Update Tomography: Reusable Learning Records via Supervision Space

Unlike homogeneous models, updates from heterogeneous architectures cannot be directly compared in a shared parameter space. We therefore turn to supervision space and show that updates from different architectures can be represented exactly as linear measurements of the same supervision contrast. Moreover, a target update remains uniquely determined as long as the supervision ambiguity left unresolved by these measurements cannot affect that target, even when the full supervision itself is not uniquely identified.We formalize these results as Update Tomography (UT), a framework for constructing updates across heterogeneous architectures without parameter alignment. Experiments on vision and language models agree with the theoretical predictions: even when full supervision cannot be recovered, UT reproduces direct-supervision learning whenever the information required by the target is retained. This learning information remains usable by heterogeneous models introduced after the original models are no longer available, with relative trajectory error remaining on the order of $10^{-5}$ across ten successive learning events.Thus, cross-architecture update reuse need not treat model-specific parameter changes as the object to be transferred, but can instead characterize and reuse the information that a learning event leaves in supervision space.