We started out training everything in full (f32) or double precision (f64), then around 2020 everyone switched to half precision (f16) with some stuff in full precision, now we are starting to move to quarter precision, and the newest Nvidia card even supports f4 (eighth precision?). And then of course there's the 1.58bit LLM paper.

So there has been a steady stream of people questioning the underlying precision, and most of the time the answer they came back with was: there's more precision than we need, a larger network with less precision is faster and better than a smaller network with more precision

What makes this especially tricky is that small models are truly 100% deterministic at temp=0 because the relative likelihoods are too coarse for FPU issues to be a factor. I had thought 3.5 was big enough that some of its token probabilities were too fine-grained for the FPU. But that's probably wrong.

On the other hand, it's not just GPT, there are currently floating-point difficulties in vllm which significantly affect the determinism of any model run on it: https://github.com/vllm-project/vllm/issues/966 Note that a suggested fix is upcasting to float32. So it's possible that GPT-3.5 is using an especially low-precision float and introducing nondeterminism by saving money on compute costs.

Sadly I do not have the money[1] to actually run a test to falsify any of this. It seems like this would be a good little research project.

[1] Or the time, or the motivation :) But this stuff is expensive.