EXL2 quantization error / fine-tuning?

[SinanAkkoyun]

Hey!

When quantizing, a quantization error occurs, which is being minimized by the use of calibration data. When quantizing a full-precision model, this is the only option.
However, when fine-tuning with qLora, one can (I think) export the quantized model directly.
Doing this "Quantization aware training" while fine-tuning seems to promise more accurate fine-tuned models than calibrating afterwards.

Let's say one fine-tunes a model with GPTQ qLora and directly exports the quantized model. Would that model perform better than one that got the whole fine-tuning dataset as calibration data only?

I am just very interested in the highest reliability of outputs from quantized models, as I hope that with the right optimization, the error could potentially be eliminated, but I'd like to get external expert optinions on that! :)