Can gzip be a language model?

  gzip -9 sports.txt   testfile.txt

  gzip -9 politics.txt testfile.txt

  gzip -9 business.txt testfile.txt

The test file belongs to the topic with the smallest size *.gz file.

Witten's group at Waikato uni were perhaps the first to work on this.

Also check out the Hutter prize if you are interested in this.

    give it a normal text prompt, and it
    continues that prompt by searching
    for the byte sequences that compress
    best.

So the result only gives us some lower bound of how well gzip works as a "plausibility tester" of a continuation of a text. The space of possible sequences is many orders of magnitude larger than what was searched. So there might be sequences in there that compress much better.

The text mentions beamsearch, but I don't see a discussion about how well beamsearch performs in finding the global optima when it comes to gzip compressibility of a text?

https://bellard.org/ts_zip/ https://corecursive.com/the-hutter-prize/

Learning being a compression is also recently proposed as Gibbs compression proposition.

See Gibbs randomness-compression proposition https://arxiv.org/abs/2505.23869v5

Video from tsoding where he implements the algorithm: https://www.youtube.com/watch?v=9n39SbRPXKQ

https://arxiv.org/abs/2506.01084

Some models are reproducible, in that the same prompt will generate the same output. Say that we could wire up such a model to generate some code.

In that case, we could create a prompt that generates, say, an entire codebase, or a large piece of text. The prompt (or really, the tokens) would then be the compressed version of the codebase or the text.

I am not talking about an "AI agent", but really a model that we call in a reproducible manner. Preferably one call, with one prompt. An agent could just run `git clone` to "decompress" a codebase, which conflates the idea of compression. If that were compression, then the "compressed version of the git kernel" would be a single line of text: `git clone https://git.kernel.org/pub/scm/linux/kernel/git/torvalds/lin...`. I am really talking about having an LLM re-generate text based on a prompt.

Does that make sense? I can imagine that this is highly impractical and inefficient. But would this count as "compression" at all?

Viz. if Language is compression (of thought / culture / the tacit je ne sait quois of being-to-being communication etc.), then definitionally, Language Modelling must also be Compression.

Except, language is an arbitrarily lossy compressor, who's "compression-prediction equivalence" is indeterminate and unstable, because Language co-evolves constantly; both as a function of or response to culture, as well as an influencer of culture.

So, the subjective-objective goodness of Language Models (of any kind of language) would be, at best, upper-bounded by the compression-prediction equivalence of the Languages corpus itself. And that is assuming the language corpus is perfect in every way---it captures all knowledge expressible by language and it is always in-sync with live evolution of all language expression and evolution (i.e. LLM training is not a batch job, but a real-time present continuous process).

For example, to my layperson eyes, the mathematical language of proofs actively weeds out ambiguity of subjective interpretation. Ideally, a proof ought to lead to the exact same conclusion on every single reading by any reader who can follow the steps. A proof also holds only if the rest of the formal, explicit, inviolable, internally-consistent set of axioms and results holds.

So it stands to reason that mathematical prose of proofs, being optimised as mechanical procedure of taking an open question to a deterministically closed solution, has better odds of approximating the tacit aspects of mathematical derivation.

Which makes an LLM able to construct a mathematical proof, which is mind-melting to say the least.

However, I wonder, can LLMs dream of mathematical sheep?

  gzipt \
      --corpus data/tinyshakespeare.txt \  
      --prompt $'MENENIUS:\n' \
      --length 200 \
      ;
  
  MENENIUS:
  MtLUMSeptuttyyyxyxyxyxyvyyyxyxyxyxyvyyyxyxyxyxywyvzyxyxyx
  yyxyyyxyxyxyxyxPlyxyxyxyxyxyxyxyxyxtoxzfTUS.zxzzzyzzzvzzz
  vzzzxvzyvyxyxyxyvyxyxyxyvy--,Vdvyxyxyxyxyxyxyxyxyxxy!zFlx
  zzyyxyxyxyvyxyxyxyvyySPffuyuy

Zstandard produces whitespace with the occasional letter thrown in. To quote MiMo: "As you can see, zstd does not speak Shakespeare. ... zstd encodes a run of one repeated byte as a near-free run-length sequence, and space and newline are the cheapest literals in the corpus: ten newlines cost about the same to append ten bytes of genuine corpus text and less than nonsense does."

Compression is a property of language.

A seemingly simple sentence like "I had lunch" has enormous amount of information compressed inside it.

The word lunch is a compressed form of "having food at noon" while "noon" in turn is a compressed form of "Sun's position against Earth's rotation" and so on and so forth.

Every sentence has layers of compressed sentences. How many layers one chooses to decompress is up to the person.

[1] https://en.wikipedia.org/wiki/Hutter_Prize

https://www.youtube.com/watch?v=l6DKRf-fAAM

In the 2023 discussion of "Demoscene accepted as UNESCO cultural heritage in The Netherlands" I posted a transcript from a video of Will Wright discussing the demo scene:

https://news.ycombinator.com/item?id=36599415

Will Wright Discusses the Demoscene:

https://www.youtube.com/watch?v=m7iuFVmTJus

>You can take any piece of content in the game, and imagine an algorithmic solution to it. Or also, you know, a way that the player could customize that object of thing.

>There's this group in Europe called the Demoscene that make these very elaborate demos for a computer that fit into very tiny little memory blocks, you know like 64K of memory, and you run the thing, and in fact it algorithmically generates about 100 megabytes worth of data, you know these rich 3D environment, generated music, generated wave files, generated animation.

>And they're developing techniques to generate, you know, huge amounts of interesting data, with very very simple, elegant, compression algorithms.

>And this is a skill that game developers used to have, back in the 8-bit days. That was the only ways to do a game like Karateka(?), was to find all these little tips and tricks to compress things and generate them algorithmically.

>But since the CD-ROM came out, and very cheap hard drives, storage is cheap, so basically we've lost that skill set, and now we attack all those problems with brute force. I think we've lost something by dropping that skill set.

[...]

https://news.ycombinator.com/item?id=36613058

[...] Here's a simple low-tech pre-LLM example that shows the equivalence of compression and procedural content generation:

Take a huge text file of HN postings, and compress it with gzip or compress or some other robust compression algorithm. The better the algorithm, the more the output will look like random noise. Then slice the compressed file in half, and replace the second half with random numbers. Then uncompress it. You'll find that at the point you sliced it, it keeps on writing out almost plausible text for a while, consisting of highly probably snippets of commonly encountered words and phrases, then goes downhill towards incoherence. It's not as coherent or confident as an LLM, but the point is to show how low the bar is for using compression for procedural content generation.

LLMs are essentially a form of compression of the world's knowledge or whatever they're trained on, not just word frequencies or pixel patterns, but also concepts and ideas. [...]

Some will say that I should 'judge the idea, not the form'.

But if the author didn't find enough strength to write alone a short ~700 words summary about his work, it means he himself isn't that interested or enthusiastic about it. Why should others bother then? Particularly since low-effort like that signals possibility the whole work is superficial and derivative.

The fact that gzip is relatively fast should be your first clue that something important is missing.

Gzip is great at predicting the next token for one very specific narrative. LLMs can predict next tokens for entire universes of narratives. Searching for the correct next token across this space scales ~quadratically with the input size. Gzip scales linearly. I can gzip a one terabyte file. Imagine feeding that much into an LLM. These are wildly different animals that happen to overlap in a very small way. Equating compression to intelligence looks increasingly silly to me.

If we must compare language models to compression, they are much more like jpeg and mp3 than they are gzip and flac. I can go fuck with a jpeg file pretty severely at the bitstream level and still have something resembling performance on the other side. Gzip cannot remotely approach this.