The subtle idea in learning from strong boards: not every agreement between them is good. Some shared placements are real structure; some are a shared trap that caps every search just short of the top. Separate the two, and attack the trap.
Reproduce this result: prose — no computation behind this page
Every technique so far treats agreement between strong boards as a good thing: where the good boards concur, follow them. This one takes agreement apart, because some of it is a trap. When many independent searches all reach a high but imperfect board, they agree on a great many placements, and some of that agreement is genuine structure while some of it is a shared bad habit: a local choice that looks good, feels forced, and quietly caps every search just short of the top. The whole idea is to tell the two apart, then attack the trap.
A single count cannot separate real structure from a trap, because both show up almost everywhere. The trick is to compute two frequencies for each candidate pattern and compare them. Over a corpus of boards scoring across a wide band, for every adjacent cell-pair and every piece-pair that ever sits there, measure:
together with a ceiling: the best score of any board that contains the pattern. Two categories fall out. Good consensus is high with a high ceiling, a pattern that strong boards share and the very best boards keep: real, trustworthy structure. A consensus trap is high with a ceiling stuck just below the top, a pattern almost every board adopts but no top board does: the agreed-upon wrong choice that locks a whole family below the record. The single-frequency view cannot distinguish them; splitting by basin is the entire move.
Knowing where the traps are turns the corpus into a map of which placements to
trust and which to pull apart. The PALIMPSEST
experiment uses it to steer an ALNS
search: take a board caught in the trap basin, find the wedge whose removal breaks
the most trap patterns while sparing the good-consensus ones, deliberately break
those cells, and hand the board back to the repair loop, whose destroy operator
tears open exactly those broken regions and rebuilds them. Steered this way, it
reached 463, the best board this project has produced (the
PALIMPSEST experiment,
whose committed board reproduces via just research-record-boards).
The caveat is the lesson. Trying to use the trap list directly, forcing the search to avoid every trapped placement, did not work and made boards worse. The value was in reading the corpus to choose where to aim the search, not in hard-coding its conclusions as a ban. A learned map is a good place to point a search and a bad set of shackles to bolt onto it, which is the same boundary between tiebreak and objective that runs through corpus priors, seen from the other side: here the danger is not over-weighting a good signal but over-trusting a signal about what is bad.
Even steered perfectly, this does not clear the top. Rebuilding the trapped regions tends to land back on the same known top board rather than a genuinely new one, because the trap is not a mistake a smarter search avoids; it is the rigidity wall itself. That is the subject of the collapse page.