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Comment by pjankiewicz | Hacker News Reader

I was thinking about the same topic and the conclusion can be wrong. LLMs are compressors, but compressors are not LLMs. Mixing this can let you believe that you can use a compressor to do the same thing as LLMs, which you cannot.

Specifically I was thinking about a way to inject knowledge into LLMs training by using statistical properties of text in such a way that you don't have to train the LLM to achieve some level of predictions. There are actually some papers that inject n-grams statistics as a part of the neural network weights.

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Any compressor actually can be used, trivially, as an autoregressive language model.

Given a context (for LLMs, this would include the entire pretraining dataset, plus the prompt), you compress `context + next_token` for every possible next token. The tokens that co-compress best with the existing context are the 'least surprising' continuations. Choose one of them and iterate.

You can easily generate text with gzip this way. It won't be very good text, because gzip compression is not as sophisticated as a transformer + SGD, but the principle is the same.

The fact that the best compression algorithms are, in the LLM setting, still catastrophically bad at prediction suggests that the overlap between compression and prediction is weak at best.

https://bellard.org/ts_zip/

This shows that prediction algorithms (AI models) are also very good at compression, but compression algorithms (like the ones used in gzip) are not likewise very good at prediction. Which is evidence that compression is necessary but not sufficient for prediction.

LLMs are both the best compression and prediction algorithm for English text.

Probably not if you account for algorithm size.

True that

That depends how much text you're compressing.

For example, LLM pretraining datasets are on the order of tens or hundreds of terabytes. If an LLM-based code for that data is ~twice as efficient as gzip, you could afford to transmit the weights of even a very large LLM and still come out ahead.

In other words: LLMs actually are excellent compressors of their training sets in the formal information-theoretic sense.

>Mixing this can let you believe that you can use a compressor to do the same thing as LLMs, which you cannot.

You can, actually! Any compressor can be losslessly converted into a generator, and vice versa.

Traditional compressors like gzip are of course very simple and can only replicate rough patterns from the input. But they are technically doing the same thing.

I agree that technically they are doing the same thing but in practice LLMs are better compressors than PNGs (learned this while I was researching this topic). That was quite surprising to me.

Actually, it's trivial. I did it for fun once when I was learning about the PPM algorithm. It took about 15 minutes to reverse the whole thing.

That sounds like boostrapping the weights involved in early layers, to obviate the need for those layers to learn (optimize) for the distribution in the training set.

Makes me wonder idly, - is this conceptually akin in some sense to a "universal grammar," and if so - with a broad enough training set, is there a latent durable universal grammar that might be similarly recovered and injected to the benefit of all training, - does that grammar go beyond morphological/syntactical/grammatical features, into e.g. semantics and pragmatics

That was my thinking as well mainly to increase the speed of training. But it may turn out that the simple statistics that you can capture like this may account for 1% of the training and are likely to be captured as the first thing during the training.

But actually these techniques are used but they are hidden as speculative decoding with increasing complexity of approximations. For example you can have a part of the network that predicts the next word based on the markov chain, the next approximation is more complex etc.

This paper proposes something similar where you can inject memory without training https://arxiv.org/abs/2605.16893

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