> It doesn't matter if the model is deterministic or probabilistic: a probabilistic model can be used to (losslessly) compress a dataset with entropy coding.

But if you can choose to lose information you can obviously achieve a higher compression score. That's literally what optical & auditory compression exploits. Indeed, we know people generally don't memorize the entire Wikipedia article. Rather they convert what they learn into some internally consistent story that they can then recite at any time & each time they recite it it's even differently worded (maybe memorizing some facts that help solidify the story).

Again, I have no problem with compression and decompression being equated to intelligence provided both are allowed to be lossy (or at least one facet of intelligence). That's because you get to inject structure into the stored representation that may not otherwise exist in the original data and you get to choose how to hydrate that representation. That's why LZMA isn't "more intelligent" than ZIP - the algorithm itself is "smarter" at compression but you're not getting to AGI by working on a better LZMA.

It's also why H264 and MP3 aren't intelligent either. While compression is lossy decompression is deterministic. That's why we can characterize LLMs as "more intelligent" than LZMA even though LZMA compresses losslessly better than LLMs.

I agree with you in spirit. I just thought you might be interested in some of the technical details regarding the relationship between compression and generalization!

I'll have a paper out next week which makes your point precise, using the language of algorithmic rate--distortion theory (lossy compression applied to algorithmic information theory + neural nets).

I think another way of understanding this is through the "Value Equivalence Principle", which points out that if we are learning a model of our environment, we don't want to model everything in full detail, we only want to model things which affect our value function, which determines how we will act. The value function, in this sense, implies a distortion function that we can define lossy compression relative to.