Researchers have discovered that input-output maps, which are widely used throughout science and engineering to model systems ranging from physics to finance, are strongly biased toward producing simple outputs. The results are surprising, as naïvely there is no reason to suspect that one output should be more likely than any other. The researchers, Kamaludin Dingle, Chico Q. Camargo, and Ard A. Louis, at the University of Oxford and at the Gulf University for Science and Technology, have published a paper on their results in a recent issue of Nature Communications.

“The greatest significance of our work is our prediction that simplicity bias—that simple outputs are exponentially more likely to be generated than complex outputs are—holds for a wide variety of systems in science and engineering,” Louis told Phys.org. “The simplicity bias implies that, for a system made of many different interacting parts—say, a circuit with many components, a network with many chemical reactions, etc.—most combinations of parameters and inputs should result in simple behavior.”

The work draws from the field of algorithmic information theory (AIT), which deals with the connections between computer science and information theory. One important result of AIT is the coding theorem.

According to this theorem, when a universal Turing machine (an abstract computing device that can compute any function) is given a random input, simple outputs have an exponentially higher probability of being generated than complex outputs. As the researchers explain, this result is completely at odds with the naïve expectation that all outputs are equally likely. Despite these intriguing findings, so far the coding theorem has rarely been applied to any real-world systems. This is because the theorem has only been formulated in a very abstract way, and one of its key components—a complexity measure called the Kolmogorov complexity—is uncomputable.

“The coding theorem of Solomonoff and Levin is a remarkable result that should really be much more widely known,” Louis said. “It predicts that low-complexity outputs are exponentially more likely to be generated by a universal Turing machine (UTM) than high-complexity outputs are. Read more from phys.org…

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