diff --git a/array_api_compat/torch/_aliases.py b/array_api_compat/torch/_aliases.py
index 982500b0..508865bb 100644
--- a/array_api_compat/torch/_aliases.py
+++ b/array_api_compat/torch/_aliases.py
@@ -21,9 +21,9 @@
 try:
     # torch >=2.3
     _int_dtypes |= {torch.uint16, torch.uint32, torch.uint64}
+    _HAS_LARGE_UINT = True
 except AttributeError:
-    pass
-
+    _HAS_LARGE_UINT = False
 
 _array_api_dtypes = {
     torch.bool,
@@ -34,47 +34,23 @@
     torch.complex128,
 }
 
-_promotion_table  = {
-    # bool
-    (torch.bool, torch.bool): torch.bool,
+_promotion_table = {
     # ints
-    (torch.int8, torch.int8): torch.int8,
     (torch.int8, torch.int16): torch.int16,
     (torch.int8, torch.int32): torch.int32,
     (torch.int8, torch.int64): torch.int64,
-    (torch.int16, torch.int8): torch.int16,
-    (torch.int16, torch.int16): torch.int16,
     (torch.int16, torch.int32): torch.int32,
     (torch.int16, torch.int64): torch.int64,
-    (torch.int32, torch.int8): torch.int32,
-    (torch.int32, torch.int16): torch.int32,
-    (torch.int32, torch.int32): torch.int32,
     (torch.int32, torch.int64): torch.int64,
-    (torch.int64, torch.int8): torch.int64,
-    (torch.int64, torch.int16): torch.int64,
-    (torch.int64, torch.int32): torch.int64,
-    (torch.int64, torch.int64): torch.int64,
-    # uints
-    (torch.uint8, torch.uint8): torch.uint8,
     # ints and uints (mixed sign)
-    (torch.int8, torch.uint8): torch.int16,
-    (torch.int16, torch.uint8): torch.int16,
-    (torch.int32, torch.uint8): torch.int32,
-    (torch.int64, torch.uint8): torch.int64,
     (torch.uint8, torch.int8): torch.int16,
     (torch.uint8, torch.int16): torch.int16,
     (torch.uint8, torch.int32): torch.int32,
     (torch.uint8, torch.int64): torch.int64,
     # floats
-    (torch.float32, torch.float32): torch.float32,
     (torch.float32, torch.float64): torch.float64,
-    (torch.float64, torch.float32): torch.float64,
-    (torch.float64, torch.float64): torch.float64,
     # complexes
-    (torch.complex64, torch.complex64): torch.complex64,
     (torch.complex64, torch.complex128): torch.complex128,
-    (torch.complex128, torch.complex64): torch.complex128,
-    (torch.complex128, torch.complex128): torch.complex128,
     # Mixed float and complex
     (torch.float32, torch.complex64): torch.complex64,
     (torch.float32, torch.complex128): torch.complex128,
@@ -82,6 +58,31 @@
     (torch.float64, torch.complex128): torch.complex128,
 }
 
+if _HAS_LARGE_UINT:  # torch >=2.3
+    _promotion_table.update(
+        {
+            # uints
+            (torch.uint8, torch.uint16): torch.uint16,
+            (torch.uint8, torch.uint32): torch.uint32,
+            (torch.uint8, torch.uint64): torch.uint64,
+            (torch.uint16, torch.uint32): torch.uint32,
+            (torch.uint16, torch.uint64): torch.uint64,
+            (torch.uint32, torch.uint64): torch.uint64,
+            # ints and uints (mixed sign)
+            (torch.uint16, torch.int8): torch.int32,
+            (torch.uint16, torch.int16): torch.int32,
+            (torch.uint16, torch.int32): torch.int32,
+            (torch.uint16, torch.int64): torch.int64,
+            (torch.uint32, torch.int8): torch.int64,
+            (torch.uint32, torch.int16): torch.int64,
+            (torch.uint32, torch.int32): torch.int64,
+            (torch.uint32, torch.int64): torch.int64,
+        }
+    )
+
+_promotion_table.update({(b, a): c for (a, b), c in _promotion_table.items()})
+_promotion_table.update({(a, a): a for a in _array_api_dtypes})
+
 
 def _two_arg(f):
     @_wraps(f)
@@ -275,6 +276,31 @@ def _reduce_multiple_axes(f, x, axis, keepdims=False, **kwargs):
             out = torch.unsqueeze(out, a)
     return out
 
+
+def _sum_prod_no_axis(x: Array, dtype: DType | None) -> Array:
+    """
+    Implements `sum(..., axis=())` and `prod(..., axis=())`.
+    
+    Works around https://github.com/pytorch/pytorch/issues/29137
+    """
+    if dtype is not None:
+        return x.clone() if dtype == x.dtype else x.to(dtype)
+
+    if x.dtype in (torch.int8, torch.int16, torch.int32):
+        return x.to(torch.int64)
+
+    if _HAS_LARGE_UINT and x.dtype in (torch.uint8, torch.uint16, torch.uint32):
+        return x.to(torch.uint64)
+
+    if x.dtype == torch.uint8:
+        # We can't upcast uint8 according to the spec because there is no
+        # torch.uint64, so at least upcast to int64 which is what prod does
+        # when axis=None.
+        return x.to(torch.int64)
+
+    return x.clone()
+
+
 def prod(x: Array,
          /,
          *,
@@ -283,20 +309,9 @@ def prod(x: Array,
          keepdims: bool = False,
          **kwargs) -> Array:
     x = torch.asarray(x)
-    ndim = x.ndim
 
-    # https://github.com/pytorch/pytorch/issues/29137. Separate from the logic
-    # below because it still needs to upcast.
     if axis == ():
-        if dtype is None:
-            # We can't upcast uint8 according to the spec because there is no
-            # torch.uint64, so at least upcast to int64 which is what sum does
-            # when axis=None.
-            if x.dtype in [torch.int8, torch.int16, torch.int32, torch.uint8]:
-                return x.to(torch.int64)
-            return x.clone()
-        return x.to(dtype)
-
+        return _sum_prod_no_axis(x, dtype)
     # torch.prod doesn't support multiple axes
     # (https://github.com/pytorch/pytorch/issues/56586).
     if isinstance(axis, tuple):
@@ -305,7 +320,7 @@ def prod(x: Array,
         # torch doesn't support keepdims with axis=None
         # (https://github.com/pytorch/pytorch/issues/71209)
         res = torch.prod(x, dtype=dtype, **kwargs)
-        res = _axis_none_keepdims(res, ndim, keepdims)
+        res = _axis_none_keepdims(res, x.ndim, keepdims)
         return res
 
     return torch.prod(x, axis, dtype=dtype, keepdims=keepdims, **kwargs)
@@ -319,25 +334,14 @@ def sum(x: Array,
          keepdims: bool = False,
          **kwargs) -> Array:
     x = torch.asarray(x)
-    ndim = x.ndim
 
-    # https://github.com/pytorch/pytorch/issues/29137.
-    # Make sure it upcasts.
     if axis == ():
-        if dtype is None:
-            # We can't upcast uint8 according to the spec because there is no
-            # torch.uint64, so at least upcast to int64 which is what sum does
-            # when axis=None.
-            if x.dtype in [torch.int8, torch.int16, torch.int32, torch.uint8]:
-                return x.to(torch.int64)
-            return x.clone()
-        return x.to(dtype)
-
+        return _sum_prod_no_axis(x, dtype)
     if axis is None:
         # torch doesn't support keepdims with axis=None
         # (https://github.com/pytorch/pytorch/issues/71209)
         res = torch.sum(x, dtype=dtype, **kwargs)
-        res = _axis_none_keepdims(res, ndim, keepdims)
+        res = _axis_none_keepdims(res, x.ndim, keepdims)
         return res
 
     return torch.sum(x, axis, dtype=dtype, keepdims=keepdims, **kwargs)