<DType>(), inputs[2].dptr<DType>(), + inputs[0].dptr<DType>(), grads[0].dptr<DType>(), grads[1].dptr<DType>()); + } +}; + +template<typename xpu, typename DType, typename pdfgrad> +struct PdfGradCaller<xpu, DType, pdfgrad, 2, false> { + static void op(const std::vector<TBlob>& inputs, + const std::vector<OpReqType>& req, + const std::vector<TBlob>& grads, + mshadow::Stream<xpu> *s) { + index_t num_samples(inputs[1].Size()/inputs[2].Size()); + mxnet_op::Kernel<LaunchExWrapper<pdfgrad>, xpu>::LaunchEx(s, inputs[0].Size(), + num_samples, req[0], + inputs[4].dptr<DType>(), inputs[1].dptr<DType>(), inputs[2].dptr<DType>(), + inputs[3].dptr<DType>(), inputs[0].dptr<DType>(), + grads[0].dptr<DType>(), grads[1].dptr<DType>(), grads[2].dptr<DType>()); + } +}; + +template<typename xpu, template<bool> class pdfgrad, int pnum, bool vparm> +void PdfOpBackward(const nnvm::NodeAttrs& attrs, + const OpContext& ctx, + const std::vector<TBlob>& inputs, + const std::vector<OpReqType>& req, + const std::vector<TBlob>& outputs) { + using namespace mshadow; + CHECK_EQ(inputs.size(), pnum+3); + CHECK_EQ(outputs.size(), pnum+1); Review comment: Nit: space around `+` ```c++ CHECK_EQ(inputs.size(), pnum + 3); CHECK_EQ(outputs.size(), pnum + 1); ``` Same applies for some other operators. ---------------------------------------------------------------- This is an automated message from the Apache Git Service. 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