diff --git a/paddle/fluid/operators/math/concat_test.cc b/paddle/fluid/operators/math/concat_test.cc
index 411dbca25bb48c99dfd16779f54e46a3e80d0d4e..270a9d3f80a80d5ea2c8b97d4a69125355ddef61 100644
--- a/paddle/fluid/operators/math/concat_test.cc
+++ b/paddle/fluid/operators/math/concat_test.cc
@@ -79,8 +79,16 @@ void ConcatCase1(DeviceContext* context) {
   concat_functor(*context, input, 0, &out);
 
   // check the dim of input_a, input_b
-  PADDLE_ENFORCE_EQ(input_a.dims(), dim_a);
-  PADDLE_ENFORCE_EQ(input_b.dims(), dim_b);
+  PADDLE_ENFORCE_EQ(input_a.dims(), dim_a,
+                    paddle::platform::errors::InvalidArgument(
+                        "The dims of Input tensor should be the same as the "
+                        "declared dims. Tensor dims: [%s], declared dims: [%s]",
+                        input_a.dims(), dim_a));
+  PADDLE_ENFORCE_EQ(input_b.dims(), dim_b,
+                    paddle::platform::errors::InvalidArgument(
+                        "The dims of Input tensor should be the same as the "
+                        "declared dims. Tensor dims: [%s], declared dims: [%s]",
+                        input_b.dims(), dim_b));
 
   int* out_ptr = nullptr;
   if (paddle::platform::is_gpu_place(Place())) {
@@ -95,10 +103,14 @@ void ConcatCase1(DeviceContext* context) {
   int idx_a = 0, idx_b = 0;
   for (int j = 0; j < 5 * 3 * 4; ++j) {
     if (j >= cols) {
-      PADDLE_ENFORCE_EQ(out_ptr[j], b_ptr[idx_b]);
+      PADDLE_ENFORCE_EQ(out_ptr[j], b_ptr[idx_b],
+                        paddle::platform::errors::InvalidArgument(
+                            "Concat test failed, the result should be equal."));
       ++idx_b;
     } else {
-      PADDLE_ENFORCE_EQ(out_ptr[j], a_ptr[idx_a]);
+      PADDLE_ENFORCE_EQ(out_ptr[j], a_ptr[idx_a],
+                        paddle::platform::errors::InvalidArgument(
+                            "Concat test failed, the result should be equal."));
       ++idx_a;
     }
   }
@@ -166,8 +178,16 @@ void ConcatCase2(DeviceContext* context) {
   concat_functor(*context, input, 1, &out);
 
   // check the dim of input_a, input_b
-  PADDLE_ENFORCE_EQ(input_a.dims(), dim_a);
-  PADDLE_ENFORCE_EQ(input_b.dims(), dim_b);
+  PADDLE_ENFORCE_EQ(input_a.dims(), dim_a,
+                    paddle::platform::errors::InvalidArgument(
+                        "The dims of Input tensor should be the same as the "
+                        "declared dims. Tensor dims: [%s], declared dims: [%s]",
+                        input_a.dims(), dim_a));
+  PADDLE_ENFORCE_EQ(input_b.dims(), dim_b,
+                    paddle::platform::errors::InvalidArgument(
+                        "The dims of Input tensor should be the same as the "
+                        "declared dims. Tensor dims: [%s], declared dims: [%s]",
+                        input_b.dims(), dim_b));
 
   int* out_ptr = nullptr;
   if (paddle::platform::is_gpu_place(Place())) {
@@ -183,10 +203,16 @@ void ConcatCase2(DeviceContext* context) {
   for (int i = 0; i < 2; ++i) {
     for (int j = 0; j < 28; ++j) {
       if (j >= cols) {
-        PADDLE_ENFORCE_EQ(out_ptr[i * 28 + j], b_ptr[idx_b]);
+        PADDLE_ENFORCE_EQ(
+            out_ptr[i * 28 + j], b_ptr[idx_b],
+            paddle::platform::errors::InvalidArgument(
+                "Concat test failed, the result should be equal."));
         ++idx_b;
       } else {
-        PADDLE_ENFORCE_EQ(out_ptr[i * 28 + j], a_ptr[idx_a]);
+        PADDLE_ENFORCE_EQ(
+            out_ptr[i * 28 + j], a_ptr[idx_a],
+            paddle::platform::errors::InvalidArgument(
+                "Concat test failed, the result should be equal."));
         ++idx_a;
       }
     }
@@ -255,8 +281,16 @@ void ConcatCase3(DeviceContext* context) {
   concat_functor(*context, input, 2, &out);
 
   // check the dim of input_a, input_b
-  PADDLE_ENFORCE_EQ(input_a.dims(), dim_a);
-  PADDLE_ENFORCE_EQ(input_b.dims(), dim_b);
+  PADDLE_ENFORCE_EQ(input_a.dims(), dim_a,
+                    paddle::platform::errors::InvalidArgument(
+                        "The dims of Input tensor should be the same as the "
+                        "declared dims. Tensor dims: [%s], declared dims: [%s]",
+                        input_a.dims(), dim_a));
+  PADDLE_ENFORCE_EQ(input_b.dims(), dim_b,
+                    paddle::platform::errors::InvalidArgument(
+                        "The dims of Input tensor should be the same as the "
+                        "declared dims. Tensor dims: [%s], declared dims: [%s]",
+                        input_b.dims(), dim_b));
 
   int* out_ptr = nullptr;
   if (paddle::platform::is_gpu_place(Place())) {
@@ -273,10 +307,16 @@ void ConcatCase3(DeviceContext* context) {
   for (int i = 0; i < 6; ++i) {
     for (int j = 0; j < 9; ++j) {
       if (j >= cols) {
-        PADDLE_ENFORCE_EQ(out_ptr[i * 9 + j], b_ptr[idx_b]);
+        PADDLE_ENFORCE_EQ(
+            out_ptr[i * 9 + j], b_ptr[idx_b],
+            paddle::platform::errors::InvalidArgument(
+                "Concat test failed, the result should be equal."));
         ++idx_b;
       } else {
-        PADDLE_ENFORCE_EQ(out_ptr[i * 9 + j], a_ptr[idx_a]);
+        PADDLE_ENFORCE_EQ(
+            out_ptr[i * 9 + j], a_ptr[idx_a],
+            paddle::platform::errors::InvalidArgument(
+                "Concat test failed, the result should be equal."));
         ++idx_a;
       }
     }
@@ -347,8 +387,16 @@ void ConcatCase4(DeviceContext* context) {
   context->Wait();
 
   // check the dim of input_a, input_b
-  PADDLE_ENFORCE_EQ(input_a.dims(), dim_a);
-  PADDLE_ENFORCE_EQ(input_b.dims(), dim_b);
+  PADDLE_ENFORCE_EQ(input_a.dims(), dim_a,
+                    paddle::platform::errors::InvalidArgument(
+                        "The dims of Input tensor should be the same as the "
+                        "declared dims. Tensor dims: [%s], declared dims: [%s]",
+                        input_a.dims(), dim_a));
+  PADDLE_ENFORCE_EQ(input_b.dims(), dim_b,
+                    paddle::platform::errors::InvalidArgument(
+                        "The dims of Input tensor should be the same as the "
+                        "declared dims. Tensor dims: [%s], declared dims: [%s]",
+                        input_b.dims(), dim_b));
 
   int* out_ptr = nullptr;
   if (paddle::platform::is_gpu_place(Place())) {
@@ -365,10 +413,16 @@ void ConcatCase4(DeviceContext* context) {
   for (int i = 0; i < 2; ++i) {
     for (int j = 0; j < 24; ++j) {
       if (j >= cols) {
-        PADDLE_ENFORCE_EQ(out_ptr[i * 24 + j], b_ptr[idx_b]);
+        PADDLE_ENFORCE_EQ(
+            out_ptr[i * 24 + j], b_ptr[idx_b],
+            paddle::platform::errors::InvalidArgument(
+                "Concat test failed, the result should be equal."));
         ++idx_b;
       } else {
-        PADDLE_ENFORCE_EQ(out_ptr[i * 24 + j], a_ptr[idx_a]);
+        PADDLE_ENFORCE_EQ(
+            out_ptr[i * 24 + j], a_ptr[idx_a],
+            paddle::platform::errors::InvalidArgument(
+                "Concat test failed, the result should be equal."));
         ++idx_a;
       }
     }
diff --git a/paddle/fluid/operators/math/context_project.h b/paddle/fluid/operators/math/context_project.h
index e9019c6d2fe6890ee92cb5a3b047666e3c2a7e04..051c6019d74f7d2820dc0ba668da3cafe8864346 100644
--- a/paddle/fluid/operators/math/context_project.h
+++ b/paddle/fluid/operators/math/context_project.h
@@ -134,7 +134,10 @@ class ContextProjectFunctor {
       }
     }
     if (padding_trainable) {
-      PADDLE_ENFORCE_NOT_NULL(padding_data);
+      PADDLE_ENFORCE_NOT_NULL(
+          padding_data,
+          platform::errors::InvalidArgument(
+              "The input tensor 'padding_data' should not be NULL."));
       for (int i = 0; i < static_cast<int>(lod_level_0.size()) - 1; ++i) {
         if (lod_level_0[i] == lod_level_0[i + 1]) continue;
 
diff --git a/paddle/fluid/operators/math/cpu_vec.h b/paddle/fluid/operators/math/cpu_vec.h
index 8940a41424b01c975f1264ca309cc09fc3c7ae85..925f3b6161ae8506107f917196e77ecb2d9c5593 100644
--- a/paddle/fluid/operators/math/cpu_vec.h
+++ b/paddle/fluid/operators/math/cpu_vec.h
@@ -621,7 +621,10 @@ class VecActivations {
     } else if (type == "identity" || type == "") {
       return vec_identity<T, isa>;
     }
-    PADDLE_THROW("Not support type: %s", type);
+    PADDLE_THROW(platform::errors::InvalidArgument(
+        "Expected type should be one of sigmod, relu, tanh, identity. But got "
+        "not support type: %s.",
+        type));
   }
 };
 
diff --git a/paddle/fluid/operators/math/cross_entropy.cu b/paddle/fluid/operators/math/cross_entropy.cu
index c7fac60dd3e663088813f795352e4d751059de39..84fa0d6af990e22083ec1a0e3993893cefad1ab5 100644
--- a/paddle/fluid/operators/math/cross_entropy.cu
+++ b/paddle/fluid/operators/math/cross_entropy.cu
@@ -27,8 +27,8 @@ __global__ void CrossEntropyKernel(T* Y, const T* X, const int64_t* label,
                                    const int ignore_index) {
   CUDA_KERNEL_LOOP(i, N) {
     PADDLE_ENFORCE(label[i] >= 0 && label[i] < D || label[i] == ignore_index,
-                   "label[%d] expected >= 0 and < %ld, or == %ld, but got "
-                   "%ld. Please check input value.",
+                   "The value of label[%d] expected >= 0 and < %ld, or == %ld, "
+                   "but got %ld. Please check input value.",
                    i, D, ignore_index, label[i]);
     Y[i] = ignore_index == label[i]
                ? static_cast<T>(0)
diff --git a/paddle/fluid/operators/math/im2col.cc b/paddle/fluid/operators/math/im2col.cc
index 094a7237826610af574061263e5b0df5eafdf239..6fb393d791cc2a077dbcd0a912bcf31b5d59ad65 100644
--- a/paddle/fluid/operators/math/im2col.cc
+++ b/paddle/fluid/operators/math/im2col.cc
@@ -34,9 +34,16 @@ class Im2ColFunctor<paddle::operators::math::ColFormat::kCFO,
                   const std::vector<int>& stride,
                   const std::vector<int>& padding, framework::Tensor* col,
                   const DataLayout data_layout) {
-    PADDLE_ENFORCE_EQ(im.dims().size(), 3, "The dimension of im should be 3.");
+    PADDLE_ENFORCE_EQ(im.dims().size(), 3,
+                      platform::errors::InvalidArgument(
+                          "The dimension of tensor 'im' should be 3. But got "
+                          "the dims of tensor 'im' is [%s].",
+                          im.dims()));
     PADDLE_ENFORCE_EQ(col->dims().size(), 5,
-                      "The dimension of col should be 5.");
+                      platform::errors::InvalidArgument(
+                          "The dimension of tensor 'col' should be 5. But got "
+                          "the dims of tensor 'col' is [%s].",
+                          col->dims()));
 
     if (stride[0] == 1 && stride[1] == 1 && dilation[0] == 1 &&
         dilation[1] == 1) {
@@ -70,9 +77,16 @@ class Col2ImFunctor<paddle::operators::math::ColFormat::kCFO,
                   const std::vector<int>& stride,
                   const std::vector<int>& padding, framework::Tensor* im,
                   const DataLayout data_layout) {
-    PADDLE_ENFORCE_EQ(im->dims().size(), 3, "The dimension of im should be 3.");
+    PADDLE_ENFORCE_EQ(im->dims().size(), 3,
+                      platform::errors::InvalidArgument(
+                          "The dimension of tensor 'im' should be 3. But got "
+                          "the dims of tensor 'im' is [%s].",
+                          im->dims()));
     PADDLE_ENFORCE_EQ(col.dims().size(), 5,
-                      "The dimension of col should be 5.");
+                      platform::errors::InvalidArgument(
+                          "The dimension of tensor 'col' should be 5. But got "
+                          "the dims of tensor 'col' is [%s].",
+                          col.dims()));
     int im_channels =
         (data_layout != DataLayout::kNHWC ? im->dims()[0] : im->dims()[2]);
     int im_height =
@@ -88,16 +102,16 @@ class Col2ImFunctor<paddle::operators::math::ColFormat::kCFO,
                        ((dilation[0] * (filter_height - 1) + 1))) /
                               stride[0] +
                           1,
-                      col_height,
-                      "Output_height and padding(padding_up, padding_down) are "
-                      "inconsistent.");
+                      col_height, platform::errors::InvalidArgument(
+                                      "Output_height and padding(padding_up, "
+                                      "padding_down) are inconsistent."));
     PADDLE_ENFORCE_EQ((im_width + padding[1] + padding[3] -
                        ((dilation[1] * (filter_width - 1) + 1))) /
                               stride[1] +
                           1,
-                      col_width,
-                      "Output_height and padding(padding_up, padding_down) are "
-                      "inconsistent.");
+                      col_width, platform::errors::InvalidArgument(
+                                     "Output_height and padding(padding_up, "
+                                     "padding_down) are inconsistent."));
 
     int channels_col = im_channels * filter_height * filter_width;
 
@@ -154,9 +168,16 @@ class Im2ColFunctor<paddle::operators::math::ColFormat::kOCF,
                   const std::vector<int>& stride,
                   const std::vector<int>& padding, framework::Tensor* col,
                   const DataLayout data_layout) {
-    PADDLE_ENFORCE_EQ(im.dims().size(), 3, "The dimension of im should be 3.");
+    PADDLE_ENFORCE_EQ(im.dims().size(), 3,
+                      platform::errors::InvalidArgument(
+                          "The dimension of tensor 'im' should be 3. But got "
+                          "the dims of tensor 'im' is [%s].",
+                          im.dims()));
     PADDLE_ENFORCE_EQ(col->dims().size(), 5,
-                      "The dimension of col should be 5.");
+                      platform::errors::InvalidArgument(
+                          "The dimension of tensor 'col' should be 5. But got "
+                          "the dims of tensor 'col' is [%s].",
+                          col->dims()));
     int im_channels = im.dims()[0];
     int im_height = im.dims()[1];
     int im_width = im.dims()[2];
@@ -218,9 +239,16 @@ class Col2ImFunctor<paddle::operators::math::ColFormat::kOCF,
                   const std::vector<int>& stride,
                   const std::vector<int>& padding, framework::Tensor* im,
                   const DataLayout data_layout) {
-    PADDLE_ENFORCE_EQ(im->dims().size(), 3, "The dimension of im should be 3.");
+    PADDLE_ENFORCE_EQ(im->dims().size(), 3,
+                      platform::errors::InvalidArgument(
+                          "The dimension of tensor 'im' should be 3. But got "
+                          "the dims of tensor 'im' is [%s].",
+                          im->dims()));
     PADDLE_ENFORCE_EQ(col.dims().size(), 5,
-                      "The dimension of col should be 5.");
+                      platform::errors::InvalidArgument(
+                          "The dimension of tensor 'col' should be 5. But got "
+                          "the dims of tensor 'col' is [%s].",
+                          col.dims()));
     int im_channels = im->dims()[0];
     int im_height = im->dims()[1];
     int im_width = im->dims()[2];
@@ -231,14 +259,14 @@ class Col2ImFunctor<paddle::operators::math::ColFormat::kOCF,
 
     PADDLE_ENFORCE_EQ(
         (im_height + padding[0] + padding[2] - filter_height) / stride[0] + 1,
-        col_height,
-        "Output_height and padding(padding_up, padding_down) are "
-        "inconsistent.");
+        col_height, platform::errors::InvalidArgument(
+                        "Output_height and padding(padding_up, padding_down) "
+                        "are inconsistent."));
     PADDLE_ENFORCE_EQ(
         (im_width + padding[1] + padding[3] - filter_width) / stride[1] + 1,
         col_width,
-        "col_width and padding(padding_left, padding_right) are "
-        "inconsistent.");
+        platform::errors::InvalidArgument("col_width and padding(padding_left, "
+                                          "padding_right) are inconsistent."));
 
     T* im_data = im->data<T>();
     const T* col_data = col.data<T>();
diff --git a/paddle/fluid/operators/math/im2col.cu b/paddle/fluid/operators/math/im2col.cu
index 97719300daed9c02a716f31d853e3a381312961c..f2a2148ba6954f50cf59ae30f4f4be6aa070739f 100644
--- a/paddle/fluid/operators/math/im2col.cu
+++ b/paddle/fluid/operators/math/im2col.cu
@@ -81,9 +81,16 @@ class Im2ColFunctor<paddle::operators::math::ColFormat::kCFO,
                   const std::vector<int>& stride,
                   const std::vector<int>& padding, framework::Tensor* col,
                   const DataLayout data_layout) {
-    PADDLE_ENFORCE_EQ(im.dims().size(), 3, "The dimension of im should be 3.");
+    PADDLE_ENFORCE_EQ(im.dims().size(), 3,
+                      platform::errors::InvalidArgument(
+                          "The dimension of tensor 'im' should be 3. But got "
+                          "the dims of tensor 'im' is [%s].",
+                          im.dims()));
     PADDLE_ENFORCE_EQ(col->dims().size(), 5,
-                      "The dimension of col should be 5.");
+                      platform::errors::InvalidArgument(
+                          "The dimension of tensor 'col' should be 5. But got "
+                          "the dims of tensor 'col' is [%s].",
+                          col->dims()));
 
     int im_channels =
         (data_layout != DataLayout::kNHWC ? im.dims()[0] : im.dims()[2]);
@@ -182,9 +189,16 @@ class Col2ImFunctor<paddle::operators::math::ColFormat::kCFO,
                   const std::vector<int>& stride,
                   const std::vector<int>& padding, framework::Tensor* im,
                   const DataLayout data_layout) {
-    PADDLE_ENFORCE_EQ(im->dims().size(), 3, "The dimension of im should be 3.");
+    PADDLE_ENFORCE_EQ(im->dims().size(), 3,
+                      platform::errors::InvalidArgument(
+                          "The dimension of tensor 'im' should be 3. But got "
+                          "the dims of tensor 'im' is [%s].",
+                          im->dims()));
     PADDLE_ENFORCE_EQ(col.dims().size(), 5,
-                      "The dimension of col should be 5.");
+                      platform::errors::InvalidArgument(
+                          "The dimension of tensor 'col' should be 5. But got "
+                          "the dims of tensor 'col' is [%s].",
+                          col.dims()));
 
     int im_channels =
         (data_layout != DataLayout::kNHWC ? im->dims()[0] : im->dims()[2]);
@@ -201,16 +215,16 @@ class Col2ImFunctor<paddle::operators::math::ColFormat::kCFO,
                        (dilation[0] * (filter_height - 1) + 1)) /
                               stride[0] +
                           1,
-                      col_height,
-                      "Output_height and padding(padding_up, padding_down) are "
-                      "inconsistent.");
+                      col_height, platform::errors::InvalidArgument(
+                                      "Output_height and padding(padding_up, "
+                                      "padding_down) are inconsistent."));
     PADDLE_ENFORCE_EQ((im_width + padding[1] + padding[3] -
                        (dilation[1] * (filter_width - 1) + 1)) /
                               stride[1] +
                           1,
-                      col_width,
-                      "col_width and padding(padding_left, padding_right) are "
-                      "inconsistent.");
+                      col_width, platform::errors::InvalidArgument(
+                                     "col_width and padding(padding_left, "
+                                     "padding_right) are inconsistent."));
 
     size_t num_kernels = im_channels * im_height * im_width;
 
@@ -285,9 +299,16 @@ class Im2ColFunctor<paddle::operators::math::ColFormat::kOCF,
                   const std::vector<int>& stride,
                   const std::vector<int>& padding, framework::Tensor* col,
                   const DataLayout data_layout) {
-    PADDLE_ENFORCE_EQ(im.dims().size(), 3, "The dimension of im should be 3.");
+    PADDLE_ENFORCE_EQ(im.dims().size(), 3,
+                      platform::errors::InvalidArgument(
+                          "The dimension of tensor 'im' should be 3. But got "
+                          "the dims of tensor 'im' is [%s].",
+                          im.dims()));
     PADDLE_ENFORCE_EQ(col->dims().size(), 5,
-                      "The dimension of col should be 5.");
+                      platform::errors::InvalidArgument(
+                          "The dimension of tensor 'col' should be 5. But got "
+                          "the dims of tensor 'col' is [%s].",
+                          col->dims()));
 
     int im_channels = im.dims()[0];
     int im_height = im.dims()[1];
@@ -370,9 +391,16 @@ class Col2ImFunctor<paddle::operators::math::ColFormat::kOCF,
                   const std::vector<int>& stride,
                   const std::vector<int>& padding, framework::Tensor* im,
                   const DataLayout data_layout) {
-    PADDLE_ENFORCE_EQ(im->dims().size(), 3, "The dimension of im should be 3.");
+    PADDLE_ENFORCE_EQ(im->dims().size(), 3,
+                      platform::errors::InvalidArgument(
+                          "The dimension of tensor 'im' should be 3. But got "
+                          "the dims of tensor 'im' is [%s].",
+                          im->dims()));
     PADDLE_ENFORCE_EQ(col.dims().size(), 5,
-                      "The dimension of col should be 5.");
+                      platform::errors::InvalidArgument(
+                          "The dimension of tensor 'col' should be 5. But got "
+                          "the dims of tensor 'col' is [%s].",
+                          col.dims()));
 
     int im_channels = im->dims()[0];
     int im_height = im->dims()[1];
@@ -386,16 +414,16 @@ class Col2ImFunctor<paddle::operators::math::ColFormat::kOCF,
                        (dilation[0] * (filter_height - 1) + 1)) /
                               stride[0] +
                           1,
-                      col_height,
-                      "Output_height and padding(padding_up, padding_down) are "
-                      "inconsistent.");
+                      col_height, platform::errors::InvalidArgument(
+                                      "Output_height and padding(padding_up, "
+                                      "padding_down) are inconsistent."));
     PADDLE_ENFORCE_EQ((im_width + padding[1] + padding[3] -
                        (dilation[1] * (filter_width - 1) + 1)) /
                               stride[1] +
                           1,
-                      col_width,
-                      "col_width and padding(padding_left, padding_right) are "
-                      "inconsistent.");
+                      col_width, platform::errors::InvalidArgument(
+                                     "col_width and padding(padding_left, "
+                                     "padding_right) are inconsistent."));
 
     int block_dim_x = 0;
     int block_dim_y = 0;