diff --git a/torch/_refs/__init__.py b/torch/_refs/__init__.py
index 2f5f4d8ce2e..80d311a16dc 100644
--- a/torch/_refs/__init__.py
+++ b/torch/_refs/__init__.py
@@ -520,6 +520,41 @@ def log10(a):
     return prims.log10(a)
 
 
+@out_wrapper
+def log_softmax(
+    a: TensorLikeType,
+    dim: int,
+    *,
+    dtype: Optional[torch.dtype] = None,
+) -> TensorLikeType:
+    result_dtype = dtype or a.dtype
+    computation_dtype = utils.get_computation_dtype(a.dtype)
+    a_ = _maybe_convert_to_dtype(a, computation_dtype)
+    return _maybe_convert_to_dtype(a_ - logsumexp(a_, dim, keepdim=True), result_dtype)  # type: ignore[return-value]
+
+
+@out_wrapper
+def logsumexp(
+    a: TensorLikeType,
+    dim: DimsType,
+    keepdim: bool = False,
+) -> TensorLikeType:
+    dim = utils.canonicalize_dims(a.ndim, dim)
+    # ATen specifies int[1] type dims which expands integers to tuples of length 1
+    if not isinstance(dim, Iterable):
+        dim = (dim,)
+    if utils.is_float_dtype(a.dtype) or utils.is_complex_dtype(a.dtype):
+        # For float and complex dtypes, we shift input to exp by a constant to avoid overflow
+        a_max = amax(a, dim, keepdim=True)
+        a_max = where(abs(a_max) == float("inf"), 0.0, a_max)
+        a_max_squeezed = prims.squeeze(a_max, dim) if not keepdim else a_max
+        result = log(sum(exp(a - a_max), dim, keepdim=keepdim)) + a_max_squeezed
+    else:
+        # This case covers boolean and integer dtypes and we use non-stabilized computation
+        result = log(sum(exp(a), dim, keepdim=keepdim))
+    return result
+
+
 @register_decomposition(torch.ops.aten.nan_to_num)
 @out_wrapper
 @elementwise_type_promotion_wrapper(
@@ -1350,7 +1385,7 @@ def amin(
 
 def amax(
     a: TensorLikeType,
-    dim: Union[Optional[int], Optional[List[int]]] = None,
+    dim: Optional[DimsType] = None,
     keepdim: bool = False,
     *,
     out: Optional[Tensor] = None,
@@ -2017,6 +2052,24 @@ def stack(tensors: TensorSequenceType, dim: int = 0) -> TensorLikeType:
     return torch.cat([t.unsqueeze(wrapped_dim) for t in tensors], dim)
 
 
+@out_wrapper
+def softmax(
+    a: TensorLikeType,
+    dim: int,
+    *,
+    dtype: Optional[torch.dtype] = None,
+) -> TensorLikeType:
+    result_dtype = dtype or a.dtype
+    computation_dtype = utils.get_computation_dtype(a.dtype)
+    a_ = _maybe_convert_to_dtype(a, computation_dtype)
+    assert isinstance(a_, TensorLike)  # to avoid MyPy error for amax
+    a_max = amax(a_, dim, keepdim=True)
+    a_exp = exp(a_ - a_max)
+    return _maybe_convert_to_dtype(
+        true_divide(a_exp, sum(a_exp, dim, keepdim=True)), result_dtype
+    )  # type: ignore[return-value]
+
+
 @out_wrapper
 def hstack(tensors: TensorSequenceType) -> TensorLikeType:
     check(len(tensors) > 0, lambda: "hstack expects a non-empty TensorList")
diff --git a/torch/testing/_internal/common_methods_invocations.py b/torch/testing/_internal/common_methods_invocations.py
index f0b25619088..67690afe2d4 100644
--- a/torch/testing/_internal/common_methods_invocations.py
+++ b/torch/testing/_internal/common_methods_invocations.py
@@ -3345,6 +3345,7 @@ def sample_inputs_logsumexp(self, device, dtype, requires_grad, **kwargs):
         ((S, S), (1,), True),
         ((S, S), (1,), False),
         ((S, S), (-2,), False),
+        ((S, S), (0, 1), False),
     )
     samples = []
     # Test large inputs to check numerical stability
@@ -17534,6 +17535,7 @@ op_db: List[OpInfo] = [
            assert_autodiffed=True,
            supports_forward_ad=True,
            supports_fwgrad_bwgrad=True,
+           gradcheck_fast_mode=False,
            sample_inputs_func=sample_inputs_logsumexp),
     OpInfo('trace',
            dtypes=all_types_and_complex(),
@@ -20064,6 +20066,22 @@ python_ref_db = [
         "_refs.log2",
         torch_opinfo_name="log2",
     ),
+    PythonRefInfo(
+        "_refs.logsumexp",
+        torch_opinfo_name="logsumexp",
+        skips=(
+            # SyntaxError: cannot assign to False
+            DecorateInfo(unittest.expectedFailure, 'TestCommon', 'test_python_ref_executor'),
+        ),
+    ),
+    PythonRefInfo(
+        "_refs.log_softmax",
+        torch_opinfo_name="log_softmax",
+        skips=(
+            # RuntimeError: Tracing expected 3 arguments but got 2 concrete arguments
+            DecorateInfo(unittest.expectedFailure, 'TestCommon', 'test_python_ref_executor'),
+        ),
+    ),
     ElementwiseUnaryPythonRefInfo(
         "_refs.nan_to_num",
         torch_opinfo_name="nan_to_num",
@@ -20122,6 +20140,14 @@ python_ref_db = [
         "_refs.sinh",
         torch_opinfo_name="sinh",
     ),
+    PythonRefInfo(
+        "_refs.softmax",
+        torch_opinfo_name="softmax",
+        skips=(
+            # RuntimeError: Tracing expected 3 arguments but got 2 concrete arguments
+            DecorateInfo(unittest.expectedFailure, 'TestCommon', 'test_python_ref_executor'),
+        ),
+    ),
     ElementwiseUnaryPythonRefInfo(
         "_refs.sqrt",
         torch_opinfo_name="sqrt",