PIN v5: Members, Scaffolding and the Cost of Not Knowing

This version reports what happened after v4 shipped, and it opens with a correction to v4 rather than an extension of it.

One number first, because every accuracy quoted here invites the wrong conclusion. On a residual architecture the same framework reaches 0.9080 on CIFAR-10 from 270,277 stored values, standing for 2,415,919,104 connections: a fold of 8,939 times. The published figure for a network of that shape is 0.9125. Folding does not cap accuracy, and at a convolution partition a folded model IS a convolutional network, so this neither beats nor should beat one. The lower figures throughout the rest of this document are properties of the architectures they were measured on, not of the framework.

Every model in this programme has ended with a head that reads every hidden unit. On the configurations used throughout, that head holds 31,370 parameters against a folded body of between 145 and 9,365. Nothing here ever pooled before the head, and once pooling is introduced two things change: storage falls by a factor of five or six at equal accuracy, and the depth curve inverts at small grids, where a flat head made depth look harmful and a pooled one shows it rising. The head had been doing work that depth should have been doing, and reporting it as though it were absent inflated every storage and arithmetic ratio in the record. Those ratios are corrected here. Every matched comparison stands, because each arm carried the same head; no accuracy finding moves.

The second half is about members. A member added to a frozen base reaches 96.7% of a model built for the task and disturbs the base by exactly zero, provided it has its own output. Fitted by a closed-form ridge solve rather than gradient descent, it beats the base from five examples and reaches 68% of everything it can give from twenty, in 0.6 milliseconds. Its weight is free at inference and behaves as a linear dial; negative weights act as targeted suppressors, improving the complement of a specialist by 0.088.

What a member is FOR turns out to be sharply bounded. Correction is nearly worthless: a converged base's held-out errors are mostly irreducible, a member recovers 17% of them, and an oracle gate is worth 0.0211. Extension is not: a base trained on seven of ten classes cannot name the other three at all, and a member supplies the whole capability.

Between those sits the result this version is named for. A base has no representation of a category it was never shown, so it cannot mark one as unfamiliar: its confidence separates what it can do from what it cannot at AUC 0.4073, below chance across three independently trained bases, and it is marginally more confident about the second. The same frozen features, read by a 200-example linear probe, separate them at 0.8286. Ignorance is invisible at the output and plain one layer down. Applied as a positive scale on the logits it cannot change any answer, so it is the first member here that can only help.

Six routing attempts had failed before this and were read as evidence that confidence is a weak signal. It is not. On material a model has seen, its own confidence separates right from wrong at 0.8681 and is perfect on its most confident fifth. On material it has not seen it is anti-correlated. Mixing the two populations produced the aggregate that looked like uselessness. Knowing you are unsure and knowing you are out of your depth are different quantities living in different places, and a gate built on the first cannot do the second's work.

With that separation made, gating works for the first time: a member claiming 40% of a test set, and serving it, lifts accuracy from 0.5936 to 0.8209, which is 0.0636 better than applying the same member everywhere. Two members fitted independently on the same 200 examples, one asserting jurisdiction and one answering, identify the same region at AUC 0.9145.

Members are also portable and sellable. A member fitted on one base is noise against another, exactly as their 0.002 alignment predicts, but a translation fitted on fifty public examples recovers 65% of a native member, and whether the two bases share a partition makes no difference this measurement can resolve. What a buyer purchases is the seller's labelled evidence, delivered through a translation that costs the buyer only unlabelled data, and a seller holding less than the buyer has nothing to sell.

Four curricula are reported and all four are null. Everything else here is subject to change and later versions supersede.