Those two metrics will converge as the size of the text being compressed goes to infinity. It's necessary to include model size for things like the Hutter prize that involve compressing a fixed text (to avoid hard-coding) but isn't usually a useful metric for compression, especially because it will cause the compression ratio to depend on the size of the data being compressed.
Edit: I thought the model in the above paper was pre-trained, but apparently it's only trained on the data as it arrives! That's indeed a very interesting approach, I wouldn't have expected that neural network models would converge quickly enough for it to be useful.
After a bit more digging, it seems Bellard also has a version using GPT-2: https://bellard.org/libnc/gpt2tc.html
Looks much cleaner and faster than my little winter break project, cool to see this implemented properly!
Oh hey I did something like this a while ago, but much less polished. I basically made an rANS encoder and hooked it up to GPT-2 (via the excellent transformers library from HuggingFace) to see what compression ratio I could get. Bellard's approach seems to use a custom model, which is probably advisable as big language models like I used are very slow. I didn't try to optimize much and only ever tested on my little personal laptop with just CPU, but I only got encoding speeds of ~0.1 Kb/s (limited mostly by available memory). However I was able to get very good compression factors of 6.5x using standard GPT-2 and 7.3x using the medium version.
Here's the code if anyone's interested: https://github.com/trsigg/lm-compression . I haven't looked at it in a while except for updating it today to work with more recent versions of the transformers library, but I think it should still function and is pretty easy to try out with different models. I thought about using something like a hidden Markov model instead which would be much faster (even more so because it would enable using tabled rather than range-based ANS), but I haven't gotten around to it.
Edit: I thought the model in the above paper was pre-trained, but apparently it's only trained on the data as it arrives! That's indeed a very interesting approach, I wouldn't have expected that neural network models would converge quickly enough for it to be useful.