Writing it down

Negative. 2026-06-26 · a principle, not a free lunch · experiment AQ

At equal memory budget, a small internal model plus an external store does not beat one bigger internal table; it loses by ~0.01 bpc, because splitting fragments the evidence. It wins only when the external store is cheaper than internal memory (−0.23 bpc). Externalizing is a cost arbitrage (the page is cheaper than the skull) not a better use of the same bytes.

The question

The bounded-memory rule has produced three experiments that all ask the same thing: under a fixed budget, what survives eviction? Two routes were already tested: evict the right tail (non-forgetting, the shape of forgetting) and consolidate the head offline (sleep). This one tests the route humans lean on hardest: we don't hold everything in our heads, we write it down. Ericsson and Kintsch's long-term working memory says an expert keeps a tiny set of cues in a narrow focus and the content in an external store the cues retrieve on demand. The question for our substrate: at equal total budget, does a small internal model plus an external store beat one big internal table, especially on the rare contexts the all-internal model evicted?

What we tried

A char-level count model, orders 1 to 5, the same counting core so peak quality is comparable. Darwin, 200k train / 20k held-out, single pass, seed 0. A, AllInternal: one bounded table, cap 4000; on overflow, evict the tail. B, IntExt: a small internal table (1000) plus an external store (3000); on overflow the internal table writes the evicted context's counts down to the store, then drops it. At predict time the internal answers when confident; when uncertain it pays a retrieval and blends. 1000 + 3000 = 4000, so A and B hold the same per-order entry budget, the fair test. A held-out position is "rare" if its order-5 context appeared 1 to 3× in training, exactly what a bounded table evicts first.

What happened

The strict equal-budget verdict is an honest negative. At equal budget, with the external store read on 71% of predictions at an 88% hit-rate, the split model is ~0.01 bpc worse, overall and on the rare slice. Writing it down, then re-reading only when unsure, buys nothing the one big table didn't already have. Two losses eat the gain. The split fragments evidence: a context's counts now live partly internal, partly on paper, and the confident-internal path answers from the internal fragment alone, missing the written-down half. And at equal budget the big table simply holds more of the live distribution at once: there is no eviction the external store uniquely rescued, because Darwin's order-5 tail is genuinely low-value (rare is hard for both, 2.40 vs 2.41).

C proves the store is doing real work: internal-only at 1000 is far worse (rare 2.77), so B's store is recovering most of the lost budget. It just doesn't exceed A. And the one regime where externalizing wins is the asymmetric one. Drop equal budget, keep internal tiny and give the store 9000 (the real human asymmetry, since paper is cheaper per entry than working memory) and D improves on the all-internal table by 0.23 bpc at the same tiny internal footprint.

The lesson

At equal byte budget, "write it down" does not beat "hold it all in one table." Externalizing is a cost arbitrage (the page is cheaper than the skull) not a better use of the same bytes. Ericsson and Kintsch's long-term working memory is cost-asymmetric by construction: the page is free to keep. So the model that matches the cognition matches its result, but the equal-budget framing is the wrong one for the human analogy even though it is the right one for the fair-comparison question. The fix for a future swing: never answer from the internal fragment alone, always blend internal and external when both hold the context.

Lineage

Grew from learning the new without losing the old and what an agent learns while it dreams, the evict-the-tail and consolidate-the-head coping routes, completing the trio with externalize, under the same bounded-memory rule.

Thread: bounded memory, online learning. The idea is Ericsson and Kintsch's long-term working memory.