> There's no fundamental reason why a transformer with low bit weights would be inherently incapable of doing high dimensional function approximation,
Sure, in fact you can train a 1 bit model to approximate any function. But that is not the point. The problem is that the capacity per weight is diminishing below ~4.5bpw.
With QaT, can you compensate for that by adding more weights. So, instead of training a 1B x 4bpw model to capacity saturation you can train a 4B x 1bpw model and achieve the same capacity. But you will end up with the same number of bits in the model, just distributed differently.
Here are some older experiments of mine with very small models:
https://github.com/cpldcpu/BitNetMCU/blob/main/docs/document...
I am quite certain that similar behavior is true also for larger models - it may be more difficult to experimentally demonstrate due to information bottlenecks and the flops required to train them to saturation.
Maybe? I am using a 3 bit quant for Qwen Next Flash in a 64G Mac using Sushi and the results for coding, design, refactoring, etc. are very good.
That said, after being satisfied with Poolside.ai’s Laguna XS 2.1 4 bit quant, when I upgraded to a 64G Mac, I now only run the 6 bit quant and the results are better.
Unfortunately, I think that benchmarks are not useful for me, and I need to take time seeing what works for me: this is one reason that when I find a combination of model, harness, etc. that works for me, then I tend to use it for a month or two before looking around for new stuff.
>As for why 4 bit is the limit, the ParetoQ paper has some interesting theories: https://arxiv.org/abs/2502.02631
Its not so clear to me what their real explanation is. Yes, it is possible to redistribute the quantization error, but this only works when the model is not trained to capacity.