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My interpretation is that while it did learn the exact computation and not just a statistical approximation, it's still limited to a grid of a given size. In that sense the attention matrix is brute forced and the network did not learn a generalization. The article itself says "The largest grid size we successfully trained was 16x16".

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They're using learned positional embeddings for each grid cell, so there's no straightforward way to extend a model trained on a small grid to a larger grid. If you go from large to small, I think it would do better than chance, but get the periodic boundary condition wrong, because the period changes with the grid size.

Using 2D RoPE instead would in principle allow scaling up as well, and maybe even period detection if you train it across a range of grids, but would eventually hit the same issues that plague long-context scaling in LLMs.

Yes, it does not understand (or has learned) the rules of the game then. For that being the case, it should be able to apply the rules correctly in a slightly different context.

Would it be possible to train an LLM on the rules how we would teach them to a human?

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