diff --git a/paddle/fluid/operators/jit/benchmark.cc b/paddle/fluid/operators/jit/benchmark.cc
index 3348778ee782ef0cdd1df4c3c4b24060436d7d79..11dc615f5ff8ea78bbbf6eeb655ee88b3a52dc13 100644
--- a/paddle/fluid/operators/jit/benchmark.cc
+++ b/paddle/fluid/operators/jit/benchmark.cc
@@ -332,6 +332,45 @@ void BenchEmbSeqPoolKernel() {
   }
 }
 
+template <jit::KernelType KT, typename T, typename PlaceType>
+void BenchSgdKernel() {
+  const T lr = 0.1;
+  auto UnDuplicatedRandomVec = [](int n, const int64_t lower,
+                                  const int64_t upper) -> std::vector<int64_t> {
+    PADDLE_ENFORCE_LE(static_cast<size_t>(upper - lower), n - 1);
+    PADDLE_ENFORCE_GT(n, 0);
+    std::vector<int64_t> all, out;
+    for (int i = 0; i < n; ++i) {
+      all.push_back(i);
+    }
+    std::random_shuffle(all.begin(), all.end());
+    out.insert(out.begin(), all.begin(), all.begin() + n);
+    return out;
+  };
+  for (int param_h : {1, 1000}) {
+    for (int grad_w : {1, 2, 8, 16, 30, 256}) {
+      // only benchmark inplace
+      Tensor param;
+      param.Resize({param_h, grad_w});
+      T* param_data = param.mutable_data<T>(PlaceType());
+      RandomVec<T>(param_h * grad_w, param_data, -2.f, 2.f);
+      for (int rows_size = 1; rows_size <= std::min(param_h, 10); ++rows_size) {
+        Tensor grad;
+        grad.Resize({rows_size, grad_w});
+        std::vector<int64_t> rows =
+            UnDuplicatedRandomVec(rows_size, 0, rows_size - 1);
+        RandomVec<T>(rows_size * grad_w, grad.mutable_data<T>(PlaceType()),
+                     -2.f, 2.f);
+        const T* grad_data = grad.data<T>();
+        const int64_t* rows_data = rows.data();
+        jit::sgd_attr_t attr(param_h, grad_w, rows_size, grad_w, rows_size);
+        BenchAllImpls<KT, jit::SgdTuples<T>, PlaceType>(
+            attr, &lr, param_data, grad_data, rows_data, param_data, &attr);
+      }
+    }
+  }
+}
+
 template <jit::KernelType KT, typename T, typename PlaceType>
 void BenchMatMulKernel() {
   for (int m : {1, 2, 3, 4}) {
@@ -477,6 +516,9 @@ BENCH_FP32_CPU(kEmbSeqPool) {
   BenchEmbSeqPoolKernel<jit::kEmbSeqPool, T, CPUPlace>();
 }
 
+// sgd function
+BENCH_FP32_CPU(kSgd) { BenchSgdKernel<jit::kSgd, T, CPUPlace>(); }
+
 // matmul
 BENCH_FP32_CPU(kMatMul) { BenchMatMulKernel<jit::kMatMul, T, CPUPlace>(); }
 
diff --git a/paddle/fluid/operators/jit/gen/CMakeLists.txt b/paddle/fluid/operators/jit/gen/CMakeLists.txt
index 294f73d9646c93132e464a032e93562094663a73..eb0c03568ddddf1c456fec6fcc81f3b40d051844 100644
--- a/paddle/fluid/operators/jit/gen/CMakeLists.txt
+++ b/paddle/fluid/operators/jit/gen/CMakeLists.txt
@@ -32,3 +32,4 @@ USE_JITKERNEL_GEN(kSeqPool)
 USE_JITKERNEL_GEN(kHMax)
 USE_JITKERNEL_GEN(kHSum)
 USE_JITKERNEL_GEN(kEmbSeqPool)
+USE_JITKERNEL_GEN(kSgd)
diff --git a/paddle/fluid/operators/jit/gen/jitcode.h b/paddle/fluid/operators/jit/gen/jitcode.h
index 689df8b1cbb7a928c9f9175d28a8231b56e2e82e..39847d1b65f771976c4dde5a3e34cc40e33851e6 100644
--- a/paddle/fluid/operators/jit/gen/jitcode.h
+++ b/paddle/fluid/operators/jit/gen/jitcode.h
@@ -31,7 +31,8 @@ namespace gen {
 // Application Binary Interface
 constexpr Xbyak::Operand::Code abi_param1(Xbyak::Operand::RDI),
     abi_param2(Xbyak::Operand::RSI), abi_param3(Xbyak::Operand::RDX),
-    abi_param4(Xbyak::Operand::RCX);
+    abi_param4(Xbyak::Operand::RCX), abi_param5(Xbyak::Operand::R8),
+    abi_param6(Xbyak::Operand::R9);
 
 constexpr Xbyak::Operand::Code g_abi_regs[] = {
     Xbyak::Operand::RBX, Xbyak::Operand::RBP, Xbyak::Operand::R12,
diff --git a/paddle/fluid/operators/jit/gen/sgd.cc b/paddle/fluid/operators/jit/gen/sgd.cc
new file mode 100644
index 0000000000000000000000000000000000000000..a745a27f9543a75f6915c9316aad62fa41305bb1
--- /dev/null
+++ b/paddle/fluid/operators/jit/gen/sgd.cc
@@ -0,0 +1,130 @@
+/* Copyright (c) 2019 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/jit/gen/sgd.h"
+#include <stddef.h>  // offsetof
+#include <vector>
+#include "paddle/fluid/operators/jit/registry.h"
+#include "paddle/fluid/platform/cpu_info.h"
+
+namespace paddle {
+namespace operators {
+namespace jit {
+namespace gen {
+
+void SgdJitCode::genCode() {
+  preCode();
+  constexpr int block = YMM_FLOAT_BLOCK;
+  constexpr int max_num_regs = 7;
+  const int num_block = w_ / block;
+  const int num_groups = num_block / max_num_regs;
+  const size_t block_size = sizeof(float) * block;
+  const size_t width_size = w_ * sizeof(float);
+  std::vector<int> groups(num_groups, max_num_regs);
+  int rest_num_regs = num_block % max_num_regs;
+  if (rest_num_regs > 0) {
+    groups.push_back(rest_num_regs);
+  }
+
+  vbroadcastss(ymm_lr, ptr[param_lr]);
+  // protect rdx
+  mov(reg_ptr_grad_i, param_grad);
+  mov(reg_ptr_rows_i, param_rows);
+
+  mov(reg_rows_size_in_byte,
+      qword[param_attr + offsetof(sgd_attr_t, selected_rows_size)]);
+  mov(rax, sizeof(int64_t));
+  mul(reg_rows_size_in_byte);
+  mov(reg_rows_size_in_byte, rax);
+  add(reg_rows_size_in_byte, reg_ptr_rows_i);
+
+  Label l_next_row;
+  L(l_next_row);
+  {
+    mov(reg_row, qword[reg_ptr_rows_i]);
+    mov(rax, width_size);
+    mul(reg_row);
+    mov(reg_row, rax);
+
+    mov(reg_ptr_param_i, param_param);
+    mov(reg_ptr_out_i, param_out);
+    add(reg_ptr_param_i, reg_row);
+    add(reg_ptr_out_i, reg_row);
+
+    size_t w_offset = 0;
+    for (int num_regs : groups) {
+      // load grad
+      size_t inner_offfset = w_offset;
+      for (int reg_i = 0; reg_i < num_regs; ++reg_i) {
+        vmovups(ymm_t(reg_i), ptr[reg_ptr_grad_i + inner_offfset]);
+        inner_offfset += block_size;
+      }
+
+      // load param
+      inner_offfset = w_offset;
+      for (int reg_i = 0; reg_i < num_regs; ++reg_i) {
+        vmovups(ymm_t(reg_i + num_regs), ptr[reg_ptr_param_i + inner_offfset]);
+        inner_offfset += block_size;
+      }
+
+      // compute out
+      for (int reg_i = 0; reg_i < num_regs; ++reg_i) {
+        vmulps(ymm_t(reg_i), ymm_t(reg_i), ymm_lr);
+        vsubps(ymm_t(reg_i + num_regs), ymm_t(reg_i + num_regs), ymm_t(reg_i));
+      }
+
+      // save out
+      inner_offfset = w_offset;
+      for (int reg_i = 0; reg_i < num_regs; ++reg_i) {
+        vmovups(ptr[reg_ptr_out_i + inner_offfset], ymm_t(reg_i + num_regs));
+        inner_offfset += block_size;
+      }
+      w_offset += (block_size * num_regs);
+    }
+
+    add(reg_ptr_grad_i, width_size);
+    add(reg_ptr_rows_i, sizeof(int64_t));
+    cmp(reg_ptr_rows_i, reg_rows_size_in_byte);
+    jl(l_next_row, T_NEAR);
+  }
+
+  postCode();
+}
+
+class SgdCreator : public JitCodeCreator<sgd_attr_t> {
+ public:
+  bool UseMe(const sgd_attr_t& attr) const override {
+    return platform::MayIUse(platform::avx) &&
+           attr.grad_width % YMM_FLOAT_BLOCK == 0;
+  }
+  size_t CodeSize(const sgd_attr_t& attr) const override {
+    return 96 + (attr.grad_width / YMM_FLOAT_BLOCK) * 32 * 8;
+  }
+  std::unique_ptr<GenBase> CreateJitCode(
+      const sgd_attr_t& attr) const override {
+    PADDLE_ENFORCE_EQ(attr.param_width, attr.grad_width);
+    PADDLE_ENFORCE_LE(attr.selected_rows_size, attr.grad_height);
+    PADDLE_ENFORCE_GE(attr.selected_rows_size, 0);
+    return make_unique<SgdJitCode>(attr, CodeSize(attr));
+  }
+};
+
+}  // namespace gen
+}  // namespace jit
+}  // namespace operators
+}  // namespace paddle
+
+namespace gen = paddle::operators::jit::gen;
+
+REGISTER_JITKERNEL_GEN(kSgd, gen::SgdCreator);
diff --git a/paddle/fluid/operators/jit/gen/sgd.h b/paddle/fluid/operators/jit/gen/sgd.h
new file mode 100644
index 0000000000000000000000000000000000000000..317edcd2bcb5fea1f14f32260fd16c9c706eaf00
--- /dev/null
+++ b/paddle/fluid/operators/jit/gen/sgd.h
@@ -0,0 +1,60 @@
+/* Copyright (c) 2018 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 <string>
+#include "glog/logging.h"
+#include "paddle/fluid/operators/jit/gen/jitcode.h"
+#include "paddle/fluid/platform/enforce.h"
+
+namespace paddle {
+namespace operators {
+namespace jit {
+namespace gen {
+
+class SgdJitCode : public JitCode {
+ public:
+  explicit SgdJitCode(const sgd_attr_t& attr, size_t code_size = 256 * 1024,
+                      void* code_ptr = nullptr)
+      : JitCode(code_size, code_ptr), w_(attr.grad_width) {
+    this->genCode();
+  }
+
+  DECLARE_JIT_CODE(SgdJitCode);
+  void genCode() override;
+
+ private:
+  int w_;
+  reg64_t param_lr{abi_param1};
+  reg64_t param_param{abi_param2};
+  reg64_t param_grad{abi_param3};
+  reg64_t param_rows{abi_param4};
+  reg64_t param_out{abi_param5};
+  reg64_t param_attr{abi_param6};
+
+  ymm_t ymm_lr = ymm_t(15);
+
+  reg64_t reg_ptr_grad_i{r10};
+  reg64_t reg_ptr_rows_i{r11};
+  reg64_t reg_rows_size_in_byte{r12};
+  reg64_t reg_row{r13};
+  reg64_t reg_ptr_param_i{r14};
+  reg64_t reg_ptr_out_i{r15};
+};
+
+}  // namespace gen
+}  // namespace jit
+}  // namespace operators
+}  // namespace paddle
diff --git a/paddle/fluid/operators/jit/helper.cc b/paddle/fluid/operators/jit/helper.cc
index a76653613289892c4bb41596f998c5f4cc131fd7..1dc60442d5c5f6acf49b6319223b190f6c81e1a6 100644
--- a/paddle/fluid/operators/jit/helper.cc
+++ b/paddle/fluid/operators/jit/helper.cc
@@ -55,6 +55,7 @@ const char* to_string(KernelType kt) {
     ONE_CASE(kHSum);
     ONE_CASE(kSoftmax);
     ONE_CASE(kEmbSeqPool);
+    ONE_CASE(kSgd);
     default:
       PADDLE_THROW("Not support type: %d, or forget to add it.", kt);
       return "NOT JITKernel";
diff --git a/paddle/fluid/operators/jit/helper.h b/paddle/fluid/operators/jit/helper.h
index 07998588a5a560f9c2ad7cc765b66e76e87da6f6..d85c719c1c58c88ec244f1f6ad8343d66391241d 100644
--- a/paddle/fluid/operators/jit/helper.h
+++ b/paddle/fluid/operators/jit/helper.h
@@ -181,6 +181,14 @@ inline std::ostream& operator<<(std::ostream& os,
   return os;
 }
 
+inline std::ostream& operator<<(std::ostream& os, const sgd_attr_t& attr) {
+  os << "param_height[" << attr.param_height << "],param_width["
+     << attr.param_width << "],grad_height[" << attr.grad_height
+     << "],grad_width[" << attr.grad_width << "],selected_rows_size["
+     << attr.selected_rows_size << "]";
+  return os;
+}
+
 inline std::ostream& operator<<(std::ostream& os, const matmul_attr_t& attr) {
   os << "M[" << attr.m << "],N[" << attr.n << "],K[" << attr.k << "]";
   return os;
diff --git a/paddle/fluid/operators/jit/kernel_base.h b/paddle/fluid/operators/jit/kernel_base.h
index 20b6a32bef9860c52ab4423395a8e00f719b0210..895e2d4d6f3809a66443ed6d6bfc1ee02d6c529a 100644
--- a/paddle/fluid/operators/jit/kernel_base.h
+++ b/paddle/fluid/operators/jit/kernel_base.h
@@ -46,6 +46,7 @@ typedef enum {
   kVMul,
   kVRelu,
   kVScal,
+  kSgd,
   kVSigmoid,
   kVSquare,
   kVSub,
@@ -173,6 +174,28 @@ struct EmbSeqPoolTuples {
                             const emb_seq_pool_attr_t*);
 };
 
+typedef struct sgd_attr_s {
+  int64_t param_height, param_width;
+  int64_t grad_height, grad_width;
+  int64_t selected_rows_size;
+  sgd_attr_s() = default;
+  explicit sgd_attr_s(int64_t param_h, int64_t param_w, int64_t grad_h,
+                      int64_t grad_w, int64_t selected_rows_sz)
+      : param_height(param_h),
+        param_width(param_w),
+        grad_height(grad_h),
+        grad_width(grad_w),
+        selected_rows_size(selected_rows_sz) {}
+} sgd_attr_t;
+
+template <typename T>
+struct SgdTuples {
+  typedef T data_type;
+  typedef sgd_attr_t attr_type;
+  typedef void (*func_type)(const T*, const T*, const T*, const int64_t*, T*,
+                            const sgd_attr_t*);
+};
+
 typedef struct matmul_attr_s {
   int m, n, k;
   void* packed_weight{nullptr};
diff --git a/paddle/fluid/operators/jit/kernel_key.cc b/paddle/fluid/operators/jit/kernel_key.cc
index e659c6d254391f09ac8692e0b7602c65e1afd47d..740d0f850a072a5ad3238e52402141a83c0b7e33 100644
--- a/paddle/fluid/operators/jit/kernel_key.cc
+++ b/paddle/fluid/operators/jit/kernel_key.cc
@@ -13,6 +13,7 @@
  * limitations under the License. */
 
 #include "paddle/fluid/operators/jit/kernel_key.h"
+#include "paddle/fluid/platform/enforce.h"
 
 namespace paddle {
 namespace operators {
@@ -23,14 +24,30 @@ size_t JitCodeKey<int>(const int& d) {
   return d;
 }
 
+// TODO(TJ): refine and benchmark JitCodeKey generatation
 constexpr int act_type_shift = 3;  // suppot 2^3 act types
+static inline int act_type_convert(KernelType type) {
+  if (type == kVIdentity) {
+    return 0;
+  } else if (type == kVExp) {
+    return 1;
+  } else if (type == kVRelu) {
+    return 2;
+  } else if (type == kVSigmoid) {
+    return 3;
+  } else if (type == kVTanh) {
+    return 4;
+  }
+  PADDLE_THROW("Unsupported act type %d", type);
+  return 0;
+}
 
 template <>
 size_t JitCodeKey<lstm_attr_t>(const lstm_attr_t& attr) {
   size_t key = attr.d;
-  int gate_key = static_cast<int>(attr.act_gate) << 1;
-  int cand_key = static_cast<int>(attr.act_cand) << (1 + act_type_shift);
-  int cell_key = static_cast<int>(attr.act_cell) << (1 + act_type_shift * 2);
+  int gate_key = act_type_convert(attr.act_gate) << 1;
+  int cand_key = act_type_convert(attr.act_cand) << (1 + act_type_shift);
+  int cell_key = act_type_convert(attr.act_cell) << (1 + act_type_shift * 2);
   return (key << (1 + act_type_shift * 3)) + gate_key + cand_key + cell_key +
          attr.use_peephole;
 }
@@ -38,8 +55,8 @@ size_t JitCodeKey<lstm_attr_t>(const lstm_attr_t& attr) {
 template <>
 size_t JitCodeKey<gru_attr_t>(const gru_attr_t& attr) {
   size_t key = attr.d;
-  return (key << (act_type_shift * 2)) + static_cast<int>(attr.act_gate) +
-         (static_cast<int>(attr.act_cand) << act_type_shift);
+  return (key << (act_type_shift * 2)) + act_type_convert(attr.act_gate) +
+         (act_type_convert(attr.act_cand) << act_type_shift);
 }
 
 template <>
@@ -61,6 +78,11 @@ size_t JitCodeKey<emb_seq_pool_attr_t>(const emb_seq_pool_attr_t& attr) {
   return attr.table_width;
 }
 
+template <>
+size_t JitCodeKey<sgd_attr_t>(const sgd_attr_t& attr) {
+  return attr.grad_width;
+}
+
 }  // namespace jit
 }  // namespace operators
 }  // namespace paddle
diff --git a/paddle/fluid/operators/jit/more/mkl/CMakeLists.txt b/paddle/fluid/operators/jit/more/mkl/CMakeLists.txt
index d209f31007255b3a90fdeeb4d609311b80bdc7b5..9a00ad56a6a909a677cb8f60bd80fe399e82952f 100644
--- a/paddle/fluid/operators/jit/more/mkl/CMakeLists.txt
+++ b/paddle/fluid/operators/jit/more/mkl/CMakeLists.txt
@@ -14,3 +14,4 @@ USE_JITKERNEL_MORE(kVTanh, mkl)
 USE_JITKERNEL_MORE(kSeqPool, mkl)
 USE_JITKERNEL_MORE(kSoftmax, mkl)
 USE_JITKERNEL_MORE(kEmbSeqPool, mkl)
+USE_JITKERNEL_MORE(kSgd, mkl)
diff --git a/paddle/fluid/operators/jit/more/mkl/mkl.cc b/paddle/fluid/operators/jit/more/mkl/mkl.cc
index 29a451f832fa745f8e1f5a45fd934f09e1f41e76..780fda02c1ff3da2e0b945f9b2fece30484e4519 100644
--- a/paddle/fluid/operators/jit/more/mkl/mkl.cc
+++ b/paddle/fluid/operators/jit/more/mkl/mkl.cc
@@ -184,6 +184,16 @@ bool EmbSeqPoolKernel<double>::UseMe(const emb_seq_pool_attr_t& attr) const {
   return true;
 }
 
+template <>
+bool SgdKernel<float>::UseMe(const sgd_attr_t& attr) const {
+  return true;
+}
+
+template <>
+bool SgdKernel<double>::UseMe(const sgd_attr_t& attr) const {
+  return true;
+}
+
 template <>
 bool MatMulKernel<float>::UseMe(const matmul_attr_t& attr) const {
   return platform::MayIUse(platform::avx);
@@ -239,5 +249,6 @@ REGISTER_MKL_KERNEL(kVTanh, VTanh);
 REGISTER_MKL_KERNEL(kSeqPool, SeqPool);
 REGISTER_MKL_KERNEL(kEmbSeqPool, EmbSeqPool);
 REGISTER_MKL_KERNEL(kSoftmax, Softmax);
+REGISTER_MKL_KERNEL(kSgd, Sgd);
 
 #undef REGISTER_MKL_KERNEL
diff --git a/paddle/fluid/operators/jit/more/mkl/mkl.h b/paddle/fluid/operators/jit/more/mkl/mkl.h
index 9a72ba83022de2beeb760772ee8489477befdd7e..a7bc2de4a3e8e7d8e2a6b00990bfa459b3029c2a 100644
--- a/paddle/fluid/operators/jit/more/mkl/mkl.h
+++ b/paddle/fluid/operators/jit/more/mkl/mkl.h
@@ -142,6 +142,32 @@ void Softmax(const T* x, T* y, int n, int bs) {
   }
 }
 
+template <typename T>
+void Sgd(const T* lr, const T* param, const T* grad, const int64_t* rows,
+         T* out, const sgd_attr_t* attr) {
+  PADDLE_ENFORCE_EQ(attr->param_width, attr->grad_width);
+  PADDLE_ENFORCE_LE(attr->selected_rows_size, attr->grad_height);
+  T scalar = -lr[0];
+  int width = attr->grad_width;
+  if (out == param) {
+    for (int64_t i = 0; i < attr->selected_rows_size; ++i) {
+      auto h_idx = rows[i];
+      PADDLE_ENFORCE_LT(h_idx, attr->param_height);
+      PADDLE_ENFORCE_GE(h_idx, 0);
+      VAXPY(scalar, grad + i * width, out + h_idx * width, width);
+    }
+  } else {
+    for (int64_t i = 0; i < attr->selected_rows_size; ++i) {
+      auto h_idx = rows[i];
+      PADDLE_ENFORCE_LT(h_idx, attr->param_height);
+      PADDLE_ENFORCE_GE(h_idx, 0);
+      VScal(&scalar, grad + i * width, out + h_idx * width, width);
+      VAdd(param + h_idx * width, out + h_idx * width, out + h_idx * width,
+           width);
+    }
+  }
+}
+
 #define DECLARE_MKL_KERNEL(name, tuples)                             \
   template <typename T>                                              \
   class name##Kernel : public KernelMore<tuples<T>> {                \
@@ -173,6 +199,8 @@ DECLARE_MKL_KERNEL(EmbSeqPool, EmbSeqPoolTuples);
 
 DECLARE_MKL_KERNEL(Softmax, SoftmaxTuples);
 
+DECLARE_MKL_KERNEL(Sgd, SgdTuples);
+
 #undef DECLARE_MKL_KERNEL
 
 }  // namespace mkl
diff --git a/paddle/fluid/operators/jit/refer/CMakeLists.txt b/paddle/fluid/operators/jit/refer/CMakeLists.txt
index 218d801c084be455538628d1c1028d8e52142894..cd19dd169d0bfdfe2cb8157ade29f48ad6428453 100644
--- a/paddle/fluid/operators/jit/refer/CMakeLists.txt
+++ b/paddle/fluid/operators/jit/refer/CMakeLists.txt
@@ -33,3 +33,4 @@ USE_JITKERNEL_REFER(kHSum)
 USE_JITKERNEL_REFER(kHMax)
 USE_JITKERNEL_REFER(kSoftmax)
 USE_JITKERNEL_REFER(kEmbSeqPool)
+USE_JITKERNEL_REFER(kSgd)
diff --git a/paddle/fluid/operators/jit/refer/refer.cc b/paddle/fluid/operators/jit/refer/refer.cc
index 7e7dd6960b66e4e2f77eca6e96604f2a86553120..0c434bd2b8cacdf4b8872da66bb8e763a6a45cee 100644
--- a/paddle/fluid/operators/jit/refer/refer.cc
+++ b/paddle/fluid/operators/jit/refer/refer.cc
@@ -59,4 +59,6 @@ REGISTER_REFER_KERNEL(kSoftmax, Softmax);
 
 REGISTER_REFER_KERNEL(kEmbSeqPool, EmbSeqPool);
 
+REGISTER_REFER_KERNEL(kSgd, Sgd);
+
 #undef REGISTER_REFER_KERNEL
diff --git a/paddle/fluid/operators/jit/refer/refer.h b/paddle/fluid/operators/jit/refer/refer.h
index fd1193aa41e50e3ede7f61588dc72389279bb95d..0f714edf85bbbf4838bfe09251bd1c2d5f3b3eb7 100644
--- a/paddle/fluid/operators/jit/refer/refer.h
+++ b/paddle/fluid/operators/jit/refer/refer.h
@@ -446,6 +446,36 @@ void EmbSeqPool(const T* table, const int64_t* idx, T* out,
   }
 }
 
+// SGD algorithm:
+// lr is pointor of learning rate scalar
+// param is an input matrix with (param_h, param_w)
+// grad is an input matrix with (grad_h, grad_w), here grad_w == param_w
+// selected_rows is a vectot<int64_t> with size selected_rows_size( <= grad_h )
+// out is an output matrix with (param_h, param_w)
+//
+// support both regular and sparse grad
+// regular SGD: out[:] = param[:] - lr[0] * grad[:];
+// sparse SGD: out[rows[i]][:] = param[rows[i]][:] - lr[0] * grad[i][:]
+//
+// Note: when use sparse SGD, and if out != param,
+// the out rows which are not selected have not beed changed, which maybe empty
+template <typename T>
+void Sgd(const T* lr, const T* param, const T* grad, const int64_t* rows,
+         T* out, const sgd_attr_t* attr) {
+  PADDLE_ENFORCE_EQ(attr->param_width, attr->grad_width);
+  PADDLE_ENFORCE_LE(attr->selected_rows_size, attr->grad_height);
+  for (int64_t i = 0; i < attr->selected_rows_size; ++i) {
+    auto h_idx = rows[i];
+    PADDLE_ENFORCE_LT(h_idx, attr->param_height);
+    PADDLE_ENFORCE_GE(h_idx, 0);
+    for (int64_t j = 0; j < attr->grad_width; ++j) {
+      out[h_idx * attr->grad_width + j] =
+          param[h_idx * attr->grad_width + j] -
+          lr[0] * grad[i * attr->grad_width + j];
+    }
+  }
+}
+
 #define DECLARE_REFER_KERNEL(name, tuples)             \
   template <typename T>                                \
   class name##Kernel : public ReferKernel<tuples<T>> { \
@@ -496,6 +526,8 @@ DECLARE_REFER_KERNEL(Softmax, SoftmaxTuples);
 
 DECLARE_REFER_KERNEL(EmbSeqPool, EmbSeqPoolTuples);
 
+DECLARE_REFER_KERNEL(Sgd, SgdTuples);
+
 #undef DECLARE_REFER_KERNEL
 
 }  // namespace refer
diff --git a/paddle/fluid/operators/jit/test.cc b/paddle/fluid/operators/jit/test.cc
index 356eba6f86ad180c7d23bf7fa91eb5d455ff5f08..b618cd6a84be752a052f9d49a4a4c772b1d7eeae 100644
--- a/paddle/fluid/operators/jit/test.cc
+++ b/paddle/fluid/operators/jit/test.cc
@@ -12,6 +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 <algorithm>
 #include <random>
 #include <string>
 #include <vector>
@@ -36,14 +37,14 @@ void RandomVec(const int n, T* a, const T lower = static_cast<T>(-20.f),
 }
 
 template <typename T>
-void ExpectEQ(const T* target, const T* refer, int n) {
+void ExpectEQ(const T* target, const T* refer, size_t n) {
   if (std::is_floating_point<T>::value) {
-    for (int i = 0; i < n; ++i) {
-      EXPECT_NEAR(target[i], refer[i], FLAGS_acc);
+    for (size_t i = 0; i < n; ++i) {
+      EXPECT_NEAR(target[i], refer[i], FLAGS_acc) << " at index : " << i;
     }
   } else {
-    for (int i = 0; i < n; ++i) {
-      EXPECT_EQ(target[i], refer[i]);
+    for (size_t i = 0; i < n; ++i) {
+      EXPECT_EQ(target[i], refer[i]) << " at index : " << i;
     }
   }
 }
@@ -296,6 +297,45 @@ struct TestFuncWithRefer<jit::EmbSeqPoolTuples<T>, std::vector<T>,
   }
 };
 
+template <typename T>
+struct TestFuncWithRefer<jit::SgdTuples<T>, T, std::vector<T>, std::vector<T>,
+                         std::vector<int64_t>, std::vector<T>,
+                         typename jit::SgdTuples<T>::attr_type> {
+  void operator()(const typename jit::SgdTuples<T>::func_type tgt, const T lr,
+                  const std::vector<T>& param, const std::vector<T>& grad,
+                  const std::vector<int64_t>& rows, const std::vector<T>& oref,
+                  const typename jit::SgdTuples<T>::attr_type& attr) {
+    EXPECT_TRUE(tgt != nullptr);
+    EXPECT_EQ(param.size(),
+              static_cast<size_t>(attr.param_height * attr.param_width));
+    EXPECT_EQ(grad.size(),
+              static_cast<size_t>(attr.grad_height * attr.grad_width));
+    EXPECT_EQ(rows.size(), static_cast<size_t>(attr.selected_rows_size));
+    EXPECT_EQ(param.size(), oref.size());
+    const T* param_data = param.data();
+    const T* grad_data = grad.data();
+    const int64_t* rows_data = rows.data();
+    const T* oref_data = oref.data();
+
+    std::vector<T> out(oref.size());
+    T* o_data = out.data();
+    tgt(&lr, param_data, grad_data, rows_data, o_data, &attr);
+    // only the selected rows should be equal
+    for (size_t i = 0; i < rows.size(); ++i) {
+      ExpectEQ<T>(o_data + rows[i] * attr.grad_width,
+                  oref_data + rows[i] * attr.grad_width, attr.grad_width);
+    }
+
+    // inplace
+    std::copy(param.begin(), param.end(), out.begin());
+    tgt(&lr, o_data, grad_data, rows_data, o_data, &attr);
+    for (size_t i = 0; i < rows.size(); ++i) {
+      ExpectEQ<T>(o_data + rows[i] * attr.grad_width,
+                  oref_data + rows[i] * attr.grad_width, attr.grad_width);
+    }
+  }
+};
+
 template <typename T>
 struct TestFuncWithRefer<jit::MatMulTuples<T>, std::vector<T>, std::vector<T>,
                          std::vector<T>,
@@ -407,7 +447,7 @@ void TestAllImpls(const typename KernelTuples::attr_type& attr, Args... args) {
 }
 
 template <jit::KernelType KT, typename T, typename PlaceType>
-void TestXYZNKernel() {
+void TestKernelXYZNTuples() {
   VLOG(10) << "===== Test JITKernel " << jit::to_string(KT);
   for (int d : TestSizes()) {
     auto ref = jit::GetRefer<KT, jit::XYZNTuples<T>>();
@@ -440,7 +480,7 @@ void TestXYZNKernel() {
 }
 
 template <jit::KernelType KT, typename T, typename PlaceType>
-void TestAXYNKernel() {
+void TestKernelAXYNTuples() {
   VLOG(10) << "===== Test JITKernel " << jit::to_string(KT);
   for (int d : TestSizes()) {
     auto ref = jit::GetRefer<KT, jit::AXYNTuples<T>>();
@@ -466,7 +506,7 @@ void TestAXYNKernel() {
 }
 
 template <jit::KernelType KT, typename T, typename PlaceType>
-void TestXRNKernel() {
+void TestKernelXRNTuples() {
   VLOG(10) << "===== Test JITKernel " << jit::to_string(KT);
   auto last_acc = FLAGS_acc;
   FLAGS_acc = 1e-4;
@@ -484,7 +524,7 @@ void TestXRNKernel() {
 }
 
 template <jit::KernelType KT, typename T, typename PlaceType>
-void TestXYNKernel() {
+void TestKernelXYNTuples() {
   VLOG(10) << "===== Test JITKernel " << jit::to_string(KT);
   for (int d : TestSizes()) {
     auto ref = jit::GetRefer<KT, jit::XYNTuples<T>>();
@@ -509,10 +549,12 @@ void TestXYNKernel() {
 }
 
 template <jit::KernelType KT, typename T, typename PlaceType>
-void TestLSTMKernel() {
+void TestKernelLSTMTuples() {
   VLOG(10) << "===== Test JITKernel " << jit::to_string(KT);
   std::vector<std::string> all_acts = {"sigmoid", "tanh", "relu", "identity"};
-  for (int d : TestSizes()) {
+  auto test_sizes = TestSizes();
+  test_sizes.erase(std::remove(test_sizes.begin(), test_sizes.end(), 1000));
+  for (int d : test_sizes) {
     for (bool use_peephole : {true, false}) {
       for (auto& act_gate : all_acts) {
         for (auto& act_cand : all_acts) {
@@ -559,10 +601,12 @@ void TestLSTMKernel() {
 }
 
 template <jit::KernelType KT, typename T, typename PlaceType>
-void TestGRUKernel() {
+void TestKernelGRUTuples() {
   VLOG(10) << "===== Test JITKernel " << jit::to_string(KT);
   std::vector<std::string> all_acts = {"sigmoid", "tanh", "relu", "identity"};
-  for (int d : TestSizes()) {
+  auto test_sizes = TestSizes();
+  test_sizes.erase(std::remove(test_sizes.begin(), test_sizes.end(), 1000));
+  for (int d : test_sizes) {
     for (auto& act_gate : all_acts) {
       for (auto& act_cand : all_acts) {
         const jit::gru_attr_t attr(d, jit::to_kerneltype(act_gate),
@@ -593,14 +637,16 @@ void TestGRUKernel() {
 }
 
 template <jit::KernelType KT, typename T, typename PlaceType>
-void TestSeqPoolKernel() {
+void TestKernelSeqPoolTuples() {
   VLOG(10) << "===== Test JITKernel " << jit::to_string(KT);
   std::vector<jit::SeqPoolType> pool_types = {
       jit::SeqPoolType::kSum, jit::SeqPoolType::kAvg, jit::SeqPoolType::kSqrt};
+  auto test_sizes = TestSizes();
+  test_sizes.erase(std::remove(test_sizes.begin(), test_sizes.end(), 1000));
   for (auto type : pool_types) {
-    for (int w : TestSizes()) {
+    for (int w : test_sizes) {
       jit::seq_pool_attr_t attr(w, type);
-      for (int h : TestSizes()) {
+      for (int h : test_sizes) {
         attr.h = h;
         auto ref = jit::GetRefer<KT, jit::SeqPoolTuples<T>>();
         EXPECT_TRUE(ref != nullptr);
@@ -618,11 +664,11 @@ void TestSeqPoolKernel() {
 }
 
 template <jit::KernelType KT, typename T, typename PlaceType>
-void TestMatMulKernel() {
+void TestKernelMatMulTuples() {
   VLOG(10) << "===== Test JITKernel " << jit::to_string(KT);
   auto last_acc = FLAGS_acc;
-  // TODO(intel): fix MKL acc issue
-  // https://github.com/PaddlePaddle/Paddle/issues/15447
+  // export MKL_CBWR=AVX would make MKL force to use AVX
+  // export KMP_DETERMINISTIC_REDUCTION=yes would make the result deterministic
   FLAGS_acc = 1e-3;
   for (int m : {1, 2, 3, 4}) {
     for (int n : {1, 2, 3, 4}) {
@@ -646,7 +692,7 @@ void TestMatMulKernel() {
 }
 
 template <jit::KernelType KT, typename T, typename PlaceType>
-void TestSoftmaxKernel() {
+void TestKernelSoftmaxTuples() {
   VLOG(10) << "===== Test JITKernel " << jit::to_string(KT);
   for (int bs : {1, 2, 10}) {
     for (int n : TestSizes()) {
@@ -671,12 +717,14 @@ void TestSoftmaxKernel() {
 }
 
 template <jit::KernelType KT, typename T, typename PlaceType>
-void TestEmbSeqPoolKernel() {
+void TestKernelEmbSeqPoolTuples() {
   VLOG(10) << "===== Test JITKernel " << jit::to_string(KT);
   int64_t tbl_h = 1e4;
   std::vector<jit::SeqPoolType> pool_types = {
       jit::SeqPoolType::kSum};  // only support sum yet
-  for (int tbl_w : TestSizes()) {
+  auto test_sizes = TestSizes();
+  test_sizes.erase(std::remove(test_sizes.begin(), test_sizes.end(), 1000));
+  for (int tbl_w : test_sizes) {
     std::vector<T> table(tbl_h * tbl_w);
     RandomVec<T>(tbl_h * tbl_w, table.data(), -2.f, 2.f);
     const T* table_data = table.data();
@@ -705,7 +753,61 @@ void TestEmbSeqPoolKernel() {
 }
 
 template <jit::KernelType KT, typename T, typename PlaceType>
-void TestNCHW16CMulNCKernel() {
+void TestKernelSgdTuples() {
+  VLOG(10) << "===== Test JITKernel " << jit::to_string(KT);
+  const T lr = 0.1;
+  auto UnDuplicatedRandomVec = [](int n, const int64_t lower,
+                                  const int64_t upper) -> std::vector<int64_t> {
+    PADDLE_ENFORCE_LE(static_cast<size_t>(upper - lower), n - 1);
+    PADDLE_ENFORCE_GT(n, 0);
+    std::vector<int64_t> all, out;
+    for (int i = 0; i < n; ++i) {
+      all.push_back(i);
+    }
+    std::random_shuffle(all.begin(), all.end());
+    out.insert(out.begin(), all.begin(), all.begin() + n);
+    return out;
+  };
+  for (int param_h : {1, 10}) {
+    for (int grad_w : TestSizes()) {
+      std::vector<T> param(param_h * grad_w);
+      std::vector<T> param_out(param_h * grad_w);
+      RandomVec<T>(param_h * grad_w, param.data(), -2.f, 2.f);
+      const T* param_data = param.data();
+      T* out_data = param_out.data();
+      for (int rows_size = 1; rows_size <= param_h; ++rows_size) {
+        std::vector<T> grad(rows_size * grad_w);
+        std::vector<int64_t> rows =
+            UnDuplicatedRandomVec(rows_size, 0, rows_size - 1);
+        RandomVec<T>(rows_size * grad_w, grad.data(), -2.f, 2.f);
+        const int64_t* rows_data = rows.data();
+        const T* grad_data = grad.data();
+        auto ref = jit::GetRefer<KT, jit::SgdTuples<T>>();
+        EXPECT_TRUE(ref != nullptr);
+        jit::sgd_attr_t attr(param_h, grad_w, rows_size, grad_w, rows_size);
+        ref(&lr, param_data, grad_data, rows_data, out_data, &attr);
+
+        // inplace test
+        std::vector<T> inp(param.size());
+        std::copy(param.begin(), param.end(), inp.begin());
+        T* inp_data = inp.data();
+        ref(&lr, inp_data, grad_data, rows_data, inp_data, &attr);
+        // only the selected rows should be equal
+        for (int i = 0; i < rows_size; ++i) {
+          ExpectEQ<T>(inp_data + rows[i] * grad_w, out_data + rows[i] * grad_w,
+                      grad_w);
+        }
+
+        TestAllImpls<KT, jit::SgdTuples<T>, PlaceType, T, std::vector<T>,
+                     std::vector<T>, std::vector<int64_t>, std::vector<T>>(
+            attr, lr, param, grad, rows, param_out, attr);
+      }
+    }
+  }
+}
+
+template <jit::KernelType KT, typename T, typename PlaceType>
+void TestKernelNCHW16CMulNCTuples() {
   VLOG(10) << "===== Test JITKernel " << jit::to_string(KT);
   const int n = 3, c = 16 * 4, h = 10, w = 10;
   auto ref = jit::GetRefer<KT, jit::NCHW16CMulNCTuples<T>>();
@@ -758,7 +860,7 @@ void TestNCHW16CMulNCKernel() {
 }
 
 template <paddle::operators::jit::KernelType KT, typename T, typename PlaceType>
-void TestLayerNormKernel() {
+void TestKernelLayerNormTuples() {
   VLOG(10) << "===== Test JITKernel " << jit::to_string(KT);
   const T epsilon = 9.99999975e-06;
   for (int n : {1, 2, 10}) {
@@ -797,11 +899,13 @@ void TestLayerNormKernel() {
 }
 
 template <paddle::operators::jit::KernelType KT, typename T, typename PlaceType>
-void TestCRFDecodingKernel() {
+void TestKernelCRFDecodingTuples() {
   VLOG(10) << "===== Test JITKernel " << jit::to_string(KT);
   constexpr int state_trans_base_idx = 2;
+  auto test_sizes = TestSizes();
+  test_sizes.erase(std::remove(test_sizes.begin(), test_sizes.end(), 1000));
   for (int seq_len : {1, 11, 17, 50}) {
-    for (int tag_num : TestSizes()) {
+    for (int tag_num : test_sizes) {
       auto ref = jit::GetRefer<KT, jit::CRFDecodingTuples<T>>();
       EXPECT_TRUE(ref != nullptr);
       int x_sz = seq_len * tag_num;
@@ -822,143 +926,76 @@ void TestCRFDecodingKernel() {
   }
 }
 
-// XYZNTuple
-TEST(JITKernel, kVMul) {
-  TestXYZNKernel<jit::kVMul, float, CPUPlace>();
-  TestXYZNKernel<jit::kVMul, double, CPUPlace>();
-}
-
-TEST(JITKernel, kVAdd) {
-  TestXYZNKernel<jit::kVAdd, float, CPUPlace>();
-  TestXYZNKernel<jit::kVAdd, double, CPUPlace>();
-}
-
-TEST(JITKernel, kVAddRelu) {
-  TestXYZNKernel<jit::kVAddRelu, float, CPUPlace>();
-  TestXYZNKernel<jit::kVAddRelu, double, CPUPlace>();
-}
-
-TEST(JITKernel, kVSub) {
-  TestXYZNKernel<jit::kVSub, float, CPUPlace>();
-  TestXYZNKernel<jit::kVSub, double, CPUPlace>();
-}
-
-// AXYNTuples
-TEST(JITKernel, kVScal) {
-  TestAXYNKernel<jit::kVScal, float, CPUPlace>();
-  TestAXYNKernel<jit::kVScal, double, CPUPlace>();
-}
-
-TEST(JITKernel, kVAddBias) {
-  TestAXYNKernel<jit::kVAddBias, float, CPUPlace>();
-  TestAXYNKernel<jit::kVAddBias, double, CPUPlace>();
-}
-
-// XRNTuples
-TEST(JITKernel, kHMax) {
-  TestXRNKernel<jit::kHMax, float, CPUPlace>();
-  TestXRNKernel<jit::kHMax, double, CPUPlace>();
-}
-
-TEST(JITKernel, kHSum) {
-  TestXRNKernel<jit::kHSum, float, CPUPlace>();
-  TestXRNKernel<jit::kHSum, double, CPUPlace>();
-}
-
-// XYNTuples
-TEST(JITKernel, kVRelu) {
-  TestXYNKernel<jit::kVRelu, float, CPUPlace>();
-  TestXYNKernel<jit::kVRelu, double, CPUPlace>();
-}
-
-TEST(JITKernel, kVIdentity) {
-  TestXYNKernel<jit::kVIdentity, float, CPUPlace>();
-  TestXYNKernel<jit::kVIdentity, double, CPUPlace>();
-}
-
-TEST(JITKernel, kVSquare) {
-  TestXYNKernel<jit::kVSquare, float, CPUPlace>();
-  TestXYNKernel<jit::kVSquare, double, CPUPlace>();
-}
-
-TEST(JITKernel, kVExp) {
-  TestXYNKernel<jit::kVExp, float, CPUPlace>();
-  TestXYNKernel<jit::kVExp, double, CPUPlace>();
-}
-
-TEST(JITKernel, kVSigmoid) {
-  TestXYNKernel<jit::kVSigmoid, float, CPUPlace>();
-  TestXYNKernel<jit::kVSigmoid, double, CPUPlace>();
-}
+#define TEST_CPU_KERNEL(test_tuple, kernel_type)                 \
+  TEST(JITKernel, kernel_type) {                                 \
+    TestKernel##test_tuple<jit::kernel_type, float, CPUPlace>(); \
+    TestKernel##test_tuple<jit::kernel_type, float, CPUPlace>(); \
+  }
 
-TEST(JITKernel, kVTanh) {
-  TestXYNKernel<jit::kVTanh, float, CPUPlace>();
-  TestXYNKernel<jit::kVTanh, double, CPUPlace>();
-}
+TEST_CPU_KERNEL(XYZNTuples, kVMul);
+TEST_CPU_KERNEL(XYZNTuples, kVAdd);
+TEST_CPU_KERNEL(XYZNTuples, kVAddRelu);
+TEST_CPU_KERNEL(XYZNTuples, kVSub);
 
-// LSTM
-TEST(JITKernel, kLSTMCtHt) {
-  TestLSTMKernel<jit::kLSTMCtHt, float, CPUPlace>();
-  TestLSTMKernel<jit::kLSTMCtHt, double, CPUPlace>();
-}
+TEST_CPU_KERNEL(AXYNTuples, kVScal);
+TEST_CPU_KERNEL(AXYNTuples, kVAddBias);
 
-TEST(JITKernel, kLSTMC1H1) {
-  TestLSTMKernel<jit::kLSTMC1H1, float, CPUPlace>();
-  TestLSTMKernel<jit::kLSTMC1H1, double, CPUPlace>();
-}
+TEST_CPU_KERNEL(XRNTuples, kHMax);
+TEST_CPU_KERNEL(XRNTuples, kHSum);
 
-// GRU
-TEST(JITKernel, kGRUH1) {
-  TestGRUKernel<jit::kGRUH1, float, CPUPlace>();
-  TestGRUKernel<jit::kGRUH1, double, CPUPlace>();
-}
+TEST_CPU_KERNEL(XYNTuples, kVRelu);
+TEST_CPU_KERNEL(XYNTuples, kVIdentity);
+TEST_CPU_KERNEL(XYNTuples, kVSquare);
+TEST_CPU_KERNEL(XYNTuples, kVExp);
+TEST_CPU_KERNEL(XYNTuples, kVSigmoid);
+TEST_CPU_KERNEL(XYNTuples, kVTanh);
 
-TEST(JITKernel, kGRUHtPart1) {
-  TestGRUKernel<jit::kGRUHtPart1, float, CPUPlace>();
-  TestGRUKernel<jit::kGRUHtPart1, double, CPUPlace>();
-}
+TEST_CPU_KERNEL(LSTMTuples, kLSTMCtHt);
+TEST_CPU_KERNEL(LSTMTuples, kLSTMC1H1);
 
-TEST(JITKernel, kGRUHtPart2) {
-  TestGRUKernel<jit::kGRUHtPart2, float, CPUPlace>();
-  TestGRUKernel<jit::kGRUHtPart2, double, CPUPlace>();
-}
+TEST_CPU_KERNEL(GRUTuples, kGRUH1);
+TEST_CPU_KERNEL(GRUTuples, kGRUHtPart1);
+TEST_CPU_KERNEL(GRUTuples, kGRUHtPart2);
 
-TEST(JITKernel, kSeqPool) {
-  TestSeqPoolKernel<jit::kSeqPool, float, CPUPlace>();
-  TestSeqPoolKernel<jit::kSeqPool, double, CPUPlace>();
-}
+TEST_CPU_KERNEL(NCHW16CMulNCTuples, kNCHW16CMulNC);
 
-TEST(JITKernel, kMatMul) {
-  TestMatMulKernel<jit::kMatMul, float, CPUPlace>();
-  TestMatMulKernel<jit::kMatMul, double, CPUPlace>();
-}
+TEST_CPU_KERNEL(SeqPoolTuples, kSeqPool);
+TEST_CPU_KERNEL(MatMulTuples, kMatMul);
+TEST_CPU_KERNEL(SoftmaxTuples, kSoftmax);
+TEST_CPU_KERNEL(EmbSeqPoolTuples, kEmbSeqPool);
+TEST_CPU_KERNEL(SgdTuples, kSgd);
+TEST_CPU_KERNEL(LayerNormTuples, kLayerNorm);
+TEST_CPU_KERNEL(CRFDecodingTuples, kCRFDecoding);
 
-TEST(JITKernel, kSoftmax) {
-  TestSoftmaxKernel<jit::kSoftmax, float, CPUPlace>();
-  TestSoftmaxKernel<jit::kSoftmax, double, CPUPlace>();
-}
+TEST(JITKernel_key, lstm) {
+  jit::lstm_attr_t attr1(8, jit::kVIdentity, jit::kVSigmoid, jit::kVTanh);
+  jit::lstm_attr_t attr2(9, jit::kVIdentity, jit::kVSigmoid, jit::kVTanh);
+  jit::lstm_attr_t attr3(9, jit::kVIdentity, jit::kVSigmoid, jit::kVTanh);
+  jit::lstm_attr_t attr4(9, jit::kVRelu, jit::kVSigmoid, jit::kVTanh);
 
-TEST(JITKernel, kEmbSeqPool) {
-  TestEmbSeqPoolKernel<jit::kEmbSeqPool, float, CPUPlace>();
-  TestEmbSeqPoolKernel<jit::kEmbSeqPool, double, CPUPlace>();
-}
+  auto key1 = jit::JitCodeKey<jit::lstm_attr_t>(attr1);
+  auto key2 = jit::JitCodeKey<jit::lstm_attr_t>(attr2);
+  auto key3 = jit::JitCodeKey<jit::lstm_attr_t>(attr3);
+  auto key4 = jit::JitCodeKey<jit::lstm_attr_t>(attr4);
 
-TEST(JITKernel, kNCHW16CMulNC) {
-  TestNCHW16CMulNCKernel<jit::kNCHW16CMulNC, float, CPUPlace>();
-  TestNCHW16CMulNCKernel<jit::kNCHW16CMulNC, double, CPUPlace>();
+  EXPECT_TRUE(key1 != key2);
+  EXPECT_TRUE(key2 == key3);
+  EXPECT_TRUE(key3 != key4);
 }
 
-TEST(JITKernel, kLayerNorm) {
-  TestLayerNormKernel<jit::kLayerNorm, float, paddle::platform::CPUPlace>();
-  TestLayerNormKernel<jit::kLayerNorm, double, paddle::platform::CPUPlace>();
-}
+TEST(JITKernel_key, gru) {
+  jit::gru_attr_t attr1(8, jit::kVSigmoid, jit::kVTanh);
+  jit::gru_attr_t attr2(9, jit::kVSigmoid, jit::kVTanh);
+  jit::gru_attr_t attr3(9, jit::kVSigmoid, jit::kVTanh);
+  jit::gru_attr_t attr4(9, jit::kVSigmoid, jit::kVIdentity);
 
-TEST(JITKernel, kCRFDecoding) {
-  TestCRFDecodingKernel<jit::kCRFDecoding, float, paddle::platform::CPUPlace>();
-  TestCRFDecodingKernel<jit::kCRFDecoding, double,
-                        paddle::platform::CPUPlace>();
-}
+  auto key1 = jit::JitCodeKey<jit::gru_attr_t>(attr1);
+  auto key2 = jit::JitCodeKey<jit::gru_attr_t>(attr2);
+  auto key3 = jit::JitCodeKey<jit::gru_attr_t>(attr3);
+  auto key4 = jit::JitCodeKey<jit::gru_attr_t>(attr4);
 
-TEST(JITKernel, pool) {
-  // TODO(TJ): add some test
+  EXPECT_TRUE(key1 != key2);
+  EXPECT_TRUE(key2 == key3);
+  EXPECT_TRUE(key3 != key4);
 }
+// TODO(TJ): add more test about key and pool
diff --git a/paddle/fluid/operators/optimizers/sgd_op.h b/paddle/fluid/operators/optimizers/sgd_op.h
index 98bae5e1d329005f9463fd7bb0751c44952dea88..c9c9f530fe846c1713ad176e05a377996d04470b 100644
--- a/paddle/fluid/operators/optimizers/sgd_op.h
+++ b/paddle/fluid/operators/optimizers/sgd_op.h
@@ -16,6 +16,7 @@ limitations under the License. */
 #include "paddle/fluid/framework/eigen.h"
 #include "paddle/fluid/framework/op_registry.h"
 #include "paddle/fluid/framework/selected_rows.h"
+#include "paddle/fluid/operators/jit/kernels.h"
 
 namespace paddle {
 namespace operators {
@@ -32,53 +33,57 @@ class SGDOpKernel : public framework::OpKernel<T> {
     if (param_var->IsType<framework::LoDTensor>()) {
       const auto *param = ctx.Input<framework::Tensor>("Param");
       auto *param_out = ctx.Output<framework::Tensor>("ParamOut");
-
       // Actually, all tensors are LoDTensor except SelectedRows.
       if (grad_var->IsType<framework::LoDTensor>()) {
-        param_out->mutable_data<T>(ctx.GetPlace());
         const auto *grad = ctx.Input<framework::Tensor>("Grad");
-
-        auto p = framework::EigenVector<T>::Flatten(*param);
-        auto g = framework::EigenVector<T>::Flatten(*grad);
-        auto o = framework::EigenVector<T>::Flatten(*param_out);
-        auto *lr = learning_rate->data<T>();
-
-        o = p - lr[0] * g;
+        auto sz = param_out->numel();
+        PADDLE_ENFORCE_EQ(param->numel(), sz);
+        PADDLE_ENFORCE_EQ(grad->numel(), sz);
+
+        jit::sgd_attr_t attr(1, sz, 1, sz, 1);
+        const T *lr = learning_rate->data<T>();
+        const T *param_data = param->data<T>();
+        const T *grad_data = grad->data<T>();
+        int64_t rows_idx = 0;
+        T *out_data = param_out->mutable_data<T>(ctx.GetPlace());
+
+        auto sgd =
+            jit::Get<jit::kSgd, jit::SgdTuples<T>, platform::CPUPlace>(attr);
+        sgd(lr, param_data, grad_data, &rows_idx, out_data, &attr);
       } else if (grad_var->IsType<framework::SelectedRows>()) {
         // TODO(qijun): In Sparse SGD operator, in-place update is enforced.
         // This manual optimization brings difficulty to track data dependency.
         // It's better to find a more elegant solution.
         PADDLE_ENFORCE_EQ(param, param_out);
         const auto *grad = ctx.Input<framework::SelectedRows>("Grad");
+        auto &grad_rows = grad->rows();
 
         // for distributed training, a sparse var may be empty,
         // just skip updating.
-        if (grad->rows().size() == 0) {
+        if (grad_rows.size() == 0) {
           return;
         }
 
-        auto grad_height = grad->height();
         auto out_dims = param_out->dims();
-        PADDLE_ENFORCE_EQ(grad_height, out_dims[0]);
-
+        PADDLE_ENFORCE_EQ(grad->height(), out_dims[0]);
         auto &grad_value = grad->value();
-        auto &grad_rows = grad->rows();
-
-        size_t grad_row_numel = grad_value.numel() / grad_rows.size();
-        PADDLE_ENFORCE_EQ(static_cast<int64_t>(grad_row_numel),
-                          param_out->numel() / grad_height);
-
-        auto *grad_data = grad_value.data<T>();
-        auto *out_data = param_out->data<T>();
-        auto *lr = learning_rate->data<T>();
-        for (size_t i = 0; i < grad_rows.size(); i++) {
-          PADDLE_ENFORCE(grad_rows[i] < grad_height,
-                         "Input rows index should less than height");
-          for (size_t j = 0; j < grad_row_numel; j++) {
-            out_data[grad_rows[i] * grad_row_numel + j] -=
-                lr[0] * grad_data[i * grad_row_numel + j];
-          }
-        }
+        const T *param_data = param->data<T>();
+        const T *grad_data = grad_value.data<T>();
+        const T *lr = learning_rate->data<T>();
+        const int64_t *rows_data = grad_rows.data();
+        T *out_data = param_out->mutable_data<T>(ctx.GetPlace());
+
+        jit::sgd_attr_t attr;
+        attr.param_height = out_dims[0];
+        attr.param_width = param_out->numel() / attr.param_height;
+        attr.grad_height = grad_rows.size();  // note: it is not grad->height()
+        attr.grad_width = grad_value.numel() / attr.grad_height;
+        attr.selected_rows_size = grad_rows.size();
+        PADDLE_ENFORCE_EQ(attr.grad_width, attr.param_width);
+
+        auto sgd =
+            jit::Get<jit::kSgd, jit::SgdTuples<T>, platform::CPUPlace>(attr);
+        sgd(lr, param_data, grad_data, rows_data, out_data, &attr);
       } else {
         PADDLE_THROW("Unsupported Variable Type of Grad");
       }
diff --git a/python/paddle/fluid/tests/unittests/test_sgd_op.py b/python/paddle/fluid/tests/unittests/test_sgd_op.py
index b46e4bfb86bd5dc9c74375693328f2506281be3e..162e6d1938c8174d342d8e4af1e4b6c424afc521 100644
--- a/python/paddle/fluid/tests/unittests/test_sgd_op.py
+++ b/python/paddle/fluid/tests/unittests/test_sgd_op.py
@@ -24,17 +24,28 @@ from op_test import OpTest
 class TestSGDOp(OpTest):
     def setUp(self):
         self.op_type = "sgd"
-        w = np.random.random((102, 105)).astype("float32")
-        g = np.random.random((102, 105)).astype("float32")
+        self.conf()
+        w = np.random.random((self.h, self.w)).astype("float32")
+        g = np.random.random((self.h, self.w)).astype("float32")
         lr = np.array([0.1]).astype("float32")
 
         self.inputs = {'Param': w, 'Grad': g, 'LearningRate': lr}
         self.outputs = {'ParamOut': w - lr * g}
 
+    def conf(self):
+        self.h = 102
+        self.w = 105
+
     def test_check_output(self):
         self.check_output()
 
 
+class TestSGDOpCase8X(TestSGDOp):
+    def conf(self):
+        self.h = 10
+        self.w = 64
+
+
 class TestSparseSGDOp(unittest.TestCase):
     def check_with_place(self, place):
         scope = core.Scope()
@@ -42,12 +53,12 @@ class TestSparseSGDOp(unittest.TestCase):
         # create and initialize Grad Variable   
         height = 10
         rows = [0, 4, 7]
-        row_numel = 12
+        self.conf()
 
         grad_selected_rows = scope.var('Grad').get_selected_rows()
         grad_selected_rows.set_height(height)
         grad_selected_rows.set_rows(rows)
-        np_array = np.ones((len(rows), row_numel)).astype("float32")
+        np_array = np.ones((len(rows), self.row_numel)).astype("float32")
         np_array[0, 0] = 2.0
         np_array[2, 8] = 4.0
 
@@ -56,7 +67,7 @@ class TestSparseSGDOp(unittest.TestCase):
 
         # create and initialize Param Variable
         param = scope.var('Param').get_tensor()
-        param_array = np.full((height, row_numel), 5.0).astype("float32")
+        param_array = np.full((height, self.row_numel), 5.0).astype("float32")
         param.set(param_array, place)
 
         # create and initialize LeraningRate Variable
@@ -98,6 +109,14 @@ class TestSparseSGDOp(unittest.TestCase):
         for place in places:
             self.check_with_place(place)
 
+    def conf(self):
+        self.row_numel = 12
+
+
+class TestSparseSGDOpCase8X(TestSparseSGDOp):
+    def conf(self):
+        self.row_numel = 16
+
 
 class TestSGDOpOptimizeSelectedRows(unittest.TestCase):
     def check_with_place(self, place):