this post was submitted on 28 May 2024
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I’m not an Information Theory guy, but I am aware that, regardless of how clever one might hope to be, there is a theoretical limit on how compressed any given set of information could possibly be; and this is particularly true for the lossless compression demanded by this challenge.
Quote from the article:
The skepticism is well-founded, said Karl Martin, chief technology officer of data science company Integrate.ai. Martin's PhD thesis at the University of Toronto focused on data compression and security.
Neuralink's brainwave signals are compressible at ratios of around 2 to 1 and up to 7 to 1, he said in an email. But 200 to 1 "is far beyond what we expect to be the fundamental limit of possibility."
I'm no expert in this subject either, but a theoretical limit could be beyond 200x - depending on the data.
For example, a basic compression approach is to use a lookup table that allows you to map large values to smaller lookup ids. So, if the possible data only contains 2 values: One consisting of 10,000 letter 'a's. The other is 10,000 letter 'b's. We can map the first to number 1 and the second to number 2. With this lookup in place, a compressed value of "12211" would uncompress to 50,000 characters. A 10,000x compression ratio. Extrapolate that example out and there is no theoretical maximum to the compression ratio.
But that's when the data set is known and small. As the complexity grows, it does seem logical that a maximum limit would be introduced.
So, it might be possible to achieve 200x compression, but only if the complexity of the data set is below some threshold I'm not smart enough to calculate.
You also have to keep in mind that, the more you compress something, the more processing power you're going to need.
Whatever compression algorithm that is proposed will also need to be able to handle the data in real-time and at low-power.
But you are correct that compression beyond 200x is absolutely achievable.
A more visual example of compression could be something like one of the Stable Diffusion AI/ML models. The model may only be a few Gigabytes, but you could generate an insane amount of images that go well beyond that initial model size. And as long as someone else is using the same model/input/seed they can also generate the exact same image as someone else. So instead of having to transmit the entire 4k image itself, you just have to tell them the prompt, along with a few variables (the seed, the CFG Scale, the # of steps, etc) and they can generate the entire 4k image on their own machine that looks exactly the same as the one you generated on your machine.
So basically, for only ~~a few bits~~ about a kilobyte, you can get 20+MB worth of data transmitted in this way. The drawback is that you need a powerful computer and a lot of energy to regenerate those images, which brings us back to the problem of making this data conveyed in real-time while using low-power.
Edit:
Tap for some quick napkin math
For transmitting the information to generate that image, you would need about 1KB to allow for 1k characters in the prompt (if you really even need that),then about 2 bytes for the height,
2 for the width,
8 bytes for the seed,
less than a byte for the CFG and the Steps (but we'll just round up to 2 bytes).
Then, you would want something better than just a parity bit for ensuring the message is transmitted correctly, so let's throw on a 32 or 64 byte hash at the end...
That still only puts us a little over 1KB (1078Bytes)... So for generating a 4k image (.PNG file) we get ~24MB worth of lossless decompression.
That's 24,000,000 Bytes which gives us roughly a compression of about 20,000x
But of course, that's still going to take time to decompress as well as a decent spike in power consumption for about 30-60+ seconds (depending on hardware) which is far from anything "real-time".
Of course you could also be generating 8k images instead of 4k images... I'm not really stressing this idea to it's full potential by any means.
So in the end you get compression at a factor of more than 20,000x for using a method like this, but it won't be for low power or anywhere near "real-time".
Before you can do that, you have to spend hours of computation to figure out a prompt and a set of variables that perfectly match the picture you want to transmit.
Sure, but this is just a more visual example of how compression using an ML model can work.
The time you spend reworking the prompt, or tweaking the steps/cfg/etc. is outside of the scope of this example.
And if we're really talking about creating a good pic it helps to use tools like control net/inpainting/etc... which could still be communicated to the receiving machine, but then you're starting to lose out on some of the compression by a factor of about 1KB for every additional additional time you need to run the model to get the correct picture.