diff --git a/python/oneflow/framework/infer_compiler/import_tools/format_utils.py b/python/oneflow/framework/infer_compiler/import_tools/format_utils.py
index d963426b140..d14026794bd 100644
--- a/python/oneflow/framework/infer_compiler/import_tools/format_utils.py
+++ b/python/oneflow/framework/infer_compiler/import_tools/format_utils.py
@@ -40,7 +40,13 @@ def _format_full_class_name(self, obj: Union[str, type, FunctionType]):
 
         elif isinstance(obj, FunctionType):
             module = inspect.getmodule(obj)
-            obj = f"{module.__name__}.{obj.__qualname__}"
+            if (
+                module.__name__ == "torch.nn.functional"
+                and obj.__qualname__ == "boolean_dispatch.<locals>.fn"
+            ):
+                obj = f"{module.__name__}.{obj.__name__}"
+            else:
+                obj = f"{module.__name__}.{obj.__qualname__}"
 
         assert isinstance(obj, str), f"obj must be str, but got {type(obj)}"
 
diff --git a/python/oneflow/framework/infer_compiler/with_fx_graph.py b/python/oneflow/framework/infer_compiler/with_fx_graph.py
index 881b720793c..3cea89ad8e3 100644
--- a/python/oneflow/framework/infer_compiler/with_fx_graph.py
+++ b/python/oneflow/framework/infer_compiler/with_fx_graph.py
@@ -38,7 +38,6 @@ def fx_node_tranform(gm):
         # Align this with env setting in `with_oneflow_compile`.
         # Otherwise, infererence using PyTorch with OneFlow backend on
         # multiple input shapes may crash
-        os.environ.setdefault("ONEFLOW_RUN_GRAPH_BY_VM", "1")
         os.environ.setdefault("ONEFLOW_GRAPH_DELAY_VARIABLE_OP_EXECUTION", "1")
         os.environ.setdefault("ONEFLOW_MLIR_CSE", "1")
         os.environ.setdefault("ONEFLOW_MLIR_ENABLE_INFERENCE_OPTIMIZATION", "1")
@@ -63,6 +62,7 @@ def fx_node_tranform(gm):
         os.environ.setdefault("ONEFLOW_MLIR_GROUP_MATMUL_QUANT", "1")
 
         class OfGraph(flow.nn.Graph):
+            @flow.nn.Graph.with_dynamic_input_shape()
             def __init__(self):
                 super().__init__()
                 self.fx_md = of_gm
@@ -70,9 +70,15 @@ def __init__(self):
                 self.config.allow_fuse_add_to_output(True)
 
             def build(self, *args, **kwargs):
-                return self.fx_md(*args, **kwargs)
+                if self.fx_md.training:
+                    return self.fx_md(*args, **kwargs)
+                with flow.no_grad():
+                    return self.fx_md(*args, **kwargs)
 
         of_g = OfGraph()
+        DEFAULT_CACHE_SIZE = 9
+        of_g._dynamic_input_graph_cache.set_cache_size(DEFAULT_CACHE_SIZE)
+        of_g._dynamic_input_graph_cache.enable_shared(True)
         oneflow_fn = lambda *args, **kwargs: of_g(*args, **kwargs)
 
     return oneflow_fn
diff --git a/python/oneflow/framework/infer_compiler/with_oneflow_backend.py b/python/oneflow/framework/infer_compiler/with_oneflow_backend.py
index 23fcb5aa684..cc5c2012765 100644
--- a/python/oneflow/framework/infer_compiler/with_oneflow_backend.py
+++ b/python/oneflow/framework/infer_compiler/with_oneflow_backend.py
@@ -46,8 +46,22 @@ def input_fn(value):
             )
         else:
             output = transformed_fn(*args, **kwargs)
-        if isinstance(output, tuple):
-            return tuple(flow.utils.tensor.to_torch(i) for i in output)
-        return flow.utils.tensor.to_torch(output)
+
+        def output_fn(value):
+            if isinstance(value, flow.Tensor):
+                return flow.utils.tensor.to_torch(value)
+            else:
+                return value
+
+        if isinstance(output, (tuple, list, flow._oneflow_internal.TensorTuple)):
+            return tuple(output_fn(i) for i in output)
+        elif isinstance(output, dict):
+            return {k: output_fn(v) for (k, v) in output.items()}
+        elif isinstance(output, flow.Tensor):
+            return output_fn(output)
+        else:
+            raise NotImplementedError(
+                f"How to handle {type(output)} output type is not implemented"
+            )
 
     return wrapped_forward