Abstention

A read that reports its own confidence gives refusal for free: the same number that answers the query says whether the query should have been answered.

Conventional systems bolt refusal on — a separate classifier, a calibration model, an out-of-distribution detector consuming the same rows a second time. A reconstruction read already carries the quantity, because reconstructing requires measuring how far the query was from what is stored.

Two kinds

Structural abstention. A key that was never composed has no address in the store. Unbinding it returns noise that resembles nothing, so a miss cannot return a confident wrong answer — the geometry has no item there to return. No threshold exists to tune, and no calibration set is required, because the refusal is a consequence of the encoding rather than a decision about a score.

Calibrated abstention. Where the question is "is this stored pattern close enough", the answer is a threshold, and a threshold is a fitted quantity. It is derived from held-out data: measure the score across inputs known to be in distribution, measure it across inputs known not to be, and place the cut in the gap between them.

The two differ in what they cost to maintain. Structural abstention holds for as long as the encoding holds. Calibrated abstention holds for as long as the conditions it was calibrated under hold — and one of those conditions is load.

Thresholds are valid only at their calibration load

A score's separation between in- and out-of-distribution inputs is a function of how much the store holds, because interference grows with occupancy. A gate calibrated on a lightly loaded collection reports a different distribution on a heavily loaded one.

An entropy gate over the attention weight distribution:

Below 0.5 the gate is anti-correlated: at the higher load it is worse than a coin. The gate is not broken — it is being read outside the regime it was measured in. A threshold carries its calibration load as part of its definition, and a collection that has grown past that load needs the threshold re-derived, exactly as a capacity budget does.

Where the signal lives

Not every similarity a read exposes carries information about confidence.

First-contact similarity carries the signal. The cosine between the query and the single-step read result measures how far the query had to move to reach the codebook. On a task separating queries that the store can answer from queries it cannot:

ROC AUC 1.0000, with an empty band at [0.61, 0.80] — no observation of either class falls inside it. A gap that wide is what makes a threshold cheap to place and stable to hold: any cut in the band separates perfectly.

Post-iteration similarity carries none. An iterative read runs until the estimate stops moving, so its final similarity is ≈ 1.0 by construction, for every input, including inputs the store has nothing to say about. The iteration did not fail to detect anything; it converged, which is what it is for. The number it leaves behind is a statement about convergence, not about the query.

The counter-property

A cleanup that returns a nearest neighbour for any input has no distance signal. It always answers, so its answer is uninformative about whether it should have answered — the answer's existence carries zero bits.

Stated as a rule: a search that cannot fail has not succeeded. The ability to return nothing is what makes returning something a measurement. This is why the read's output is a pair — reconstruction and fidelity — rather than a bare vector, and why exposing only the vector to an application throws away the half that governs whether the other half should be used.

Building a gate

1. Use the first-contact read, not the iterative one, wherever the result feeds a decision.
2. Prefer structural abstention where the encoding allows it — an address that does not exist needs no threshold.
3. Where a threshold is needed, derive it on held-out data at the collection's operating load, from both classes.
4. Record the load the threshold was calibrated at, and re-derive when the collection moves materially past it.
5. Report the band, not just the cut. An empty band says the gate is safe; a band that has closed says the gate has stopped separating.

Related

• How the memory works — fidelity as a free by-product of the read.
• The cleanup loop — why iterative reads discard the signal.
• Capacity and interference — the load that moves the threshold.
• Boundary conditions — the case where saturation looks like confidence.
• Fidelity, cleanup memory.