I think OmniQuant is notable because it shifts the bend of the curve to 3-bit. While < 3-bit still ramps up, it's notable in that it's usable and doesn't go asymptotic: https://github.com/OpenGVLab/OmniQuant/blob/main/imgs/weight...

What EXL2 seems to bring to the table is that you can target an arbitrary quantize bit-weight (eg, if you're a bit short on VRAM, you don't need to go from 4->3 or 3->2, but can specify say 3.75bwp). You have some control w/ other schemes by setting group size, or with k-quants, but EXL2 is definitely allows you to be finer grained. I haven't gotten a chance to sit down with EXL2 yet, but if no one else does it, it's on my todo-list to be able to do 1:1 perplexity and standard benchmark evals on all the various new quantization methods, just as a matter of curiosity.

Can you do tuning/training on quantized models? Or are they inference only?

This paper[1] attempts to do LoRA fine tuning on quantised LLMs. The LoRa weights themselves are full precision, but they're much smaller. Although, I haven't had a chance to try it yet.

[1]: https://arxiv.org/abs/2306.08162