diff --git a/paddle/fluid/operators/lu_op.h b/paddle/fluid/operators/lu_op.h
index 214b2eccae9f75e9bfcfa3df0b823918e2b0c353..6e2ac4617da4df8e4ebaf92d4193ef8b3368b97a 100644
--- a/paddle/fluid/operators/lu_op.h
+++ b/paddle/fluid/operators/lu_op.h
@@ -18,8 +18,8 @@ limitations under the License. */
 #include "paddle/fluid/framework/phi_utils.h"
 #include "paddle/fluid/operators/set_value_op.h"
 #include "paddle/fluid/operators/svd_helper.h"
-#include "paddle/fluid/operators/tril_triu_op.h"
 #include "paddle/phi/kernels/funcs/lapack/lapack_function.h"
+#include "paddle/phi/kernels/funcs/tril_triu_compute.h"
 #include "paddle/phi/kernels/math_kernel.h"
 #include "paddle/phi/kernels/triangular_solve_kernel.h"
 
@@ -404,11 +404,12 @@ void LU_Unpack(const DeviceContext& dev_ctx, const framework::Tensor* LU,
   const auto W = udims[udims.size() - 1];
   auto L_dataptr = L->mutable_data<T>(dev_ctx.GetPlace());
   platform::ForRange<DeviceContext> x_for_range(dev_ctx, LU->numel());
-  TrilTriuCompute<T> tril_computer(LU->data<T>(), -1, true, H, W, L_dataptr);
+  phi::funcs::TrilTriuCompute<T> tril_computer(LU->data<T>(), -1, true, H, W,
+                                               L_dataptr);
   x_for_range(tril_computer);
 
-  TrilTriuCompute<T> triu_computer(LU->data<T>(), 0, false, H, W,
-                                   U->mutable_data<T>(dev_ctx.GetPlace()));
+  phi::funcs::TrilTriuCompute<T> triu_computer(
+      LU->data<T>(), 0, false, H, W, U->mutable_data<T>(dev_ctx.GetPlace()));
   x_for_range(triu_computer);
 
   // set L's diagonal 1
@@ -532,15 +533,15 @@ class LUGradKernel : public framework::OpKernel<T> {
     auto phil_rank = LmHdims.size();
     auto phiu_rank = UmHdims.size();
     platform::ForRange<DeviceContext> l_for_range(dev_ctx, phi_L.numel());
-    TrilTriuCompute<T> tril_computer(phi_L.data<T>(), -1, true,
-                                     LmHdims[phil_rank - 2],
-                                     LmHdims[phil_rank - 1], phi_L.data<T>());
+    phi::funcs::TrilTriuCompute<T> tril_computer(
+        phi_L.data<T>(), -1, true, LmHdims[phil_rank - 2],
+        LmHdims[phil_rank - 1], phi_L.data<T>());
     l_for_range(tril_computer);
 
     platform::ForRange<DeviceContext> u_for_range(dev_ctx, phi_U.numel());
-    TrilTriuCompute<T> triu_computer(phi_U.data<T>(), 0, false,
-                                     UmHdims[phiu_rank - 2],
-                                     UmHdims[phiu_rank - 1], phi_U.data<T>());
+    phi::funcs::TrilTriuCompute<T> triu_computer(
+        phi_U.data<T>(), 0, false, UmHdims[phiu_rank - 2],
+        UmHdims[phiu_rank - 1], phi_U.data<T>());
     u_for_range(triu_computer);
 
     Tensor_Add<DeviceContext, T>(dev_ctx, phi_L, phi_U, &phi);
@@ -591,8 +592,9 @@ class LUGradKernel : public framework::OpKernel<T> {
         const auto W = phidims[phidims.size() - 1];
         platform::ForRange<DeviceContext> x_for_range(dev_ctx,
                                                       phi_complement.numel());
-        TrilTriuCompute<T> tril_computer(phi_complement.data<T>(), -1, true, H,
-                                         W, phi_complement_l.data<T>());
+        phi::funcs::TrilTriuCompute<T> tril_computer(
+            phi_complement.data<T>(), -1, true, H, W,
+            phi_complement_l.data<T>());
         x_for_range(tril_computer);
 
         Tensor_Sub<DeviceContext, T>(dev_ctx, phi, phi_complement_l, &phi);
@@ -664,8 +666,8 @@ class LUGradKernel : public framework::OpKernel<T> {
       const auto W = phidims[phidims.size() - 1];
       platform::ForRange<DeviceContext> x_for_range(dev_ctx,
                                                     phi_complement.numel());
-      TrilTriuCompute<T> triu_computer(phi_complement.data<T>(), 0, false, H, W,
-                                       phi_complement_u.data<T>());
+      phi::funcs::TrilTriuCompute<T> triu_computer(
+          phi_complement.data<T>(), 0, false, H, W, phi_complement_u.data<T>());
       x_for_range(triu_computer);
 
       Tensor_Sub<DeviceContext, T>(dev_ctx, phi, phi_complement_u, &phi);
diff --git a/paddle/fluid/operators/lu_unpack_op.h b/paddle/fluid/operators/lu_unpack_op.h
index d2303f2c08da8e98053e314f9756e4e375e27775..e4100867dc685ef68cd01b22ab7972aa8b436a06 100644
--- a/paddle/fluid/operators/lu_unpack_op.h
+++ b/paddle/fluid/operators/lu_unpack_op.h
@@ -16,7 +16,8 @@ limitations under the License. */
 
 #include "paddle/fluid/framework/op_registry.h"
 #include "paddle/fluid/operators/lu_op.h"
-#include "paddle/fluid/operators/tril_triu_op.h"
+#include "paddle/fluid/platform/for_range.h"
+#include "paddle/phi/kernels/funcs/tril_triu_compute.h"
 
 namespace paddle {
 namespace operators {
@@ -87,7 +88,8 @@ class LU_UnpackGradKernel : public framework::OpKernel<T> {
     auto W = ldims[ldims.size() - 1];
     auto L_dataptr = dl_tril.mutable_data<T>(dev_ctx.GetPlace());
     platform::ForRange<DeviceContext> l_for_range(dev_ctx, dl->numel());
-    TrilTriuCompute<T> tril_computer(dl->data<T>(), -1, true, H, W, L_dataptr);
+    phi::funcs::TrilTriuCompute<T> tril_computer(dl->data<T>(), -1, true, H, W,
+                                                 L_dataptr);
     l_for_range(tril_computer);
 
     const auto udims = du->dims();
@@ -96,7 +98,8 @@ class LU_UnpackGradKernel : public framework::OpKernel<T> {
     W = udims[udims.size() - 1];
     auto U_dataptr = du_triu.mutable_data<T>(dev_ctx.GetPlace());
     platform::ForRange<DeviceContext> u_for_range(dev_ctx, du->numel());
-    TrilTriuCompute<T> triu_computer(du->data<T>(), 0, false, H, W, U_dataptr);
+    phi::funcs::TrilTriuCompute<T> triu_computer(du->data<T>(), 0, false, H, W,
+                                                 U_dataptr);
     u_for_range(triu_computer);
 
     auto xdims = dx->dims();
diff --git a/paddle/fluid/operators/multiplex_op.cc b/paddle/fluid/operators/multiplex_op.cc
index 313a479ea301bb2c7dac0d0a27ca6064de99536a..8771a6573cba044d182aced752d3a65c446ad32e 100644
--- a/paddle/fluid/operators/multiplex_op.cc
+++ b/paddle/fluid/operators/multiplex_op.cc
@@ -12,9 +12,9 @@ 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. */
 
-#include "paddle/fluid/operators/multiplex_op.h"
 #include <memory>
 #include <vector>
+#include "paddle/fluid/framework/op_registry.h"
 
 namespace paddle {
 namespace operators {
@@ -169,15 +169,3 @@ REGISTER_OPERATOR(multiplex, ops::MultiplexOp, ops::MultiplexOpMaker,
                   ops::MultiplexGradMaker<paddle::framework::OpDesc>,
                   ops::MultiplexGradMaker<paddle::imperative::OpBase>);
 REGISTER_OPERATOR(multiplex_grad, ops::MultiplexGradOp);
-REGISTER_OP_CPU_KERNEL(
-    multiplex,
-    ops::MultiplexCPUKernel<paddle::platform::CPUDeviceContext, float>,
-    ops::MultiplexCPUKernel<paddle::platform::CPUDeviceContext, double>,
-    ops::MultiplexCPUKernel<paddle::platform::CPUDeviceContext, int>,
-    ops::MultiplexCPUKernel<paddle::platform::CPUDeviceContext, int64_t>);
-REGISTER_OP_CPU_KERNEL(
-    multiplex_grad,
-    ops::MultiplexGradCPUKernel<paddle::platform::CPUDeviceContext, float>,
-    ops::MultiplexGradCPUKernel<paddle::platform::CPUDeviceContext, double>,
-    ops::MultiplexGradCPUKernel<paddle::platform::CPUDeviceContext, int>,
-    ops::MultiplexGradCPUKernel<paddle::platform::CPUDeviceContext, int64_t>);
diff --git a/paddle/fluid/operators/multiplex_op.cu b/paddle/fluid/operators/multiplex_op.cu
deleted file mode 100644
index 0a32ee96fb6938157364dc717724ce9193286f27..0000000000000000000000000000000000000000
--- a/paddle/fluid/operators/multiplex_op.cu
+++ /dev/null
@@ -1,117 +0,0 @@
-/* Copyright (c) 2016 PaddlePaddle Authors. All Rights Reserved.
-
-Licensed 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. */
-
-#include "paddle/fluid/framework/op_registry.h"
-#include "paddle/fluid/operators/multiplex_op.h"
-
-namespace paddle {
-namespace operators {
-
-using Tensor = framework::Tensor;
-
-template <typename Place, typename T>
-class MultiplexGPUKernel : public framework::OpKernel<T> {
- public:
-  void Compute(const framework::ExecutionContext& ctx) const {
-    auto ins = ctx.MultiInput<Tensor>("X");
-    auto* ids = ctx.Input<Tensor>("Ids");
-    auto* out = ctx.Output<Tensor>("Out");
-    out->mutable_data<T>(ctx.GetPlace());
-
-    for (size_t i = 0; i < ins.size(); ++i) {
-      PADDLE_ENFORCE_GT(
-          ins[i]->numel(), 0,
-          platform::errors::OutOfRange(
-              "indexing will be out of bounds with size 0 for the %d-th input.",
-              i));
-    }
-
-    auto rows = ins[0]->dims()[0];
-    auto cols = ins[0]->numel() / rows;
-    // copy index to cpu
-    Tensor index_t_cpu;
-    paddle::framework::TensorCopySync(*ids, platform::CPUPlace(), &index_t_cpu);
-    auto* index = index_t_cpu.data<int32_t>();
-    auto stream = ctx.cuda_device_context().stream();
-    platform::CUDAPlace place = ctx.GetPlace();
-    for (auto i = 0; i < rows; i++) {
-      int32_t k = index[i];
-      PADDLE_ENFORCE_GE(k, 0, platform::errors::PreconditionNotMet(
-                                  "index must be nonnegative."));
-      PADDLE_ENFORCE_LT(static_cast<size_t>(k), ins.size(),
-                        platform::errors::PreconditionNotMet(
-                            "index exceeds the number of candidate tensors."));
-      memory::Copy(place, out->data<T>() + i * cols, place,
-                   ins[k]->data<T>() + i * cols, cols * sizeof(T), stream);
-    }
-  }
-};
-
-template <typename Place, typename T>
-class MultiplexGradGPUKernel : public framework::OpKernel<T> {
- public:
-  void Compute(const framework::ExecutionContext& ctx) const {
-    auto* d_out = ctx.Input<Tensor>(framework::GradVarName("Out"));
-    auto* ids = ctx.Input<Tensor>("Ids");
-    auto d_ins = ctx.MultiOutput<Tensor>(framework::GradVarName("X"));
-
-    size_t idx = -1UL;
-    for (size_t i = 0; i < d_ins.size(); i++) {
-      if (d_ins[i]) {
-        d_ins[i]->mutable_data<T>(ctx.GetPlace());
-        auto t = framework::EigenVector<T>::Flatten(*d_ins[i]);
-        t.device(*ctx.template device_context<Place>().eigen_device()) =
-            t.constant(static_cast<T>(0));
-
-        idx = i;
-      }
-    }
-
-    if (idx == -1UL) return;
-
-    auto rows = d_ins[idx]->dims()[0];
-    auto cols = d_ins[idx]->numel() / rows;
-    // copy index to cpu
-    Tensor index_t_cpu;
-    paddle::framework::TensorCopySync(*ids, platform::CPUPlace(), &index_t_cpu);
-    auto* index = index_t_cpu.data<int32_t>();
-
-    auto stream = ctx.cuda_device_context().stream();
-    platform::CUDAPlace place = ctx.GetPlace();
-    for (auto i = 0; i < rows; i++) {
-      size_t k = static_cast<size_t>(index[i]);
-      if (d_ins[k]) {
-        memory::Copy(place, d_ins[k]->data<T>() + i * cols, place,
-                     d_out->data<T>() + i * cols, cols * sizeof(T), stream);
-      }
-    }
-  }
-};
-}  // namespace operators
-}  // namespace paddle
-
-namespace ops = paddle::operators;
-
-REGISTER_OP_CUDA_KERNEL(
-    multiplex,
-    ops::MultiplexGPUKernel<paddle::platform::CUDADeviceContext, float>,
-    ops::MultiplexGPUKernel<paddle::platform::CUDADeviceContext, double>,
-    ops::MultiplexGPUKernel<paddle::platform::CUDADeviceContext, int>,
-    ops::MultiplexGPUKernel<paddle::platform::CUDADeviceContext, int64_t>);
-REGISTER_OP_CUDA_KERNEL(
-    multiplex_grad,
-    ops::MultiplexGradGPUKernel<paddle::platform::CUDADeviceContext, float>,
-    ops::MultiplexGradGPUKernel<paddle::platform::CUDADeviceContext, double>,
-    ops::MultiplexGradGPUKernel<paddle::platform::CUDADeviceContext, int>,
-    ops::MultiplexGradGPUKernel<paddle::platform::CUDADeviceContext, int64_t>);
diff --git a/paddle/fluid/operators/multiplex_op.h b/paddle/fluid/operators/multiplex_op.h
deleted file mode 100644
index 1d0a009edeedcad746853bb286af52cce474df87..0000000000000000000000000000000000000000
--- a/paddle/fluid/operators/multiplex_op.h
+++ /dev/null
@@ -1,96 +0,0 @@
-/* Copyright (c) 2016 PaddlePaddle Authors. All Rights Reserved.
-
-Licensed 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. */
-
-#pragma once
-
-#include "paddle/fluid/framework/eigen.h"
-#include "paddle/fluid/framework/op_registry.h"
-#include "paddle/fluid/memory/memcpy.h"
-
-namespace paddle {
-namespace operators {
-
-template <typename DeviceContext, typename T>
-class MultiplexCPUKernel : public framework::OpKernel<T> {
- public:
-  void Compute(const framework::ExecutionContext& ctx) const {
-    auto ins = ctx.MultiInput<framework::Tensor>("X");
-    auto ids = ctx.Input<framework::Tensor>("Ids");
-    auto* out = ctx.Output<framework::Tensor>("Out");
-
-    out->mutable_data<T>(ctx.GetPlace());
-
-    for (size_t i = 0; i < ins.size(); ++i) {
-      PADDLE_ENFORCE_GT(
-          ins[i]->numel(), 0,
-          platform::errors::OutOfRange(
-              "indexing will be out of bounds with size 0 for the %d-th input.",
-              i));
-    }
-
-    auto rows = ins[0]->dims()[0];
-    auto cols = ins[0]->numel() / rows;
-    auto index = ids->data<int32_t>();
-    platform::CPUPlace place = ctx.GetPlace();
-    for (auto i = 0; i < rows; i++) {
-      int32_t k = index[i];
-      PADDLE_ENFORCE_GE(k, 0, platform::errors::PreconditionNotMet(
-                                  "index must be nonnegative."));
-      PADDLE_ENFORCE_LT(static_cast<size_t>(k), ins.size(),
-                        platform::errors::PreconditionNotMet(
-                            "index exceeds the number of candidate tensors."));
-      memory::Copy(place, out->data<T>() + i * cols, place,
-                   ins[k]->data<T>() + i * cols, cols * sizeof(T));
-    }
-  }
-};
-
-template <typename DeviceContext, typename T>
-class MultiplexGradCPUKernel : public framework::OpKernel<T> {
- public:
-  void Compute(const framework::ExecutionContext& ctx) const {
-    auto* d_out = ctx.Input<framework::Tensor>(framework::GradVarName("Out"));
-    auto* ids = ctx.Input<framework::Tensor>("Ids");
-    auto d_ins =
-        ctx.MultiOutput<framework::Tensor>(framework::GradVarName("X"));
-
-    size_t idx = -1UL;
-    for (size_t i = 0; i < d_ins.size(); i++) {
-      if (d_ins[i]) {
-        d_ins[i]->mutable_data<T>(ctx.GetPlace());
-        auto t = framework::EigenVector<T>::Flatten(*d_ins[i]);
-        t.device(*ctx.template device_context<DeviceContext>().eigen_device()) =
-            t.constant(static_cast<T>(0));
-
-        idx = i;
-      }
-    }
-
-    if (idx == -1UL) return;
-
-    auto rows = d_ins[idx]->dims()[0];
-    auto cols = d_ins[idx]->numel() / rows;
-    auto* index = ids->data<int32_t>();
-    platform::CPUPlace place = ctx.GetPlace();
-    for (auto i = 0; i < rows; i++) {
-      size_t k = static_cast<size_t>(index[i]);
-      if (d_ins[k]) {
-        memory::Copy(place, d_ins[k]->data<T>() + i * cols, place,
-                     d_out->data<T>() + i * cols, cols * sizeof(T));
-      }
-    }
-  }
-};
-}  // namespace operators
-}  // namespace paddle
diff --git a/paddle/fluid/operators/qr_op.cc b/paddle/fluid/operators/qr_op.cc
index 40e3cbde3b00917ee5952b8aebd412b357683018..82fc9ef1b7858992c49f537ce8608856ef6b6fde 100644
--- a/paddle/fluid/operators/qr_op.cc
+++ b/paddle/fluid/operators/qr_op.cc
@@ -145,8 +145,6 @@ REGISTER_OPERATOR(qr, ops::QrOp, ops::QrOpMaker,
 
 REGISTER_OPERATOR(qr_grad, ops::QrGradOp);
 
-REGISTER_OP_CPU_KERNEL(qr, ops::QrCPUKernel<float>, ops::QrCPUKernel<double>);
-
 REGISTER_OP_CPU_KERNEL(
     qr_grad, ops::QrGradKernel<paddle::platform::CPUDeviceContext, float>,
     ops::QrGradKernel<paddle::platform::CPUDeviceContext, double>);
diff --git a/paddle/fluid/operators/qr_op.h b/paddle/fluid/operators/qr_op.h
index f09a07e96cd34e1b631ef9484fe23b12a3b58543..5ef02d8942797a720d18358d425cf45f77be82ad 100644
--- a/paddle/fluid/operators/qr_op.h
+++ b/paddle/fluid/operators/qr_op.h
@@ -48,85 +48,6 @@ static inline std::tuple<bool, bool> _parse_qr_mode(std::string mode) {
   return std::make_tuple(compute_q, reduced);
 }
 
-template <typename T>
-class QrCPUKernel : public framework::OpKernel<T> {
- public:
-  void Compute(const framework::ExecutionContext& context) const override {
-    bool compute_q;
-    bool reduced_mode;
-    const Tensor& x = *context.Input<Tensor>("X");
-    Tensor& q = *context.Output<Tensor>("Q");
-    Tensor& r = *context.Output<Tensor>("R");
-    std::string mode = context.Attr<std::string>("mode");
-    std::tie(compute_q, reduced_mode) = _parse_qr_mode(mode);
-
-    auto numel = x.numel();
-    PADDLE_ENFORCE_GT(numel, 0, platform::errors::PreconditionNotMet(
-                                    "The input of QR is empty."));
-    auto x_dims = x.dims();
-    int x_rank = x_dims.size();
-    int m = x_dims[x_rank - 2];
-    int n = x_dims[x_rank - 1];
-    int min_mn = std::min(m, n);
-    int k = reduced_mode ? min_mn : m;
-    int batch_size = numel / (m * n);
-    int x_stride = m * n;
-    int q_stride = m * k;
-    int r_stride = k * n;
-
-    auto* x_data = x.data<phi::dtype::Real<T>>();
-    T* q_data = nullptr;
-    if (compute_q) {
-      q_data = q.mutable_data<phi::dtype::Real<T>>(
-          context.GetPlace(),
-          size_t(batch_size * m * k * sizeof(phi::dtype::Real<T>)));
-      memset(q_data, 0,
-             size_t(batch_size * m * k * sizeof(phi::dtype::Real<T>)));
-    }
-    auto* r_data = r.mutable_data<phi::dtype::Real<T>>(
-        context.GetPlace(),
-        size_t(batch_size * k * n * sizeof(phi::dtype::Real<T>)));
-    memset(r_data, 0, size_t(batch_size * k * n * sizeof(phi::dtype::Real<T>)));
-
-    // Implement QR by calling Eigen
-    for (int i = 0; i < batch_size; ++i) {
-      const T* x_matrix_ptr = x_data + i * x_stride;
-      T* r_matrix_ptr = r_data + i * r_stride;
-      using EigenDynamicMatrix =
-          Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>;
-      auto x_matrix = Eigen::Map<const EigenDynamicMatrix>(x_matrix_ptr, m, n);
-      Eigen::HouseholderQR<EigenDynamicMatrix> qr(x_matrix);
-      if (reduced_mode) {
-        auto qr_top_matrix = qr.matrixQR().block(0, 0, min_mn, n);
-        auto r_matrix_view =
-            qr_top_matrix.template triangularView<Eigen::Upper>();
-        auto r_matrix = EigenDynamicMatrix(r_matrix_view);
-        memcpy(r_matrix_ptr, r_matrix.data(), r_matrix.size() * sizeof(T));
-      } else {
-        auto r_matrix_view =
-            qr.matrixQR().template triangularView<Eigen::Upper>();
-        auto r_matrix = EigenDynamicMatrix(r_matrix_view);
-        memcpy(r_matrix_ptr, r_matrix.data(), r_matrix.size() * sizeof(T));
-      }
-
-      if (compute_q) {
-        T* q_matrix_ptr = q_data + i * q_stride;
-        if (reduced_mode) {
-          auto q_matrix =
-              qr.householderQ() * EigenDynamicMatrix::Identity(m, min_mn);
-          q_matrix.transposeInPlace();
-          memcpy(q_matrix_ptr, q_matrix.data(), q_matrix.size() * sizeof(T));
-        } else {
-          auto q_matrix =
-              qr.householderQ() * EigenDynamicMatrix::Identity(m, m);
-          q_matrix.transposeInPlace();
-          memcpy(q_matrix_ptr, q_matrix.data(), q_matrix.size() * sizeof(T));
-        }
-      }
-    }
-  }
-};
-
 template <typename DeviceContext, typename T>
 class QrGradKernel : public framework::OpKernel<T> {
  public:
diff --git a/paddle/fluid/operators/tril_triu_op.cc b/paddle/fluid/operators/tril_triu_op.cc
index 3e943c62e1ce17857e78e140efeb50e627e80a4e..c8010e8a128e0b2483c93ed38047b17060bfb0e9 100644
--- a/paddle/fluid/operators/tril_triu_op.cc
+++ b/paddle/fluid/operators/tril_triu_op.cc
@@ -12,8 +12,8 @@ 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. */
 
-#include "paddle/fluid/operators/tril_triu_op.h"
 #include <memory>
+#include "paddle/fluid/framework/op_registry.h"
 
 namespace paddle {
 namespace operators {
@@ -104,19 +104,3 @@ REGISTER_OPERATOR(tril_triu, ops::TrilTriuOp, ops::TrilTriuOpMaker,
                   ops::TrilTriuGradOpMaker<paddle::framework::OpDesc>,
                   ops::TrilTriuGradOpMaker<paddle::imperative::OpBase>);
 REGISTER_OPERATOR(tril_triu_grad, ops::TrilTriuGradOp);
-REGISTER_OP_CPU_KERNEL(
-    tril_triu, ops::TrilTriuOpKernel<paddle::platform::CPUDeviceContext, bool>,
-    ops::TrilTriuOpKernel<paddle::platform::CPUDeviceContext, float>,
-    ops::TrilTriuOpKernel<paddle::platform::CPUDeviceContext, double>,
-    ops::TrilTriuOpKernel<paddle::platform::CPUDeviceContext, int>,
-    ops::TrilTriuOpKernel<paddle::platform::CPUDeviceContext, int64_t>,
-    ops::TrilTriuOpKernel<paddle::platform::CPUDeviceContext, plat::float16>);
-REGISTER_OP_CPU_KERNEL(
-    tril_triu_grad,
-    ops::TrilTriuGradOpKernel<paddle::platform::CPUDeviceContext, bool>,
-    ops::TrilTriuGradOpKernel<paddle::platform::CPUDeviceContext, float>,
-    ops::TrilTriuGradOpKernel<paddle::platform::CPUDeviceContext, double>,
-    ops::TrilTriuGradOpKernel<paddle::platform::CPUDeviceContext, int>,
-    ops::TrilTriuGradOpKernel<paddle::platform::CPUDeviceContext, int64_t>,
-    ops::TrilTriuGradOpKernel<paddle::platform::CPUDeviceContext,
-                              plat::float16>);
diff --git a/paddle/fluid/operators/tril_triu_op.cu b/paddle/fluid/operators/tril_triu_op.cu
deleted file mode 100644
index 9cbbdeeb2ce28453f2c22d063975fa82aae5d3b3..0000000000000000000000000000000000000000
--- a/paddle/fluid/operators/tril_triu_op.cu
+++ /dev/null
@@ -1,35 +0,0 @@
-/* Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
-
-Licensed 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. */
-
-#include "paddle/fluid/operators/tril_triu_op.h"
-
-namespace ops = paddle::operators;
-namespace plat = paddle::platform;
-
-REGISTER_OP_CUDA_KERNEL(
-    tril_triu, ops::TrilTriuOpKernel<paddle::platform::CUDADeviceContext, bool>,
-    ops::TrilTriuOpKernel<paddle::platform::CUDADeviceContext, float>,
-    ops::TrilTriuOpKernel<paddle::platform::CUDADeviceContext, double>,
-    ops::TrilTriuOpKernel<paddle::platform::CUDADeviceContext, int>,
-    ops::TrilTriuOpKernel<paddle::platform::CUDADeviceContext, int64_t>,
-    ops::TrilTriuOpKernel<paddle::platform::CUDADeviceContext, plat::float16>);
-REGISTER_OP_CUDA_KERNEL(
-    tril_triu_grad,
-    ops::TrilTriuGradOpKernel<paddle::platform::CUDADeviceContext, bool>,
-    ops::TrilTriuGradOpKernel<paddle::platform::CUDADeviceContext, float>,
-    ops::TrilTriuGradOpKernel<paddle::platform::CUDADeviceContext, double>,
-    ops::TrilTriuGradOpKernel<paddle::platform::CUDADeviceContext, int>,
-    ops::TrilTriuGradOpKernel<paddle::platform::CUDADeviceContext, int64_t>,
-    ops::TrilTriuGradOpKernel<paddle::platform::CUDADeviceContext,
-                              plat::float16>);
diff --git a/paddle/fluid/operators/tril_triu_op.h b/paddle/fluid/operators/tril_triu_op.h
deleted file mode 100644
index 3150b7617d10a8f9c2f60dd2e74ab2cbbb2d655e..0000000000000000000000000000000000000000
--- a/paddle/fluid/operators/tril_triu_op.h
+++ /dev/null
@@ -1,102 +0,0 @@
-/* Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
-
-Licensed 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. */
-
-#pragma once
-
-#include "paddle/fluid/framework/op_registry.h"
-#include "paddle/fluid/platform/float16.h"
-#include "paddle/fluid/platform/for_range.h"
-
-namespace paddle {
-namespace operators {
-
-template <typename T>
-class TrilTriuCompute {
- public:
-  HOSTDEVICE TrilTriuCompute(const T* in, const int diagonal, const bool lower,
-                             const int64_t H, const int64_t W, T* out)
-      : in_(in), diagonal_(diagonal), lower_(lower), H_(H), W_(W), out_(out) {}
-
-  HOSTDEVICE void operator()(int64_t idx) {
-    const int64_t row = (idx / W_) % H_;
-    const int64_t col = idx % W_;
-    const bool mask =
-        lower_ ? (col - row > diagonal_) : (col - row < diagonal_);
-    out_[idx] = mask ? static_cast<T>(0) : in_[idx];
-  }
-
- private:
-  const T* in_;
-  const int diagonal_;
-  const bool lower_;
-  const int64_t H_;
-  const int64_t W_;
-  T* out_;
-};
-
-template <typename DeviceContext, typename T>
-class TrilTriuOpKernel : public framework::OpKernel<T> {
- public:
-  void Compute(const framework::ExecutionContext& context) const override {
-    const auto* x = context.Input<framework::Tensor>("X");
-    const auto* x_data = x->data<T>();
-    auto* out = context.Output<framework::Tensor>("Out");
-    auto* out_data = out->mutable_data<T>(context.GetPlace());
-
-    const int diagonal = context.Attr<int>("diagonal");
-    const bool lower = context.Attr<bool>("lower");
-
-    const auto& dims = x->dims();
-    const auto H = dims[dims.size() - 2];
-    const auto W = dims[dims.size() - 1];
-
-    platform::ForRange<DeviceContext> for_range(
-        context.template device_context<DeviceContext>(),
-        static_cast<size_t>(x->numel()));
-
-    paddle::operators::TrilTriuCompute<T> tril_triu_computer(
-        x_data, diagonal, lower, H, W, out_data);
-    for_range(tril_triu_computer);
-  }
-};
-
-template <typename DeviceContext, typename T>
-class TrilTriuGradOpKernel : public framework::OpKernel<T> {
- public:
-  void Compute(const framework::ExecutionContext& context) const override {
-    const auto* d_out =
-        context.Input<framework::Tensor>(framework::GradVarName("Out"));
-    const auto* dout_data = d_out->data<T>();
-    auto* d_x = context.Output<framework::Tensor>(framework::GradVarName("X"));
-    auto* dx_data = d_x->mutable_data<T>(context.GetPlace());
-
-    const int diagonal = context.Attr<int>("diagonal");
-    const bool lower = context.Attr<bool>("lower");
-
-    const auto& dims = d_out->dims();
-    const auto H = dims[dims.size() - 2];
-    const auto W = dims[dims.size() - 1];
-
-    platform::ForRange<DeviceContext> for_range(
-        context.template device_context<DeviceContext>(),
-        static_cast<size_t>(d_out->numel()));
-
-    paddle::operators::TrilTriuCompute<T> tril_triu_grad_computer(
-        dout_data, diagonal, lower, H, W, dx_data);
-    for_range(tril_triu_grad_computer);
-  }
-};
-
-}  // namespace operators
-}  // namespace paddle
diff --git a/paddle/fluid/operators/tril_triu_op_npu.cc b/paddle/fluid/operators/tril_triu_op_npu.cc
index ad1c1814c05cdf7f96a6f3c05a5cf1a00d2a2e93..4145730357d6007368d26c46d2b1bd47c9085982 100644
--- a/paddle/fluid/operators/tril_triu_op_npu.cc
+++ b/paddle/fluid/operators/tril_triu_op_npu.cc
@@ -12,7 +12,7 @@ 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. */
 
-#include "paddle/fluid/operators/tril_triu_op.h"
+#include "paddle/fluid/framework/op_registry.h"
 #include "paddle/fluid/platform/device/npu/npu_op_runner.h"
 
 namespace paddle {
diff --git a/paddle/fluid/operators/tril_triu_op_xpu.cc b/paddle/fluid/operators/tril_triu_op_xpu.cc
index e36cbcf228cfbf30c8fcd5562ac40f38a5467cdb..a44ea8ff689b85d9f718572c45b4f8fafaf1565d 100644
--- a/paddle/fluid/operators/tril_triu_op_xpu.cc
+++ b/paddle/fluid/operators/tril_triu_op_xpu.cc
@@ -11,7 +11,7 @@ limitations under the License. */
 
 #ifdef PADDLE_WITH_XPU
 
-#include "paddle/fluid/operators/tril_triu_op.h"
+#include "paddle/fluid/framework/op_registry.h"
 #include "paddle/fluid/platform/device/device_wrapper.h"
 
 namespace paddle {
diff --git a/paddle/phi/kernels/cpu/multiplex_grad_kernel.cc b/paddle/phi/kernels/cpu/multiplex_grad_kernel.cc
new file mode 100644
index 0000000000000000000000000000000000000000..f5a426e93db2cf23962276632fead69565999d37
--- /dev/null
+++ b/paddle/phi/kernels/cpu/multiplex_grad_kernel.cc
@@ -0,0 +1,65 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed 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.
+
+#include "paddle/phi/kernels/multiplex_grad_kernel.h"
+
+#include "paddle/fluid/memory/memcpy.h"
+
+#include "paddle/phi/backends/cpu/cpu_context.h"
+#include "paddle/phi/core/kernel_registry.h"
+#include "paddle/phi/kernels/funcs/eigen/common.h"
+
+namespace phi {
+
+template <typename T, typename Context>
+void MultiplexGradKernel(const Context& ctx,
+                         const DenseTensor& ids,
+                         const DenseTensor& out_grad,
+                         std::vector<DenseTensor*> ins_grad) {
+  size_t idx = -1UL;
+  for (size_t i = 0; i < ins_grad.size(); i++) {
+    if (ins_grad[i]) {
+      ctx.template Alloc<T>(ins_grad[i]);
+      auto t = phi::EigenVector<T>::Flatten(*ins_grad[i]);
+      t.device(*ctx.eigen_device()) = t.constant(static_cast<T>(0));
+      idx = i;
+    }
+  }
+  if (idx == -1UL) return;
+
+  auto rows = ins_grad[idx]->dims()[0];
+  auto cols = ins_grad[idx]->numel() / rows;
+  auto* index = ids.data<int32_t>();
+  for (auto i = 0; i < rows; i++) {
+    size_t k = static_cast<size_t>(index[i]);
+    if (ins_grad[k]) {
+      paddle::memory::Copy(ctx.GetPlace(),
+                           ins_grad[k]->data<T>() + i * cols,
+                           ctx.GetPlace(),
+                           out_grad.data<T>() + i * cols,
+                           cols * sizeof(T));
+    }
+  }
+}
+
+}  // namespace phi
+
+PD_REGISTER_KERNEL(multiplex_grad,
+                   CPU,
+                   ALL_LAYOUT,
+                   phi::MultiplexGradKernel,
+                   float,
+                   double,
+                   int,
+                   int64_t) {}
diff --git a/paddle/phi/kernels/cpu/multiplex_kernel.cc b/paddle/phi/kernels/cpu/multiplex_kernel.cc
new file mode 100644
index 0000000000000000000000000000000000000000..2d9f4c51a981ed8701afe0aa4e7d6a8955f4348c
--- /dev/null
+++ b/paddle/phi/kernels/cpu/multiplex_kernel.cc
@@ -0,0 +1,65 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed 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.
+
+#include "paddle/phi/kernels/multiplex_kernel.h"
+
+#include "paddle/fluid/memory/memcpy.h"
+#include "paddle/phi/backends/cpu/cpu_context.h"
+#include "paddle/phi/core/kernel_registry.h"
+
+namespace phi {
+
+template <typename T, typename Context>
+void MultiplexKernel(const Context& ctx,
+                     const std::vector<const DenseTensor*>& ins,
+                     const DenseTensor& ids,
+                     DenseTensor* out) {
+  ctx.template Alloc<T>(out);
+  for (size_t i = 0; i < ins.size(); ++i) {
+    PADDLE_ENFORCE_GT(
+        ins[i]->numel(),
+        0,
+        errors::OutOfRange(
+            "indexing will be out of bounds with size 0 for the %d-th input.",
+            i));
+  }
+  auto rows = ins[0]->dims()[0];
+  auto cols = ins[0]->numel() / rows;
+  auto index = ids.data<int32_t>();
+  for (auto i = 0; i < rows; i++) {
+    int32_t k = index[i];
+    PADDLE_ENFORCE_GE(
+        k, 0, errors::PreconditionNotMet("index must be nonnegative."));
+    PADDLE_ENFORCE_LT(static_cast<size_t>(k),
+                      ins.size(),
+                      errors::PreconditionNotMet(
+                          "index exceeds the number of candidate tensors."));
+    paddle::memory::Copy(ctx.GetPlace(),
+                         out->data<T>() + i * cols,
+                         ctx.GetPlace(),
+                         ins[k]->data<T>() + i * cols,
+                         cols * sizeof(T));
+  }
+}
+
+}  // namespace phi
+
+PD_REGISTER_KERNEL(multiplex,
+                   CPU,
+                   ALL_LAYOUT,
+                   phi::MultiplexKernel,
+                   float,
+                   double,
+                   int,
+                   int64_t) {}
diff --git a/paddle/phi/kernels/cpu/qr_kernel.cc b/paddle/phi/kernels/cpu/qr_kernel.cc
new file mode 100644
index 0000000000000000000000000000000000000000..e2e32567441ae8ff5315856e3f9132c9553f6d62
--- /dev/null
+++ b/paddle/phi/kernels/cpu/qr_kernel.cc
@@ -0,0 +1,116 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed 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.
+
+#include <Eigen/Dense>
+
+#include "paddle/phi/kernels/qr_kernel.h"
+
+#include "paddle/phi/backends/cpu/cpu_context.h"
+#include "paddle/phi/core/kernel_registry.h"
+#include "paddle/phi/kernels/funcs/complex_functors.h"
+
+namespace phi {
+
+static inline std::tuple<bool, bool> ParseQrMode(const std::string& mode) {
+  bool compute_q;
+  bool reduced;
+  if (mode == "reduced") {
+    compute_q = true;
+    reduced = true;
+  } else if (mode == "complete") {
+    compute_q = true;
+    reduced = false;
+  } else if (mode == "r") {
+    compute_q = false;
+    reduced = true;
+  } else {
+    PADDLE_THROW(errors::InvalidArgument(
+        "QR received unrecognized mode '%s'"
+        " but expected one of 'reduced' (default), 'r', or 'complete'",
+        mode));
+  }
+  return std::make_tuple(compute_q, reduced);
+}
+
+template <typename T, typename Context>
+void QrKernel(const Context& ctx,
+              const DenseTensor& x,
+              const std::string& mode,
+              DenseTensor* q,
+              DenseTensor* r) {
+  bool compute_q;
+  bool reduced_mode;
+  std::tie(compute_q, reduced_mode) = ParseQrMode(mode);
+  auto numel = x.numel();
+  PADDLE_ENFORCE_GT(
+      numel, 0, errors::PreconditionNotMet("The input of QR is empty."));
+  auto x_dims = x.dims();
+  int x_rank = x_dims.size();
+  int m = x_dims[x_rank - 2];
+  int n = x_dims[x_rank - 1];
+  int min_mn = std::min(m, n);
+  int k = reduced_mode ? min_mn : m;
+  int batch_size = numel / (m * n);
+  int x_stride = m * n;
+  int q_stride = m * k;
+  int r_stride = k * n;
+  auto* x_data = x.data<phi::dtype::Real<T>>();
+  T* q_data = nullptr;
+  if (compute_q) {
+    q_data = ctx.template Alloc<phi::dtype::Real<T>>(
+        q, batch_size * m * k * sizeof(phi::dtype::Real<T>));
+  }
+  auto* r_data = ctx.template Alloc<phi::dtype::Real<T>>(
+      r, batch_size * k * n * sizeof(phi::dtype::Real<T>));
+
+  // Implement QR by calling Eigen
+  for (int i = 0; i < batch_size; ++i) {
+    const T* x_matrix_ptr = x_data + i * x_stride;
+    T* r_matrix_ptr = r_data + i * r_stride;
+    using EigenDynamicMatrix =
+        Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>;
+    auto x_matrix = Eigen::Map<const EigenDynamicMatrix>(x_matrix_ptr, m, n);
+    Eigen::HouseholderQR<EigenDynamicMatrix> qr(x_matrix);
+    if (reduced_mode) {
+      auto qr_top_matrix = qr.matrixQR().block(0, 0, min_mn, n);
+      auto r_matrix_view =
+          qr_top_matrix.template triangularView<Eigen::Upper>();
+      auto r_matrix = EigenDynamicMatrix(r_matrix_view);
+      memcpy(r_matrix_ptr, r_matrix.data(), r_matrix.size() * sizeof(T));
+    } else {
+      auto r_matrix_view =
+          qr.matrixQR().template triangularView<Eigen::Upper>();
+      auto r_matrix = EigenDynamicMatrix(r_matrix_view);
+      memcpy(r_matrix_ptr, r_matrix.data(), r_matrix.size() * sizeof(T));
+    }
+
+    if (compute_q) {
+      T* q_matrix_ptr = q_data + i * q_stride;
+      if (reduced_mode) {
+        auto q_matrix =
+            qr.householderQ() * EigenDynamicMatrix::Identity(m, min_mn);
+        q_matrix.transposeInPlace();
+        memcpy(q_matrix_ptr, q_matrix.data(), q_matrix.size() * sizeof(T));
+      } else {
+        auto q_matrix = qr.householderQ() * EigenDynamicMatrix::Identity(m, m);
+        q_matrix.transposeInPlace();
+        memcpy(q_matrix_ptr, q_matrix.data(), q_matrix.size() * sizeof(T));
+      }
+    }
+  }
+}
+
+}  // namespace phi
+
+PD_REGISTER_KERNEL(qr, CPU, ALL_LAYOUT, phi::QrKernel, float, double) {}
diff --git a/paddle/phi/kernels/cpu/tril_triu_grad_kernel.cc b/paddle/phi/kernels/cpu/tril_triu_grad_kernel.cc
new file mode 100644
index 0000000000000000000000000000000000000000..14aca258a2c71a0651868f6917e2707987179ee0
--- /dev/null
+++ b/paddle/phi/kernels/cpu/tril_triu_grad_kernel.cc
@@ -0,0 +1,29 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed 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.
+
+#include "paddle/phi/kernels/impl/tril_triu_grad_kernel_impl.h"
+
+#include "paddle/phi/backends/cpu/cpu_context.h"
+#include "paddle/phi/core/kernel_registry.h"
+
+PD_REGISTER_KERNEL(tril_triu_grad,
+                   CPU,
+                   ALL_LAYOUT,
+                   phi::TrilTriuGradKernel,
+                   bool,
+                   float,
+                   double,
+                   int,
+                   int64_t,
+                   phi::dtype::float16) {}
diff --git a/paddle/phi/kernels/cpu/tril_triu_kernel.cc b/paddle/phi/kernels/cpu/tril_triu_kernel.cc
new file mode 100644
index 0000000000000000000000000000000000000000..a3d20e55e21fb6e11f63ef05f5de63fbc51caf5e
--- /dev/null
+++ b/paddle/phi/kernels/cpu/tril_triu_kernel.cc
@@ -0,0 +1,29 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed 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.
+
+#include "paddle/phi/kernels/impl/tril_triu_kernel_impl.h"
+
+#include "paddle/phi/backends/cpu/cpu_context.h"
+#include "paddle/phi/core/kernel_registry.h"
+
+PD_REGISTER_KERNEL(tril_triu,
+                   CPU,
+                   ALL_LAYOUT,
+                   phi::TrilTriuKernel,
+                   bool,
+                   float,
+                   double,
+                   int,
+                   int64_t,
+                   phi::dtype::float16) {}
diff --git a/paddle/phi/kernels/funcs/tril_triu_compute.h b/paddle/phi/kernels/funcs/tril_triu_compute.h
new file mode 100644
index 0000000000000000000000000000000000000000..d2b6f1e559d2b5bfc333b60359f5b1e56e9aaadb
--- /dev/null
+++ b/paddle/phi/kernels/funcs/tril_triu_compute.h
@@ -0,0 +1,48 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed 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.
+
+#pragma once
+
+namespace phi {
+namespace funcs {
+
+template <typename T>
+class TrilTriuCompute {
+ public:
+  HOSTDEVICE TrilTriuCompute(const T* in,
+                             const int diagonal,
+                             const bool lower,
+                             const int64_t H,
+                             const int64_t W,
+                             T* out)
+      : in_(in), diagonal_(diagonal), lower_(lower), H_(H), W_(W), out_(out) {}
+
+  HOSTDEVICE void operator()(int64_t idx) {
+    const int64_t row = (idx / W_) % H_;
+    const int64_t col = idx % W_;
+    const bool mask =
+        lower_ ? (col - row > diagonal_) : (col - row < diagonal_);
+    out_[idx] = mask ? static_cast<T>(0) : in_[idx];
+  }
+
+ private:
+  const T* in_;
+  const int diagonal_;
+  const bool lower_;
+  const int64_t H_;
+  const int64_t W_;
+  T* out_;
+};
+}  // namespace funcs
+}  // namespace phi
diff --git a/paddle/phi/kernels/gpu/multiplex_grad_kernel.cu b/paddle/phi/kernels/gpu/multiplex_grad_kernel.cu
new file mode 100644
index 0000000000000000000000000000000000000000..21576ab608d269340322782c8113c6054c791e74
--- /dev/null
+++ b/paddle/phi/kernels/gpu/multiplex_grad_kernel.cu
@@ -0,0 +1,68 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed 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.
+
+#include "paddle/phi/kernels/multiplex_grad_kernel.h"
+
+#include "paddle/phi/api/lib/utils/tensor_utils.h"
+#include "paddle/phi/backends/gpu/gpu_context.h"
+#include "paddle/phi/core/kernel_registry.h"
+#include "paddle/phi/kernels/funcs/eigen/common.h"
+
+namespace phi {
+
+template <typename T, typename Context>
+void MultiplexGradKernel(const Context& ctx,
+                         const DenseTensor& ids,
+                         const DenseTensor& out_grad,
+                         std::vector<DenseTensor*> ins_grad) {
+  size_t idx = -1UL;
+  for (size_t i = 0; i < ins_grad.size(); i++) {
+    if (ins_grad[i]) {
+      ctx.template Alloc<T>(ins_grad[i]);
+      auto t = phi::EigenVector<T>::Flatten(*ins_grad[i]);
+      t.device(*ctx.eigen_device()) = t.constant(static_cast<T>(0));
+      idx = i;
+    }
+  }
+  if (idx == -1UL) return;
+
+  auto rows = ins_grad[idx]->dims()[0];
+  auto cols = ins_grad[idx]->numel() / rows;
+  DenseTensor index_t_cpu;
+  paddle::framework::TensorCopySync(ids, phi::CPUPlace(), &index_t_cpu);
+  auto* index = index_t_cpu.data<int32_t>();
+  auto stream = ctx.stream();
+  for (auto i = 0; i < rows; i++) {
+    size_t k = static_cast<size_t>(index[i]);
+    if (ins_grad[k]) {
+      paddle::memory::Copy(ctx.GetPlace(),
+                           ins_grad[k]->data<T>() + i * cols,
+                           ctx.GetPlace(),
+                           out_grad.data<T>() + i * cols,
+                           cols * sizeof(T),
+                           stream);
+    }
+  }
+}
+
+}  // namespace phi
+
+PD_REGISTER_KERNEL(multiplex_grad,
+                   GPU,
+                   ALL_LAYOUT,
+                   phi::MultiplexGradKernel,
+                   float,
+                   double,
+                   int,
+                   int64_t) {}
diff --git a/paddle/phi/kernels/gpu/multiplex_kernel.cu b/paddle/phi/kernels/gpu/multiplex_kernel.cu
new file mode 100644
index 0000000000000000000000000000000000000000..743448a46866687cf2ac68be522a306281289252
--- /dev/null
+++ b/paddle/phi/kernels/gpu/multiplex_kernel.cu
@@ -0,0 +1,70 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed 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.
+
+#include "paddle/phi/kernels/multiplex_kernel.h"
+
+#include "paddle/phi/api/lib/utils/tensor_utils.h"
+#include "paddle/phi/backends/gpu/gpu_context.h"
+#include "paddle/phi/core/kernel_registry.h"
+
+namespace phi {
+
+template <typename T, typename Context>
+void MultiplexKernel(const Context& ctx,
+                     const std::vector<const DenseTensor*>& ins,
+                     const DenseTensor& ids,
+                     DenseTensor* out) {
+  ctx.template Alloc<T>(out);
+  for (size_t i = 0; i < ins.size(); ++i) {
+    PADDLE_ENFORCE_GT(
+        ins[i]->numel(),
+        0,
+        errors::OutOfRange(
+            "indexing will be out of bounds with size 0 for the %d-th input.",
+            i));
+  }
+
+  auto rows = ins[0]->dims()[0];
+  auto cols = ins[0]->numel() / rows;
+  DenseTensor index_t_cpu;
+  paddle::framework::TensorCopySync(ids, phi::CPUPlace(), &index_t_cpu);
+  auto* index = index_t_cpu.data<int32_t>();
+  auto stream = ctx.stream();
+  for (auto i = 0; i < rows; i++) {
+    int32_t k = index[i];
+    PADDLE_ENFORCE_GE(
+        k, 0, errors::PreconditionNotMet("index must be nonnegative."));
+    PADDLE_ENFORCE_LT(static_cast<size_t>(k),
+                      ins.size(),
+                      errors::PreconditionNotMet(
+                          "index exceeds the number of candidate tensors."));
+    paddle::memory::Copy(ctx.GetPlace(),
+                         out->data<T>() + i * cols,
+                         ctx.GetPlace(),
+                         ins[k]->data<T>() + i * cols,
+                         cols * sizeof(T),
+                         stream);
+  }
+}
+
+}  // namespace phi
+
+PD_REGISTER_KERNEL(multiplex,
+                   GPU,
+                   ALL_LAYOUT,
+                   phi::MultiplexKernel,
+                   float,
+                   double,
+                   int,
+                   int64_t) {}
diff --git a/paddle/phi/kernels/gpu/tril_triu_grad_kernel.cu b/paddle/phi/kernels/gpu/tril_triu_grad_kernel.cu
new file mode 100644
index 0000000000000000000000000000000000000000..bc3ef1bc623bb27ac2452d1e908c389543598011
--- /dev/null
+++ b/paddle/phi/kernels/gpu/tril_triu_grad_kernel.cu
@@ -0,0 +1,29 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed 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.
+
+#include "paddle/phi/kernels/impl/tril_triu_grad_kernel_impl.h"
+
+#include "paddle/phi/backends/gpu/gpu_context.h"
+#include "paddle/phi/core/kernel_registry.h"
+
+PD_REGISTER_KERNEL(tril_triu_grad,
+                   GPU,
+                   ALL_LAYOUT,
+                   phi::TrilTriuGradKernel,
+                   bool,
+                   float,
+                   double,
+                   int,
+                   int64_t,
+                   phi::dtype::float16) {}
diff --git a/paddle/phi/kernels/gpu/tril_triu_kernel.cu b/paddle/phi/kernels/gpu/tril_triu_kernel.cu
new file mode 100644
index 0000000000000000000000000000000000000000..8c48edf9eff25aa68abcfe0b08dd7ab659aaa0fb
--- /dev/null
+++ b/paddle/phi/kernels/gpu/tril_triu_kernel.cu
@@ -0,0 +1,29 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed 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.
+
+#include "paddle/phi/kernels/impl/tril_triu_kernel_impl.h"
+
+#include "paddle/phi/backends/gpu/gpu_context.h"
+#include "paddle/phi/core/kernel_registry.h"
+
+PD_REGISTER_KERNEL(tril_triu,
+                   GPU,
+                   ALL_LAYOUT,
+                   phi::TrilTriuKernel,
+                   bool,
+                   float,
+                   double,
+                   int,
+                   int64_t,
+                   phi::dtype::float16) {}
diff --git a/paddle/phi/kernels/impl/cholesky_solve_grad_kernel_impl.h b/paddle/phi/kernels/impl/cholesky_solve_grad_kernel_impl.h
index 9f557e746378939e32a32955e758cdc5c510f229..72741e6d3a01ae374c43a24ac519ff5106b5733e 100644
--- a/paddle/phi/kernels/impl/cholesky_solve_grad_kernel_impl.h
+++ b/paddle/phi/kernels/impl/cholesky_solve_grad_kernel_impl.h
@@ -24,13 +24,12 @@
 #include "paddle/phi/kernels/funcs/blas/blas.h"
 #include "paddle/phi/kernels/funcs/common_shape.h"
 #include "paddle/phi/kernels/funcs/complex_functors.h"
+#include "paddle/phi/kernels/funcs/for_range.h"
 #include "paddle/phi/kernels/funcs/matrix_reduce.h"
+#include "paddle/phi/kernels/funcs/tril_triu_compute.h"
 #include "paddle/phi/kernels/math_kernel.h"
 #include "paddle/phi/kernels/transpose_kernel.h"
 
-// See Note [ Why still include the fluid headers? ]
-#include "paddle/fluid/operators/tril_triu_op.h"
-
 namespace phi {
 
 template <typename T, typename Context>
@@ -115,7 +114,7 @@ void CholeskySolveGradKernel(const Context& dev_ctx,
   const auto H = y_bst_dims_vec[y_bst_ndim - 2];
   const auto W = y_bst_dims_vec[y_bst_ndim - 1];
   phi::funcs::ForRange<Context> y_for_range(dev_ctx, dy_bst.numel());
-  paddle::operators::TrilTriuCompute<T> tril_triu_functor(
+  phi::funcs::TrilTriuCompute<T> tril_triu_functor(
       dy_bst.data<T>(), 0, !upper, H, W, dy_bst_upper.data<T>());
   y_for_range(tril_triu_functor);
 
diff --git a/paddle/phi/kernels/impl/triangular_solve_grad_kernel_impl.h b/paddle/phi/kernels/impl/triangular_solve_grad_kernel_impl.h
index 9b1e4b1d3a65d5c0da831a36152cff85a3353fa3..044adb0230cac4d0dc6bf9e9348968e4d7c60b5d 100644
--- a/paddle/phi/kernels/impl/triangular_solve_grad_kernel_impl.h
+++ b/paddle/phi/kernels/impl/triangular_solve_grad_kernel_impl.h
@@ -21,12 +21,11 @@
 #include "paddle/phi/kernels/funcs/blas/blas.h"
 #include "paddle/phi/kernels/funcs/common_shape.h"
 #include "paddle/phi/kernels/funcs/complex_functors.h"
+#include "paddle/phi/kernels/funcs/for_range.h"
 #include "paddle/phi/kernels/funcs/matrix_reduce.h"
+#include "paddle/phi/kernels/funcs/tril_triu_compute.h"
 #include "paddle/phi/kernels/triangular_solve_kernel.h"
 
-// See Note [ Why still include the fluid headers? ]
-#include "paddle/fluid/operators/tril_triu_op.h"
-
 namespace phi {
 
 template <typename T, typename Context>
@@ -119,7 +118,7 @@ void TriangularSolveGradKernel(const Context& dev_ctx,
     const auto H = dims[dims.size() - 2];
     const auto W = dims[dims.size() - 1];
     phi::funcs::ForRange<Context> x_for_range(dev_ctx, dx_bst.numel());
-    paddle::operators::TrilTriuCompute<T> tril_triu_functor(
+    phi::funcs::TrilTriuCompute<T> tril_triu_functor(
         dx_bst.data<T>(), unitriangular, !upper, H, W, dx_bst_upper.data<T>());
     x_for_range(tril_triu_functor);
 
diff --git a/paddle/phi/kernels/impl/tril_triu_grad_kernel_impl.h b/paddle/phi/kernels/impl/tril_triu_grad_kernel_impl.h
new file mode 100644
index 0000000000000000000000000000000000000000..dcc7224b5075ca77db813089af6048f0809c9f35
--- /dev/null
+++ b/paddle/phi/kernels/impl/tril_triu_grad_kernel_impl.h
@@ -0,0 +1,44 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed 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.
+
+#pragma once
+
+#include "paddle/phi/kernels/tril_triu_grad_kernel.h"
+
+#include "paddle/phi/kernels/funcs/for_range.h"
+#include "paddle/phi/kernels/funcs/tril_triu_compute.h"
+
+namespace phi {
+
+template <typename T, typename Context>
+void TrilTriuGradKernel(const Context& ctx,
+                        const DenseTensor& out_grad,
+                        int diagonal,
+                        bool lower,
+                        DenseTensor* x_grad) {
+  const auto* dout_data = out_grad.data<T>();
+  auto* dx_data = ctx.template Alloc<T>(x_grad);
+
+  const auto& dims = out_grad.dims();
+  const auto H = dims[dims.size() - 2];
+  const auto W = dims[dims.size() - 1];
+
+  phi::funcs::ForRange<Context> for_range(
+      ctx, static_cast<size_t>(out_grad.numel()));
+  phi::funcs::TrilTriuCompute<T> tril_triu_grad_computer(
+      dout_data, diagonal, lower, H, W, dx_data);
+  for_range(tril_triu_grad_computer);
+}
+
+}  // namespace phi
diff --git a/paddle/phi/kernels/impl/tril_triu_kernel_impl.h b/paddle/phi/kernels/impl/tril_triu_kernel_impl.h
new file mode 100644
index 0000000000000000000000000000000000000000..959169d87cefd877a4fb056218dd761a96f23136
--- /dev/null
+++ b/paddle/phi/kernels/impl/tril_triu_kernel_impl.h
@@ -0,0 +1,43 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed 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.
+
+#pragma once
+
+#include "paddle/phi/kernels/tril_triu_kernel.h"
+
+#include "paddle/phi/kernels/funcs/for_range.h"
+#include "paddle/phi/kernels/funcs/tril_triu_compute.h"
+
+namespace phi {
+
+template <typename T, typename Context>
+void TrilTriuKernel(const Context& ctx,
+                    const DenseTensor& x,
+                    int diagonal,
+                    bool lower,
+                    DenseTensor* out) {
+  const auto* x_data = x.data<T>();
+  auto* out_data = ctx.template Alloc<T>(out);
+
+  const auto& dims = x.dims();
+  const auto H = dims[dims.size() - 2];
+  const auto W = dims[dims.size() - 1];
+  phi::funcs::ForRange<Context> for_range(ctx, static_cast<size_t>(x.numel()));
+
+  phi::funcs::TrilTriuCompute<T> tril_triu_computer(
+      x_data, diagonal, lower, H, W, out_data);
+  for_range(tril_triu_computer);
+}
+
+}  // namespace phi
diff --git a/paddle/phi/kernels/multiplex_grad_kernel.h b/paddle/phi/kernels/multiplex_grad_kernel.h
new file mode 100644
index 0000000000000000000000000000000000000000..b32c9dbe100584f7076f34d848d3e5112315f83d
--- /dev/null
+++ b/paddle/phi/kernels/multiplex_grad_kernel.h
@@ -0,0 +1,27 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed 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.
+
+#pragma once
+
+#include "paddle/phi/core/dense_tensor.h"
+
+namespace phi {
+
+template <typename T, typename Context>
+void MultiplexGradKernel(const Context& ctx,
+                         const DenseTensor& ids,
+                         const DenseTensor& out_grad,
+                         std::vector<DenseTensor*> ins_grad);
+
+}  // namespace phi
diff --git a/paddle/phi/kernels/multiplex_kernel.h b/paddle/phi/kernels/multiplex_kernel.h
new file mode 100644
index 0000000000000000000000000000000000000000..341c6d5cabb7ce1d67090c7533bc8c45622f4786
--- /dev/null
+++ b/paddle/phi/kernels/multiplex_kernel.h
@@ -0,0 +1,27 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed 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.
+
+#pragma once
+
+#include "paddle/phi/core/dense_tensor.h"
+
+namespace phi {
+
+template <typename T, typename Context>
+void MultiplexKernel(const Context& ctx,
+                     const std::vector<const DenseTensor*>& ins,
+                     const DenseTensor& ids,
+                     DenseTensor* out);
+
+}  // namespace phi
diff --git a/paddle/phi/kernels/qr_kernel.h b/paddle/phi/kernels/qr_kernel.h
new file mode 100644
index 0000000000000000000000000000000000000000..9c3dfb16601267ec8a1d2535f6854c2a31dba5a8
--- /dev/null
+++ b/paddle/phi/kernels/qr_kernel.h
@@ -0,0 +1,28 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed 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.
+
+#pragma once
+
+#include "paddle/phi/core/dense_tensor.h"
+
+namespace phi {
+
+template <typename T, typename Context>
+void QrKernel(const Context& ctx,
+              const DenseTensor& x,
+              const std::string& mode,
+              DenseTensor* q,
+              DenseTensor* r);
+
+}  // namespace phi
diff --git a/paddle/phi/kernels/tril_triu_grad_kernel.h b/paddle/phi/kernels/tril_triu_grad_kernel.h
new file mode 100644
index 0000000000000000000000000000000000000000..10faf5c48d5bffab9f5199ebeefe7d5a2267ecea
--- /dev/null
+++ b/paddle/phi/kernels/tril_triu_grad_kernel.h
@@ -0,0 +1,28 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed 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.
+
+#pragma once
+
+#include "paddle/phi/core/dense_tensor.h"
+
+namespace phi {
+
+template <typename T, typename Context>
+void TrilTriuGradKernel(const Context& ctx,
+                        const DenseTensor& out_grad,
+                        int diagonal,
+                        bool lower,
+                        DenseTensor* x_grad);
+
+}  // namespace phi
diff --git a/paddle/phi/kernels/tril_triu_kernel.h b/paddle/phi/kernels/tril_triu_kernel.h
new file mode 100644
index 0000000000000000000000000000000000000000..4daa84e25c373d6bd5a26f2682385921dc2ce880
--- /dev/null
+++ b/paddle/phi/kernels/tril_triu_kernel.h
@@ -0,0 +1,28 @@
+// Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed 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.
+
+#pragma once
+
+#include "paddle/phi/core/dense_tensor.h"
+
+namespace phi {
+
+template <typename T, typename Context>
+void TrilTriuKernel(const Context& ctx,
+                    const DenseTensor& x,
+                    int diagonal,
+                    bool lower,
+                    DenseTensor* out);
+
+}  // namespace phi
diff --git a/paddle/phi/ops/compat/multiplex_sig.cc b/paddle/phi/ops/compat/multiplex_sig.cc
new file mode 100644
index 0000000000000000000000000000000000000000..9dab4655d172312a7389d0bb243e31ee39ef5981
--- /dev/null
+++ b/paddle/phi/ops/compat/multiplex_sig.cc
@@ -0,0 +1,32 @@
+/* Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+
+Licensed 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. */
+
+#include "paddle/phi/core/compat/op_utils.h"
+
+namespace phi {
+
+KernelSignature MultiplexOpArgumentMapping(const ArgumentMappingContext& ctx) {
+  return KernelSignature("multiplex", {"X", "Ids"}, {}, {"Out"});
+}
+
+KernelSignature MultiplexGradOpArgumentMapping(
+    const ArgumentMappingContext& ctx) {
+  return KernelSignature(
+      "multiplex_grad", {"Ids", GradVarName("Out")}, {}, {GradVarName("X")});
+}
+
+}  // namespace phi
+
+PD_REGISTER_ARG_MAPPING_FN(multiplex, phi::MultiplexOpArgumentMapping);
+PD_REGISTER_ARG_MAPPING_FN(multiplex_grad, phi::MultiplexGradOpArgumentMapping);
diff --git a/paddle/phi/ops/compat/qr_sig.cc b/paddle/phi/ops/compat/qr_sig.cc
new file mode 100644
index 0000000000000000000000000000000000000000..dd424d590ee113adfab0e9643c3c7ffc519f86e4
--- /dev/null
+++ b/paddle/phi/ops/compat/qr_sig.cc
@@ -0,0 +1,25 @@
+/* Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+
+Licensed 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. */
+
+#include "paddle/phi/core/compat/op_utils.h"
+
+namespace phi {
+
+KernelSignature QrOpArgumentMapping(const ArgumentMappingContext& ctx) {
+  return KernelSignature("qr", {"X"}, {"mode"}, {"Q", "R"});
+}
+
+}  // namespace phi
+
+PD_REGISTER_ARG_MAPPING_FN(qr, phi::QrOpArgumentMapping);
diff --git a/paddle/phi/ops/compat/tril_triu_sig.cc b/paddle/phi/ops/compat/tril_triu_sig.cc
new file mode 100644
index 0000000000000000000000000000000000000000..4f79f8650decfc6556287be2caefa6d1074ecf7f
--- /dev/null
+++ b/paddle/phi/ops/compat/tril_triu_sig.cc
@@ -0,0 +1,34 @@
+/* Copyright (c) 2022 PaddlePaddle Authors. All Rights Reserved.
+
+Licensed 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. */
+
+#include "paddle/phi/core/compat/op_utils.h"
+
+namespace phi {
+
+KernelSignature TrilTriuOpArgumentMapping(const ArgumentMappingContext& ctx) {
+  return KernelSignature("tril_triu", {"X"}, {"diagonal", "lower"}, {"Out"});
+}
+
+KernelSignature TrilTriuGradOpArgumentMapping(
+    const ArgumentMappingContext& ctx) {
+  return KernelSignature("tril_triu_grad",
+                         {GradVarName("Out")},
+                         {"diagonal", "lower"},
+                         {GradVarName("X")});
+}
+
+}  // namespace phi
+
+PD_REGISTER_ARG_MAPPING_FN(tril_triu, phi::TrilTriuOpArgumentMapping);
+PD_REGISTER_ARG_MAPPING_FN(tril_triu_grad, phi::TrilTriuGradOpArgumentMapping);