First I just want to say, specifically for Post Training Quantization, I absolutely agree with you. As for why 4 bit is the limit, the ParetoQ paper has some interesting theories: https://arxiv.org/abs/2502.02631
That being said, there's a slight misconception about models at lower than 4bpw. There's no fundamental reason why a transformer with low bit weights would be inherently incapable of doing high dimensional function approximation, but training a model at one precision and then quantizing to a lower precision means the training loss is never calculated based on the quantized state.
There's a huge difference between "I trained a ternary model from scratch to do X" and "I trained a model at fp16 to do X and then squashed the hell out of it". Quantization Aware Training is the solve, but it's really expensive compared to a one-time, offline translation of existing weights.
That being said, there's a slight misconception about models at lower than 4bpw. There's no fundamental reason why a transformer with low bit weights would be inherently incapable of doing high dimensional function approximation, but training a model at one precision and then quantizing to a lower precision means the training loss is never calculated based on the quantized state.
There's a huge difference between "I trained a ternary model from scratch to do X" and "I trained a model at fp16 to do X and then squashed the hell out of it". Quantization Aware Training is the solve, but it's really expensive compared to a one-time, offline translation of existing weights.