diff --git a/paddle/fluid/operators/math/cpu_vec.h b/paddle/fluid/operators/math/cpu_vec.h
index 57726956cfba802183903b436c82b15c34d8fcc9..65b601fc6783c20da50ca7cfcb6316bb412bc4f4 100644
--- a/paddle/fluid/operators/math/cpu_vec.h
+++ b/paddle/fluid/operators/math/cpu_vec.h
@@ -54,7 +54,14 @@ inline void vec_scal(const int n, const T a, T* x) {
 #ifdef PADDLE_WITH_MKLML
 template <>
 inline void vec_exp<float>(const int n, const float* x, float* y) {
-  platform::dynload::vsExp(n, x, y);
+  constexpr int small_enough = 128;
+  if (n < small_enough) {
+    for (int i = 0; i < n; ++i) {
+      y[i] = std::exp(x[i]);
+    }
+  } else {
+    platform::dynload::vsExp(n, x, y);
+  }
 }
 
 template <>
@@ -128,6 +135,47 @@ inline void vec_scal<float, platform::avx512f>(const int n, const float a,
   vec_scal<float, platform::avx2>(n, a, x, y);
 }
 
+template <typename T, platform::cpu_isa_t isa = platform::isa_any>
+inline void vec_sum(const size_t n, const T* x, T* s) {
+  s[0] = x[0];
+  for (size_t i = 1; i < n; ++i) {
+    s[0] += x[i];
+  }
+}
+
+template <>
+inline void vec_sum<float, platform::avx>(const size_t n, const float* x,
+                                          float* s) {
+#ifdef __AVX__
+  constexpr unsigned int block = YMM_FLOAT_BLOCK;
+  if (n < block) {
+    vec_sum<float, platform::isa_any>(n, x, s);
+    return;
+  }
+
+  unsigned int i, end;
+  i = end = 0;
+  s[0] = 0.f;
+
+  end = n & ~(block - 1);
+  __m256 tmp = _mm256_setzero_ps();
+  for (i = 0; i < end; i += block) {
+    tmp = _mm256_add_ps(tmp, _mm256_load_ps(x + i));
+  }
+
+  __m256 hsum = _mm256_hadd_ps(tmp, tmp);
+  hsum = _mm256_add_ps(hsum, _mm256_permute2f128_ps(hsum, hsum, 0x1));
+  _mm_store_ss(s, _mm_hadd_ps(_mm256_castps256_ps128(hsum),
+                              _mm256_castps256_ps128(hsum)));
+
+  for (; i < n; i++) {
+    s[0] += x[i];
+  }
+#else
+  vec_sum<float, platform::isa_any>(n, x, s);
+#endif
+}
+
 template <typename T, platform::cpu_isa_t isa = platform::isa_any>
 inline void vec_bias_sub(const int n, const T a, const T* x, T* y) {
   for (int i = 0; i < n; ++i) {
@@ -242,6 +290,39 @@ inline void vec_cross<float, platform::avx512f>(const int n, const float* x,
   vec_cross<float, platform::avx>(n, x, y, z, out);
 }
 
+template <typename T, platform::cpu_isa_t isa = platform::isa_any>
+inline void vec_clip(const size_t n, const T a, const T* x, T* y) {
+  for (size_t i = 0; i < n; ++i) {
+    y[i] = x[i] < a ? a : x[i];
+  }
+}
+
+template <>
+inline void vec_clip<float, platform::avx>(const size_t n, const float a,
+                                           const float* x, float* y) {
+#ifdef __AVX__
+  constexpr unsigned int block = YMM_FLOAT_BLOCK;
+  if (n < block) {
+    vec_clip<float, platform::isa_any>(n, a, x, y);
+    return;
+  }
+
+  unsigned int i = 0, end = 0;
+  end = n & ~(block - 1);
+  __m256 threshold = _mm256_set1_ps(a);
+
+  for (i = 0; i < end; i += block) {
+    _mm256_storeu_ps(y + i, _mm256_max_ps(_mm256_loadu_ps(x + i), threshold));
+  }
+
+  for (; i < n; i++) {
+    y[i] = x[i] < a ? a : x[i];
+  }
+#else
+  vec_clip<float, platform::isa_any>(n, a, x, y);
+#endif
+}
+
 template <typename T, platform::cpu_isa_t isa = platform::isa_any>
 inline void vec_add_bias(const int n, const T a, const T* x, T* y) {
   for (int i = 0; i < n; ++i) {
diff --git a/paddle/fluid/operators/math/cpu_vec_test.cc b/paddle/fluid/operators/math/cpu_vec_test.cc
index 28eb9cadc9d4258bf4f8f71a06e029531e448014..04932a07094968d1984ea369c1e8c218c0d57fd2 100644
--- a/paddle/fluid/operators/math/cpu_vec_test.cc
+++ b/paddle/fluid/operators/math/cpu_vec_test.cc
@@ -65,12 +65,11 @@ void ref_relu(const int n, const T* x, T* y) {
 }
 
 template <typename T>
-void RandomVec(const int n, T* a) {
+void RandomVec(const int n, T* a, const T lower = static_cast<T>(-20.f),
+               const T upper = static_cast<T>(20.f)) {
   static unsigned int seed = 100;
   std::mt19937 rng(seed++);
   std::uniform_real_distribution<double> uniform_dist(0, 1);
-  const T lower = static_cast<T>(-20.f);
-  const T upper = static_cast<T>(20.f);
   for (int i = 0; i < n; ++i) {
     a[i] = static_cast<T>(uniform_dist(rng) * (upper - lower) + lower);
   }
@@ -144,6 +143,62 @@ TEST(CpuVecTest, relu) {
   TestAndBench<double>(30, vec_relu<double>, ref_relu<double>);
 }
 
+template <typename T>
+void compare_sum(size_t n, std::function<void(const size_t, const T*, T*)> tgt,
+                 std::function<void(const size_t, const T*, T*)> ref) {
+  std::vector<T> x(n);
+  T ytgt_data, yref_data;
+  RandomVec<T>(n, x.data(), static_cast<T>(-2), static_cast<T>(2));
+
+  const T* x_data = x.data();
+  tgt(n, x_data, &ytgt_data);
+  ref(n, x_data, &yref_data);
+  EXPECT_NEAR(ytgt_data, yref_data, 1e-3);
+}
+
+TEST(CpuVecTest, vec_sum) {
+  namespace platform = paddle::platform;
+  using namespace paddle::operators::math;  // NOLINT
+  for (size_t sz : {1, 2, 15, 16, 30, 32, 128, 200, 512}) {
+    compare_sum<float>(sz, vec_sum<float>, vec_sum<float, platform::isa_any>);
+    compare_sum<float>(sz, vec_sum<float, platform::avx>,
+                       vec_sum<float, platform::isa_any>);
+  }
+  compare_sum<double>(30U, vec_sum<double>, vec_sum<double, platform::isa_any>);
+}
+
+template <typename T>
+void compare_clip(
+    size_t n, T threshold,
+    std::function<void(const size_t, const T, const T*, T*)> tgt,
+    std::function<void(const size_t, const T, const T*, T*)> ref) {
+  std::vector<T> x(n);
+  std::vector<T> ytgt(n), yref(n);
+  RandomVec<T>(n, x.data(), static_cast<T>(-2), static_cast<T>(2));
+
+  const T* x_data = x.data();
+  T* yref_data = yref.data();
+  T* ytgt_data = ytgt.data();
+  tgt(n, threshold, x_data, ytgt_data);
+  ref(n, threshold, x_data, yref_data);
+  for (int i = 0; i < n; ++i) {
+    EXPECT_NEAR(ytgt_data[i], yref_data[i], 1e-3);
+  }
+}
+
+TEST(CpuVecTest, vec_clip) {
+  namespace platform = paddle::platform;
+  using namespace paddle::operators::math;  // NOLINT
+  for (size_t sz : {1, 2, 15, 16, 30, 32, 128, 200, 512}) {
+    compare_clip<float>(sz, -4.f, vec_clip<float>,
+                        vec_clip<float, platform::isa_any>);
+    compare_clip<float>(sz, -1.1f, vec_clip<float, platform::avx>,
+                        vec_clip<float, platform::isa_any>);
+  }
+  compare_clip<double>(30U, 1.0, vec_clip<double>,
+                       vec_clip<double, platform::isa_any>);
+}
+
 template <typename T>
 void TestInplace(const int n, std::function<void(const int, const T*, T*)> tgt,
                  std::function<void(const int, const T*, T*)> ref) {
diff --git a/paddle/fluid/operators/math/softmax_impl.h b/paddle/fluid/operators/math/softmax_impl.h
index 6f6f33345f5336a8b8ff100c0286914ef629283f..30790c9c1a98e9cc1bc81e6941d7abfc604e8a48 100644
--- a/paddle/fluid/operators/math/softmax_impl.h
+++ b/paddle/fluid/operators/math/softmax_impl.h
@@ -17,6 +17,8 @@ limitations under the License. */
 #include "paddle/fluid/framework/eigen.h"
 #include "paddle/fluid/framework/tensor.h"
 #include "paddle/fluid/operators/jit/kernels.h"
+#include "paddle/fluid/operators/math/cpu_vec.h"
+#include "paddle/fluid/platform/cpu_info.h"
 
 namespace paddle {
 namespace operators {
@@ -34,16 +36,15 @@ struct ValueClip {
   }
 };
 
-template <typename DeviceContext, typename T, bool is_test, typename Enable>
-void SoftmaxFunctor<DeviceContext, T, is_test, Enable>::operator()(
-    const DeviceContext& context, const int axis_dim,
-    const framework::Tensor* X, framework::Tensor* Y) {
+template <typename DeviceContext, typename T, bool is_test>
+void SoftmaxEigen(const DeviceContext& context, const int axis_dim,
+                  const framework::Tensor* X, framework::Tensor* Y) {
+  constexpr int kBatchDim = 0;
+  constexpr int kClassDim = 1;
+
   auto logits = EigenMatrix<T>::From(*X);
   auto softmax = EigenMatrix<T>::From(*Y);
 
-  const int kBatchDim = 0;
-  const int kClassDim = 1;
-
   const int batch_size = logits.dimension(kBatchDim);
   const int num_classes = logits.dimension(kClassDim);
   const int num_remain = num_classes / axis_dim;
@@ -70,12 +71,58 @@ void SoftmaxFunctor<DeviceContext, T, is_test, Enable>::operator()(
                                                  .broadcast(one_axis));
 }
 
+template <typename DeviceContext, typename T, bool is_test, typename Enable>
+void SoftmaxFunctor<DeviceContext, T, is_test, Enable>::operator()(
+    const DeviceContext& context, const int axis_dim,
+    const framework::Tensor* X, framework::Tensor* Y) {
+  SoftmaxEigen<DeviceContext, T, is_test>(context, axis_dim, X, Y);
+}
+
 template <class DeviceContext>
 using enable_if_CPU = typename std::enable_if<
     std::is_same<DeviceContext, platform::CPUDeviceContext>::value>::type;
 
+template <typename DeviceContext, typename T, bool is_test>
+class SoftmaxFunctor<DeviceContext, T, is_test, enable_if_CPU<DeviceContext>> {
+ public:
+  void operator()(const DeviceContext& context, const int axis_dim,
+                  const framework::Tensor* X, framework::Tensor* Y) {
+    auto in_dims = X->dims();
+    constexpr int kBatchDim = 0;
+    constexpr int kClassDim = 1;
+
+    const int num_classes = in_dims[kClassDim];
+    const int batch_size = in_dims[kBatchDim];
+    const int num_remain = num_classes / axis_dim;
+
+    if (num_remain == 1 && platform::MayIUse(platform::avx)) {
+      const T* in_data = X->data<T>();
+      T* out_data = Y->data<T>();
+      for (int bs = 0; bs < batch_size; ++bs) {
+        T max_val = *std::max_element(in_data, in_data + num_classes);
+        max_val *= static_cast<T>(-1);
+        vec_add_bias<T, platform::avx>(num_classes, max_val, in_data, out_data);
+        vec_clip<T, platform::avx>(num_classes, static_cast<T>(-64), out_data,
+                                   out_data);
+        vec_exp<T>(num_classes, out_data, out_data);
+
+        T sum = 0;
+        vec_sum<T, platform::avx>(num_classes, out_data, &sum);
+        sum = static_cast<T>(1) / sum;
+        vec_scal<T, platform::avx>(num_classes, sum, out_data, out_data);
+
+        in_data += num_classes;
+        out_data += num_classes;
+      }
+    } else {
+      SoftmaxEigen<DeviceContext, T, is_test>(context, axis_dim, X, Y);
+    }
+  }
+};
+
 template <typename DeviceContext>
 class SoftmaxFunctor<DeviceContext, float, true, enable_if_CPU<DeviceContext>> {
+ public:
   void operator()(const DeviceContext& context, const int axis_dim,
                   const framework::Tensor* X, framework::Tensor* Y) {
     auto in_dims = X->dims();