Learning what a long-lived board looks like

Train a classifier to tell boards from very long games apart from ordinary boards, then use that opinion to guide play. It could tell them apart almost perfectly, and still chose worse moves.

The intuition

A clairvoyant planner that can see every hidden gray disc plays very long games. The positions it passes through must have some visible structure in common — call it the shape of a board with a future. If a public classifier can learn to recognise that shape, then "does my move lead toward that shape?" becomes a signal any legal policy can use.

The delicate part is making the classifier learn the right difference. A board from a 250-move oracle game is fuller and taller than a board from a 60-move ordinary game, so a lazy classifier can hit high accuracy by counting discs and learning nothing about structure. This experiment therefore matched every positive with a negative having exactly the same rise phase, the same number of occupied cells, and the same maximum column height, and used only invariant aggregates of causal-graph and trigger features as inputs.

Three ways of using the resulting signal were tried, in increasing caution: as a dense reward for policy-gradient training, as a tie-break between nearly equal moves, and as a shaping term added to a fixed training run.

How it works, step by step

1. Collect. 4,096 checksum-locked public positions from oracle trajectories as positives; positions from exactly 1,024 fresh games of an exact one-move fair search as negatives.
2. Match. Pair each positive with a negative on rise phase, occupied count, and maximum height, so load cannot be the discriminating feature.
3. Train and check honestly. Two complementary small networks (295 inputs, 24 hidden units, 7,129 parameters), each trained on one half of the positions split by board identity, evaluated only on the other. The negatives inherit the split of their whole origin game, so no game straddles the boundary.
4. Gate before using it. Held-out separation had to pass fixed thresholds, and the matched pairs had to cover at least 80% of the positives without reusing any negative.
5. Deploy cautiously. In the tie-break variant, an exact two-move fair search proposes; at most two columns within 2,500 points of its best are admitted; each is scored by the mean classifier opinion of seven public successors; exact ties fall back to the search's own choice.

What happened, in plain English

The classifier was excellent and the gate still stopped it. Held-out separation was about 0.92 — far above the 0.62 threshold — but only 74.0% of positives could be matched without reusing a negative, against an 80% requirement. Execution stopped there. No policy training started, no final classifier was saved, and every reserved seed range stayed shut. The gate was not loosened, the matching was not redone, and nothing was retried after the number was seen.

Used as a tie-break, a near-perfect classifier made play worse. A separate experiment fit one final scalar on the 3,032 pairs that had matched, reaching about 0.95 separation, and let it choose only between nearly-tied moves. On 16 games it averaged 253,799 points and 73.9 moves, against the unmodified search's 301,101 and 88.9. It cleared and revealed fewer discs per move, and it won both score and moves in only 5 of 16 games. Every improvement gate failed.

The ledger's own conclusion is the lesson: strong matched-state classification does not by itself rank close root actions correctly.

Two further attempts using it as a training reward were not retained. One shaped a fixed policy-gradient run with the classifier and improved training slightly while missing every floor; a second raised only the shaping strength and made things materially worse. Neither has a ledger record.

The technical record

Statuses in the experiment index: the oracle-manifold discriminator and the manifold root prior are rejected, ledger-recorded; both GAIL-shaping variants are rejected, task-record only with no ledger protocol, artifact hash, or per-game data retained.

From the ledger:

Discriminator. Fold 0 held-out AUC 0.924806 and paired ranking 0.930140; fold 1, 0.915419 and 0.912361 — against frozen thresholds of 0.62 and 0.58. Coverage 3,032 of 4,096 positives (74.0234%) against an 80% admission gate, so the run stopped in 12.574 seconds. Proposed policy-training seeds 0x3d6b1000...0x3d6b6fff, Stage-A seeds 0x3d6c0000...0x3d6c001f, and every protected and final cohort remain unopened.

Root prior. Whole-fit AUC 0.945853, matched-pair ranking 0.941953, logistic loss 0.291224. On 16 fitting games 0x3d6f0000...0x3d6f000f:

Policy	Mean score	Mean moves	Clears / reveals per move
Manifold root prior	253,798.875	73.938	1.826 / 0.986
Exact fair D3	301,101.062	88.938	1.936 / 1.063

It changed 31.53% of the search's moves, had two admissible candidates on 74.81% of moves, and won both score and moves in 5 of 16 games. The 32-game screen 0x3d6f1000...0x3d6f101f was never opened. docs/exploratory/audit-03-claim-arithmetic.md classifies both rows as corrected 17,000-point scoring; the ledger section itself does not state the mode.

GAIL variants. From the source comments and docs/exploratory/audit-05-optimistic-curriculum.md: the development variant trains a reflection-invariant 295-24-1 discriminator from the 3,032 matched pairs and shapes one fixed policy-gradient run; the scaled variant changes only the shaping coefficients (centred term 0.10 to 0.75, potential shaping 0.15 to 0.50) on a disjoint evaluation lane, holding the checkpoint, architecture, schedule, update, reward, and selection rule fixed. No achieved numbers from either were retained, so none are quoted here.

Sources: oracle-manifold-ppo.cpp, manifold-root-prior.cpp, manifold-gail-development.cpp, manifold-gail-scaled.cpp.

What this taught us, and what is still open

This is the cleanest "prediction is not ranking" result in the repository. A classifier at 0.95 separation is, by any normal standard, an excellent model. Given the job of choosing between two nearly equal columns, it lost score, survival, and disc throughput. Recognising the kind of board that survives is a different skill from knowing which move gets you one. The sibling-ranking page is the general statement of this.

It also shows what a matched control is worth. Because positives and negatives were matched on load and height, nobody can dismiss the 0.92 as "it learned to count discs." That rigour is exactly what makes the negative result usable.

And what an honest gate is worth. The 80% coverage requirement stopped a model that had already passed its accuracy thresholds. It would have been easy to relax; the record states plainly that it was not.

Still open. Whether the manifold signal helps as a feature inside a value function, rather than as a reward or a tie-break, was never tested. The two shaping experiments that came closest left no retained measurements, so they constrain nothing.