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How well can the GPT architecture solve the parity task?

by FactorialCode1 min read11th Jul 20203 comments

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Suppose I give it pairs of strings and ask it to output 1 if the the number of 1s in the string is even and zero if it's odd.

e. g.

0 -> 0

1 -> 1

11 -> 0

101 -> 0

1101-> 1

10101001 -> 0

111000101110 -> 1

How well does it do on this task? What if we finetune it on sample data?

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1 Answers

It does not, sad to say. I tried space-separating each digit for the BPE issue, and its general completion is to just copy the previous line. The log probs of the possible completions are generally 50:50 for 0/1, showing it's not tapping into any parity counting.

One interesting update: we've been increasingly unlocking GPT-3 solutions by rewriting them as multi-step procedures. So parity might be doable by somewhat cheating and writing out a series of steps for computing the parity for each example: https://twitter.com/bucketofkets/status/1285100951271952384 https://twitter.com/Malcolm_Ocean/status/1285099206781341696

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If you try this, reformat to work around the BPE problem as detailed in https://www.gwern.net/GPT-3#bpes