Can gzip be a language model?

I wanted to see how this would work with bzip2 and zstd. The source is public at https://github.com/nathanrs/gzipt, and I asked MiMo-V2.6-Flash to fork and modify it. The answer is that bzip2 produces sequences that don't resemble human language:

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

(Line breaks added.) This looks roughly optimized for the most repetitive Burrows-Wheeler transform (https://en.wikipedia.org/wiki/Burrows%E2%80%93Wheeler_transf...).

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."

I've been pondering on something related: can an LLM be a chat?

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?

Yes: you can classify a test file by topic with gzip as follows:

  gzip -9 sports.txt   testfile.txt

  gzip -9 politics.txt testfile.txt

  gzip -9 business.txt testfile.txt

(ass. sports.txt politics.txt and business.txt are text docs pertaining from the sports, politics and business domains, respectively, and have equal size)

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.

This tracks perfectly with Winrar being more profitable than OpenAI... coincidence? I think not!

3blue1brown did a series on this topic: https://www.youtube.com/watch?v=l6DKRf-fAAM https://www.youtube.com/watch?v=GlYgs6v2YfU (i think one more is yet to release)

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

One moment, how are we supposed to know how well that search was done? There is no way to search a meaningful part of the search space.

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?

R. Hendricks, D. Chugtai, and J. Dunn, "Lossless compression via optimized middle-out bitstream processing," Pied Piper Inc., Palo Alto, CA, Tech. Rep. 42, Apr. 2014.

This is fun, but historically people have gone a bit overboard with saying that models like this, or n-gram language models, are anywhere close to large neural network models. There is certainly a connection though.

I think language itself is compression, so the arxiv paper tracks for me.

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?

I'm more interested in the converse question: how well does an LLM perform as a compressor, compared to gzip (ignoring its insanely lower speed)?

Yay, another mostly AI authored piece with vibe-coded aesthetics.

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.

Good article.

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" and "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.

Previous discussions of that specific page https://news.ycombinator.com/item?id=48557691

Interesting approach, I wonder how this could be used as a classifier. :)

Only if it can run DOOM.

.

Not without attention or something approximating it.

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.