Earlier quoted context omitted.
early int4 experiments seem to indicate it's possible but you do lose performance, see this thread https://www.reddit.com/r/MachineLearning/comments/11i4olx/d_... edit: to clarify, it may be possible to get this loss back and there is reason to be optimistic
Probably the best method is to just train it on int4 in the first place. Fine tuning after quantization would definitely help though.
Unclear why you think that since experiments show the opposite.
In general the gradient seems to get too "bumpy" to do good gradient decent at lower levels of precision.
There are some papers showing that making the training loop aware of quantitization can help ultimate quantizied performance but I'm not aware of this being implemented at large scale.