diff --git a/onnxscript/function_libs/torch_lib/ops/core.py b/onnxscript/function_libs/torch_lib/ops/core.py
index b46d999b3..6aaddd65f 100644
--- a/onnxscript/function_libs/torch_lib/ops/core.py
+++ b/onnxscript/function_libs/torch_lib/ops/core.py
@@ -81,7 +81,7 @@ def aten_acosh(self: TFloat) -> TFloat:
     return op.Acosh(self)
 
 
-@torch_op("aten::add")
+@torch_op(("aten::add", "aten::add.Tensor"))
 def aten_add(self: TReal, other: TReal, alpha: float = 1.0) -> TReal:
     """add.Tensor(Tensor self, Tensor other, *, Scalar alpha=1) -> Tensor"""
     # TODO(microsoft/onnxruntime#15977): Improve fp16 precision
@@ -1235,7 +1235,7 @@ def aten_chunk(self: TTensor, chunks: int, dim: int = 0) -> Sequence[TTensor]:
     return op.SplitToSequence(self, list_split, axis=dim)
 
 
-@torch_op("aten::clamp", trace_only=True)
+@torch_op(("aten::clamp", "aten::clamp.Tensor"), trace_only=True)
 def aten_clamp(self: TReal, min: Optional[TReal] = None, max: Optional[TReal] = None) -> TReal:
     """clamp(Tensor self, Tensor? min=None, Tensor? max=None) -> Tensor"""
     clamped = self
@@ -2184,7 +2184,7 @@ def aten_dist(self: TensorType, other: TensorType, p: float = 2.0) -> TensorType
     raise NotImplementedError()
 
 
-@torch_op("aten::div")
+@torch_op(("aten::div", "aten::div.Tensor"))
 def aten_div(self: TFloat, other: TFloat) -> TFloat:
     """div.Tensor(Tensor self, Tensor other) -> Tensor"""
 
@@ -2299,7 +2299,7 @@ def aten_embedding_sparse_backward(
     raise NotImplementedError()
 
 
-@torch_op("aten::empty")
+@torch_op(("aten::empty", "aten::empty.memory_format"))
 def aten_empty(size: IntType, dtype: int = FLOAT.dtype) -> TTensor:  # type: ignore[type-var]
     # empty(SymInt[] size, *, ScalarType? dtype=None, Layout? layout=None, Device? device=None, bool? pin_memory=None, MemoryFormat? memory_format=None) -> Tensor
 
@@ -2353,7 +2353,7 @@ def aten_empty_strided(
     return op.Expand(zero, size)
 
 
-@torch_op("aten::eq")
+@torch_op(("aten::eq", "aten::eq.Tensor", "aten::eq.Scalar"))
 def aten_eq(self: TTensor, other: TTensor) -> BOOL:
     """eq.Tensor(Tensor self, Tensor other) -> Tensor"""
 
@@ -2563,7 +2563,7 @@ def aten_feature_dropout(input: TensorType, p: float, train: bool) -> TensorType
     raise NotImplementedError()
 
 
-@torch_op("aten::fill")
+@torch_op(("aten::fill", "aten::fill.Tensor"))
 def aten_fill(self: TTensor, value: TTensor) -> TTensor:
     """fill.Tensor(Tensor self, Tensor value) -> Tensor"""
 
@@ -2748,7 +2748,7 @@ def aten_gcd(self: TensorType, other: TensorType) -> TensorType:
     raise NotImplementedError()
 
 
-@torch_op("aten::ge")
+@torch_op(("aten::ge", "aten::ge.Tensor", "aten::ge.Scalar"))
 def aten_ge(self: TReal, other: TReal) -> BOOL:
     """ge.Tensor(Tensor self, Tensor other) -> Tensor"""
 
@@ -2905,7 +2905,7 @@ def aten_gru_cell(
     raise NotImplementedError()
 
 
-@torch_op("aten::gt")
+@torch_op(("aten::gt", "aten::gt.Scalar"))
 def aten_gt(self: TReal, other: TReal) -> BOOL:
     """gt.Tensor(Tensor self, Tensor other) -> Tensor"""
 
@@ -3595,7 +3595,7 @@ def aten_ldexp(self: TensorType, other: TensorType) -> TensorType:
     raise NotImplementedError()
 
 
-@torch_op("aten::le")
+@torch_op(("aten::le", "aten::le.Tensor"))
 def aten_le(self: TReal, other: TReal) -> BOOL:
     """le.Tensor(Tensor self, Tensor other) -> Tensor"""
 
@@ -3884,7 +3884,7 @@ def aten_lstm_mps_backward(
     raise NotImplementedError()
 
 
-@torch_op("aten::lt")
+@torch_op(("aten::lt", "aten::lt.Scalar"))
 def aten_lt(self: TReal, other: TReal) -> BOOL:
     """lt.Tensor(Tensor self, Tensor other) -> Tensor"""
 
@@ -3957,7 +3957,7 @@ def aten_margin_ranking_loss(
     raise NotImplementedError()
 
 
-@torch_op("aten::masked_fill")
+@torch_op(("aten::masked_fill", "aten::masked_fill.Scalar", "aten::masked_fill.Tensor"))
 def aten_masked_fill(self: TTensor, mask: BOOL, value: TTensor) -> TTensor:
     """masked_fill.Tensor(Tensor self, Tensor mask, Tensor value) -> Tensor"""
     # NOTE: Do not attempt to cast `mask` to BOOL because mask should not take any other types.
@@ -4462,7 +4462,7 @@ def aten_msort(self: TensorType) -> TensorType:
     raise NotImplementedError()
 
 
-@torch_op("aten::mul")
+@torch_op(("aten::mul", "aten::mul.Tensor"))
 def aten_mul(self: TReal, other: TReal) -> TReal:
     """mul.Tensor(Tensor self, Tensor other) -> Tensor"""
     # FIXME(titaiwang): get rid of this when we have type_promotion
@@ -4470,7 +4470,7 @@ def aten_mul(self: TReal, other: TReal) -> TReal:
     return op.Mul(self, other)
 
 
-@torch_op("aten::mul")
+@torch_op(("aten::mul", "aten::mul.Tensor"))
 def aten_mul_bool(self: BOOL, other: BOOL) -> BOOL:
     """ONNX Mul doesn't support Boolean, so use And as an equivalent operator."""
 
@@ -4883,7 +4883,7 @@ def aten_native_norm(self: TensorType, p: float = 2.0) -> TensorType:
     raise NotImplementedError()
 
 
-@torch_op("aten::ne")
+@torch_op(("aten::ne", "aten::ne.Scalar", "aten::ne.Tensor"))
 def aten_ne(self: TReal, other: TReal) -> BOOL:
     """ne.Tensor(Tensor self, Tensor other) -> Tensor"""
 
@@ -5223,7 +5223,7 @@ def aten_positive(self: TensorType) -> TensorType:
     raise NotImplementedError()
 
 
-@torch_op("aten::pow")
+@torch_op(("aten::pow", "aten::pow.Tensor_Tensor", "aten::pow.Tensor_Scalar"))
 def aten_pow(self: TReal, exponent: TTensor) -> TReal:
     """pow(Tensor self, Tensor exponent) -> Tensor"""
 
@@ -5756,7 +5756,7 @@ def aten_rsqrt(self: TFloatOrBFloat16) -> TFloatOrBFloat16:
     return op.Reciprocal(op.Sqrt(self))
 
 
-@torch_op("aten::rsub")
+@torch_op(("aten::rsub", "aten::rsub.Scalar"))
 def aten_rsub(self: TReal, other: TReal, alpha: float = 1.0) -> TReal:
     """rsub.Tensor(Tensor self, Tensor other, *, Scalar alpha=1) -> Tensor"""
     # FIXME(titaiwang): get rid of this when we have type_promotion
@@ -5785,7 +5785,7 @@ def aten_scatter_add(
     return op.ScatterElements(self, index, src, axis=dim, reduction="add")
 
 
-@torch_op("aten::scatter_reduce", trace_only=True)
+@torch_op(("aten::scatter_reduce", "aten::scatter_reduce.two"), trace_only=True)
 def aten_scatter_reduce(
     self: TReal,
     dim: int,  # we have to use int here because ScatterElements() will use this attribute
@@ -5855,7 +5855,7 @@ def aten_segment_reduce(
     raise NotImplementedError()
 
 
-@torch_op("aten::select")
+@torch_op(("aten::select", "aten::select.int"))
 def aten_select(self: TTensor, dim: int, index: int) -> TTensor:
     """select(Tensor self, int dim, int index) -> Tensor"""
 
@@ -5935,7 +5935,7 @@ def aten_sinh(self: TFloat) -> TFloat:
     return op.Sinh(self)
 
 
-@torch_op("aten::slice", trace_only=True)
+@torch_op(("aten::slice", "aten::slice.Tensor"), trace_only=True)
 def aten_slice(
     self: TTensor,
     dim: int = 0,
@@ -6081,7 +6081,7 @@ def aten_sparse_mask(self: TensorType, mask: TensorType) -> TensorType:
     raise NotImplementedError()
 
 
-@torch_op("aten::split")
+@torch_op(("aten::split", "aten::split.Tensor"))
 def aten_split(self: TTensor, split_size: INT64, dim: int = 0) -> TTensor:
     """split.Tensor(Tensor(a -> *) self, SymInt split_size, int dim=0) -> Tensor(a)[]"""
 
@@ -6309,7 +6309,7 @@ def aten_stft(
     return result
 
 
-@torch_op("aten::sub")
+@torch_op(("aten::sub", "aten::sub.Tensor"))
 def aten_sub(self: TReal, other: TReal, alpha: float = 1.0) -> TReal:
     """sub.Tensor(Tensor self, Tensor other, *, Scalar alpha=1) -> Tensor"""
     alpha = op.CastLike(alpha, other)
@@ -6324,7 +6324,7 @@ def aten_subtract(self: TensorType, other: TensorType, alpha: float = 1.0) -> Te
     raise NotImplementedError()
 
 
-@torch_op("aten::sum", trace_only=True)
+@torch_op(("aten::sum", "aten::sum.dim_IntList"), trace_only=True)
 def aten_sum_dim_IntList(
     self: TReal, dim: Optional[INT64] = None, keepdim: bool = False, dtype: int = -1
 ) -> TReal:
@@ -6634,7 +6634,7 @@ def aten_trace_backward(grad: TensorType, sizes: INT64) -> TensorType:
     raise NotImplementedError()
 
 
-@torch_op("aten::transpose", trace_only=True)
+@torch_op(("aten::transpose", "aten::transpose.int"), trace_only=True)
 def aten_transpose(self, dim0: int, dim1: int):
     """transpose.int(Tensor(a) self, int dim0, int dim1) -> Tensor(a)"""
 
@@ -6729,7 +6729,7 @@ def aten_type_as(self: TensorType, other: TensorType) -> TensorType:
     raise NotImplementedError()
 
 
-@torch_op("aten::unbind")
+@torch_op(("aten::unbind", "aten::unbind.int"))
 def aten_unbind(self: TTensor, dim: int = 0) -> Sequence[TTensor]:
     """unbind.int(Tensor(a -> *) self, int dim=0) -> Tensor(a)[]"""
 
@@ -7082,7 +7082,7 @@ def aten_vstack(tensors: Sequence[TTensor]) -> TTensor:
     return op.ConcatFromSequence(tensors, axis=0)
 
 
-@torch_op("aten::where")
+@torch_op(("aten::where", "aten::where.self"))
 def aten_where(condition: BOOL, self: TTensor, other: TTensor) -> TTensor:
     """where.self(Tensor condition, Tensor self, Tensor other) -> Tensor"""