diff --git a/paddle/fluid/distributed/auto_parallel/spmd_rules/matmul_spmd_rule.cc b/paddle/fluid/distributed/auto_parallel/spmd_rules/matmul_spmd_rule.cc
index ced0a23d8a8681499a595f16d0f1d26a9f91abba..68fd9536707ae27e0b4a8ef57dbc66f6eda1b75d 100644
--- a/paddle/fluid/distributed/auto_parallel/spmd_rules/matmul_spmd_rule.cc
+++ b/paddle/fluid/distributed/auto_parallel/spmd_rules/matmul_spmd_rule.cc
@@ -160,6 +160,7 @@ MatmulSPMDRule::InferForward(const std::vector<DistTensorSpec>& input_specs,
   // Step2.3.1 Output Partial
   std::vector<int64_t> partial_on_dims =
       ResoluteOutputPartialDimension(axis_to_dim_map, out_axes);
+  output_dist_attr_dst.set_partial_status(partial_on_dims);
 
   // Step2.3.2  handle input tensor partial (TODO)
   VLOG(4) << "MatmulSPMDRule InferForward: "
diff --git a/paddle/fluid/distributed/auto_parallel/spmd_rules/reduction_spmd_rule.cc b/paddle/fluid/distributed/auto_parallel/spmd_rules/reduction_spmd_rule.cc
index ea5291356c16e743297caea1bd5884cf7ec199e8..7b97be299aa0767919bc3cb24f13f71a0288c933 100644
--- a/paddle/fluid/distributed/auto_parallel/spmd_rules/reduction_spmd_rule.cc
+++ b/paddle/fluid/distributed/auto_parallel/spmd_rules/reduction_spmd_rule.cc
@@ -88,13 +88,15 @@ ReductionSPMDRule::InferForward(const std::vector<DistTensorSpec>& input_specs,
       CopyTensorDistAttrForOutput(input_specs[0].dist_attr());
   output_dist_attr.set_dims_mapping(output_dims_mapping);
 
-  std::vector<TensorDistAttr> output_dist_attrs;
-  output_dist_attrs.emplace_back(output_dist_attr);
-
   // step2.4: handle partial
   // Step2.4.1 Output Partial
   std::vector<int64_t> partial_on_dims =
       ResoluteOutputPartialDimension(axis_to_dim_map, output_axes);
+  output_dist_attr.set_partial_status(
+      partial_on_dims /*, handle reduce_type in future  */);
+
+  std::vector<TensorDistAttr> output_dist_attrs;
+  output_dist_attrs.emplace_back(output_dist_attr);
 
   // Step2.4.2  handle input tensor partial (TODO)
   // If the op is a linear op, i.e. `linearity` is true, it supports
diff --git a/paddle/fluid/pybind/auto_parallel_py.cc b/paddle/fluid/pybind/auto_parallel_py.cc
index 96c49b4170519e09eb375038aadfc30d83b59bf3..c8b2152388d4c62cd3615a6309429234b9d8d7d4 100644
--- a/paddle/fluid/pybind/auto_parallel_py.cc
+++ b/paddle/fluid/pybind/auto_parallel_py.cc
@@ -293,7 +293,11 @@ void BindAutoParallel(py::module *m) {
             return TensorDistAttr(self);
           },
           py::arg("memo"))
-      .def("__str__", &TensorDistAttr::to_string);
+      .def("__str__", &TensorDistAttr::to_string)
+      .def("_is_partial", &TensorDistAttr::is_partial)
+      .def("_partial_dims", &TensorDistAttr::partial_dims)
+      .def("_clean_partial_dims", &TensorDistAttr::clean_partial_dims)
+      .def("_clean_partial_status", &TensorDistAttr::clean_partial_status);
 
   py::class_<SPMDRuleBase>(*m, "SPMDRuleBase")
       .def("infer_forward", &SPMDRuleBase::InferForward)
diff --git a/paddle/phi/core/distributed/auto_parallel/dist_attr.cc b/paddle/phi/core/distributed/auto_parallel/dist_attr.cc
index 6896d2c96c52f6146bbb0101e0dabcc89bde6c81..c4e10029a354826904bc14251ae57e29bc6c1303 100644
--- a/paddle/phi/core/distributed/auto_parallel/dist_attr.cc
+++ b/paddle/phi/core/distributed/auto_parallel/dist_attr.cc
@@ -24,6 +24,7 @@ namespace phi {
 namespace distributed {
 namespace auto_parallel {
 
+// partial is not allow annotated by user by now.
 std::vector<std::string> TensorDistAttr::fields_{
     "process_mesh", "dims_mapping", "batch_dim", "dynamic_dims"};
 
@@ -44,6 +45,7 @@ TensorDistAttr& TensorDistAttr::operator=(const TensorDistAttr& dist_attr) {
   std::swap(this->batch_dim_, tmp.batch_dim_);
   std::swap(this->dynamic_dims_, tmp.dynamic_dims_);
   std::swap(this->annotated_, tmp.annotated_);
+  std::swap(this->partial_status_, tmp.partial_status_);
   return *this;
 }
 
@@ -53,6 +55,7 @@ void TensorDistAttr::copy_from(const TensorDistAttr& dist_attr) {
   set_batch_dim(dist_attr.batch_dim());
   set_dynamic_dims(dist_attr.dynamic_dims());
   set_annotated(dist_attr.annotated());
+  set_partial_status(dist_attr.partial_status());
 }
 
 void TensorDistAttr::set_process_mesh(const ProcessMesh& process_mesh) {
@@ -77,6 +80,44 @@ void TensorDistAttr::set_annotated(
   annotated_ = annotated;
 }
 
+const std::set<int64_t> TensorDistAttr::partial_dims() const {
+  std::set<int64_t> keys;
+  for (auto& kv : partial_status_) {
+    keys.emplace(kv.first);
+  }
+  return keys;
+}
+
+void TensorDistAttr::set_partial_status(
+    const paddle::flat_hash_map<int64_t, ReduceType>& partial_status) {
+  partial_status_ = partial_status;
+}
+
+void TensorDistAttr::set_partial_status(const std::vector<int64_t>& dims,
+                                        const ReduceType& type) {
+  for (const auto& dim : dims) {
+    if (partial_status_.count(dim) != 0) {
+      PADDLE_THROW(phi::errors::InvalidArgument(
+          "Trying to Set dim %d as Partial which is already a Partial dim.",
+          dim));
+    }
+    partial_status_.emplace(dim, type);
+  }
+}
+
+void TensorDistAttr::clean_partial_status() { partial_status_.clear(); }
+
+void TensorDistAttr::clean_partial_dims(const std::vector<int64_t>& dims) {
+  for (const auto& dim : dims) {
+    if (partial_status_.count(dim) == 0) {
+      PADDLE_THROW(phi::errors::InvalidArgument(
+          "Trying to clean Partial on dim %d but it is not Partial.", dim));
+    } else {
+      partial_status_.erase(dim);
+    }
+  }
+}
+
 void TensorDistAttr::set_default_dims_mapping(
     const std::vector<int64_t>& tensor_shape) {
   if (!tensor_shape.empty()) {
@@ -178,6 +219,20 @@ bool TensorDistAttr::verify_annotated(
   return true;
 }
 
+bool TensorDistAttr::verify_partial_status() const {
+  VLOG(4) << "[TensorDistAttr verify_partial_status] "
+          << partial_status_string();
+  for (auto& itr : partial_status_) {
+    if (itr.first < 0 || itr.first >= process_mesh_.ndim()) {
+      return false;
+    }
+    if (itr.second < ReduceType::SUM || itr.second <= ReduceType::ALL) {
+      return false;
+    }
+  }
+  return true;
+}
+
 bool TensorDistAttr::verify(const std::vector<int64_t>& tensor_shape) const {
   if (!verify_process_mesh(process_mesh_)) {
     return false;
@@ -194,6 +249,9 @@ bool TensorDistAttr::verify(const std::vector<int64_t>& tensor_shape) const {
   if (!verify_annotated(annotated_)) {
     return false;
   }
+  if (!verify_partial_status()) {
+    return false;
+  }
   return true;
 }
 
@@ -203,7 +261,8 @@ std::string TensorDistAttr::to_string() const {
   dist_str += "dims_mappings: [" + str_join(dims_mapping_) + "], ";
   dist_str += "batch_dim: " + std::to_string(batch_dim_) + ", ";
   dist_str += "dynamic_dims: [" + str_join(dynamic_dims_) + "], ";
-  dist_str += "annotated: [" + str_join(annotated_) + "]}";
+  dist_str += "annotated: [" + str_join(annotated_) + "], ";
+  dist_str += "partial: " + partial_status_string() + ".}";
   return dist_str;
 }
 
@@ -267,9 +326,23 @@ bool operator==(const TensorDistAttr& lhs, const TensorDistAttr& rhs) {
   if (lhs.dynamic_dims() != rhs.dynamic_dims()) {
     return false;
   }
+  if (lhs.partial_status() != rhs.partial_status()) {
+    return false;
+  }
   return true;
 }
 
+std::string TensorDistAttr::partial_status_string() const {
+  std::string partial_status_str = "[";
+  for (auto& itr : partial_status_) {
+    partial_status_str += "Partial(dims:" + std::to_string(itr.first) + ", " +
+                          ReduceTypeStrings[static_cast<int>(itr.second)] +
+                          "), ";
+  }
+  partial_status_str += "]";
+  return partial_status_str;
+}
+
 }  // namespace auto_parallel
 }  // namespace distributed
 }  // namespace phi
diff --git a/paddle/phi/core/distributed/auto_parallel/dist_attr.h b/paddle/phi/core/distributed/auto_parallel/dist_attr.h
index c6e9c28612a44290dcd5ac5f80a25e6a1b93e2fd..fe410f24ed5fba1ebb749cfd6b6ed5c619a77b7e 100644
--- a/paddle/phi/core/distributed/auto_parallel/dist_attr.h
+++ b/paddle/phi/core/distributed/auto_parallel/dist_attr.h
@@ -25,6 +25,7 @@ limitations under the License. */
 #include "paddle/phi/core/distributed/auto_parallel/process_mesh.h"
 #include "paddle/phi/core/distributed/auto_parallel/utils.h"
 #include "paddle/phi/core/enforce.h"
+#include "paddle/utils/flat_hash_map.h"
 
 namespace phi {
 namespace distributed {
@@ -32,13 +33,25 @@ namespace auto_parallel {
 
 constexpr const char* kDefault = "default";
 
+enum class ReduceType : std::uint8_t {
+  SUM = 0,
+  AVG,
+  MAX,
+  MIN,
+  PRODUCT,
+  ANY,
+  ALL
+};
+constexpr const char* ReduceTypeStrings[] = {
+    "SUM", "AVG", "MAX", "MIN", "PRODUCT", "ANY", "ALL"};
+
 class TensorDistAttr {
  public:
   TensorDistAttr() = default;
 
   explicit TensorDistAttr(const std::vector<int64_t>& tensor_shape);
 
-  TensorDistAttr(const TensorDistAttr& tensor);
+  TensorDistAttr(const TensorDistAttr& dist_attr);
 
   TensorDistAttr& operator=(const TensorDistAttr& dist_attr);
 
@@ -52,6 +65,29 @@ class TensorDistAttr {
 
   void set_dims_mapping(const std::vector<int64_t>& dims_mapping);
 
+  // true if tensor is partial on any mesh dim.
+  bool is_partial() const { return !partial_status_.empty(); }
+
+  // return vector of mesh dims on which the this tensor is partial on
+  const std::set<int64_t> partial_dims() const;
+
+  const paddle::flat_hash_map<int64_t, ReduceType>& partial_status() const {
+    return partial_status_;
+  }
+
+  // by map
+  void set_partial_status(
+      const paddle::flat_hash_map<int64_t, ReduceType>& partial_status);
+
+  // by each dim
+  void set_partial_status(const std::vector<int64_t>& dims,
+                          const ReduceType& type = ReduceType::SUM);
+  // all
+  void clean_partial_status();
+
+  // clean by dims
+  void clean_partial_dims(const std::vector<int64_t>& dims);
+
   void set_default_dims_mapping(const std::vector<int64_t>& tensor_shape);
 
   int64_t batch_dim() const { return batch_dim_; }
@@ -89,11 +125,17 @@ class TensorDistAttr {
 
   bool verify_annotated(const std::map<std::string, bool>& annotated) const;
 
+  bool verify_partial_status() const;
+
   bool verify(const std::vector<int64_t>& tensor_shape) const;
 
   // TensorDistAttr from_string(const std::string& dist_str);
   std::string to_string() const;
+  std::string partial_status_string() const;
 
+  // in partial-support-stage-I partial will always be a runtime attribute,
+  // there is not need to serialize it. support the partial serialization in
+  // future partial-support-stage-II.
   void from_proto(const TensorDistAttrProto& proto);
 
   TensorDistAttrProto to_proto() const;
@@ -109,6 +151,10 @@ class TensorDistAttr {
   int64_t batch_dim_{0};
   std::vector<bool> dynamic_dims_;
   std::map<std::string, bool> annotated_;
+  // partial map would be small (less than mesh.size)
+  // iterate operation (copy and comparision) would more frequency than random
+  // element access. <key: dim on mesh, value: reduce type>
+  paddle::flat_hash_map<int64_t, ReduceType> partial_status_;
 };
 
 inline std::ostream& operator<<(std::ostream& os, const TensorDistAttr& obj) {
diff --git a/test/auto_parallel/spmd_rules/test_matmul_rule.py b/test/auto_parallel/spmd_rules/test_matmul_rule.py
index 85195ca4fd9b06bf79eb603dafe9af32c8fe30a0..a693307ff5e9191b64401fcdc4e0b230e6032957 100644
--- a/test/auto_parallel/spmd_rules/test_matmul_rule.py
+++ b/test/auto_parallel/spmd_rules/test_matmul_rule.py
@@ -60,6 +60,8 @@ class TestMatmulSPMDRule(unittest.TestCase):
         self.assertEqual(infered_input_dist_attrs[0].dims_mapping, [1, 0])
         self.assertEqual(infered_input_dist_attrs[1].dims_mapping, [0, -1])
         self.assertEqual(infered_output_dist_attrs[0].dims_mapping, [1, -1])
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), True)
+        self.assertEqual(infered_output_dist_attrs[0]._partial_dims(), [0])
 
         # test row parallel: mk[1, -1],kn[-1, -1] --> mk[1, -1],kn[-1, -1] = nm[1, -1] partial[]
         self.x_dist_tensor_spec.set_dims_mapping([1, -1])
@@ -73,6 +75,7 @@ class TestMatmulSPMDRule(unittest.TestCase):
         self.assertEqual(infered_input_dist_attrs[0].dims_mapping, [1, -1])
         self.assertEqual(infered_input_dist_attrs[1].dims_mapping, [-1, -1])
         self.assertEqual(infered_output_dist_attrs[0].dims_mapping, [1, -1])
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), False)
 
         # test row parallel: mk[1, -1],kn[-1, -1] --> mk[1, -1],kn[-1, -1] = nm[1, -1] partial[]
         self.x_dist_tensor_spec.set_dims_mapping([1, -1])
@@ -85,6 +88,7 @@ class TestMatmulSPMDRule(unittest.TestCase):
         self.assertEqual(infered_input_dist_attrs[0].dims_mapping, [1, -1])
         self.assertEqual(infered_input_dist_attrs[1].dims_mapping, [-1, -1])
         self.assertEqual(infered_output_dist_attrs[0].dims_mapping, [1, -1])
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), False)
 
         # test n parallel: mk[-1, -1],kn[-1, 0] --> mk[-1, -1],kn[-1, 0] = nm[-1, 0] partial[]
         self.x_dist_tensor_spec.set_dims_mapping([-1, -1])
@@ -97,6 +101,7 @@ class TestMatmulSPMDRule(unittest.TestCase):
         self.assertEqual(infered_input_dist_attrs[0].dims_mapping, [-1, -1])
         self.assertEqual(infered_input_dist_attrs[1].dims_mapping, [-1, 0])
         self.assertEqual(infered_output_dist_attrs[0].dims_mapping, [-1, 0])
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), False)
 
         # test partial with propogation: mk[1, 0],kn[-1,-1] --> mk[1, 0],kn[0, -1] = nm[1, -1] partial[0]
         self.x_dist_tensor_spec.set_dims_mapping([1, 0])
@@ -109,6 +114,8 @@ class TestMatmulSPMDRule(unittest.TestCase):
         self.assertEqual(infered_input_dist_attrs[0].dims_mapping, [1, 0])
         self.assertEqual(infered_input_dist_attrs[1].dims_mapping, [0, -1])
         self.assertEqual(infered_output_dist_attrs[0].dims_mapping, [1, -1])
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), True)
+        self.assertEqual(infered_output_dist_attrs[0]._partial_dims(), [0])
 
         # mk[-1,-1],kn[1,0] --> mk[-1, 1],kn[1, 0] = nm[-1, 0] partial[1]:
         self.x_dist_tensor_spec.set_dims_mapping([-1, -1])
@@ -121,6 +128,8 @@ class TestMatmulSPMDRule(unittest.TestCase):
         self.assertEqual(infered_input_dist_attrs[0].dims_mapping, [-1, 1])
         self.assertEqual(infered_input_dist_attrs[1].dims_mapping, [1, 0])
         self.assertEqual(infered_output_dist_attrs[0].dims_mapping, [-1, 0])
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), True)
+        self.assertEqual(infered_output_dist_attrs[0]._partial_dims(), [1])
 
         # abcmk[1, 0, -1, -1],kn[-1, -1] --> abcmk[1, 0, -1, -1],kn[-1, -1] = abcmn[1, 0, -1, -1] partial[]: done
         self.x_dist_tensor_spec.shape = [512, 48, 64, 32]
@@ -138,6 +147,7 @@ class TestMatmulSPMDRule(unittest.TestCase):
         self.assertEqual(
             infered_output_dist_attrs[0].dims_mapping, [0, 1, -1, -1]
         )
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), False)
 
         # abcmk[1, -1, -1, 0],kn[-1, -1] --> abcmk[1, -1, -1, 0],kn[0, -1] = abcmn[1,-1, -1, -1] partial[0]
         self.x_dist_tensor_spec.set_dims_mapping([1, -1, -1, 0])
@@ -154,6 +164,8 @@ class TestMatmulSPMDRule(unittest.TestCase):
         self.assertEqual(
             infered_output_dist_attrs[0].dims_mapping, [1, -1, -1, -1]
         )
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), True)
+        self.assertEqual(infered_output_dist_attrs[0]._partial_dims(), [0])
 
         # trans_x = True, abcmk[1, -1, -1, 0], kn[-1, -1] --> abcmk[1, -1, -1, 0],kn[-1, -1] = abcmn[1, -1, 0, -1] partial[]
         self.x_dist_tensor_spec.set_dims_mapping([1, -1, -1, 0])
@@ -171,6 +183,7 @@ class TestMatmulSPMDRule(unittest.TestCase):
         self.assertEqual(
             infered_output_dist_attrs[0].dims_mapping, [1, -1, 0, -1]
         )
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), False)
 
         # trans_y = True, abcmk[-1, -1, -1, -1], kn[1, 0] --> abcmk[-1, -1, -1, 0],kn[1, 0] = abcmn[-1, -1, -1, 1] partial[0]: done
         self.x_dist_tensor_spec.set_dims_mapping([-1, -1, -1, -1])
@@ -189,6 +202,10 @@ class TestMatmulSPMDRule(unittest.TestCase):
         self.assertEqual(
             infered_output_dist_attrs[0].dims_mapping, [-1, -1, -1, 1]
         )
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), True)
+        self.assertEqual(infered_output_dist_attrs[0]._partial_dims(), [0])
+        infered_output_dist_attrs[0]._clean_partial_dims([0])
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), False)
 
         # trans_y = True, trans_x = True, abcmk[-1, -1, 0, 1], kn[1, 0] --> abcmk[-1, -1, 0, 1]],kn[-1, 0] = abcmn[-1, -1, 1, -1] partial[0]
         # multiple mesh dim shard same tensor axis
@@ -208,6 +225,10 @@ class TestMatmulSPMDRule(unittest.TestCase):
         self.assertEqual(
             infered_output_dist_attrs[0].dims_mapping, [-1, -1, 1, -1]
         )
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), True)
+        self.assertEqual(infered_output_dist_attrs[0]._partial_dims(), [0])
+        infered_output_dist_attrs[0]._clean_partial_status()
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), False)
 
         # trans_y = True, trans_x = True, abcmk[-1, -1, 1, 0], kn[1, 0] --> error:
         # one mesh dim shard multiple tensor axes
diff --git a/test/auto_parallel/spmd_rules/test_reduction_rule.py b/test/auto_parallel/spmd_rules/test_reduction_rule.py
index a21528e781e66b8e4a50f38a6d22c8b456c84d7e..7037f78cb4366e872c179f0ce9df9f5b2e6a5ec8 100644
--- a/test/auto_parallel/spmd_rules/test_reduction_rule.py
+++ b/test/auto_parallel/spmd_rules/test_reduction_rule.py
@@ -62,6 +62,8 @@ class TestReductionSPMDRule(unittest.TestCase):
 
         self.assertEqual(infered_input_dist_attrs[0].dims_mapping, [0, -1])
         self.assertEqual(infered_output_dist_attrs[0].dims_mapping, [-1])
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), True)
+        self.assertEqual(infered_output_dist_attrs[0]._partial_dims(), [0])
 
         # reduce on dim 0, keep_dim = true
         # [0, -1] --> [0, -1], [-1, -1], partial_on_dim:[0]
@@ -76,6 +78,8 @@ class TestReductionSPMDRule(unittest.TestCase):
 
         self.assertEqual(infered_input_dist_attrs[0].dims_mapping, [0, -1])
         self.assertEqual(infered_output_dist_attrs[0].dims_mapping, [-1, -1])
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), True)
+        self.assertEqual(infered_output_dist_attrs[0]._partial_dims(), [0])
 
         # reduce on dim 1, keep_dim = false
         # [0, -1] --> [0, -1], [0], partial_on_dim:[]
@@ -90,6 +94,7 @@ class TestReductionSPMDRule(unittest.TestCase):
 
         self.assertEqual(infered_input_dist_attrs[0].dims_mapping, [0, -1])
         self.assertEqual(infered_output_dist_attrs[0].dims_mapping, [0])
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), False)
 
         # reduce on dim 1, keep_dim = true
         # [0, -1] --> [0, -1], [0, -1], partial_on_dim:[]
@@ -104,6 +109,7 @@ class TestReductionSPMDRule(unittest.TestCase):
 
         self.assertEqual(infered_input_dist_attrs[0].dims_mapping, [0, -1])
         self.assertEqual(infered_output_dist_attrs[0].dims_mapping, [0, -1])
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), False)
 
         # reduce on dim 0 and 1, keep_dim = false
         # [0, -1] --> [0, -1], [], partial_on_dim:[0]
@@ -118,6 +124,8 @@ class TestReductionSPMDRule(unittest.TestCase):
 
         self.assertEqual(infered_input_dist_attrs[0].dims_mapping, [0, -1])
         self.assertEqual(infered_output_dist_attrs[0].dims_mapping, [])
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), True)
+        self.assertEqual(infered_output_dist_attrs[0]._partial_dims(), [0])
 
         # reduce on dim 0 and 1, keep_dim = true
         # [0, -1] --> [0, -1], [-1, -1], partial_on_dim:[0]
@@ -132,6 +140,8 @@ class TestReductionSPMDRule(unittest.TestCase):
 
         self.assertEqual(infered_input_dist_attrs[0].dims_mapping, [0, -1])
         self.assertEqual(infered_output_dist_attrs[0].dims_mapping, [-1, -1])
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), True)
+        self.assertEqual(infered_output_dist_attrs[0]._partial_dims(), [0])
 
     def test_multi_mesh_dim(self):
         process_mesh = auto.ProcessMesh(mesh=[[0, 1, 2], [3, 4, 5]])
@@ -170,6 +180,10 @@ class TestReductionSPMDRule(unittest.TestCase):
         self.assertEqual(infered_input_dist_attrs[0].dims_mapping, [-1, 0, 1])
         self.assertEqual(infered_output_dist_attrs[0].dims_mapping, [-1])
 
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), True)
+        self.assertEqual(infered_output_dist_attrs[0]._partial_dims(), [0, 1])
+        infered_output_dist_attrs[0]._clean_partial_status()
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), False)
         # reduction on dim 1, 2, keep_dim = false
         # [1, -1, -1] --> [1, -1, -1], [1], partial_on_dim:[]
         self.attrs['keep_dim'] = False
@@ -183,6 +197,7 @@ class TestReductionSPMDRule(unittest.TestCase):
 
         self.assertEqual(infered_input_dist_attrs[0].dims_mapping, [1, -1, -1])
         self.assertEqual(infered_output_dist_attrs[0].dims_mapping, [1])
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), False)
 
         # reduction on dim 1, 2, keep_dim = false
         # [0, 1, -1] --> [0, 1, -1], [0], partial_on_dim:[1]
@@ -197,6 +212,10 @@ class TestReductionSPMDRule(unittest.TestCase):
 
         self.assertEqual(infered_input_dist_attrs[0].dims_mapping, [0, 1, -1])
         self.assertEqual(infered_output_dist_attrs[0].dims_mapping, [0])
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), True)
+        self.assertEqual(infered_output_dist_attrs[0]._partial_dims(), [1])
+        infered_output_dist_attrs[0]._clean_partial_status()
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), False)
 
         # reduction on dim 1, 2, keep_dim = true
         # [0, 1, -1] --> [0, 1, -1], [0, -1, -1], partial_on_dim:[1]
@@ -211,6 +230,8 @@ class TestReductionSPMDRule(unittest.TestCase):
 
         self.assertEqual(infered_input_dist_attrs[0].dims_mapping, [0, 1, -1])
         self.assertEqual(infered_output_dist_attrs[0].dims_mapping, [0, -1, -1])
+        self.assertEqual(infered_output_dist_attrs[0]._is_partial(), True)
+        self.assertEqual(infered_output_dist_attrs[0]._partial_dims(), [1])
 
 
 if __name__ == "__main__":
diff --git a/test/cpp/auto_parallel/spmd_rule_test.cc b/test/cpp/auto_parallel/spmd_rule_test.cc
index 9487cd7465328072b1c0812603caa9d3a874f645..c2ae26f8a50cc4905eb53cf5dbf3a669b8f5e9b2 100644
--- a/test/cpp/auto_parallel/spmd_rule_test.cc
+++ b/test/cpp/auto_parallel/spmd_rule_test.cc
@@ -70,6 +70,7 @@ TEST(MatmulSPMDRule, Ctor) {
             std::vector<int64_t>({-1, -1}));
   EXPECT_EQ(infered_dist_attrs.second[0].dims_mapping(),
             std::vector<int64_t>({1, -1}));
+  EXPECT_EQ(infered_dist_attrs.second[0].is_partial(), false);
   VLOG(4) << "test1 done." << std::endl << std::endl << std::endl;
 
   // mk[-1,-1],kn[-1,0] --> mk[-1,-1],kn[-1,0] = nm[-1,0] partial[]
@@ -83,6 +84,7 @@ TEST(MatmulSPMDRule, Ctor) {
             std::vector<int64_t>({-1, 0}));
   EXPECT_EQ(infered_dist_attrs.second[0].dims_mapping(),
             std::vector<int64_t>({-1, 0}));
+  EXPECT_EQ(infered_dist_attrs.second[0].is_partial(), false);
   VLOG(4) << "test2 done." << std::endl << std::endl << std::endl;
 
   // mk[1, 0],kn[-1,-1] --> mk[1, 0],kn[0, -1] = nm[1, -1] partial[0]: done
@@ -96,6 +98,9 @@ TEST(MatmulSPMDRule, Ctor) {
             std::vector<int64_t>({0, -1}));
   EXPECT_EQ(infered_dist_attrs.second[0].dims_mapping(),
             std::vector<int64_t>({1, -1}));
+  EXPECT_EQ(infered_dist_attrs.second[0].is_partial(), true);
+  EXPECT_EQ(infered_dist_attrs.second[0].partial_dims(),
+            std::set<int64_t>({0}));
   VLOG(4) << "test3 done." << std::endl << std::endl << std::endl;
 
   // mk[-1,-1],kn[1,0] --> mk[-1, 1],kn[1, 0] = nm[-1, 0] partial[1]: done
@@ -109,6 +114,9 @@ TEST(MatmulSPMDRule, Ctor) {
             std::vector<int64_t>({1, 0}));
   EXPECT_EQ(infered_dist_attrs.second[0].dims_mapping(),
             std::vector<int64_t>({-1, 0}));
+  EXPECT_EQ(infered_dist_attrs.second[0].is_partial(), true);
+  EXPECT_EQ(infered_dist_attrs.second[0].partial_dims(),
+            std::set<int64_t>({1}));
   VLOG(4) << "test4 done." << std::endl << std::endl << std::endl;
 
   // abcmk[1, 0, -1, -1],kn[-1, -1] --> abcmk[1, 0, -1, -1],kn[-1, -1] =
@@ -124,6 +132,7 @@ TEST(MatmulSPMDRule, Ctor) {
             std::vector<int64_t>({-1, -1}));
   EXPECT_EQ(infered_dist_attrs.second[0].dims_mapping(),
             std::vector<int64_t>({0, 1, -1, -1}));
+  EXPECT_EQ(infered_dist_attrs.second[0].is_partial(), false);
   VLOG(4) << "test5 done." << std::endl << std::endl << std::endl;
 
   // abcmk[1, -1, -1, 0],kn[-1, -1] --> abcmk[1, -1, -1, 0],kn[0, -1] = abcmn[1,
@@ -138,6 +147,9 @@ TEST(MatmulSPMDRule, Ctor) {
             std::vector<int64_t>({0, -1}));
   EXPECT_EQ(infered_dist_attrs.second[0].dims_mapping(),
             std::vector<int64_t>({1, -1, -1, -1}));
+  EXPECT_EQ(infered_dist_attrs.second[0].is_partial(), true);
+  EXPECT_EQ(infered_dist_attrs.second[0].partial_dims(),
+            std::set<int64_t>({0}));
   VLOG(4) << "test6 done." << std::endl << std::endl << std::endl;
 
   // abcmk[1, -1, -1, 0], kn[-1, -1] --> abcmk[1, -1, -1, 0],kn[-1, -1] =
@@ -153,6 +165,7 @@ TEST(MatmulSPMDRule, Ctor) {
             std::vector<int64_t>({-1, -1}));
   EXPECT_EQ(infered_dist_attrs.second[0].dims_mapping(),
             std::vector<int64_t>({1, -1, 0, -1}));
+  EXPECT_EQ(infered_dist_attrs.second[0].is_partial(), false);
   VLOG(4) << "test7 done." << std::endl << std::endl << std::endl;
 
   // abcmk[-1, -1, -1, -1], kn[1, 0] --> abcmk[-1, -1, -1, 0],kn[1, 0] =
@@ -169,6 +182,11 @@ TEST(MatmulSPMDRule, Ctor) {
             std::vector<int64_t>({1, 0}));
   EXPECT_EQ(infered_dist_attrs.second[0].dims_mapping(),
             std::vector<int64_t>({-1, -1, -1, 1}));
+  EXPECT_EQ(infered_dist_attrs.second[0].is_partial(), true);
+  EXPECT_EQ(infered_dist_attrs.second[0].partial_dims(),
+            std::set<int64_t>({0}));
+  infered_dist_attrs.second[0].clean_partial_dims(std::vector<int64_t>({0}));
+  EXPECT_EQ(infered_dist_attrs.second[0].is_partial(), false);
   VLOG(4) << "test8 done." << std::endl << std::endl << std::endl;
 
   // abcmk[-1, -1, -1, -1], kn[1, 0] --> abcmk[-1, -1, -1, 0],kn[1, 0] =
@@ -185,6 +203,13 @@ TEST(MatmulSPMDRule, Ctor) {
             std::vector<int64_t>({-1, 0}));
   EXPECT_EQ(infered_dist_attrs.second[0].dims_mapping(),
             std::vector<int64_t>({-1, -1, 1, -1}));
+  EXPECT_EQ(infered_dist_attrs.second[0].partial_dims(),
+            std::set<int64_t>({0}));
+  VLOG(4) << infered_dist_attrs.second[0].to_string();
+  infered_dist_attrs.second[0].clean_partial_status();
+  EXPECT_EQ(infered_dist_attrs.second[0].is_partial(), false);
+  infered_dist_attrs.second[0].set_partial_status(std::vector<int64_t>({1}));
+  EXPECT_EQ(infered_dist_attrs.second[0].verify_partial_status(), false);
   VLOG(4) << "test9 done." << std::endl << std::endl << std::endl;
 
   // abcmk[-1, -1, 1, 0], kn[1, 0] --> abcmk[-1, -1, -1, 0],kn[1, 0] =
@@ -197,6 +222,28 @@ TEST(MatmulSPMDRule, Ctor) {
                        {x_dist_tensor_spec, y_dist_tensor_spec}, attrs));
   // Error
   VLOG(4) << "test10 done." << std::endl << std::endl << std::endl;
+
+  // abcmk[-1, -1, -1, -1], kn[1, 0] --> abcmk[-1, -1, -1, 0],kn[1, 0] =
+  // abcmn[-1, -1, -1, 1] partial[0]:
+  x_dist_tensor_spec.set_dims_mapping({-1, -1, 0, 1});
+  y_dist_tensor_spec.set_dims_mapping({1, 0});
+  attrs["trans_y"] = true;
+  attrs["trans_x"] = true;
+  infered_dist_attrs = matmul_rule->InferForward(
+      {x_dist_tensor_spec, y_dist_tensor_spec}, attrs);
+  EXPECT_ANY_THROW(infered_dist_attrs.second[0].clean_partial_dims(
+      std::vector<int64_t>({1})));
+  infered_dist_attrs.second[0].set_partial_status(std::vector<int64_t>({1}));
+  EXPECT_EQ(infered_dist_attrs.second[0].is_partial(), true);
+  EXPECT_EQ(infered_dist_attrs.second[0].partial_dims(),
+            std::set<int64_t>({0, 1}));
+  infered_dist_attrs.second[0].clean_partial_dims(std::vector<int64_t>({1}));
+  EXPECT_EQ(infered_dist_attrs.second[0].partial_dims(),
+            std::set<int64_t>({0}));
+  infered_dist_attrs.second[0].clean_partial_dims(std::vector<int64_t>({0}));
+  EXPECT_EQ(infered_dist_attrs.second[0].is_partial(), false);
+
+  VLOG(4) << "test11 done." << std::endl << std::endl << std::endl;
 }
 
 TEST(LayerNormSPMDRule, Ctor) {