diff --git a/paddle/fluid/pybind/eager_method.cc b/paddle/fluid/pybind/eager_method.cc
index 37ace14d145c66995a8b567cbc4d3098d4146f8d..d9face124bd82ad86ed588eba78d8e8b3df0749e 100644
--- a/paddle/fluid/pybind/eager_method.cc
+++ b/paddle/fluid/pybind/eager_method.cc
@@ -1279,6 +1279,15 @@ static PyObject* tensor__inplace_version(TensorObject* self, PyObject* args,
   EAGER_CATCH_AND_THROW_RETURN_NULL
 }
 
+static PyObject* tensor_method_element_size(TensorObject* self, PyObject* args,
+                                            PyObject* kwargs) {
+  EAGER_TRY
+  uint32_t element_size = framework::DataTypeSize(self->tensor.dtype());
+
+  return ToPyObject(element_size);
+  EAGER_CATCH_AND_THROW_RETURN_NULL
+}
+
 static PyObject* tensor__bump_inplace_version(TensorObject* self,
                                               PyObject* args,
                                               PyObject* kwargs) {
@@ -1417,6 +1426,8 @@ PyMethodDef variable_methods[] = {
      METH_VARARGS | METH_KEYWORDS, NULL},
     {"to_dense", (PyCFunction)(void (*)(void))tensor_method_to_dense,
      METH_VARARGS | METH_KEYWORDS, NULL},
+    {"element_size", (PyCFunction)(void (*)(void))tensor_method_element_size,
+     METH_VARARGS | METH_KEYWORDS, NULL},
     /***the method of sparse tensor****/
     {"_inplace_version", (PyCFunction)(void (*)(void))tensor__inplace_version,
      METH_VARARGS | METH_KEYWORDS, NULL},
diff --git a/python/paddle/__init__.py b/python/paddle/__init__.py
index bba9c226dc07b68a9ee9835486658478cc8a59b9..e532633b6eb3537e98dff4c669bb1b9d075ba3cb 100755
--- a/python/paddle/__init__.py
+++ b/python/paddle/__init__.py
@@ -48,7 +48,10 @@ from .framework.dtype import bfloat16  # noqa: F401
 from .framework.dtype import bool  # noqa: F401
 from .framework.dtype import complex64  # noqa: F401
 from .framework.dtype import complex128  # noqa: F401
-from .framework import VarBase as Tensor  # noqa: F401
+if fluid.framework._in_eager_mode_:
+    Tensor = framework.core.eager.Tensor
+else:
+    from .framework import VarBase as Tensor  # noqa: F401
 Tensor.__qualname__ = 'Tensor'  # noqa: F401
 import paddle.compat  # noqa: F401
 import paddle.distributed  # noqa: F401
diff --git a/python/paddle/fluid/tests/unittests/test_cross_op.py b/python/paddle/fluid/tests/unittests/test_cross_op.py
index 6cba72213ff9798ddbc128c88bfcbbcb208c86e1..8b884583646a7ffb9e6d63a2e0c7ee4a53d3da56 100644
--- a/python/paddle/fluid/tests/unittests/test_cross_op.py
+++ b/python/paddle/fluid/tests/unittests/test_cross_op.py
@@ -48,10 +48,10 @@ class TestCrossOp(OpTest):
         self.outputs = {'Out': np.array(z_list).reshape(self.shape)}
 
     def test_check_output(self):
-        self.check_output(check_eager=False)
+        self.check_output(check_eager=True)
 
     def test_check_grad_normal(self):
-        self.check_grad(['X', 'Y'], 'Out', check_eager=False)
+        self.check_grad(['X', 'Y'], 'Out', check_eager=True)
 
 
 class TestCrossOpCase1(TestCrossOp):
diff --git a/python/paddle/tensor/linalg.py b/python/paddle/tensor/linalg.py
index 818ce2f5c6757d489a5442201645b703474964bf..8afab2e05f26b3e59c3ac1f0bd9f8edd5ac623fa 100644
--- a/python/paddle/tensor/linalg.py
+++ b/python/paddle/tensor/linalg.py
@@ -27,6 +27,9 @@ from paddle import _C_ops
 
 __all__ = []
 
+# Consistent with kDefaultDim from C++ Backend
+K_DEFAULT_DIM = 9
+
 
 def matmul(x, y, transpose_x=False, transpose_y=False, name=None):
     """
@@ -1157,6 +1160,7 @@ def cross(x, y, axis=None, name=None):
             #  [0. 0. 0.]]
     """
     if in_dygraph_mode():
+        axis = K_DEFAULT_DIM if axis is None else axis
         return _C_ops.final_state_cross(x, y, axis)
     else:
         if _in_legacy_dygraph():
diff --git a/python/paddle/tensor/logic.py b/python/paddle/tensor/logic.py
index e3ffd36d77972e8f426087377eb526bcdb87f4df..3896fa535ff22143e6ffa1b6824d80cb4de9b838 100755
--- a/python/paddle/tensor/logic.py
+++ b/python/paddle/tensor/logic.py
@@ -280,7 +280,8 @@ def greater_than(x, y, name=None):
             print(result1)  # result1 = [False False True]
     """
     if in_dygraph_mode():
-        return _C_ops.final_state_greater_than(x, y)
+        axis = -1  # default value
+        return _C_ops.final_state_greater_than(x, y, axis)
     else:
         if _in_legacy_dygraph():
             return _C_ops.greater_than(x, y)
diff --git a/python/paddle/utils/code_gen/api.yaml b/python/paddle/utils/code_gen/api.yaml
index ece46837c6def9f3d09a7e1c9dbec2f8923f4887..b46accfb11b017b840891dd0530cf4fc74cc3dc8 100644
--- a/python/paddle/utils/code_gen/api.yaml
+++ b/python/paddle/utils/code_gen/api.yaml
@@ -610,21 +610,21 @@
     func : gelu
   backward : gelu_grad
 
-- api : greater
+- api : greater_equal
   args : (Tensor x, Tensor y, int axis = -1)
   output : Tensor
   infer_meta :
     func : CompareInferMeta
   kernel :
-    func : greater
+    func : greater_equal
 
-- api : greater_equal
+- api : greater_than
   args : (Tensor x, Tensor y, int axis = -1)
   output : Tensor
   infer_meta :
     func : CompareInferMeta
   kernel :
-    func : greater_equal
+    func : greater_than
 
 - api : gumbel_softmax
   args : (Tensor x, float temperature, bool hard, int axis)