refine notation in bilinear_tensor_product_op.h

Author: peterzhang2029

paddle/operators/bilinear_tensor_product_op.h

@@ -27,10 +27,6 @@ template <typename T, int MajorType = Eigen::RowMajor,
           typename IndexType = Eigen::DenseIndex>
 using EigenMatrix = framework::EigenMatrix<T, MajorType, IndexType>;
 
-template <typename T, int MajorType = Eigen::RowMajor,
-          typename IndexType = Eigen::DenseIndex>
-using EigenVector = framework::EigenVector<T, MajorType, IndexType>;
-
 template <typename Place, typename T>
 class BilinearTensorProductKernel : public framework::OpKernel<T> {
  public:
@@ -49,7 +45,9 @@ class BilinearTensorProductKernel : public framework::OpKernel<T> {
     auto weight_dims = weight->dims();
     auto place = ctx.GetEigenDevice<Place>();
 
-    // Create the intermediate variables.
+    // Create the intermediate variable to caculate the result of
+    // Input(X) multiplied by Input(Weight_i), the formula is:
+    // left_mul = X Weight_i.
     Tensor left_mul;
     left_mul.mutable_data<T>(framework::make_ddim({batch_size, weight_dims[2]}),
                              ctx.GetPlace());
@@ -95,31 +93,33 @@ class BilinearTensorProductGradKernel : public framework::OpKernel<T> {
     auto d_out_mat = EigenMatrix<T>::From(*d_out);
     auto place = ctx.GetEigenDevice<Place>();
 
-    // Create the intermediate variables for gradient.
+    // Create the intermediate variable to caculate the Output(Y@Grad).
     Tensor x_scale;
     x_scale.mutable_data<T>(framework::make_ddim({batch_size, weight_dims[1]}),
                             ctx.GetPlace());
     auto x_scale_mat = EigenMatrix<T>::From(x_scale);
+
+    // Create the intermediate variable to caculate the Output(X@Grad).
     Tensor y_scale;
     y_scale.mutable_data<T>(framework::make_ddim({batch_size, weight_dims[2]}),
                             ctx.GetPlace());
     auto y_scale_mat = EigenMatrix<T>::From(y_scale);
 
     math::SetConstant<Place, T> set_zero;
 
-    // Set X@Grad be zero at first.
+    // Set Output(X@Grad) be zero.
     if (d_x) {
       d_x->mutable_data<T>(ctx.GetPlace());
       set_zero(ctx.device_context(), d_x, static_cast<T>(0));
     }
 
-    // Set Y@Grad be zero at first.
+    // Set Output(Y@Grad) be zero.
     if (d_y) {
       d_y->mutable_data<T>(ctx.GetPlace());
       set_zero(ctx.device_context(), d_y, static_cast<T>(0));
     }
 
-    // Caculate the X@Grad and Y@Grad.
+    // Caculate the Output(X@Grad) and Output(Y@Grad).
     if (d_x || d_y) {
       Eigen::DSizes<int, 2> bcast_for_x(1, weight_dims[2]);
       Eigen::DSizes<int, 2> bcast_for_y(1, weight_dims[1]);
@@ -150,7 +150,7 @@ class BilinearTensorProductGradKernel : public framework::OpKernel<T> {
       }
     }
 
-    // Caculate the gradient of Weight.
+    // Caculate the gradient of Input(Weight).
     if (d_weight) {
       d_weight->mutable_data<T>(ctx.GetPlace());
       Eigen::DSizes<int, 2> bcast_for_weight(1, weight_dims[1]);
@@ -169,7 +169,7 @@ class BilinearTensorProductGradKernel : public framework::OpKernel<T> {
       }
     }
 
-    // Caculate the gradient of Bias.
+    // Caculate the gradient of Input(Bias).
     if (d_bias) {
       d_bias->mutable_data<T>(ctx.GetPlace());
       auto d_bias_mat = EigenMatrix<T>::From(*d_bias);