Is Complexity an Illusion?

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 measure the complexity of weak constraints, and show that if one does not presuppose an abstraction layer, then all have equal complexity. However, in the context of a spatially and temporally extended abstraction layer, efficiency demands weak constraints take simple forms, and simplicity becomes correlated with generalisation. Simplicity has no causal influence on generalisation, but appears to due to confounding.