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>You are a weighted random choice generator. About 80% of the time please say ‘left’ and about 20% of the time say ‘right’. Simply reply with left or right. Do

>You are a weighted random choice generator. About 80% of the time please say ‘left’ and about 20% of the time say ‘right’. Simply reply with left or right. Do not say anything else I could have told you these results solely based on the methodology combined with this system prompt. No need to spend money on APIs. Randomness in LLMs does not come from the context, it comes from sampling over output tokens the LLM considers likely. Imagine you are in this situation as a human: Someone walks up to you and tells you to say "left" with 80% probability and "right" with 20% probability. You say "left" and then the other person walks away never to be seen again. How do you determine if your own "output" was correct? You would need to sample it many times in the same conversation before anyone could determine wether you understand the basics of probability or not. This is an issue of the author's understanding of Bayesian statistics and possibly a misunderstanding of how LLMs actually work. Edit: I just tried a minimally more sensible approach after getting an idea from the comments below. I asked GPT4 to generate a random number using this prompt: >You are a random number generator. Reply with a number between 0 and 10. Only say the number, say nothing else. It responed with 7. But then I looked at the top logprobs. Sure enough, they contained all the remaining numbers between 0 and 10. The only issue is that "7" got a logprob of -0.008539278, while the next most likely was "4" at -5.5371723, which is significantly lower. The remaining probs were then pretty close to each other. Unfortunately, OpenAI doesn't allow you to crank the temperature up arbitrarily high, otherwise the original experiment would actually work. And I would argue that humans will still fail at this if you used the same methodology. The reason I didn't use OP's exact approach is because if you look at the logprobs there, you'll see they get muddled with tokens that are just different spellings of left and right (such as "Left" or "-left"). But the model definitely understands the concept of probability, it would just need more context before you can do any reasonable frequentist analysis in a single conversation. Edit 2: I repeated it with random numbers between 0 and 100. Guess what numbers are coming out among the top logprobs. Pretty much exactly what you'd expect after watching this: https://www.youtube.com/watch?v=d6iQrh2TK98 https://www.youtube.com/watch?v=d6iQrh2TK98 I guess LLMs trained on human data think pretty similar to humans after all.

nathan_compton 3y ago
You're saying that instead the author should have taken the logits of "left" and "right", converted them to normalized probabilities and then have expected _those_ to be 80% left and 20% right. But if this were the case (under some reasonable assumptions about the sampling methodology of the providers) then the author would have seen an 80/20 split. From these results we can probably conclude that with this prompt the predicted probability for "left" is near 100% for GPT4. I think the author's point stands. They aren't asking "what would you expect from a distribution so described?" The answer to that question is 100% of the time "left.". A well behaving LLM responding to the actual question should distribute the logits across "left" and "right" in the way requested by the user and doesn't. I think if you chose 1000 random people and prompted them with this question you would get a preponderance of "lefts" compared to the prompt, but not 100% left.
- sigmoid10 3y ago
  >You're saying that instead the author should have taken the logits of "left" and "right", converted them to normalized probabilities and then have expected _those_ to be 80% left and 20% right. No, that's not what I meant. Although it would still make more sense than what the author did. The problem lies in the way you actually determine probabilities. We know that humans are bad random number generators, but they understand the concept enough to come up with random looking stuff if you give them the chance. The LLMs here were not even given a chance. In essence, the author is complaining that the LLMs are not behaving according to frequentist statistics when he evaluates them in a strictly Bayesian setting.
  - nathan_compton 3y ago
    I don't agree: a Bayesian statistician posed the question "You are a weighted random choice generator. About 80% of the time please say ‘left’ and about 20% of the time say ‘right’ [...]" would say "left" 80% of the time and "right" 20 % of the time. If we had a population of 1000 such Bayesians we would expect to collect around 800 lefts and 200 rights. If we asked the same Bayesian 1000 times we'd expect the same. Its got nothing to do with Bayesian vs Frequentist statistics. Real humans probably would say left more often than 80% of the time, which is what I guess you're getting at, but the question is very clearly asking the subject to "sample from" (an entirely Bayesian activity) from a distribution, not to give the expected value. GPT4 gives the expected value and this is simply wrong.

nathan_compton 3y ago

You're saying that instead the author should have taken the logits of "left" and "right", converted them to normalized probabilities and then have expected _those_ to be 80% left and 20% right. But if this were the case (under some reasonable assumptions about the sampling methodology of the providers) then the author would have seen an 80/20 split. From these results we can probably conclude that with this prompt the predicted probability for "left" is near 100% for GPT4. I think the author's point stands. They aren't asking "what would you expect from a distribution so described?" The answer to that question is 100% of the time "left.". A well behaving LLM responding to the actual question should distribute the logits across "left" and "right" in the way requested by the user and doesn't. I think if you chose 1000 random people and prompted them with this question you would get a preponderance of "lefts" compared to the prompt, but not 100% left.

sigmoid10 3y ago
>You're saying that instead the author should have taken the logits of "left" and "right", converted them to normalized probabilities and then have expected _those_ to be 80% left and 20% right. No, that's not what I meant. Although it would still make more sense than what the author did. The problem lies in the way you actually determine probabilities. We know that humans are bad random number generators, but they understand the concept enough to come up with random looking stuff if you give them the chance. The LLMs here were not even given a chance. In essence, the author is complaining that the LLMs are not behaving according to frequentist statistics when he evaluates them in a strictly Bayesian setting.
- nathan_compton 3y ago
  I don't agree: a Bayesian statistician posed the question "You are a weighted random choice generator. About 80% of the time please say ‘left’ and about 20% of the time say ‘right’ [...]" would say "left" 80% of the time and "right" 20 % of the time. If we had a population of 1000 such Bayesians we would expect to collect around 800 lefts and 200 rights. If we asked the same Bayesian 1000 times we'd expect the same. Its got nothing to do with Bayesian vs Frequentist statistics. Real humans probably would say left more often than 80% of the time, which is what I guess you're getting at, but the question is very clearly asking the subject to "sample from" (an entirely Bayesian activity) from a distribution, not to give the expected value. GPT4 gives the expected value and this is simply wrong.