As long as the serial dependency of “you have to compute X before you can even start computing Y” holds, it shouldn’t matter if X comes before Y in the input sequence or after.
No, I think it does matter if you get X before Y vs Y before X. Serial depth isn’t everything—fanout matters too.
But first, I agree with your point that in a pure transformer attention architecture[1] you are limited in serial steps to the layer count; additional input tokens don’t give you more serial steps. And I shouldn’t have mentioned “Even stackless O(1) memory machines can ‘compute as they read’” as a weak architecture, because that architecture doesn’t have that step-layer limit.
But despite the inescapable step-layer limit, I think order of data presentation and “computing as you read” still matters a lot for transformers! Take this example:
Add these ciphered numbers, where the digits have been replaced
with letters according to this cipher code:
f=0, d=1, g=2, k=3 a=4, e=5, c=6, b=7, h=8, i=9
hgi + bci + kie + bbc + gca + cab + ggg + hcb
If a transformer sees the cipher key before the encrypted numbers, it can sum
(Layer 5) 4769 ← no CoT needed!
(Layer 4) 2769 + 2000
(Layer 3) 1598 + 1171 + 911 + 1089
(Layer 2) 829 + 769 + 395 + 777 + 264 + 647 + 222 + 867
(input) hgi + bci + kie + bbc + gca + cab + ggg + hcb
You could sum a lot of numbers with divide and conquer. 20 layers lets you sum a million numbers.
But what if the transformer sees the encrypted numbers before the cipher key? Now the transformer has a problem. It can’t do much as it reads the ciphered numbers[3] before it had the cipher key. It has very little room, O(1), to do computation after its reads the cipher key. A looped architecture might be able to decipher and add the numbers on the last token’s residual stream, but a pure transformer couldn’t.
- ^
I think most modern architectures aren’t pure attention anymore, and use recurrent stuff (recurrent in the text direction, not the layer direction)
- ^
Pedantic note: you’d need an extra layer I’m not including here to decipher the numbers with induction heads
- ^
There probably are some clever ways to help “add” cyphered numbers but let’s ignore that for now.
I think the limiting bit isn’t the physical hands, but the ability to control what you squeeze by touch and feel.