Preserve reads of shared storage across tensor updates

Let X=[[1,2],[3,4]], and let v be its first-column view rather than a copy. The view reads locations [0,0] and [1,0]. A write adding ten to X[0,0] overlaps one of those locations, so a later sum of v must observe the update under ordinary sequential semantics. A view of only the second column would not overlap that particular write. This distinction is about accessed locations and operation semantics, not whether two variables have different spelling.

Now compare a read before the mutation with a read after it. Their shapes are identical, but their expected sums differ. Moving the later read earlier is not common-subexpression elimination because the intervening write changes its inputs through shared storage. Conversely, a proof that a write touches a disjoint region can enable motion that a conservative whole-buffer alias model would refuse. Unknown aliasing generally requires conservative handling; inventing disjointness to remove a copy trades correctness for an unproved assumption.

A functional representation can replace an update with a new tensor value and redirect later dependent uses. That can make dataflow easier to optimize, but externally observable mutations still need the required treatment at the function boundary. PyTorch 2.9 functionalization documents such fix-ups and limitations, including problematic global state and overlapping as_strided cases. Calling an intermediate graph functional does not authorize forgetting what callers see through an input alias after the original function returns.

MLIR bufferization approaches the opposite direction: it starts with tensor value semantics and chooses storage implementations. If an old tensor value remains needed after an operation that could overwrite its future buffer, the analysis must prevent that read-after-write conflict, potentially by copying. Safe in-place reuse depends on the old value's users and writability. It is not guaranteed merely because the new tensor has the same shape, or forbidden merely because it has a new SSA name.

A useful test pair passes a view in one case and a real copy with the same initial contents in another. After mutating the base, the view must reflect the update while the copy need not. Also return or inspect the mutated input when that is part of the API contract; checking only a detached output can miss a dropped write-back. Add a nonoverlapping view case so a conservative optimization can be distinguished from an incorrect one, without requiring the compiler to optimize every provably safe opportunity.

The network lab illustrates only the distinction between evaluating an old value and a changed value. Reset, set both x=1,w=1, predict output about 0.6225, then Play or Step. Reset and set both x=2,w=1 for the changed-input output about 0.8176. Naming both results on paper prevents silently substituting one for the other. The lab has no shared tensor buffers, views, mutation, or functionalization pass, so the alias relationship itself must be established in a separate program fixture.