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Compression is prediction

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Re: Compression is prediction

#21

Post by aaroninsf »

pjankiewicz wrote: post #10

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 lev…

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

Re: Compression is prediction

#22

Post by cyanydeez »

glial wrote: post #15
throwaway_7274 wrote: post #5

This perspective is a useful source of intuition against the “LLMs can’t have new ideas, they’re just next-token-predictors” style arguments. What if you shift your perspective to thinking of training as optimization over a vast parametrized family of compression algorithms? Well, it suddenly looks a lot more plausible that “new” “ideas” can emerge from that process!

> it suddenly looks a lot more plausible that “new” “ideas” can emerge from that process This is not intuitive to me. It seems like a "new idea" is something that (almost by definition) isn't in the training set. Can you elaborate a bit? Edit: but perhaps a good model could arise from training, which would be a good idea in the sense that parsimonious ideas are good scientific ideas.

Once MP3s were invented, I had the idea for the Apple IPOD; but obviously I didn't have a giant manufacturing wing, the ability to make small hard drives, or anything else.

I don't think Apple invented the ipod anymore than I invented it; LLMs likely would have also come to the same conclusion about an ipod like device.

Original ideas either dont exist or have a functionally irrelevent definition in comparison with inputing tokens to LLMs to get novel ideas out.

Re: Compression is prediction

#23

Post by jparishy »

Cool visuals and breakdown. I wrote something in early 2025 about how LLMs seem to be an emergent behavior of lossy compression, but did not have the knowledge or verbiage at the time to get this detailed. In retrospect my writing seems naive and I'm happy to have found this and the Google paper linked inside. To be a fly on the wall in some of the labs, man.

Another thought that came from the same post is that, insofar as we see LLMs as human-style intelligence, they're more like stream of consciousness devices. Essentially incessant talking and buying enough time until you get to a usable answer. I think I associate some subset of intelligence with what you don't say, which is impossible with the SOC-style outputs, so this is something I think about a fair bit.

What could maybe differentiate current gen models from next gen is the ability to call tools modeled within the layers themselves, not externally. I think as far as I understand it, model trainers expect the model to do this itself in a way we don't understand or control, like a version of the bitter lesson. But I posit we can model many determinate tools as NNs themselves and figure out how to get the internal states of the LLM to make use of them during inference, e.g. calculators, indexes, citations. Just an enthusiast though, so grain of salt and all.

Re: Compression is prediction

#24

Post by pjankiewicz »

Legend2440 wrote: post #17
pjankiewicz wrote: post #10

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 lev…

>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.

Re: Compression is prediction

#25

Post by redhed »

glial wrote: post #15
throwaway_7274 wrote: post #5

This perspective is a useful source of intuition against the “LLMs can’t have new ideas, they’re just next-token-predictors” style arguments. What if you shift your perspective to thinking of training as optimization over a vast parametrized family of compression algorithms? Well, it suddenly looks a lot more plausible that “new” “ideas” can emerge from that process!

> it suddenly looks a lot more plausible that “new” “ideas” can emerge from that process This is not intuitive to me. It seems like a "new idea" is something that (almost by definition) isn't in the training set. Can you elaborate a bit? Edit: but perhaps a good model could arise from training, which would be a good idea in the sense that parsimonious ideas are good scientific ideas.

How I see it, is if the human brain does lossy compression/prediction of the natural world that learns from its "training set" (sensory inputs) and we have been able to come up with new ideas, then it seems like AI would be able to as well.

Re: Compression is prediction

#26

Post by duskwuff »

variadix wrote: post #11

This is a lot less surprising when you learn how non-LZ compressors work, that is, by modeling a probability distribution and using those probabilities to encode information in the minimum number of bits required to transmit the data. A less obvious conclusion is that LZ compressors do this to implicitly, the length of each symbol they could emit (literal or match, etc.) can be converted to the probability distributi…

A common design in compressors is to use LZ as a first step, but to then represent the constant data and/or offset-length pairs from LZ using an entropy coder.

Deflate (as used in gzip) uses a Huffman coder. LZMA (as used by xz) uses a predictive range coder. Zstandard can use either Huffman or FSE. Some high-speed compressors like LZ4 skip the entropy coding stage entirely at the expense of compression ratio.

Bzip2 is an interesting aversion of this pattern - it uses the Burrows-Wheeler transform as a first pass instead of LZ. Unfortunately, this is one of the major reasons why it's so slow.

Re: Compression is prediction

#27

Post by kailanb »

Unrelated to the content: I was really pleased to see that this site defaults to the bare minimum for cookie consent. I reflexively clicked "Reject all" only to see that it was already the default, which threw me off.

Re: Compression is prediction

#28

Post by baron3dl »

I stumbled across a connection between LLMs and compression when researching N-dim polytope emergence in neural networks. Toy Models of Superposition (Anthropic, 2022) suggests that gradient descent can independently discover efficient geometric packing arrangements for sparse features. LVQ compression uses regular lattice structures, including some based on 4D lattices.

I found this interesting and wonder whether LLMs have a higher density ceiling, since training and inference don't rely on a fixed lattice and can instead learn their own representational geometry.

Re: Compression is prediction

#30

Post by pjankiewicz »

aaroninsf wrote: post #21
pjankiewicz wrote: post #10

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 lev…

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 trai…

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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