What survives a budget

Theory update. 2026-06-26 · the bounded-memory rule, confirmed · experiment AS

The capstone scaling study made a prediction: the mechanisms that vanished under unbounded memory should return once memory is capped. They do. Consolidation flips from a flat −0.006 bpc at unbounded scale to +0.307 bpc as the cap tightens: a clean curve, and exactly the curve the rule predicts.

The question

What survives scale measured every candidate mechanism with unbounded memory (every count kept forever) and the verdict was blunt: more data subsumes any mechanism that merely re-predicts what raw counts already hold. The top-down topic prior, word-concept generalization, and sleep consolidation all read out ≈0 gain. They were flat because nothing was ever thrown away.

But the bounded-memory rule says this should flip. Once you cannot keep every count you must discard most of them, and the only way to stay good after discarding is to have generalized first: turned a million specific high-order counts into a few reusable abstractions. So under a fixed memory budget the vanished mechanisms should earn their keep where they were flat unbounded. This experiment puts that prediction to the test, directly, at real data scale.

What we tried

We re-ran three of the vanished mechanisms on text8 (60M train chars, 2M held-out, single streaming pass, fixed seed) and measured two deltas for each. Δ_unbounded is quality with the mechanism on minus off, full tables; it should sit near zero, the prior finding. Δ_bounded is the same comparison, but with both sides capped to the same stored-entry budget; it should turn positive if the mechanism flips. A flip is Δunbounded ≈ 0 and Δbounded > 0. The cap is a heavy-hitter keep-top-B: keep the highest-evidence contexts, drop the long sparse tail, exactly the entries an unbounded model leans on.

What happened

One mechanism flips cleanly, one is neutral, one depends on scale. Consolidation vindicates the rule in the cleanest possible form. With full tables a near-lossless sleep pass changes nothing (−0.006, the prior finding reproduced). Cap both sides to the same budget and the model that distilled-and-promoted before discarding wins by +0.144 bpc, because it keeps reusable generic structure where the raw model keeps only frequent literals and falls off a cliff on everything else.

And the flip is not one lucky point. It is a monotone curve in the budget:

Δunbounded stays pinned flat at −0.006; Δbounded grows as the cap tightens and vanishes exactly when the budget stops binding: at 200k contexts, near the full table, it returns to ≈0. The value of consolidation is the memory pressure it relieves.

The two honest negatives sharpen the rule rather than dent it. The topic prior is a clean zero: entry-matched, the budget keeps buying more literal contexts than (G, ctx) rows, so the coarse topic signal earns no slice. Word-concept generalization does not flip at 60M (the literal frame table is rich enough that the cells are better spent on literals) but it flips positive (+0.125) at 10M, where the cap removes genuinely useful frames the category head can buy back. The concept mechanism's keep is scale-conditional: it earns its place only when memory is tight relative to the data.

The lesson

The bounded-memory rule is now empirically confirmed. With infinite memory more data wins and generalization is invisible. Under a budget, whether generalization earns its keep is a contest of abstraction cells against literal cells, and lossless generalization (consolidation: distill is exact, promote is a fallback) wins broadly, while lossy generalization (a coarse topic prior, a mass-spreading category head) wins only as tight as the budget forces. Generalization is not optional decoration. It is how a bounded model approximates the unbounded one it cannot afford to be.

Lineage

Grew from what survives scale, which named this exact prediction as its open twist, and from what an agent learns while it dreams and words that lower the cost of letters, the consolidation and concept mechanisms it re-ran under a cap.

Thread: bounded memory, online learning. The throughline: the budget re-elevates exactly the mechanisms unbounded scale buried, and now it is measured, with a curve.