PaddlePaddle
diff --git a/‎paddle/fluid/pybind/pir.cc
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+10-7Lines changed: 10 additions & 7 deletions b/‎paddle/fluid/pybind/pir.cc
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+10-7Lines changed: 10 additions & 7 deletions
diff --git a/‎python/paddle/autograd/backward_utils.py
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+142-7Lines changed: 142 additions & 7 deletions b/‎python/paddle/autograd/backward_utils.py
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+142-7Lines changed: 142 additions & 7 deletions
@@ -761,8 +761,8 @@ void BindValue(py::module *m) {
            [](Value self) {
              return paddle::dialect::scale(self, -1.0, 0.0, true);
            })
-      .def("__eq__", &Value::operator==)
-      .def("__hash__", [](Value self) { return std::hash<pir::Value>{}(self); })
+      .def("is_same", &Value::operator==)
+      .def("hash", [](Value self) { return std::hash<pir::Value>{}(self); })
       .def("__repr__", &Value2String);
   // For basaic operators
   OVERRIDE_OPERATOR_FOR_EACH(__add__, add, 1.0, other, true);
@@ -1029,7 +1029,8 @@ static auto GetNoNeedBufferValue(const ::pir::Block *whole_block,
                                    no_need_buffer_values.end());
 }
 
-using OpResultMap = std::unordered_map<pir::OpResult, pir::OpResult>;
+using OpResultMap =
+    std::pair<std::vector<pir::OpResult>, std::vector<pir::OpResult>>;
 std::pair<std::shared_ptr<Program>, OpResultMap> CloneProgram(
     const Program &program) {
   // Limitation of this function:
@@ -1042,12 +1043,14 @@ std::pair<std::shared_ptr<Program>, OpResultMap> CloneProgram(
     auto *cloned_op = BuildOpFrom(&op, value_map);
     cloned_program->block()->push_back(cloned_op);
   }
-  std::unordered_map<pir::OpResult, pir::OpResult> op_result_map;
+  std::vector<pir::OpResult> associated_array_key, associated_array_value;
   for (auto &pair : value_map) {
-    op_result_map[pair.first.dyn_cast<pir::OpResult>()] =
-        pair.second.dyn_cast<pir::OpResult>();
+    associated_array_key.push_back(pair.first.dyn_cast<pir::OpResult>());
+    associated_array_value.push_back(pair.second.dyn_cast<pir::OpResult>());
   }
-  return std::make_pair(cloned_program, op_result_map);
+  return std::make_pair(
+      cloned_program,
+      std::make_pair(associated_array_key, associated_array_value));
 }
 
 void AppendSetParameter(Program *forward_program,
 
@@ -11,14 +11,149 @@
 # 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.
+from __future__ import annotations
 
 import collections
 import warnings
+from collections.abc import Sequence
+from typing import Any
 
+from paddle import pir
 from paddle.base import core
 from paddle.base.wrapped_decorator import signature_safe_contextmanager
 
 
+class ValueWrapper:
+    def __init__(self, value) -> None:
+        if isinstance(value, ValueWrapper):
+            assert isinstance(value._value, (type(None), pir.Value))
+        else:
+            assert isinstance(value, (type(None), pir.Value))
+        self._value = value._value if isinstance(value, ValueWrapper) else value
+
+    def __hash__(self) -> int:
+        if isinstance(self._value, pir.Value):
+            return self._value.hash()
+        else:
+            return hash(self._value)
+
+    def __eq__(self, other) -> bool:
+        if not isinstance(other, ValueWrapper):
+            warnings.warn(
+                f'In ValueWrapper.__eq__ expected type of `other` is ValueWrapper but received {other.__class__}.'
+            )
+            return False
+
+        if self._value is None or other._value is None:
+            return self._value is None and other._value is None
+        return self._value.is_same(other._value)
+
+
+class ValueDict:
+    def __init__(
+        self,
+        iter=None,
+        *,
+        default_factory=None,
+    ):
+        self._items: dict[ValueWrapper] = {}
+        self._default_factory = default_factory
+        if iter is not None:
+            for key, val in iter.items():
+                self[key] = val
+
+    def copy(self):
+        ret = ValueDict()
+        ret._items = self._items.copy()
+        ret._default_factory = self._default_factory
+        return ret
+
+    def update(self, other_dict):
+        for key, val in other_dict.items():
+            self[key] = val
+
+    def keys(self):
+        for key in self._items.keys():
+            yield key._value
+
+    def values(self):
+        return self._items.values()
+
+    def items(self):
+        for key, val in self._items.items():
+            yield key._value, val
+
+    def pop(self, key):
+        if not self.__contains__(key):
+            raise KeyError(f'{key} is not in ValueDict')
+        return self._items.pop(ValueWrapper(key))
+
+    def __setitem__(self, key, val: Any):
+        self._items[ValueWrapper(key)] = val
+
+    def __getitem__(self, key):
+        if not self.__contains__(key):
+            if self._default_factory is not None:
+                self[key] = self._default_factory()
+            else:
+                raise KeyError(f'{key} is not in ValueDict')
+        return self._items[ValueWrapper(key)]
+
+    def __bool__(self):
+        return bool(self._items)
+
+    def __len__(self):
+        return len(self._items)
+
+    def __iter__(self):
+        return self.keys()
+
+    def __contains__(self, key):
+        return ValueWrapper(key) in self._items
+
+
+class ValueSet:
+    def __init__(
+        self, iter: Sequence[ValueWrapper] | set[ValueWrapper] | None = None
+    ):
+        self._set: set[ValueWrapper] = set()
+        if iter is not None:
+            for val in iter:
+                self.add(val)
+
+    def copy(self):
+        ret = ValueSet()
+        ret._set = self._set.copy()
+        return ret
+
+    def add(self, val):
+        if not self.__contains__(val):
+            self._set.add(ValueWrapper(val))
+
+    def update(self, other: set):
+        for val in other:
+            self.add(val)
+
+    def __and__(self, other: ValueSet):
+        return ValueSet(self._set & other._set)
+
+    def __or__(self, other: ValueSet):
+        return ValueSet(self._set | other._set)
+
+    def __bool__(self):
+        return bool(self._set)
+
+    def __len__(self):
+        return len(self._set)
+
+    def __iter__(self):
+        for val in self._set:
+            yield val._value
+
+    def __contains__(self, val):
+        return ValueWrapper(val) in self._set
+
+
 class State:
     """
     record relationship of forward op/value and backward op/value
@@ -30,24 +165,24 @@ class State:
     def __init__(self, block):
         self.block = block
         # opresult -> list(list(opresult))
-        self.value_to_valuegrad = collections.defaultdict(list)
-        self.value_to_sumvaluegrad = collections.defaultdict(list)
+        self.value_to_valuegrad = ValueDict(default_factory=list)
+        self.value_to_sumvaluegrad = ValueDict(default_factory=list)
         # operation -> list(operation)
         self.op_to_opgrad = collections.defaultdict(list)
 
         # opresult -> list(opresult)
-        self.valuegrad_to_value = collections.defaultdict(list)
-        self.sumvaluegrad_to_value = collections.defaultdict(list)
+        self.valuegrad_to_value = ValueDict(default_factory=list)
+        self.sumvaluegrad_to_value = ValueDict(default_factory=list)
         # operation -> list(operation)
         self.opgrad_to_op = collections.defaultdict(list)
         # only for controlflow
         # inside_value is sub block value, which will yield to parent block,
         # parant block value is outside_value
-        self.inside_value_to_outside_value_map = {}
+        self.inside_value_to_outside_value_map = ValueDict()
 
     def turn_map(self) -> None:
-        self.valuegrad_to_value = collections.defaultdict(list)
-        self.sumvaluegrad_to_value = collections.defaultdict(list)
+        self.valuegrad_to_value = ValueDict(default_factory=list)
+        self.sumvaluegrad_to_value = ValueDict(default_factory=list)
         self.opgrad_to_op = collections.defaultdict(list)
 
         for k, v in self.value_to_valuegrad.items():