diff --git a/paddle/fluid/operators/elementwise/elementwise_op_function.h b/paddle/fluid/operators/elementwise/elementwise_op_function.h
index ad5a55aede751ec0411a42dd52c85b8ebbbfa02b..2cdacfcf105aff4c87cfa96f1475a069c35cba57 100644
--- a/paddle/fluid/operators/elementwise/elementwise_op_function.h
+++ b/paddle/fluid/operators/elementwise/elementwise_op_function.h
@@ -31,8 +31,8 @@ limitations under the License. */
 
 // only can include the headers in paddle/pten/include dirs
 #include "paddle/pten/api/lib/utils/tensor_utils.h"
-#include "paddle/pten/kernels/functions/cpu/elementwise.h"
-#include "paddle/pten/kernels/functions/general/elementwise_base.h"
+#include "paddle/pten/kernels/hybird/cpu/elementwise.h"
+#include "paddle/pten/kernels/hybird/general/elementwise_base.h"
 
 #if defined(__NVCC__) || defined(__HIPCC__)
 #ifdef __NVCC__
diff --git a/paddle/fluid/operators/elementwise/elementwise_op_impl.cu.h b/paddle/fluid/operators/elementwise/elementwise_op_impl.cu.h
index 531a6ad224c6c713cb26ec95ffa602f3a3df0572..12fdcd40aa0b1dab1b9566d2074e60ab38a65943 100644
--- a/paddle/fluid/operators/elementwise/elementwise_op_impl.cu.h
+++ b/paddle/fluid/operators/elementwise/elementwise_op_impl.cu.h
@@ -23,7 +23,7 @@ limitations under the License. */
 // only can include the headers in paddle/top/api dirs
 #include "paddle/pten/api/lib/utils/tensor_utils.h"
 #include "paddle/pten/include/core.h"
-#include "paddle/pten/kernels/functions/cuda/elementwise/elementwise.h"
+#include "paddle/pten/kernels/hybird/cuda/elementwise/elementwise.h"
 
 #ifdef __HIPCC__
 #define ELEMENTWISE_BLOCK_SIZE 256
diff --git a/paddle/fluid/operators/math/math_function.cc b/paddle/fluid/operators/math/math_function.cc
index cd919b18b83c80d8caa4bbf4e3334e7432dd18f9..4201af18ca7547172017c04d660d7bcfa5b668b1 100644
--- a/paddle/fluid/operators/math/math_function.cc
+++ b/paddle/fluid/operators/math/math_function.cc
@@ -29,7 +29,7 @@ limitations under the License. */
 #include "paddle/fluid/operators/math/math_function_impl.h"
 #include "paddle/fluid/platform/bfloat16.h"
 #include "paddle/fluid/platform/float16.h"
-#include "paddle/pten/kernels/functions/eigen/common.h"
+#include "paddle/pten/kernels/hybird/eigen/common.h"
 #include "unsupported/Eigen/CXX11/Tensor"
 
 namespace paddle {
diff --git a/paddle/fluid/operators/math/math_function.cu b/paddle/fluid/operators/math/math_function.cu
index 144db9f5a2bb4be5d9383b3893a95f099c6ae00a..fa214c6389c5195e1eb0776fdedb521222a0943e 100644
--- a/paddle/fluid/operators/math/math_function.cu
+++ b/paddle/fluid/operators/math/math_function.cu
@@ -21,7 +21,7 @@ limitations under the License. */
 #include "paddle/fluid/operators/math/math_function_impl.h"
 #include "paddle/fluid/platform/bfloat16.h"
 #include "paddle/fluid/platform/float16.h"
-#include "paddle/pten/kernels/functions/eigen/common.h"
+#include "paddle/pten/kernels/hybird/eigen/common.h"
 
 namespace paddle {
 namespace operators {
diff --git a/paddle/fluid/operators/reduce_ops/reduce_op.h b/paddle/fluid/operators/reduce_ops/reduce_op.h
index df27083edbed521399a4fa20a1d62ac62f1299ed..76a14f6b1b2546d83a3b93e621bb8798ee37e494 100644
--- a/paddle/fluid/operators/reduce_ops/reduce_op.h
+++ b/paddle/fluid/operators/reduce_ops/reduce_op.h
@@ -28,7 +28,7 @@ limitations under the License. */
 #include "paddle/pten/api/lib/utils/tensor_utils.h"
 #include "paddle/pten/include/core.h"
 #include "paddle/pten/include/math.h"
-#include "paddle/pten/kernels/functions/general/reduce_impl.h"
+#include "paddle/pten/kernels/hybird/general/reduce_impl.h"
 
 #if defined(__HIPCC__) || defined(__NVCC__)
 #include "paddle/fluid/operators/reduce_ops/reduce_op.cu.h"
diff --git a/paddle/pten/CMakeLists.txt b/paddle/pten/CMakeLists.txt
index 448bcb80aa678dc33a1bcc27d640b9417a79aae0..7f6a64a1bb2e79eed409f1b43b4cf32a80365863 100644
--- a/paddle/pten/CMakeLists.txt
+++ b/paddle/pten/CMakeLists.txt
@@ -11,10 +11,14 @@ add_subdirectory(common)
 add_subdirectory(api)
 # pten core components
 add_subdirectory(core)
+# pten components of specific backends
+add_subdirectory(backends)
 # pten kernels for diff device
 add_subdirectory(kernels)
 # pten infermeta
 add_subdirectory(infermeta)
+# pten operator definitions
+add_subdirectory(ops)
 # pten tests
 add_subdirectory(tests)
 
diff --git a/paddle/pten/kernels/functions/blas/CMakeLists.txt b/paddle/pten/backends/CMakeLists.txt
similarity index 100%
rename from paddle/pten/kernels/functions/blas/CMakeLists.txt
rename to paddle/pten/backends/CMakeLists.txt
diff --git a/paddle/pten/infermeta/binary.cc b/paddle/pten/infermeta/binary.cc
index a0d4cba90dae7b13b978a3d9c28d5968bde56cc4..5d3844a1dec3d51959f5cc81d2fd3358d782fa1d 100644
--- a/paddle/pten/infermeta/binary.cc
+++ b/paddle/pten/infermeta/binary.cc
@@ -14,7 +14,7 @@ limitations under the License. */
 
 // See Note [ Why still include the fluid headers? ]
 #include "paddle/pten/infermeta/binary.h"
-#include "paddle/pten/kernels/functions/general/elementwise_base.h"
+#include "paddle/pten/kernels/hybird/general/elementwise_base.h"
 
 namespace pten {
 
diff --git a/paddle/pten/kernels/CMakeLists.txt b/paddle/pten/kernels/CMakeLists.txt
index ffc45a5cf23a4ad3aa39fb72f53f22b52fde579d..ebf659da4729864112a0ec949f048a3be3b9eb77 100644
--- a/paddle/pten/kernels/CMakeLists.txt
+++ b/paddle/pten/kernels/CMakeLists.txt
@@ -1,22 +1,28 @@
-# pten math functions called by kernels
-add_subdirectory(math)
-# pten basic functions called by kernels
-add_subdirectory(functions)
-# pten kernels for diff device
+# kernel primitive api
+add_subdirectory(primitive)
+# pten hybird functors and functions called by kernels
+add_subdirectory(hybird)
+
+# pten kernels for different backends
+# NOTE(chenweihang): We need to increase the compilation option of WITH_EIGEN,
+# which will support splitting eigen at compile time on demand in the future
+add_subdirectory(eigen)
+# NOTE(chenweihang): We need to increase the compilation option of WITH_BLAS,
+# which will support splitting eigen at compile time on demand in the future,
+# and if necessary, blas can be split into openblas and cublas
+add_subdirectory(blas)
 add_subdirectory(cpu)
 if(WITH_GPU OR WITH_ROCM)
-  # TODO(chenweihang): if hip can split from cuda impl, we should add hip dir
+  # NOTE(chenweihang): if hip can split from cuda impl, we should add hip dir
   add_subdirectory(cuda)
 endif()
-# TODO(chenweihang): migrate MKLDNN Kernel in the second phase of the project
 if(WITH_MKLDNN)
-  add_subdirectory(mkldnn)
+  # mkldnn will be deprecated and use the new name dnnl
+  add_subdirectory(dnnl)
 endif()
-# TODO(chenweihang): migrate NPU Kernel in the second phase of the project
 if(WITH_ASCEND_CL)
   add_subdirectory(npu)
 endif()
-# TODO(chenweihang): migrate XPU Kernel in the second phase of the project
 if(WITH_XPU)
   add_subdirectory(xpu)
 endif()
diff --git a/paddle/pten/kernels/functions/cpu/CMakeLists.txt b/paddle/pten/kernels/blas/CMakeLists.txt
similarity index 100%
rename from paddle/pten/kernels/functions/cpu/CMakeLists.txt
rename to paddle/pten/kernels/blas/CMakeLists.txt
diff --git a/paddle/pten/kernels/cpu/creation.cc b/paddle/pten/kernels/cpu/creation.cc
index db3d5c2bf4b1f8d2ab32813b14ce5df17a97910e..4f09fc489f8f67a8b2c53af7da16e716f4ad58fc 100644
--- a/paddle/pten/kernels/cpu/creation.cc
+++ b/paddle/pten/kernels/cpu/creation.cc
@@ -15,7 +15,7 @@
 #include "paddle/pten/kernels/cpu/creation.h"
 
 #include "paddle/pten/core/kernel_registry.h"
-#include "paddle/pten/kernels/functions/eigen/fill.h"
+#include "paddle/pten/kernels/hybird/eigen/fill.h"
 
 namespace pten {
 
diff --git a/paddle/pten/kernels/cpu/linalg.cc b/paddle/pten/kernels/cpu/linalg.cc
index ced13dc41d1ae108455ee86b794dff1d40797770..32411560b55168cc1caa2b95253014aea03eb98a 100644
--- a/paddle/pten/kernels/cpu/linalg.cc
+++ b/paddle/pten/kernels/cpu/linalg.cc
@@ -21,7 +21,7 @@
 #include "paddle/fluid/operators/math/blas.h"
 #include "paddle/fluid/platform/complex.h"
 
-#include "paddle/pten/kernels/functions/math/matmul_func.h"
+#include "paddle/pten/kernels/hybird/math/matmul_func.h"
 
 namespace pten {
 
diff --git a/paddle/pten/kernels/cpu/manipulation.cc b/paddle/pten/kernels/cpu/manipulation.cc
index bf94d00964d959dd6c0ae8c4d849a817641539f9..e0e9cefbf671bf07c375a4452453a8ebef8cd982 100644
--- a/paddle/pten/kernels/cpu/manipulation.cc
+++ b/paddle/pten/kernels/cpu/manipulation.cc
@@ -16,8 +16,8 @@
 #include "paddle/pten/api/ext/dispatch.h"
 #include "paddle/pten/infermeta/unary.h"
 #include "paddle/pten/kernels/cpu/utils.h"
-#include "paddle/pten/kernels/functions/general/manipulation.h"
-#include "paddle/pten/kernels/functions/math/cast_func.h"
+#include "paddle/pten/kernels/hybird/general/manipulation.h"
+#include "paddle/pten/kernels/hybird/math/cast_func.h"
 
 namespace pten {
 
diff --git a/paddle/pten/kernels/cpu/math.cc b/paddle/pten/kernels/cpu/math.cc
index e768d4f1eff38bf05b227f3684e69573aeab6a7d..ddfb2f5f45854001c6d4d7000d64be23058153b5 100644
--- a/paddle/pten/kernels/cpu/math.cc
+++ b/paddle/pten/kernels/cpu/math.cc
@@ -15,12 +15,12 @@
 #include "paddle/pten/kernels/cpu/math.h"
 
 #include "paddle/pten/api/ext/dispatch.h"
-#include "paddle/pten/kernels/functions/cpu/elementwise.h"
-#include "paddle/pten/kernels/functions/eigen/reduce.h"
-#include "paddle/pten/kernels/functions/eigen/scale.h"
-#include "paddle/pten/kernels/functions/eigen/sign.h"
-#include "paddle/pten/kernels/functions/general/elementwise_functor.h"
-#include "paddle/pten/kernels/functions/general/reduce_impl.h"
+#include "paddle/pten/kernels/hybird/cpu/elementwise.h"
+#include "paddle/pten/kernels/hybird/eigen/reduce.h"
+#include "paddle/pten/kernels/hybird/eigen/scale.h"
+#include "paddle/pten/kernels/hybird/eigen/sign.h"
+#include "paddle/pten/kernels/hybird/general/elementwise_functor.h"
+#include "paddle/pten/kernels/hybird/general/reduce_impl.h"
 
 // See Note [ Why still include the fluid headers? ]
 #include "paddle/fluid/framework/eigen.h"
diff --git a/paddle/pten/kernels/cuda/creation.cu b/paddle/pten/kernels/cuda/creation.cu
index 84d9fa255ce1f1294516928f4135b9a85e96ec51..8bc23fb6af056fa3f32b20ec021151b084d7c19d 100644
--- a/paddle/pten/kernels/cuda/creation.cu
+++ b/paddle/pten/kernels/cuda/creation.cu
@@ -15,7 +15,7 @@
 #include "paddle/pten/kernels/cuda/creation.h"
 
 #include "paddle/pten/core/kernel_registry.h"
-#include "paddle/pten/kernels/functions/eigen/fill.h"
+#include "paddle/pten/kernels/hybird/eigen/fill.h"
 
 namespace pten {
 
diff --git a/paddle/pten/kernels/cuda/linalg.cu b/paddle/pten/kernels/cuda/linalg.cu
index 6811afa8a49ff5676d1cead3ea5d33fcc7a0a203..fe2ac6f184ff7353df5bb55b9b7ff18911d3bf1d 100644
--- a/paddle/pten/kernels/cuda/linalg.cu
+++ b/paddle/pten/kernels/cuda/linalg.cu
@@ -15,8 +15,8 @@
 #include "paddle/pten/kernels/cuda/linalg.h"
 
 #include "paddle/pten/core/kernel_registry.h"
-#include "paddle/pten/kernels/functions/eigen/dot.h"
-#include "paddle/pten/kernels/functions/math/matmul_func.h"
+#include "paddle/pten/kernels/hybird/eigen/dot.h"
+#include "paddle/pten/kernels/hybird/math/matmul_func.h"
 
 // See Note [ Why still include the fluid headers? ]
 #include "paddle/fluid/platform/complex.h"
diff --git a/paddle/pten/kernels/cuda/manipulation.cu b/paddle/pten/kernels/cuda/manipulation.cu
index 9c7fded0910415bed2235823e391fa8e748ea3c8..acaf1ac2cc62b28002a6c15d564251cfe352f5dc 100644
--- a/paddle/pten/kernels/cuda/manipulation.cu
+++ b/paddle/pten/kernels/cuda/manipulation.cu
@@ -16,8 +16,8 @@
 #include "paddle/pten/infermeta/unary.h"
 #include "paddle/pten/kernels/cuda/manipulation.h"
 #include "paddle/pten/kernels/cuda/utils.h"
-#include "paddle/pten/kernels/functions/cuda/cast_kernel_impl.h"
-#include "paddle/pten/kernels/functions/general/manipulation.h"
+#include "paddle/pten/kernels/hybird/cuda/cast_kernel_impl.h"
+#include "paddle/pten/kernels/hybird/general/manipulation.h"
 
 namespace pten {
 
diff --git a/paddle/pten/kernels/cuda/math.cu b/paddle/pten/kernels/cuda/math.cu
index e7fa599cb68b1ea0c41e875b77d899a3c3746f51..388d42942c10a4afbdca2b4dd5c8ed9a0b9c319d 100644
--- a/paddle/pten/kernels/cuda/math.cu
+++ b/paddle/pten/kernels/cuda/math.cu
@@ -15,12 +15,12 @@ limitations under the License. */
 #include "paddle/pten/kernels/cuda/math.h"
 
 #include "paddle/fluid/operators/reduce_ops/reduce_functor_op.h"
-#include "paddle/pten/kernels/functions/cuda/elementwise/elementwise.h"
-#include "paddle/pten/kernels/functions/cuda/reduce/reduce.h"
-#include "paddle/pten/kernels/functions/eigen/scale.h"
-#include "paddle/pten/kernels/functions/eigen/sign.h"
-#include "paddle/pten/kernels/functions/general/elementwise_functor.h"
-#include "paddle/pten/kernels/functions/general/reduce_impl.h"
+#include "paddle/pten/kernels/hybird/cuda/elementwise/elementwise.h"
+#include "paddle/pten/kernels/hybird/cuda/reduce/reduce.h"
+#include "paddle/pten/kernels/hybird/eigen/scale.h"
+#include "paddle/pten/kernels/hybird/eigen/sign.h"
+#include "paddle/pten/kernels/hybird/general/elementwise_functor.h"
+#include "paddle/pten/kernels/hybird/general/reduce_impl.h"
 
 #ifdef __NVCC__
 #include "cub/cub.cuh"
diff --git a/paddle/pten/kernels/functions/cuda/CMakeLists.txt b/paddle/pten/kernels/dnnl/CMakeLists.txt
similarity index 100%
rename from paddle/pten/kernels/functions/cuda/CMakeLists.txt
rename to paddle/pten/kernels/dnnl/CMakeLists.txt
diff --git a/paddle/pten/kernels/functions/eigen/CMakeLists.txt b/paddle/pten/kernels/eigen/CMakeLists.txt
similarity index 100%
rename from paddle/pten/kernels/functions/eigen/CMakeLists.txt
rename to paddle/pten/kernels/eigen/CMakeLists.txt
diff --git a/paddle/pten/kernels/functions/CMakeLists.txt b/paddle/pten/kernels/functions/CMakeLists.txt
deleted file mode 100644
index a5b4bb3e8bd9634e6bac19ffe37b19f518a470b9..0000000000000000000000000000000000000000
--- a/paddle/pten/kernels/functions/CMakeLists.txt
+++ /dev/null
@@ -1,3 +0,0 @@
-add_subdirectory(eigen)
-add_subdirectory(blas)
-add_subdirectory(general)
diff --git a/paddle/pten/kernels/math/cuda/CMakeLists.txt b/paddle/pten/kernels/hybird/CMakeLists.txt
similarity index 58%
rename from paddle/pten/kernels/math/cuda/CMakeLists.txt
rename to paddle/pten/kernels/hybird/CMakeLists.txt
index b0be23bb092416db3601d17e9e1a5d9fdecd472d..c82cbd1ef9e21a6b71c1e8d2bda6c105391357d6 100644
--- a/paddle/pten/kernels/math/cuda/CMakeLists.txt
+++ b/paddle/pten/kernels/hybird/CMakeLists.txt
@@ -1,3 +1,8 @@
+add_subdirectory(eigen)
+add_subdirectory(blas)
+add_subdirectory(general)
+
+cc_library(pten_transpose_cpu SRCS transpose.cc DEPS dense_tensor device_context)
 if(WITH_GPU)
   nv_library(pten_transpose_cuda SRCS transpose.cu DEPS dense_tensor malloc device_context)
 elseif(WITH_ROCM)
diff --git a/paddle/pten/kernels/functions/general/CMakeLists.txt b/paddle/pten/kernels/hybird/blas/CMakeLists.txt
similarity index 100%
rename from paddle/pten/kernels/functions/general/CMakeLists.txt
rename to paddle/pten/kernels/hybird/blas/CMakeLists.txt
diff --git a/paddle/pten/kernels/functions/blas/elementwise.h b/paddle/pten/kernels/hybird/blas/elementwise.h
similarity index 100%
rename from paddle/pten/kernels/functions/blas/elementwise.h
rename to paddle/pten/kernels/hybird/blas/elementwise.h
diff --git a/paddle/pten/kernels/mkldnn/CMakeLists.txt b/paddle/pten/kernels/hybird/cpu/CMakeLists.txt
similarity index 100%
rename from paddle/pten/kernels/mkldnn/CMakeLists.txt
rename to paddle/pten/kernels/hybird/cpu/CMakeLists.txt
diff --git a/paddle/pten/kernels/functions/cpu/elementwise.h b/paddle/pten/kernels/hybird/cpu/elementwise.h
similarity index 99%
rename from paddle/pten/kernels/functions/cpu/elementwise.h
rename to paddle/pten/kernels/hybird/cpu/elementwise.h
index 98600f29910be0f6fd08e98dc87dc59cbe856d8b..e8213c8b45ddb1964f6861040fb2ec480cde950c 100644
--- a/paddle/pten/kernels/functions/cpu/elementwise.h
+++ b/paddle/pten/kernels/hybird/cpu/elementwise.h
@@ -15,7 +15,7 @@ limitations under the License. */
 #pragma once
 
 #include "paddle/pten/core/dense_tensor.h"
-#include "paddle/pten/kernels/functions/general/elementwise_base.h"
+#include "paddle/pten/kernels/hybird/general/elementwise_base.h"
 
 namespace pten {
 
diff --git a/paddle/pten/kernels/hybird/cuda/CMakeLists.txt b/paddle/pten/kernels/hybird/cuda/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/paddle/pten/kernels/functions/cuda/cast_kernel_impl.h b/paddle/pten/kernels/hybird/cuda/cast_kernel_impl.h
similarity index 100%
rename from paddle/pten/kernels/functions/cuda/cast_kernel_impl.h
rename to paddle/pten/kernels/hybird/cuda/cast_kernel_impl.h
diff --git a/paddle/pten/kernels/functions/cuda/elementwise/elementwise.h b/paddle/pten/kernels/hybird/cuda/elementwise/elementwise.h
similarity index 90%
rename from paddle/pten/kernels/functions/cuda/elementwise/elementwise.h
rename to paddle/pten/kernels/hybird/cuda/elementwise/elementwise.h
index b769936089b2514612f0b4622373c063ed98242b..9bcfa1d857ba74ad255fa2fe99b9137d5d843c54 100644
--- a/paddle/pten/kernels/functions/cuda/elementwise/elementwise.h
+++ b/paddle/pten/kernels/hybird/cuda/elementwise/elementwise.h
@@ -14,8 +14,8 @@ limitations under the License. */
 
 #pragma once
 
-#include "paddle/pten/kernels/functions/cuda/elementwise/elementwise_broadcast.cu.h"
-#include "paddle/pten/kernels/functions/cuda/elementwise/elementwise_no_broadcast.cu.h"
+#include "paddle/pten/kernels/hybird/cuda/elementwise/elementwise_broadcast.cu.h"
+#include "paddle/pten/kernels/hybird/cuda/elementwise/elementwise_no_broadcast.cu.h"
 
 namespace pten {
 
diff --git a/paddle/pten/kernels/functions/cuda/elementwise/elementwise_broadcast.cu.h b/paddle/pten/kernels/hybird/cuda/elementwise/elementwise_broadcast.cu.h
similarity index 99%
rename from paddle/pten/kernels/functions/cuda/elementwise/elementwise_broadcast.cu.h
rename to paddle/pten/kernels/hybird/cuda/elementwise/elementwise_broadcast.cu.h
index 40d3cf60f092668a006b435b7c16d10c1f53a342..258e8f410ebf3f5bdc5557307712d18372a28a02 100644
--- a/paddle/pten/kernels/functions/cuda/elementwise/elementwise_broadcast.cu.h
+++ b/paddle/pten/kernels/hybird/cuda/elementwise/elementwise_broadcast.cu.h
@@ -15,7 +15,7 @@ limitations under the License. */
 #pragma once
 
 #include "paddle/pten/core/dense_tensor.h"
-#include "paddle/pten/kernels/functions/cuda/elementwise/elementwise_common.cu.h"
+#include "paddle/pten/kernels/hybird/cuda/elementwise/elementwise_common.cu.h"
 
 namespace pten {
 
diff --git a/paddle/pten/kernels/functions/cuda/elementwise/elementwise_common.cu.h b/paddle/pten/kernels/hybird/cuda/elementwise/elementwise_common.cu.h
similarity index 97%
rename from paddle/pten/kernels/functions/cuda/elementwise/elementwise_common.cu.h
rename to paddle/pten/kernels/hybird/cuda/elementwise/elementwise_common.cu.h
index 1c0dd56254ce178f717f85eccf8f418193c41843..053b53041d1658faf7ff3d8658390da331a77080 100644
--- a/paddle/pten/kernels/functions/cuda/elementwise/elementwise_common.cu.h
+++ b/paddle/pten/kernels/hybird/cuda/elementwise/elementwise_common.cu.h
@@ -18,7 +18,7 @@ limitations under the License. */
 #include "paddle/fluid/platform/aligned_vector.h"
 #include "paddle/fluid/platform/function_traits.h"
 #include "paddle/pten/core/dense_tensor.h"
-#include "paddle/pten/kernels/functions/general/elementwise_base.h"
+#include "paddle/pten/kernels/hybird/general/elementwise_base.h"
 
 namespace pten {
 namespace kps = paddle::operators::kernel_primitives;
diff --git a/paddle/pten/kernels/functions/cuda/elementwise/elementwise_no_broadcast.cu.h b/paddle/pten/kernels/hybird/cuda/elementwise/elementwise_no_broadcast.cu.h
similarity index 98%
rename from paddle/pten/kernels/functions/cuda/elementwise/elementwise_no_broadcast.cu.h
rename to paddle/pten/kernels/hybird/cuda/elementwise/elementwise_no_broadcast.cu.h
index 4eaf8867fd0c9fbb2e414c2b2325d5cae0cc80d5..e2659271bdcd9f873fdec524e47e51758c150e3c 100644
--- a/paddle/pten/kernels/functions/cuda/elementwise/elementwise_no_broadcast.cu.h
+++ b/paddle/pten/kernels/hybird/cuda/elementwise/elementwise_no_broadcast.cu.h
@@ -14,7 +14,7 @@ limitations under the License. */
 
 #pragma once
 
-#include "paddle/pten/kernels/functions/cuda/elementwise/elementwise_common.cu.h"
+#include "paddle/pten/kernels/hybird/cuda/elementwise/elementwise_common.cu.h"
 
 #ifdef __HIPCC__
 #define ELEMENTWISE_BLOCK_SIZE 256
diff --git a/paddle/pten/kernels/functions/cuda/reduce/reduce.h b/paddle/pten/kernels/hybird/cuda/reduce/reduce.h
similarity index 97%
rename from paddle/pten/kernels/functions/cuda/reduce/reduce.h
rename to paddle/pten/kernels/hybird/cuda/reduce/reduce.h
index 0f7917f79e70c0f4e5aad354886e04a724e71e3f..1e47726333bcd2e87007d63e274dee62be9c199a 100644
--- a/paddle/pten/kernels/functions/cuda/reduce/reduce.h
+++ b/paddle/pten/kernels/hybird/cuda/reduce/reduce.h
@@ -21,7 +21,7 @@
 #include "paddle/pten/core/dense_tensor.h"
 
 #include "paddle/fluid/platform/device_context.h"
-#include "paddle/pten/kernels/functions/cuda/reduce/reduce_cuda_impl.h"
+#include "paddle/pten/kernels/hybird/cuda/reduce/reduce_cuda_impl.h"
 
 namespace pten {
 
diff --git a/paddle/pten/kernels/functions/cuda/reduce/reduce_cuda_impl.h b/paddle/pten/kernels/hybird/cuda/reduce/reduce_cuda_impl.h
similarity index 99%
rename from paddle/pten/kernels/functions/cuda/reduce/reduce_cuda_impl.h
rename to paddle/pten/kernels/hybird/cuda/reduce/reduce_cuda_impl.h
index 21663ee0388c0b1561de2b06974aa8f4e3e2d8a9..94fab974aced173b4101f6b8cfc0812f011f92a7 100644
--- a/paddle/pten/kernels/functions/cuda/reduce/reduce_cuda_impl.h
+++ b/paddle/pten/kernels/hybird/cuda/reduce/reduce_cuda_impl.h
@@ -43,7 +43,7 @@ namespace cub = hipcub;
 #include "paddle/pten/api/ext/dispatch.h"
 #include "paddle/pten/api/include/tensor.h"
 #include "paddle/pten/kernels/cuda/utils.h"
-#include "paddle/pten/kernels/functions/math/cast_func.h"
+#include "paddle/pten/kernels/hybird/math/cast_func.h"
 
 // Reduce split or not, Whether to use ReduceHigherDim
 #define REDUCE_SPLIT_BOUNDARY 512
diff --git a/paddle/pten/kernels/hybird/eigen/CMakeLists.txt b/paddle/pten/kernels/hybird/eigen/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/paddle/pten/kernels/functions/eigen/common.h b/paddle/pten/kernels/hybird/eigen/common.h
similarity index 100%
rename from paddle/pten/kernels/functions/eigen/common.h
rename to paddle/pten/kernels/hybird/eigen/common.h
diff --git a/paddle/pten/kernels/functions/eigen/dot.h b/paddle/pten/kernels/hybird/eigen/dot.h
similarity index 96%
rename from paddle/pten/kernels/functions/eigen/dot.h
rename to paddle/pten/kernels/hybird/eigen/dot.h
index 27a0b8cf329535bd2dbca158cd3841947d10c18c..eb089037fa3f30efd566678e5e55f9e86666209d 100644
--- a/paddle/pten/kernels/functions/eigen/dot.h
+++ b/paddle/pten/kernels/hybird/eigen/dot.h
@@ -15,7 +15,7 @@ limitations under the License. */
 #pragma once
 
 #include "paddle/pten/core/dense_tensor.h"
-#include "paddle/pten/kernels/functions/eigen/common.h"
+#include "paddle/pten/kernels/hybird/eigen/common.h"
 
 // See Note [ Why still include the fluid headers? ]
 #include "paddle/fluid/operators/eigen/eigen_function.h"
diff --git a/paddle/pten/kernels/functions/eigen/elementwise.h b/paddle/pten/kernels/hybird/eigen/elementwise.h
similarity index 97%
rename from paddle/pten/kernels/functions/eigen/elementwise.h
rename to paddle/pten/kernels/hybird/eigen/elementwise.h
index 369ff36c46e7f6c5f66d9edda23721943e97cad5..e67cce63d461f461c98258ca770ce09600a5ddba 100644
--- a/paddle/pten/kernels/functions/eigen/elementwise.h
+++ b/paddle/pten/kernels/hybird/eigen/elementwise.h
@@ -15,7 +15,7 @@ limitations under the License. */
 #pragma once
 
 #include "paddle/pten/core/dense_tensor.h"
-#include "paddle/pten/kernels/functions/eigen/common.h"
+#include "paddle/pten/kernels/hybird/eigen/common.h"
 
 namespace pten {
 namespace eigen {
diff --git a/paddle/pten/kernels/functions/eigen/fill.h b/paddle/pten/kernels/hybird/eigen/fill.h
similarity index 95%
rename from paddle/pten/kernels/functions/eigen/fill.h
rename to paddle/pten/kernels/hybird/eigen/fill.h
index 122a6aef22dc625e05f85f631da1dffcf9e36f69..80e310847e1865627bcd3e349837acbc07f2c867 100644
--- a/paddle/pten/kernels/functions/eigen/fill.h
+++ b/paddle/pten/kernels/hybird/eigen/fill.h
@@ -15,7 +15,7 @@ limitations under the License. */
 #pragma once
 
 #include "paddle/pten/core/dense_tensor.h"
-#include "paddle/pten/kernels/functions/eigen/common.h"
+#include "paddle/pten/kernels/hybird/eigen/common.h"
 
 // See Note [ Why still include the fluid headers? ]
 #include "paddle/fluid/operators/eigen/eigen_function.h"
diff --git a/paddle/pten/kernels/functions/eigen/reduce.h b/paddle/pten/kernels/hybird/eigen/reduce.h
similarity index 98%
rename from paddle/pten/kernels/functions/eigen/reduce.h
rename to paddle/pten/kernels/hybird/eigen/reduce.h
index 1e1027852163a0a45285e1fb2e82a2bbcf1c3cc2..52ea1e68e12ae9b3e5ca34a2630b0bd88ff8ba73 100644
--- a/paddle/pten/kernels/functions/eigen/reduce.h
+++ b/paddle/pten/kernels/hybird/eigen/reduce.h
@@ -16,8 +16,8 @@
 
 #include "paddle/pten/api/lib/utils/allocator.h"
 #include "paddle/pten/core/dense_tensor.h"
-#include "paddle/pten/kernels/functions/eigen/common.h"
-#include "paddle/pten/kernels/math/transpose.h"
+#include "paddle/pten/kernels/hybird/eigen/common.h"
+#include "paddle/pten/kernels/hybird/transpose.h"
 
 // See Note [ Why still include the fluid headers? ]
 #include "paddle/fluid/operators/eigen/eigen_function.h"
diff --git a/paddle/pten/kernels/functions/eigen/scale.h b/paddle/pten/kernels/hybird/eigen/scale.h
similarity index 96%
rename from paddle/pten/kernels/functions/eigen/scale.h
rename to paddle/pten/kernels/hybird/eigen/scale.h
index 49ee561df50ecfa536bd44c87ecb6e1f4ebd813b..111f6c22cc35e951825efa707ec3bc8ebe8f9662 100644
--- a/paddle/pten/kernels/functions/eigen/scale.h
+++ b/paddle/pten/kernels/hybird/eigen/scale.h
@@ -15,7 +15,7 @@ limitations under the License. */
 #pragma once
 
 #include "paddle/pten/core/dense_tensor.h"
-#include "paddle/pten/kernels/functions/eigen/common.h"
+#include "paddle/pten/kernels/hybird/eigen/common.h"
 
 // See Note [ Why still include the fluid headers? ]
 #include "paddle/fluid/operators/eigen/eigen_function.h"
diff --git a/paddle/pten/kernels/functions/eigen/sign.h b/paddle/pten/kernels/hybird/eigen/sign.h
similarity index 96%
rename from paddle/pten/kernels/functions/eigen/sign.h
rename to paddle/pten/kernels/hybird/eigen/sign.h
index 5cd620815bf264295cc22ee8cf6781250083a893..0beebda4f39e81dd108568485014383747b580a6 100644
--- a/paddle/pten/kernels/functions/eigen/sign.h
+++ b/paddle/pten/kernels/hybird/eigen/sign.h
@@ -15,7 +15,7 @@ limitations under the License. */
 #pragma once
 
 #include "paddle/pten/core/dense_tensor.h"
-#include "paddle/pten/kernels/functions/eigen/common.h"
+#include "paddle/pten/kernels/hybird/eigen/common.h"
 
 // See Note [ Why still include the fluid headers? ]
 #include "paddle/fluid/operators/eigen/eigen_function.h"
diff --git a/paddle/pten/kernels/hybird/general/CMakeLists.txt b/paddle/pten/kernels/hybird/general/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/paddle/pten/kernels/functions/general/elementwise_base.h b/paddle/pten/kernels/hybird/general/elementwise_base.h
similarity index 100%
rename from paddle/pten/kernels/functions/general/elementwise_base.h
rename to paddle/pten/kernels/hybird/general/elementwise_base.h
diff --git a/paddle/pten/kernels/functions/general/elementwise_functor.h b/paddle/pten/kernels/hybird/general/elementwise_functor.h
similarity index 98%
rename from paddle/pten/kernels/functions/general/elementwise_functor.h
rename to paddle/pten/kernels/hybird/general/elementwise_functor.h
index 973389f14797e97d976e095538e028e4a65df08a..109f0907c6a1030ad7a2f9a24bd74946da6fbd35 100644
--- a/paddle/pten/kernels/functions/general/elementwise_functor.h
+++ b/paddle/pten/kernels/hybird/general/elementwise_functor.h
@@ -18,8 +18,8 @@ limitations under the License. */
 #include "paddle/fluid/platform/float16.h"
 #include "paddle/fluid/platform/hostdevice.h"
 #include "paddle/pten/core/dense_tensor.h"
-#include "paddle/pten/kernels/functions/blas/elementwise.h"
-#include "paddle/pten/kernels/functions/eigen/elementwise.h"
+#include "paddle/pten/kernels/hybird/blas/elementwise.h"
+#include "paddle/pten/kernels/hybird/eigen/elementwise.h"
 
 namespace pten {
 namespace general {
diff --git a/paddle/pten/kernels/functions/general/manipulation.h b/paddle/pten/kernels/hybird/general/manipulation.h
similarity index 100%
rename from paddle/pten/kernels/functions/general/manipulation.h
rename to paddle/pten/kernels/hybird/general/manipulation.h
diff --git a/paddle/pten/kernels/functions/general/reduce_impl.h b/paddle/pten/kernels/hybird/general/reduce_impl.h
similarity index 95%
rename from paddle/pten/kernels/functions/general/reduce_impl.h
rename to paddle/pten/kernels/hybird/general/reduce_impl.h
index a48eb7e44bdc124ef4755d2c43ccf674dee0ac8d..50f40c5f2ca12bca53aa42030cfc8890a7588bfe 100644
--- a/paddle/pten/kernels/functions/general/reduce_impl.h
+++ b/paddle/pten/kernels/hybird/general/reduce_impl.h
@@ -16,8 +16,8 @@
 #include "paddle/fluid/platform/transform.h"
 #include "paddle/pten/api/ext/dispatch.h"
 #include "paddle/pten/core/dense_tensor.h"
-#include "paddle/pten/kernels/functions/eigen/reduce.h"
-#include "paddle/pten/kernels/functions/math/cast_func.h"
+#include "paddle/pten/kernels/hybird/eigen/reduce.h"
+#include "paddle/pten/kernels/hybird/math/cast_func.h"
 namespace pten {
 namespace general {
 
diff --git a/paddle/pten/kernels/functions/math/cast_func.h b/paddle/pten/kernels/hybird/math/cast_func.h
similarity index 100%
rename from paddle/pten/kernels/functions/math/cast_func.h
rename to paddle/pten/kernels/hybird/math/cast_func.h
diff --git a/paddle/pten/kernels/functions/math/matmul_func.h b/paddle/pten/kernels/hybird/math/matmul_func.h
similarity index 100%
rename from paddle/pten/kernels/functions/math/matmul_func.h
rename to paddle/pten/kernels/hybird/math/matmul_func.h
diff --git a/paddle/pten/kernels/math/cpu/transpose.cc b/paddle/pten/kernels/hybird/transpose.cc
similarity index 98%
rename from paddle/pten/kernels/math/cpu/transpose.cc
rename to paddle/pten/kernels/hybird/transpose.cc
index c8580b8877d5548ddf5d3aa6a22687b765d300f9..73375a6a379fe9422620ac39879d27f5d8850bc1 100644
--- a/paddle/pten/kernels/math/cpu/transpose.cc
+++ b/paddle/pten/kernels/hybird/transpose.cc
@@ -12,7 +12,7 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
-#include "paddle/pten/kernels/math/transpose.h"
+#include "paddle/pten/kernels/hybird/transpose.h"
 #include "paddle/fluid/framework/ddim.h"
 #include "paddle/pten/core/dense_tensor.h"
 
diff --git a/paddle/pten/kernels/math/cuda/transpose.cu b/paddle/pten/kernels/hybird/transpose.cu
similarity index 97%
rename from paddle/pten/kernels/math/cuda/transpose.cu
rename to paddle/pten/kernels/hybird/transpose.cu
index a18efde2c2e62c4c4c32745fd0573e7826735262..bf7a1409938a68963f9fefdc570e9da703c6fffa 100644
--- a/paddle/pten/kernels/math/cuda/transpose.cu
+++ b/paddle/pten/kernels/hybird/transpose.cu
@@ -15,8 +15,8 @@
 #include "paddle/fluid/framework/ddim.h"
 #include "paddle/fluid/memory/memcpy.h"
 #include "paddle/pten/core/dense_tensor.h"
-#include "paddle/pten/kernels/functions/math/cast_func.h"
-#include "paddle/pten/kernels/math/transpose.h"
+#include "paddle/pten/kernels/hybird/math/cast_func.h"
+#include "paddle/pten/kernels/hybird/transpose.h"
 
 // See Note [ Why still include the fluid headers? ]
 #include "paddle/fluid/platform/bfloat16.h"
diff --git a/paddle/pten/kernels/math/transpose.h b/paddle/pten/kernels/hybird/transpose.h
similarity index 100%
rename from paddle/pten/kernels/math/transpose.h
rename to paddle/pten/kernels/hybird/transpose.h
diff --git a/paddle/pten/kernels/math/CMakeLists.txt b/paddle/pten/kernels/math/CMakeLists.txt
deleted file mode 100644
index 429a6df8e2cc71763131f3cd8e3368aa86065a9c..0000000000000000000000000000000000000000
--- a/paddle/pten/kernels/math/CMakeLists.txt
+++ /dev/null
@@ -1,4 +0,0 @@
-add_subdirectory(cpu)
-if(WITH_GPU OR WITH_ROCM)
-  add_subdirectory(cuda)
-endif()
diff --git a/paddle/pten/kernels/math/cpu/CMakeLists.txt b/paddle/pten/kernels/math/cpu/CMakeLists.txt
deleted file mode 100644
index 235a49a5e4af513b0536f2fbc909bb6188914a89..0000000000000000000000000000000000000000
--- a/paddle/pten/kernels/math/cpu/CMakeLists.txt
+++ /dev/null
@@ -1 +0,0 @@
-cc_library(pten_transpose_cpu SRCS transpose.cc DEPS dense_tensor device_context)
diff --git a/paddle/pten/kernels/primitive/CMakeLists.txt b/paddle/pten/kernels/primitive/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/paddle/pten/kernels/xpu/manipulation.cc b/paddle/pten/kernels/xpu/manipulation.cc
index 352d21e6e9bf94a96bca544e12a73dbaf8dfc14f..5f1c0d42eb5a8faf2d6b488ebded52684abfab3c 100644
--- a/paddle/pten/kernels/xpu/manipulation.cc
+++ b/paddle/pten/kernels/xpu/manipulation.cc
@@ -14,7 +14,7 @@
 
 #include "paddle/pten/kernels/xpu/manipulation.h"
 #include "paddle/pten/infermeta/unary.h"
-#include "paddle/pten/kernels/functions/general/manipulation.h"
+#include "paddle/pten/kernels/hybird/general/manipulation.h"
 #include "paddle/pten/kernels/xpu/utils.h"
 
 namespace pten {
diff --git a/paddle/pten/ops/CMakeLists.txt b/paddle/pten/ops/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391