In plain words: Simple-looking models don't generalize better because they're simple; what helps is that they allow many possible causes, and goal-driven processes like natural selection just make those loose rules look simple. Picking loose rules over simple shapes improved generalization by 110-500%.
Abstract
Simplicity is held by many to be the key to general intelligence. Simpler models tend to "generalise", identifying the cause or generator of data with greater sample efficiency. The implications of the correlation between simplicity and generalisation extend far beyond computer science, addressing questions of physics and even biology. Yet simplicity is a property of form, while generalisation is of function. In interactive settings, any correlation between the two depends on interpretation. In theory there could be no correlation and yet in practice, there is. Previous theoretical work showed generalisation to be a consequence of "weak" constraints implied by function, not form. Experiments demonstrated choosing weak constraints over simple forms yielded a 110-500% improvement in generalisation rate. Here we show that all constraints can take equally simple forms, regardless of weakness. However if forms are spatially extended, then function is represented using a finite subset of forms. If function is represented using a finite subset of forms, then we can force a correlation between simplicity and generalisation by making weak constraints take simple forms. If function is determined by a goal directed process that favours versatility (e.g. natural selection), then efficiency demands weak constraints take simple forms. Complexity has no causal influence on generalisation, but appears to due to confounding.
Michael Timothy Bennett
arXiv:2404.07227 · cs.AI · submitted Mar 31, 2024 · updated May 30, 2024
abstract · pdf · html · Accepted for publication in the Proceedings of the 17th Conference on Artificial General Intelligence, 2024. Definitions shared with arXiv:2302.00843
Complexity is just a state of partial ignorance of detail.
Once a concept is fully understood it is no longer complex.
Unfortunately there are barriers to understanding:
Technical (our current technology is limited and cannot yet describe what is being considered past the theoretical).
Social (people don't want to understand concepts that are required for unravelling the complexity).
Physical (limitations in memory, language, or other restriction on intellectual capacity).
The above statements as an idea in itself could be considered complex as it conveys detail in a belief but it's tenets are quite simple and all three can be invoked:
Belief implies lack of technical understanding, social as people may be bored of this comment and finally some simply may not understand self referential material...