diff --git a/decomposition_tensor.py b/decomposition_tensor.py
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--- /dev/null
+++ b/decomposition_tensor.py
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+
+from functools import wraps
+import torch
+from torch._decomp import decomposition_table
+import torch.nn.functional as F
+from torch.utils._pytree import tree_map
+from torch.testing._internal.logging_tensor import LoggingTensor, capture_logs
+from torch.testing._internal.common_utils import run_tests, TestCase
+
+# Goals:
+# - we want something reusable that can compose with any subclass
+# Non-goal:
+# - should work with both __torch_dispatch__ and __torch_function__
+#   - decomposition table is aten to aten (alternatively, parametrize on decomposition table?)
+#
+# Should this be a wrapper subclass ("has-a") or just use inheritance? Both are implemented below.
+# - Wrapper subclass API `DecompositionTensor(LoggingTensor(t))`
+#   - will need to redispatch
+# - OR provide helper dynamically inherit from the provided subclass and just override its __torch_dispatch__
+#   function to the decorated version
+#   + won't need to redispatch
+# - OR User just writes inline if necessary
+#   + more customizability
+#
+# How does this work with torch function?
+# - It doesn't. torch function will try to rewrap the output again and error if we don't disable it
+#
+# What is progressive lowering tensor and how does this compare?
+# - TODO
+
+aten = torch.ops.aten
+
+skip_list = [aten.add.Tensor, aten.to.dtype, aten.div.Tensor, aten.clamp.default]
+
+# 1) Wrapper subclass inline version
+class DecompositionTensor(torch.Tensor):
+    @staticmethod
+    def __new__(cls, e):
+        r = torch.Tensor._make_wrapper_subclass(cls, e.shape, dtype=e.dtype, requires_grad=False)
+        r.elem = e
+        return r
+
+    # We may be able to remove this line in the future when Ed's PR lands
+    __torch_function__ = torch._C._disabled_torch_function_impl
+
+    @classmethod
+    def __torch_dispatch__(cls, func, types, args=(), kwargs=None):  # type: ignore
+        def unwrap(e):
+            return e.elem if isinstance(e, DecompositionTensor) else e
+
+        def wrap(e):
+            return DecompositionTensor(e) if isinstance(e, torch.Tensor) else e
+
+        if func in skip_list:
+            # Check skip-list first, so "backend" has a chance to see non-decomposed ops
+            return tree_map(wrap, func(*tree_map(unwrap, args), **tree_map(unwrap, kwargs)))
+        elif func in decomposition_table:
+            return decomposition_table[func](*args, **kwargs)
+        else:
+            raise NotImplementedError(f"{func.__name__} does not have a decomposition and is not in skip_list")
+
+# 2) Decorator (Alban's suggestion)
+def decompose(skip_list, missing_ops=None):
+    def _decompose(f):
+        @wraps(f)
+        def wrapper(cls, func, types, args=(), kwargs=None):
+            if func in skip_list:
+                # Functions that the layers below are able to handle
+                return f(cls, func, types, args, kwargs)
+            elif func in decomposition_table:
+                return decomposition_table[func](*args, **kwargs)
+            else:
+                if missing_ops is not None:
+                    missing_ops.add(func.__name__)
+                    return f(cls, func, types, args, kwargs)
+                else:
+                    raise NotImplementedError(f"{func.__name__} does not have a decomposition and is not in skip_list")
+        return wrapper
+    return _decompose
+
+# 2.1) Using the decorator
+class DecompositionTensor2(torch.Tensor):
+    @staticmethod
+    def __new__(cls, e):
+        r = torch.Tensor._make_wrapper_subclass(cls, e.shape, dtype=e.dtype, requires_grad=False)
+        r.elem = e
+        return r
+
+    __torch_function__ = torch._C._disabled_torch_function_impl
+
+    @classmethod
+    @decompose(skip_list, missing_ops=None)
+    def __torch_dispatch__(cls, func, types, args=(), kwargs=None):  # type: ignore
+        def unwrap(e):
+            return e.elem if isinstance(e, DecompositionTensor2) else e
+
+        def wrap(e):
+            return DecompositionTensor2(e) if isinstance(e, torch.Tensor) else e
+
+        return tree_map(wrap, func(*tree_map(unwrap, args), **tree_map(unwrap, kwargs)))
+
+# 3) Version using inheritance
+def apply_decomposition_before_cls(cls, skip_list, missing_ops=None):
+    # skip_list here could be the list of ops that your subclass/transform/backend supports
+    # Inherits from cls and then wraps its __torch_dispatch__
+    cls_new = type(f'Decomposed{cls.__name__}', (cls,), {})
+    # Is this always safe to do? What properties does cls need to have for this to be OK?
+    # - cls should not be a plain tenosr, which would not have __torch_dispatch__
+    #   or we could just check has_attr (?)
+    assert cls is not torch.Tensor
+    cls_new.__torch_dispatch__ = classmethod(decompose(skip_list, missing_ops)(cls.__torch_dispatch__.__func__))
+    return cls_new
+
+
+class TestDecompositionTensor(TestCase):
+    def test_decompose_logging_tensor(self):
+        def f(t):
+            return F.hardsigmoid(t.add(t))
+
+        # Start off only with LoggingTensor
+        with capture_logs() as logs:
+            f(LoggingTensor(torch.tensor(1.)))
+        self.assertExpectedInline('\n'.join(logs), """\
+$1 = torch._ops.aten.add.Tensor($0, $0)
+$2 = torch._ops.aten.hardsigmoid.default($1)""")
+
+        # Now we try with LoggingTensor wrapped with a DecompositionTensor (inline version)
+        with capture_logs() as logs1:
+            f(DecompositionTensor(LoggingTensor(torch.tensor(1.))))
+        # We shouldn't see hardsigmoid here anymore because it has been decomposed!
+        self.assertExpectedInline('\n'.join(logs1), """\
+$1 = torch._ops.aten.add.Tensor($0, $0)
+$2 = torch._ops.aten.to.dtype($1, torch.float32)
+$3 = torch._ops.aten.add.Tensor($2, 3)
+$4 = torch._ops.aten.clamp.default($3, 0)
+$5 = torch._ops.aten.clamp.default($4, None, 6)
+$6 = torch._ops.aten.div.Tensor($5, 6)
+$7 = torch._ops.aten.to.dtype($6, torch.float32)""")
+        # With the decorator version
+        with capture_logs() as logs2:
+            f(DecompositionTensor2(LoggingTensor(torch.tensor(1.))))
+
+        # Patch an existing class
+        DecomposedLoggingTensor = apply_decomposition_before_cls(LoggingTensor, skip_list)
+
+        with capture_logs() as logs3:
+            f(DecomposedLoggingTensor(torch.tensor(1.)))
+
+        # How would one obtain the skip_list in the first place without having to iterate
+        # through errors and add them one-by-one?
+        # - We allow users to pass in an empty set to the decorator/wrapper, and this set would
+        #   get populated as the program runs
+        missing_ops = set()
+        DecomposedLoggingTensor2 = apply_decomposition_before_cls(LoggingTensor, [], missing_ops=missing_ops)
+        t = DecomposedLoggingTensor2(torch.tensor(1.))
+        with capture_logs() as logs4:
+            f(t)
+        self.assertEqual(missing_ops, set(str(op).split('aten.')[1] for op in skip_list))
+        self.assertTrue(logs1 == logs2 == logs3 == logs4)
+
+if __name__ == "__main__":
+    run_tests()