the average information content of transformer LLMs at about 3-4 bits per parameter

The problem is that 4-bit block-wise quantization does not guarantee preserving 4 bits of useful information per parameter - not even on average. It simply assigns one of 16 quantization levels to each weight, with the whole block sharing the same scale/range.

How efficiently those 16 levels preserve the model’s information depends on the weight distribution, block size, range/clipping strategy, outliers, and which weights are actually important. Some weights may be represented almost exactly, while others lose much of their useful information.

A simple example is an outlier: if you choose the range to preserve a very large weight, much of the 16-level dynamic range is spent on that outlier, leaving coarse resolution for all the smaller weights in the block. So 4 bits of storage does not imply 4 bits of useful information preserved. Yes, QAT helps, but usually at the cost of learning efficiency. It takes longer to train a model to the same quality when using less precision, and sometimes we simply cannot get to the same quality level with not enough precision in the right places.

Another problem in quantization is that we don't really know which weights are sensitive - we can compute various sensitivity metrics, and some of these metrics will correlate with accuracy on some benchmarks, but not on others.

Another complementary option is, if the model is fast enough, we should be able to push up correctness by self-consistency voting at close to T=1. Smart/fast Zero-shot classifiers like the recent Jev could help with aggregation across answers too, extending applicability.

I'm not convinced by this argument - if such a method improves accuracy of a degraded quantized model, then it could in theory also help non-degraded full precision model. And if so, then we are back to square one, because this composite model will then get degraded due to quantization (baseline has improved!)

We do know one thing - increasing the size of the model usually makes it more robust to quantization. If going from 8 bits to 2 bits speeds things up by a factor of, say, 4x, then if we double the size of the model, we might still end up with an overall speedup. Finding this balance might become a hot area of research.

Breaking the 1.58-bit Barrier for Ternary LLMs