Comment by augment_me | Hacker News Reader

Comment by augment_me | Hacker News Reader

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As much as I want to, I sadly don't think Information Theory makes sense in this setting, and I really wanted to believe this. When Shannon made his theory of information, he was always dealing with informational representations on the abstraction level of bits. At Bell Labs, a lot of the work was on the compression of data for transfer over telephone wires. Entropy coding, later codexes like algorithmic coding, and all compression on this level assumes that you have a bit-based X, and you compress it.

However, in deep neural networks, you are dealing with compression on different levels of abstraction. How do you decide what shared features a peacock and a palm tree have? At what scale should they be represented? How do you deal with invariance under affine transforms? Do you want to open the box of invariance under non-affine transforms?

When you start looking at what it would mean to compress feature representations, you immediately get to the question of data. You realize that Shannon simply was given a form of a very low abstraction data and that information theory came out to handle data at this level, but it's not suited for the data representations of many higher level modalities.

If you read Society of Mind by Marvin Minsky, which has aged well to about 80%, you can get the hint of the kind of abstractions that humans make and what would be needed to represent them, this is not representable in bits, you need to go to higher level shared features, and then you open all of the questions above as well as credit assignment, mutual information approximation, Fischer information between bayesians, etc.

> How do you decide what shared features a peacock and a palm tree have? At what scale should they be represented? How do you deal with invariance under affine transforms? Do you want to open the box of invariance under non-affine transforms?

The whole point is that the representation is learned. When you talk about various levels of abstraction, you're missing that all of these levels are representable with words and the relationships between them. That is verbatim what LLMs are optimized for. Interestingly, when you take an embedding, you do see that some transformations in embedding space actually hold which is quite interesting (e.g. tree + many ~ forest)

1) I am talking about representations beyond language models and language embeddings. If you take for example image, video, audio, 3D-spatial DICOM or combinations like VLMs. If you ask a language model to make an image of a Begonia ferox leaf without training it with images as well, it will not be able to represent this.

2) Language is already a higher-order lossy compressed abstraction made by humans to communicate fast and fill out the left out information with a learned prior. If you train a model on language only, it will not have the opportunity to have a non-compressed representation to make its own abstraction from.

3) If you are LLM-pilled and believe that we will be able to reach arbitrary levels of precise informational representation using language only, and that all abstractions that we may ever want can live on every single embedding layer in an LLM, your argument is fair.

1) If you ask a language model to make an image of a Begonia ferox leaf without training it with images as well

is this not true also of humans?

2) The idea that there is a non-compressed prior is already philosophical no? It seems to just be a rehash of whether an example of a "Chair" is a representation of a perfect Idea of a chair, or whether accidental things put together read as a chair. Its just dualism or not, Plato vs aristotle but for LLMs vs human learning.

If we do happen to just form an abstraction from less examples than an LLM, then its a question of efficiency in the learning algo and the capability to fill the gaps faster/better.

Obvs a world model and multi modal learning would close the gap between LLM latent space and what the human mind encodings might look like. But you can formulate a reality where humans do not have access to a non compressed representation (or even say that doesnt exist) and we are just more efficient at abstraction and recollection

3) There are multiple answers to this. One is that language can just be a prong in the learning modes available. Another is that language is many times redundant and includes supplemental information and nuances that despite being a higher order abstraction has enough additional information to reconstruct entire messages even after the lossy transmission.

Btw I am pretty against LLMs as path forward, but I have been interested in their ability to solve problems with Convergent solutions and their learning model as a lossy compression algorithm where instead of saving the actual data, you save a very good guesser of the next word. So if a text is part of its traning algo then you get almost a 1:1 (like a zip dictionary) but if its not, then he gives you something that plausibly could be in an imaginary Zip with that title.

Check out https://en.wikipedia.org/wiki/Kolmogorov_complexity

AKA why Component Content Systems usually fall flat on their face over time.

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