Ultimate Intelligence Part II: Physical Complexity and Limits of Inductive Inference Systems
We continue our analysis of volume and energy measures that are appropriate for quantifying inductive inference systems. We extend logical depth and conceptual jump size measures in AIT to stochastic problems, and physical measures that involve volume and
- PDF / 194,068 Bytes
- 10 Pages / 439.37 x 666.142 pts Page_size
- 57 Downloads / 145 Views
G¨ ok Us Sibernetik Ar&Ge Ltd. S ¸ ti, Istanbul, Turkey [email protected]
Abstract. We continue our analysis of volume and energy measures that are appropriate for quantifying inductive inference systems. We extend logical depth and conceptual jump size measures in AIT to stochastic problems, and physical measures that involve volume and energy. We introduce a graphical model of computational complexity that we believe to be appropriate for intelligent machines. We show several asymptotic relations between energy, logical depth and volume of computation for inductive inference. In particular, we arrive at a “black-hole equation” of inductive inference, which relates energy, volume, space, and algorithmic information for an optimal inductive inference solution. We introduce energy-bounded algorithmic entropy. We briefly apply our ideas to the physical limits of intelligent computation in our universe.
“Everything must be made as simple as possible. But not simpler.” — Albert Einstein
1
Introduction
We initiated the ultimate intelligence research program in 2014 inspired by Seth Lloyd’s similarly titled article on the ultimate physical limits to computation [6], intended as a book-length treatment of the theory of general-purpose AI. In similar spirit to Lloyd’s research, we investigate the ultimate physical limits and conditions of intelligence. A main motivation is to extend the theory of intelligence using physical units, emphasizing the physicalism inherent in computer science. This is the second installation of the paper series, the first part [13] proposed that universal induction theory is physically complete arguing that the algorithmic entropy of a physical stochastic source is always finite, and argued that if we choose the laws of physics as the reference machine, the loophole in algorithmic information theory (AIT) of choosing a reference machine is closed. We also introduced several new physically meaningful complexity measures adequate for reasoning about intelligent machinery using the concepts of minimum volume, energy and action, which are applicable to both classical and quantum computers. Probably the most important of the new measures was the minimum energy required to physically transmit a message. The minimum energy c Springer International Publishing Switzerland 2016 B. Steunebrink et al. (Eds.): AGI 2016, LNAI 9782, pp. 33–42, 2016. DOI: 10.1007/978-3-319-41649-6 4
34
¨ E. Ozkural
complexity also naturally leads to an energy prior, complementing the speed prior [15] which inspired our work on incorporating physical resource limits to inductive inference theory. In this part, we generalize logical depth and conceptual jump size to stochastic sources and consider the influence of volume, space and energy. We consider the energy efficiency of computing as an important parameter for an intelligent system, forgoing other details of a universal induction approximation. We thus relate the ultimate limits of intelligence to physical limits of computation.
2
Notation and Background
Let us rec
Data Loading...
