When several pieces fit, which do you place next? Instead of one rule of thumb, carry several signals learned from strong boards and let them vote. Voting keeps the search from over-trusting any one hunch and marching into the same dead end.
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Building a board one piece at a time, the hard decision is which piece to place next when several would fit equally well. A single rule of thumb, cheapest cost first, most-constrained cell first, tends to march the search into the same dead end every run. A corpus prior improves on that with one learned signal. This technique improves on it again by carrying several learned signals at once and letting them vote, so no single hunch owns the decision.
From the corpus of strong boards you can learn more than one thing at a time, and the signals are cheap counts over the same board set:
At each step the beam scores every candidate placement by its matched-edge gain plus a weighted sum of the three signals, and keeps the top few. A little injected randomness stops the parallel beams collapsing onto one path.
This is the KEYRING experiment, a keyring of hunches rather than one. It reached 460 in a corner family no earlier search had cracked, which is the real payoff: because the strong boards are known to sit in isolated basins, a signal diverse enough to reach a new family is worth more than one that re-derives a known board.
A single learned signal has the same failure mode as a single hand-written rule: wherever it is wrong, it is wrong every time, and it drags every beam the same way. Three signals that were learned from different views of the corpus, position, adjacency, and patch quality, disagree in different places, and their disagreement is exactly the randomness that keeps the beams exploring different regions. The patch prior carries the most weight because it alone encodes bad: it can push the search away from a placement, not just toward one, which is the seed of the idea that grows into anti-pattern mining.
The same caveat as every learned signal applies. The three priors are mined from a corpus that is itself sub-perfect, so they encode the community's ceiling as much as its wisdom, and the vote reaches the top of the search's range reliably without lifting that range. Where that boundary sits is its own page.