diff --git a/pyinfinitensor/src/pyinfinitensor/onnx.py b/pyinfinitensor/src/pyinfinitensor/onnx.py
index a5248b28..7fdcfc5f 100644
--- a/pyinfinitensor/src/pyinfinitensor/onnx.py
+++ b/pyinfinitensor/src/pyinfinitensor/onnx.py
@@ -1,4 +1,4 @@
-import backend
+import backend
 from onnx import (
     ModelProto,
     TensorProto,
@@ -538,9 +538,6 @@ class OnnxStub:
                 else:
                     assert False, "Unsupported Tensor Type: {}".format(tensor.data_type)
 
-        for output in model.graph.output:
-            self.outputs[output.name] = tensors[output.name]
-
         return ans
 
     @classmethod
@@ -571,6 +568,8 @@ class OnnxStub:
             outputs: List[ValueInfoProto] = []
             # saves global input tensors
             initializers: List[TensorProto] = []
+            # saves global output tensors
+            value_info: List[ValueInfoProto] = []
 
             enable_check = False
             def __init__(self, enable_check):
@@ -586,12 +585,15 @@ class OnnxStub:
 
             def push_output(self, name: str, tensor: backend.Tensor) -> str:
                 self.names[tensor] = name
-                if not tensor.has_target():
-                    shape = tensor.shape()
-                    dtype = backend.tensor_dtype(tensor)
-                    value_info = make_tensor_value_info(name, dtype, shape)
-                    check_value_info(value_info)
+
+                shape = tensor.shape()
+                dtype = backend.tensor_dtype(tensor)
+                value_info = make_tensor_value_info(name, dtype, shape)
+                check_value_info(value_info)
+                if not tensor.has_target(): # if this output is a global output
                     self.outputs.append(value_info)
+                else: # if this output is a local output
+                    self.value_info.append(value_info)
                 return name
 
             def push_input(
@@ -635,7 +637,8 @@ class OnnxStub:
 
             def build(self, name: str) -> ModelProto:
                 graph = make_graph(
-                    self.nodes, name, self.inputs, self.outputs, self.initializers
+                    self.nodes, name, self.inputs, self.outputs, self.initializers,
+                    value_info=self.value_info
                 )
                 if self.enable_check:
                     check_graph(graph)