# Learning from strong boards

> A study in five experiments of one idea: instead of searching Eternity II from first principles, mine the corpus of strong boards already found for structure and feed it back into a search. A position prior, a learned move-vote, a scarce-demand compass, an anti-pattern miner, and a record decode, ordered from the simplest signal to the subtlest, and the one wall all five reach.

- Canonical page (with interactive figures/demos): https://eternity2.dev/research/lab/experiments/raphael-anjou/learning/
- Updated: 2026-07-16
- Topics: learning, construction

---
Most of this notebook searches Eternity II from first principles: a beam builds a
board from an empty grid, a backtracker digs and retreats, a repair loop polishes
a full board by moves. Each reasons only from the rules of the puzzle and the
board in front of it. This study is the exception, and it is a study rather than a
loose set of runs because all five experiments in it ask one question from
different angles: **what can a search learn from the boards people have already
found, and how far does that carry it?**

The raw material is a corpus of strong boards, every arrangement the community and
this project have pushed above 400 of 480. The move, in every experiment here, is
to read that corpus for structure (where pieces sit, which pieces touch, which
local patterns recur, which agreements are traps) and feed the structure back into
a search as a bias. It is closer to imitation learning than to search design, and
it earns its own home because the same handful of ideas keep returning, each a
little sharper than the last.

The corpus itself is [published](/research/build/dataset): 7,658 distinct boards
scoring 400 to 469, released under CC0, with the diversity check that stops a
learned signal from merely re-encoding one board. The method-agnostic write-up of
each technique lives in the theory section on
[learning from strong boards](/research/build/learning); the pages here are the
lab side, the runs that put each technique on the real 16×16 board, with their
scores and the questions they left open.

## The five experiments, simplest signal to subtlest

The study reads as a sequence. Each experiment adds one turn of the screw over the
one before it, and the pages are ordered to be read in that order.

| # | Experiment | The learned signal | Reached (of 480) |
|---|---|---|---|
| 1 | [PRIOR](/research/lab/experiments/raphael-anjou/learning/prior) | where each piece tends to sit, a single position count | 460 |
| 2 | [KEYRING](/research/lab/experiments/raphael-anjou/learning/keyring) | three signals (position, adjacency, 2×2 patch) voting together | 460 |
| 3 | [LODESTONE](/research/lab/experiments/raphael-anjou/learning/lodestone) | which pieces serve a scarce colour demand, a faint compass | 451 |
| 4 | [PALIMPSEST](/research/lab/experiments/raphael-anjou/learning/palimpsest) | the shared bad habits that cap boards, mining the trap not the structure | 463 |
| 5 | [REPLAY](/research/lab/experiments/raphael-anjou/learning/replay) | the one move a single record board used that our search could not | 460 |

**[PRIOR](/research/lab/experiments/raphael-anjou/learning/prior)** is the simplest
form the idea can take, a count: over the strong boards, how often does each piece
sit in each cell? Used as a construction tiebreak it builds a competitive board
from nothing and reaches 460. **[KEYRING](/research/lab/experiments/raphael-anjou/learning/keyring)**
adds signals rather than trusting one, letting a position count, an adjacency
count, and a learned 2×2-patch quality vote on each placement, which carries a
build into a corner family no earlier search had cracked.
**[LODESTONE](/research/lab/experiments/raphael-anjou/learning/lodestone)** goes the
other way, to a single deliberately faint signal (a per-piece scarce-demand
weight) and, in doing so, finds the knife-edge that runs through the whole study:
the moment a learned signal stops being a tiebreak and starts being the objective,
the search collapses.

**[PALIMPSEST](/research/lab/experiments/raphael-anjou/learning/palimpsest)** is the
subtle turn. Every experiment before it trusts agreement between strong boards;
this one asks which agreements are *traps*, placements every board adopts but no
top board keeps, and steers a repair search to attack them. It produced this
project's best board, 463. **[REPLAY](/research/lab/experiments/raphael-anjou/learning/replay)**
learns from a single board rather than a statistic: rebuild a community record
exactly, and whatever you must add to your search to make it walk that path is the
ingredient it was missing. Here that was the double break, the move that lifted the
strict ladder from 458 to 460.

## The one wall all five reach

The through-line is what makes this a study and not a bag of tricks, and it is a
sobering one. Every signal here is safe only as a gentle bias: over-trust it and
the search falls apart (LODESTONE drops from 451 to 380 as its weight climbs;
PALIMPSEST's trap list helps as a steer and hurts as a ban). And even used
perfectly, none of these signals raises the ceiling. They reach the top of a
search's own range, fast and reliably, and stop, because the corpus they learn
from is made of boards that all hit the same
[rigidity wall](/research/why/rigidity-wall). Learning from strong boards is the
fastest way *to* the plateau and, on its own, no way *past* it. That failure mode
is the subject of the theory section's
[collapse capstone](/research/build/learning/when-learning-collapses), and it is
the note the whole study resolves on.

This is one of three studies in the [experiments notebook](/research/lab/experiments/raphael-anjou).
Its siblings, the [DFS study](/research/lab/experiments/raphael-anjou/dfs-study)
and the [repair study](/research/lab/experiments/raphael-anjou/repair-study), take a
single search paradigm apart one decision at a time; this one holds the paradigm
loose and varies what the search is allowed to *know*.

## Pages in this section

- [PRIOR](https://eternity2.dev/research/lab/experiments/raphael-anjou/learning/prior) — Build a board from nothing, breaking ties by where pieces tend to sit in the strong boards we already have. It reaches a high score with no starting board to copy.
- [KEYRING](https://eternity2.dev/research/lab/experiments/raphael-anjou/learning/keyring) — Build a board from scratch, ranking each next piece by three signals learned from past strong boards. Reached 460 in a board family no earlier search had cracked.
- [LODESTONE](https://eternity2.dev/research/lab/experiments/raphael-anjou/learning/lodestone) — A faint compass for a from-scratch search: nudge it to commit the rare pieces early, where they're needed. It doesn't raise the ceiling; it makes the search reliably reach the top of its own range.
- [PALIMPSEST](https://eternity2.dev/research/lab/experiments/raphael-anjou/learning/palimpsest) — Read every strong board to find the habits that quietly hold a board back, then break them. This experiment produced the project's best board: 463 of 480.
- [REPLAY](https://eternity2.dev/research/lab/experiments/raphael-anjou/learning/replay) — Rebuild the community's strict 460 boards exactly, and in doing so discover the move ordinary solvers can't make: paying two mismatches at a single cell.

## Related

- [Learn from strong boards](https://eternity2.dev/research/build/learning) — Most attacks on Eternity II search from first principles. A distinct family does the opposite: it mines the corpus of boards people have already found for structure, then feeds that structure back into the search. Position priors, learned move-ordering, anti-pattern mining, record decoding, and the failure mode where a learned signal collapses.
- [The dataset](https://eternity2.dev/research/build/dataset) — A public, CC0 dataset for Eternity II in two parts: fourteen benchmark instances to solve, and a corpus of 7,658 distinct strong boards to learn from. Every score is recomputed from the board itself, and the corpus is checked to be genuinely diverse rather than a thousand copies of one board.
- [Raphaël Anjou's experiments](https://eternity2.dev/research/lab/experiments/raphael-anjou) — A notebook of Eternity II search experiments, organised into the shared engines they run on, the combination pipelines that chase the score, three studies that take one search paradigm apart a decision at a time, and exact endgame solves. Each has its idea, its best board, and the questions it left open. The best reaches 463 of 480.
- [The DFS study](https://eternity2.dev/research/lab/experiments/raphael-anjou/dfs-study) — One question, asked carefully: among depth-first backtrackers for Eternity II, what does each fill order, each heuristic, and the break mechanism actually buy? A family of from-scratch backtrackers, each one change apart, run on the same ten corner-pinned variants, single core, sixty seconds.
- [The repair study](https://eternity2.dev/research/lab/experiments/raphael-anjou/repair-study) — The sibling of the DFS study, for the other way people attack Eternity II: destroy part of a board, rebuild it, keep the change if it helps. One question, asked carefully. What does each decision in that loop buy: which region to destroy, how to rebuild it, when to keep a move, when to restart, and what board to start from?
- [The rigidity wall](https://eternity2.dev/research/why/rigidity-wall) — Every record board we have is frozen in place. You cannot nudge your way from a great board to a perfect one, and we can prove it.