diff --git a/onnxscript/function_libs/torch_aten/ops/nn.py b/onnxscript/function_libs/torch_aten/ops/nn.py
index beb5f16ddd..f7813ba8ec 100644
--- a/onnxscript/function_libs/torch_aten/ops/nn.py
+++ b/onnxscript/function_libs/torch_aten/ops/nn.py
@@ -239,7 +239,7 @@ def aten_conv_depthwise3d(
     raise NotImplementedError()
 
 
-@torch_op("aten::cross_entropy_loss", trace_only=True)
+@torch_op("aten::cross_entropy_loss")
 def aten_cross_entropy_loss(
     self: TFloatOrBFloat16,
     target: Sequence[int],
@@ -251,30 +251,16 @@ def aten_cross_entropy_loss(
     """cross_entropy_loss(Tensor self, Tensor target, Tensor? weight=None, int reduction=Mean, SymInt ignore_index=-100, float label_smoothing=0.0) -> Tensor"""
 
     if reduction == 0:  # "none"
-        result = _aten_cross_entropy_loss_onnx(self, target, weight, "none", ignore_index)
-    elif reduction == 1:  # "mean"
-        result = _aten_cross_entropy_loss_onnx(self, target, weight, "mean", ignore_index)
-    else:  # "sum"
-        result = _aten_cross_entropy_loss_onnx(self, target, weight, "sum", ignore_index)
-
-    return result
-
-
-@torch_op("aten::cross_entropy_loss", private=True)
-def _aten_cross_entropy_loss_onnx(
-    self: TFloatOrBFloat16,
-    target: Sequence[int],
-    weight: Optional[TFloatOrBFloat16],
-    reduction_str: str,
-    ignore_index: int,
-):
-    if op.OptionalHasElement(weight):
         result, _ = op.SoftmaxCrossEntropyLoss(
-            self, target, weight, reduction=reduction_str, ignore_index=ignore_index
+            self, target, weight, reduction="none", ignore_index=ignore_index
         )
-    else:
+    elif reduction == 2:  # "sum"
+        result, _ = op.SoftmaxCrossEntropyLoss(
+            self, target, weight, reduction="sum", ignore_index=ignore_index
+        )
+    else:  # "mean", default
         result, _ = op.SoftmaxCrossEntropyLoss(
-            self, target, reduction=reduction_str, ignore_index=ignore_index
+            self, target, weight, reduction="mean", ignore_index=ignore_index
         )
 
     return result
diff --git a/onnxscript/tests/function_libs/torch_aten/ops_correctness_test.py b/onnxscript/tests/function_libs/torch_aten/ops_correctness_test.py
index aa9696a635..f1967dde98 100644
--- a/onnxscript/tests/function_libs/torch_aten/ops_correctness_test.py
+++ b/onnxscript/tests/function_libs/torch_aten/ops_correctness_test.py
@@ -486,6 +486,11 @@ def _where_input_wrangler(
     "nn.functional.adaptive_avg_pool2d": nn_ops.aten_adaptive_avg_pool2d,
     "nn.functional.adaptive_avg_pool3d": nn_ops.aten_adaptive_avg_pool3d,
     "nn.functional.celu": nn_ops.aten_celu,
+    # use cross_entropy as test case instead of cross_entropy_loss (not in OPS_DB)
+    "nn.functional.cross_entropy": (
+        nn_ops.aten_cross_entropy_loss,
+        _cross_entropy_input_wrangler,
+    ),
     "nn.functional.dropout": (core_ops.aten_dropout, _dropout_input_wrangler),
     "nn.functional.elu": nn_ops.aten_elu,
     "nn.functional.embedding": (core_ops.aten_embedding, _embedding_input_wrangler),
@@ -566,11 +571,6 @@ def _where_input_wrangler(
     "nn.functional.conv1d": core_ops.aten_conv1d,
     "nn.functional.conv2d": core_ops.aten_conv2d,
     "nn.functional.conv3d": core_ops.aten_conv3d,
-    # use cross_entropy as test case instead of cross_entropy_loss (not in OPS_DB)
-    "nn.functional.cross_entropy": (
-        nn_ops.aten_cross_entropy_loss,
-        _cross_entropy_input_wrangler,
-    ),
     "nn.functional.gelu": nn_ops.aten_gelu,
     "nn.functional.linear": nn_ops.aten_linear,
     "nn.functional.upsample_nearest2d": (
diff --git a/onnxscript/values.py b/onnxscript/values.py
index f9e035abf2..9c8dd80e1a 100644
--- a/onnxscript/values.py
+++ b/onnxscript/values.py
@@ -315,7 +315,13 @@ def param_schemas(self) -> tuple[ParamSchema, ...]:
         # args with default value are attributes
         schemas = []
         for arg in inputs:
-            param_schema = ParamSchema(name=arg.name, type=arg.typeinfo, is_input=True)
+            if isinstance(arg.typeinfo, onnx.TypeProto.Optional):
+                required = False
+            else:
+                required = True
+            param_schema = ParamSchema(
+                name=arg.name, type=arg.typeinfo, is_input=True, required=required
+            )
             schemas.append(param_schema)
 
         for attr_name in attributes: