Simplicity bias (also called Algorithmic randomness deficit) is a bias observed in many GP maps (see Bias in GP maps), and in many Complex systems (which can often be seen as GP maps). Simplicity is defined as low complexity.

Simplicity bias in discrete systems

Simplicity bias in finite-state transducers

Simplicity bias in continuous systems

See MMathPhys oral presentation, Simplicity, Order

Origin of the bias

A map that shows simplicity bias seems to need to be simple itself (having short description / low Kolmogorov complexity).

A priori probability estimates from structural complexity

Universal probability

Origin of bias in GP maps

Sloppy models (Why is science possible?)

Types of bias

• Algorithmic Randomness deficit of the set of outputs (p-sampled) (ARD1).
• Algorithmic Randomness deficit over the g-sampled distribution of outputs (ARD2).

Other features of simple maps

• Low probability – low complexity outputs have inputs which are simple. This is because a description of the inputs can be constructed from a description of the output, plus an index, which is at most $\log{A}$, where $A$ is the size of the input set producing that output. If the output has low probability, $A$ is small, and so this term is small. If the output is simple, then its description is small. Both these terms are small, and therefore, the input set must be composed of simple strings.

Effects of simplicity bias

Effectiveness of Learning: Simplicity and learning

Effectiveness of Evolution (see Biological complexity)