The last time I saw any NaN's, they were a result of numeric overflow inside llama.cpp inference engine due to limited numeric range on fp16 (which was used on Vulkan) and gpt-oss-120b. The problem appears as the model suddenly getting stuck and only repeated G from there on. Sampler saw nothing usable due to the NaN being generated, all tokens had the same probability which was something like 0, and it chose one.

This is probably something similar: a value near the extreme range in some floating point accumulator that occurs during inference and happens to get triggered in Q4 quantization, but happens to not trigger on higher bit quantization. They fixed the issue on Vulkan by post-processing the results and replacing infinity values with the maximum representable real values. Downside of this is that it costs some performance.

As to perplexity, I think this is not a good measurement of quality for models with a chat template, as the perplexity is influenced by the missing chat template in the perplexity evaluation context. A large value like 8 is not reasonable, even 1B models probably have lower perplexity than this. I think we should see some value around 2 if the testing is done correctly. I have no every reason to expect that modern good large models like MiniMax and Qwen3.5 would get fairly comparable numbers appropriate for their parameter count if only we used the correct chat templates during the test.

I'm not sure how much this affects K-L divergence measurements, but I expect it's probably harming them as well. As long as the text being given to model is unnatural, i.e. not following its chat template, it is in some quasi-trained state, and measuring its performance in this condition and making quantization decisions could be a fool's errand.