We still need to figure out the framework.
In a modeling framework (and we started in the context of neural nets which are models) "noise" is generally interpreted as model residuals -- the part of data that you are unwilling or unable to model. In the same context "simplicity" usually means that the model has few parameters and an uncomplicated structure. As you can see, they are not opposites at all.
In the information/entropy framework simplicity usually means low Kolmogorov complexity and I am not sure what would "noise" mean.
When you say "randomness is a type of noise", can you define the terms you are using?
Let me start over.
Randomness is maximally complex, in the sense that a true random output cannot easily be predicted or efficiently be described. Simplicity is minimally complex, in that a simple process is easy to describe and its output easy to predict. Sometimes, part of the complexity of a complex explanation will be the result of "exploited" randomness. Randomness cannot be exploited for long, however. After all, it's not randomness if it is predictable. Thus a neural net might overfit its data only to fail at out of sample predictions, or a...
This essay claims to refute a popularized understanding of Occam's Razor that I myself adhere to. It is confusing me, since I hold this belief at a very deep level that it's difficult for me to examine. Does anyone see any problems in its argument, or does it seem compelling? I specifically feel as though it might be summarizing the relevant Machine Learning research badly, but I'm not very familiar with the field. It also might be failing to give any credit to simplicity as a general heuristic when simplicity succeeds in a specific field, and it's unclear whether such credit would be justified. Finally, my intuition is that situations in nature where there is a steady bias towards growing complexity are more common than the author claims, and that such tendencies are stronger for longer. However, for all of this, I have no clear evidence to back up the ideas in my head, just vague notions that are difficult to examine. I'd appreciate someone else's perspective on this, as mine seems to be distorted.
Essay: http://bruce.edmonds.name/sinti/