Intelligence _may arise_ from information. Information _necessarily arises_ from compression.
It is very similar, to me, to the concept of humors (https://en.wikipedia.org/wiki/Humorism). Empirically, it was observed that these things had some correlation, and they occurred together, but they are not directly causative. Similarly with the theory of spontaneous generation (https://en.wikipedia.org/wiki/Spontaneous_generation), which was another theory spawned (heh, as it were), from casual causal correlation (again, as it were).
This can be shown rather easily when you show that the time-dynamics of an exemplar system with high information diverge from the time dynamics of a system with high intelligence, i.e. there is a structural component to the information embedded in the system such that the temporal aspects of applied information are somehow necessary for intelligence.
I hope to release some work at least tangentially related to this within the next few years (though of course it is a bit more high-flying and depends on some other in-flight work). If we are to attempt to move towards AGI, I really think we need to stick with the mathematical basics. Neural networks, although they've been made out to be really complicated, are actually quite simple in terms of the concepts powering them, I believe. That's something I'm currently working on putting together and trying to distill to its essence. That will also be at least 1-2 years out, and likely before any temporally-related work, all going well. In my experience, this all is just a personal belief from a great deal of time and thought with the minutia of neural networks. That said, I could perhaps be biased with some notion of simplicity, since I've worked with them long enough for some concepts to feel comfortably second-nature.