An Observation on Generalization

Noting the theory papers on Kolmorogov complexity. For those not familiar, Ilya argues that the reason why neural networks generalize -- why they work at all -- is because they are effectively finding a simple description of their training data , converging down onto the limit of the Kolmorogov complexity. [1] [1] ▶ this video

> We are now getting an equivalent definition of what neural nets are being trained for! LLMs are trained to compress the internet as much as possible! Nice payoff. Others have also called out the relationship to compression ( ▶ this video ).

I am curious why isn't the network always in an "interference" state, but sometimes it collapses into a "restricted" ONB? > the neural networks we observe in practice are in some sense noisily simulating larger, highly sparse networks This seems somewhat related to a point made by Ilya Sutskever here [1]: NNs can be though of an approximation to the Kolmogorov compressor. Speculating, one could say any network is a projection of the ideal compressor (which argualy perfectly represents all n-features in an n-dimensional ONB) into a lower dimentional space, hence the interference. But why is there not always such an interference? [1] ▶ this video