The claim
CLAIM-125 leaves open when a transport between scenarios preserves decision-relevant information, and CLAIM-050 takes Blackwell’s order (THEORY-156) as the measure of that. Model stitching is the machine-learning practice closest to a test of it. A learned map s carries one network’s representation r into another network at layer ℓ, and the result is judged by what the second network can then do.
Stitching comes in two forms, and only one of them is a test of Blackwell’s order:
- Reconstruction form. Here s is fitted so that s ∘ r reproduces the target layers, φ′ ≈ E φ in Lenc and Vedaldi (LIT-363). If it succeeds on the input distribution, then given each label the target representation is a function of r. The target is then a garbling of r, and r is at least as informative for every decision problem on the label (THEORY-176, relation 4). Success certifies one direction of sufficiency.
- Task-loss form. Here s is fitted to minimise the second network’s task loss, the protocol of Bansal, Nakkiran and Barak (LIT-850). The stitching penalty then compares one decision problem, through a fixed head and a restricted map class. Both of its losses are upper bounds on the best attainable risk, so the penalty orders neither, and it is not invariant under invertible reparametrisation (THEORY-176, relations 1–3). A negative penalty, the paper’s evidence that “more is better”, shows that the fitted map did not reproduce the layers it replaced.
In both forms the test runs in one direction. A failure to stitch says only that no map in the class works. The information may still be there in a form the class cannot reach: Lenc and Vedaldi’s identity stitch fails between networks that a learned linear map makes interchangeable.
Relative representations (THEORY-175) are a third route. The map is replaced by a fixed construction, cosine similarity to matched anchor points, and that construction is blind exactly to the cosine-preserving maps. It moves the correspondence problem into the choice of anchors. What it transports is judged by task performance alone, so it is the task-loss form’s evidence, not the reconstruction form’s.
What it does not say
It does not say stitching answers CLAIM-125. Even in reconstruction form the certificate covers one pair of representations on one input distribution, for decisions about the label used to define the experiment. It gives no characterisation of which transports preserve information, and no measure of how much a non-sufficient transport loses; that is Le Cam’s deficiency (THEORY-156). It does not say task-loss stitching is useless. It is the right test when the decision problem really is fixed in advance, which is CLAIM-050’s point that fidelity is relative to the receiver’s decisions. It says that the penalty is not, by itself, an order of information.
Note of 2026-10-13: the general content is filed separately
Under ADR-040, the result about the two forms of stitching is filed on its own as CLAIM-268, in the formal-apparatus line, resting on no claim. This claim now rests on it for the general content, and keeps CLAIM-050, for reading stitching as a test of decision-relevant transport. Claims in other lines that need only the general content cite CLAIM-268, so setting pragmatic-transport aside does not take it from them.
Note of 2026-10-19: the warrant is the reading’s
Everything a derivation can give here is in CLAIM-268, which is Active. In the reconstruction form, success makes the target a deterministic garbling of r about the label, on any outcome space. In the task-loss form, the penalty is a difference of upper bounds that orders neither minimum, and it changes under invertible reparametrisation. What remains in this claim is CLAIM-050’s reading, that these facts test whether a transport keeps the information a receiver’s decisions need. That reading is interpretive, and so is this claim’s warrant now. The defeat condition still names the formal failures. Since CLAIM-268 holds them, meeting either one would defeat both claims. The claim stays Proposed while CLAIM-050 is.
Note of 2026-10-27: grounded in what it uses of Blackwell
The status review of this date (ADR-057) moved this claim’s ground from THEORY-156 to THEORY-1096. It uses Blackwell’s definitions (an experiment, a garbling, the informativeness order) or the easy direction, that a garbling never helps a decision-maker free to choose any rule. Both hold on any outcome spaces, with the proof written out there. THEORY-156’s general converse, which stays Proposed, is not used. Quotations of THEORY-156 above are of the definitions it states.
Note of 2026-10-29: promoted
The eleventh status review (ADR-057) promoted this claim on the owner’s assent. The note of 2026-10-19 said it stays Proposed while CLAIM-050 is, and CLAIM-050 has been Active since 2026-10-28; CLAIM-268, its other premise, is Active, and so is every ground. CLAIM-230 no longer objects to it: that claim cites this one’s certificate, for decisions about the label used to define the experiment, as a parallel, and says that for stitching the label comes with the data set. Nothing in the record meets the defeat condition, whose formal failures CLAIM-268 holds.