Low Complexity, Low Probability Patterns and Consequences for Algorithmic Probability Applications

Figure 1

Simplicity bias plots with low complexity, low probability outputs. Blue dots represent different binary string output patterns. The black line is the upper bound of equation (3). Probabilities are the fraction of random inputs that map to output . are estimated complexity values for each output . There are many data points far below the upper bound; these points are low Kolmogorov complexity, low probability (LKLP) output patterns. The maps studied are (a) a finite state transducer (FST) with data taken from [7]; (b) time series patterns from the World Bank open data, with data taken from [8]; (c) computationally predicted RNA secondary structures from 1 million randomly sampled input sequences; and (d) discretised polynomials curves generated with (0, 1) and random coefficients, data taken from [9].

(a)

(b)

(c)

(d)