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Compression is prediction

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Re: Compression is prediction

#41

Post by melenaboija »

farfatched wrote: post #36

This is the thesis behind the "Information Theory, Inference, and Learning Algorithms" course that was taught at Cambridge University. > Why unify information theory and machine learning? Because they are two sides of the same coin. In the 1960s, a single field, cybernetics, was populated by information theorists, computer scientists, and neuroscientists, all studying common problems. Information theory and machine l…

This is basically a thesis supported by Shannon’s information theory.

Any rigorous CS program should cover this in depth.

Re: Compression is prediction

#42

Post by porphyra »

ssivark wrote: post #14

Nope; there is a bit more nuance and the distinction is important. Compression is functionally equivalent to prediction when the data distribution is exactly representative of all future problems . The story changes drastically if you want generalization -- because the test distribution could be arbitrarily different, even if it had the same support ! Eg: you observe a rare edge case in your training data and (lossy)…

How does that invalidate the "compression is prediction"? If the future data is different and you failed to generalize, then the failure to predict means you got worse at compressing and have to spend more bits storing the new information. Conversely, if the future data is the same as that you've seen previously, you could predict it very well, and compress better as a result.

Re: Compression is prediction

#43

Post by throwaway_7274 »

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.

Wow, I didn’t even notice how badly I underexplained that! Yeah, thanks, your edit is what I had in mind. jbay808 explains it well, too.

Re: Compression is prediction

#44

Post by gr_norm »

porphyra wrote: post #42
ssivark wrote: post #14

Nope; there is a bit more nuance and the distinction is important. Compression is functionally equivalent to prediction when the data distribution is exactly representative of all future problems . The story changes drastically if you want generalization -- because the test distribution could be arbitrarily different, even if it had the same support ! Eg: you observe a rare edge case in your training data and (lossy)…

How does that invalidate the "compression is prediction"? If the future data is different and you failed to generalize, then the failure to predict means you got worse at compressing and have to spend more bits storing the new information. Conversely, if the future data is the same as that you've seen previously, you could predict it very well, and compress better as a result.

A maximally efficient compressor for the existing data distribution is not in general (and often will not be) maximally efficient for future data. The former may only be enabled by convenient local optima of the input distribution that a compressor accounting for the latter could not take advantage of.

For instance, consider the distribution of strings drawn from the language '0+'. Now consider the same for the language '[01]+'. A compressor looking at only the strings of the first language within those of the second can do a much better job if it does not have to account for future data.

This also relates distantly to the idea of overfitting in machine learning.

Re: Compression is prediction

#45

Post by nonameiguess »

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!

There's another element to this that I almost never see discussed. Ideas are not facts. Neither LLMs nor humans can generate new knowledge, as opposed to ideas, by thinking alone. Physical investigation and experimentation is necessary.

The exception being pure mathematics since it exists solely in the realm of ideas. I'm willing to call that knowledge, but it's still a distinction, the old analytic/synthetic dichotomy of Kant.

Re: Compression is prediction

#46

Post by tcgv »

porphyra wrote: post #42
ssivark wrote: post #14

Nope; there is a bit more nuance and the distinction is important. Compression is functionally equivalent to prediction when the data distribution is exactly representative of all future problems . The story changes drastically if you want generalization -- because the test distribution could be arbitrarily different, even if it had the same support ! Eg: you observe a rare edge case in your training data and (lossy)…

How does that invalidate the "compression is prediction"? If the future data is different and you failed to generalize, then the failure to predict means you got worse at compressing and have to spend more bits storing the new information. Conversely, if the future data is the same as that you've seen previously, you could predict it very well, and compress better as a result.

"Compression can be prediction" would be more accurate.

Re: Compression is prediction

#47

Post by westurner »

Perhaps a similar observation; https://news.ycombinator.com/item?id=48703636 :

> Compression, Predictive modeling, or Complexity?

Perhaps a bad example: https://news.ycombinator.com/item?id=38400380 :

> "78% MNIST accuracy using GZIP in under 10 lines of code" (2023) https://news.ycombinator.com/item?id=37583593

Re: Compression is prediction

#48

Post by chermi »

farfatched wrote: post #36

This is the thesis behind the "Information Theory, Inference, and Learning Algorithms" course that was taught at Cambridge University. > Why unify information theory and machine learning? Because they are two sides of the same coin. In the 1960s, a single field, cybernetics, was populated by information theorists, computer scientists, and neuroscientists, all studying common problems. Information theory and machine l…

I had a long ranting comment I deleted. I just don't like this trend of people presenting work in a way that makes you think some combo of 1) they discovered from scratch themselves 2) it's new 3) they didn't try to cite or acknowledge where they learned it/point to good sources 4) they don't really care about trying to teach something deeply, they want shiny stuff that makes them seem deep.

This post references specific parts/calculations, but you'd never know it was not news if you didn't know better.

Re: Compression is prediction

#49

Post by sigbottle »

I keep on seeing this claim, especially from popular creators such as 3Blue1Brown. How is this not borderline vacuous?

I'm not a LessWrong^TM rationalist guy, but one really good thought experiment I always keep in the back of my mind from them is Solomonoff induction. AIT people take it as a framework to work with - it's pretty cool, I agree. But I (and some other people, such as certain AI execs at Amazon - according to my interpretation of their public interviews) think it just highlights the trap - given an arbitrarily powerful oracle, you can get compression down pat. Like, if you assume the source is generatable with a turing machine, and you write a function to brute force over all turing machines, then whoa, your compression works. You will necessarily find the optimal compression at some point because your search function is literally searching over all possible turing machines that could've generated the input sequence, anyways (because the input sequence was generated by a turing machine)

These are the kinds of results you can get if you don't have any actual constraints on what the compressor can do.

(Of course, again - this is not the point of solomonoff induction - it's to use this as a base truth, to then layer parsimony on top of that. There are infinite number of turing machines that could match your prefix, parsimony filters, throw some bayesian inference on top of that, and you get Solomonoff induction. They constrain it afterwards. But I think to that intuition as a base whenever people claim new results.).

But I see in casual conversation, people constantly making claims like, "LLM's are so good because they compress a model of the world". What is that model then? Scott Aaronson has made points like this before - your "model" could just be a massive lookup table, so you can't just claim "compression" and win - the compressor must be reasonably small, too.

I don't object to the notion that LLM's have some notion of world models more sophisticated than memorization. That's proven by actual interventional experiments, such as the ones that actual interperability researchers do. But mere compression is vacuously powerful. "Vacuous" not in the sense that "oh, you might be suboptimal and be a little more complex", vacuous as in "the philosophical point you were trying to make is vacuous because you make a vacuously powerful statement".

(I'm not a total fan of intervention either, as an end-all gospel as some people use, but it's far, far better than not having it).

Re: Compression is prediction

#50

Post by vanviegen »

jbs789 wrote: post #32
ssivark wrote: post #14

Nope; there is a bit more nuance and the distinction is important. Compression is functionally equivalent to prediction when the data distribution is exactly representative of all future problems . The story changes drastically if you want generalization -- because the test distribution could be arbitrarily different, even if it had the same support ! Eg: you observe a rare edge case in your training data and (lossy)…

That’s interesting. Also sparked the thought that the assumption only holds if the future looks like the present.

If your compression algrotihm is deep enough (think LLM), it will capture a lot of abstraction, making it compress well even in future cases that differ from the passed but fit the scheme in some other way.
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