Turing machines, Rule 110, and A::B reversal using Claude 3 Opus.
License: MIT License
Given only a series of input tapes, Opus learns to compute solutions for the A::B problem with 100% accuracy at 24 steps, and Rule 110 for a 12-token tape over 12 steps (accuracy over large runs not yet measured).
See:
Again, a really weird example of the copy error.
The last test run showed 4 errors, but it was actually the same error for Rule 1 four times. The batch start index was wrong after the refactor, it basically ran the same tests over and over again. Whoops.
For Rule 1 (and presumably other 1-y rules that were not tested, e.g. 11, 111), the LOOP token fails to indicate the following sequence correctly, and the model writes a 1. It's pretty hard to understand how it makes this mistake, since it has never seen a one in that position, but again I chalk it up to it having its attention balanced between several other things at once and it being slightly overwhelmed. Hard to reach a more technical conclusion at this point.
2024-04-21T22:37:02.4949028Z TAPE 1/9 0░ 1░ 2░ 3░ 4░ 5█ 6█ 7█ 8█ 9█ | TAPE 1/9 0░ 1░ 2░ 3░ 4░ 5█ 6█ 7█ 8█ 9█
2024-04-21T22:37:02.4949791Z PRINT 1/9 ░ ░ ░ ░ ░ █ █ █ █ █ | PRINT 1/9 ░ ░ ░ ░ ░ █ █ █ █ █
2024-04-21T22:37:02.4950371Z LOOP | LOOP
2024-04-21T22:37:02.4951008Z ░ 0░ 1░ ░ ░ ░: 0 → █ 0█ | 1
Goal will be to adjust the tape so this transition is less error-prone somehow, from the PRINT to the looping over the indices.
Notes for later.
Run:
https://github.com/SpellcraftAI/turing/actions/runs/8773913109
Errors: 6
TAPE statement.[2][1]
2024-04-21T17:41:57.7013398Z TAPE 5/9 0█ 1░ 2█ 3░ 4█ 5█ 6█ 7█ 8░ 9█ | TAPE 5/9 0█ 1░ 2█ 3░ 4█ 5█ 6█ 7█ 8░ 9█
2024-04-21T17:41:57.7014289Z PRINT 5/9 █ ░ █ ░ █ █ █ █ ░ █ | PRINT 5/9 █ ░ █ ░ █ █ █ █ ░ █
2024-04-21T17:41:57.7014817Z |
2024-04-21T17:41:57.7015386Z ░ 0█ 1░ ░ █ ░: 2 → █ 0█ | 5
[2]
2024-04-21T19:16:37.1773857Z TAPE 0/9 0░ 1░ 2░ 3░ 4░ 5░ 6░ 7░ 8█ 9█ | TAPE 0/9 0
Again, own notes for later.
This shows a good example of how sensitive this system is to copy errors given everything that it's doing at once.
2024-04-21T20:53:54.1557534Z TAPE 0/9 0░ 1░ 2░ 3░ 4░ 5█ 6░ 7█ 8░ 9░ | TAPE 0/9 0░ 1░ 2░ 3░ 4░ 5█ 6░ 7█ 8░ 9░
2024-04-21T20:53:54.1558294Z PRINT 0/9 ░ ░ ░ ░ ░ █ ░ █ ░ ░ | PRINT 0/9 ░ ░ ░ ░ ░ █ ░ █ ░ ░
2024-04-21T20:53:54.1558862Z LOOP | LOOP
2024-04-21T20:53:54.1559498Z ░ 0░ 1░ ░ ░ ░: 0 → ░ 0░ | ░ 0░ 1░ ░ ░ ░: 0 → ░ 0░
2024-04-21T20:53:54.1560163Z 0░ 1░ 2░ ░ ░ ░: 0 → ░ 1░ | 0░ 1░ 2░ ░ ░ ░: 0 → ░ 1░
2024-04-21T20:53:54.1560950Z 1░ 2░ 3░ ░ ░ ░: 0 → ░ 2░ | 1░ 2░ 3░ ░ ░ ░: 0 → ░ 2░
2024-04-21T20:53:54.1561585Z 2░ 3░ 4░ ░ ░ ░: 0 → ░ 3░ | 2░ 3░ 4░ ░ ░ ░: 0 → ░ 3░
2024-04-21T20:53:54.1562216Z 3░ 4░ 5█ ░ ░ █: 1 → █ 4█ | 3░ 4░ 5█ ░ ░ █: 1 → █ 4█
2024-04-21T20:53:54.1562850Z 4░ 5█ 6░ ░ █ ░: 2 → █ 5█ | 4░ 5█ 6░ ░ █ ░: 2 → █ 5█
2024-04-21T20:53:54.1563478Z 5█ 6░ 7█ █ ░ █: 5 → █ 6█ | 5█ 6░ 7█ █ ░ █: 5 → █ 6█
2024-04-21T20:53:54.1564128Z 6░ 7█ 8░ ░ █ ░: 2 → █ 7█ | 6░ 7█ 8░ ░ █ ░: 2 → █ 7█
2024-04-21T20:53:54.1564918Z 7█ 8░ 9░ █ ░ ░: 4 → █ 8█ | 7█ 8░ 9░ █ ░ ░: 4 → █ 8█
2024-04-21T20:53:54.1565580Z 8░ 9░ ░ ░ ░ ░: 0 → ░ 9░ 9/9 | 8░ 9░ ░ ░ ░ ░: 0 → ░ 9░ 8
Somehow, the termination index is actually what's breaking here. It will always be the same as the last index, in this example, 9/9, because the tape's final index is 9:
9░ 9/9
Yet it writes:
9░ 8
And probably was going to write 8/9 or 8/8 (the tape is currently stopped when there's an error). Either way, it's a surprising error to make, since the correct token is only 2 or 3 tokens away, 9[token] 9/9.
So, this has to be changed. There still should remain a stop token, but it will not be the index. I assume (hope) it's just one too many numeric series to keep track of, and just attending to the final missing position:
8░ 9░ ░ [IMPLIES STOP]
Might help, though the hope was that including the index would allow for it to learn the association of the final index as the stop token for that step in the training set, and removing it may make it stop the loop less reliably, which would be a problem.
Will try to change to a separate unique token. In past situations with this problem, when it's this stable and just on the edge, removing a little bit of data from each step log can get it over the finish line.
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