diff --git a/onnxslim/core/optimization/dead_node_elimination.py b/onnxslim/core/optimization/dead_node_elimination.py
index 61bdea4..6985124 100644
--- a/onnxslim/core/optimization/dead_node_elimination.py
+++ b/onnxslim/core/optimization/dead_node_elimination.py
@@ -10,17 +10,18 @@
 logger = logging.getLogger("onnxslim")
 
 
-def dead_node_elimination(graph):
+def dead_node_elimination(graph, is_subgraph=False):
     """Perform in-place constant folding optimizations on the given computational graph by eliminating redundant
     nodes.
     """
     for subgraph in graph.subgraphs():
-        dead_node_elimination(subgraph)
+        dead_node_elimination(subgraph, is_subgraph=True)
 
     for node in graph.nodes:
         if node.op in {"Identity", "Dropout"}:
-            delete_node(node)
-            logger.debug(f"removing {node.op} op: {node.name}")
+            if not is_subgraph:
+                delete_node(node)
+                logger.debug(f"removing {node.op} op: {node.name}")
         elif node.op == "Pad":
             if len(node.inputs) > 1 and isinstance(node.inputs[1], Constant):
                 pad_value = node.inputs[1].values.tolist()
diff --git a/onnxslim/core/utils.py b/onnxslim/core/utils.py
index d4d53a3..bcbd798 100644
--- a/onnxslim/core/utils.py
+++ b/onnxslim/core/utils.py
@@ -1,4 +1,4 @@
-from onnxslim.core.pattern import get_node_users
+from onnxslim.core.pattern import get_node_users, get_node_feeds
 from onnxslim.third_party.onnx_graphsurgeon.ir.tensor import Variable
 
 
@@ -15,10 +15,12 @@ def delete_node(node, input_var_idx=0, output_var_idx=0):
             break
 
     if output_var:
-        input_node = node.i()
-        input_node.outputs.remove(node.inputs[input_var_idx])
-        input_node.outputs.append(node.outputs[output_var_idx])
-        node.outputs.clear()
+        feeds = get_node_feeds(node)
+        feed = feeds[0]
+        if not isinstance(feed, Variable):
+            feed.outputs.remove(node.inputs[input_var_idx])
+            feed.outputs.append(node.outputs[output_var_idx])
+            node.outputs.clear()
     else:
         for next_node in next_nodes:
             index = next_node.inputs.index(node_variable)