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@scaling01

A few more observations after replicating the Tower of Hanoi game with their exact prompts: - You need AT LEAST 2^N - 1 moves and the output format requires 10 tokens per move + some constant stuff. - Furthermore the output limit for Sonnet 3.7 is 128k, DeepSeek R1 64K, and… https://t.co/ax5ZK4WkGx

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                                      "text": "I was wondering why LLMs can do so many steps on Hanoi but not in the other games...\n\nIn the paper they use the minimum/optimal path length as a proxy for problem difficulty or compositional depth, like 2^N - 1 for Towers of Hanoi, (N+1)^2 - 1 for Checker Jumping and some linear term for River Crossing and Blocks World.\n\nBut optimal-path length is a bad measure for the problems complexity. Because it doesn't tell us anything about how hard it is to find any solution at all, it just tells us the length of the solution.\n\nEven though the search space of Towers of Hanoi is huge you don't actually have to perform any kind of search or backtracking because there is only 1 simple rule to apply (that the LLMs know) and therefore only 1 possible path.\n\nI'm no combinatorics freak, but I let o3 and Gemini 2.5 Pro search some other, maybe better suited metrics for the games complexity. And they consistently ranked the games difficulty like this:\nRiver Crossing >> Blocks World > Checker Jumping > Tower of Hanoi. And this is also what you can see in their charts.\n\nSo their claim in blue doesn't hold or their framing that \"Models may struggle with puzzles of lower compositional depth while succeeding on different puzzles with higher compositional depth\".\n\nAnd with that their \"Open Questions and Puzzling Behavior of Reasoning Models\" aren't all that puzzling lol",
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