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RoboticsAI Safety & AlignmentZenn AI/MLPublished: Oct 4, 2026, 22:00 JST

Yielding robots hit 74–77% on Penrose tiling

Yielding robots hit 74–77% on Penrose tiling

3 Key Points

  1. What happened

    On a Penrose tiling floor with 90 tile vertices, robots with only integer addition and comparison guessed unseen bar orientations at 74–77% with passes, 12–13 points above the no-pass majority vote.

  2. Why it matters

    The jump from 61.7–64.2% to 73.7–77.2% came from yielding rules — passes, sidesteps, waiting, and layer switching — not from more computing power, suggesting coordination itself can carry information.

  3. What to watch

    The author notes this does not surpass existing AI, and whether accuracy holds with more than two answers or a larger floor is left to future work.

WHO IT HITSThis is a research demo rather than a product, so it lands mainly on researchers exploring robot swarms, multi-agent coordination, and hardware-free AI that runs on integer arithmetic. It may be relevant to anyone weighing whether simple local rules and mutual yielding can substitute for heavier floating-point computation.

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Context & Analysis

The experiment sits on a Penrose rhombus floor whose 90 vertices are addresses; the left 32 form a retina, where an average of 2.8 addresses light up. Each exit has a scent layer computed by adding neighbors' values, and robots step toward the strongest neighboring scent. The core change is stacking yielding rules on top — one robot per address at a time, sidestep if the strongest neighbor is taken, wait if both are blocked, and switch layers if a pass is standing at the blocked spot.

What the results show is that coordination rules do more than prevent jams. When passes are removed, robots overlap and slip through, turning the task into a simple majority vote per address, and accuracy drops from 73.7–77.2% to 61.7–64.2%. The author also found that learning layer-switching passes produced 14 passes split by orientation: some work only for vertical bars while others fire only for horizontal ones. Waiting itself differs by orientation, measured at 2.03 times per bar for vertical and 1.61 for horizontal.

The author frames this as a companion to local-rule research in swarm robotics, not a new method. The test ahead is whether the same approach holds when the answer has three or more categories, or when the floor and image scale up.

FAQ
What exactly did the model learn?
It learned only 0 and 1 passes: one set deciding which layer each robot starts from per retina address, and another deciding whether a blocked robot switches layers.
How does this compare to existing AI?
The article says it is not about surpassing existing AI — it is a re-examination of how AI works from the single angle of addition-only computation.
What are the conditions that made the answer possible?
Two things together: robots staying under 10% of the floor (spare room) and yielding rules (passes, sidestepping, waiting, layer switching).

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