Some Theorems on Incremental Compression

Franz, Arthur

doi:10.1007/978-3-319-41649-6_8

Cited by 4 publications

(2 citation statements)

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“…It still requires exponential or double-exponential computation time, however [18]. Recent results show that program-based compression can be done incrementally [19]. These results can potentially lead to the development of a more efficient anytime-version of the speed prior.…”

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confidence: 99%

Universal Artificial Intelligence

Hutter

2018

Foundations of Trusted Autonomy

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Artificial intelligence (AI) bears the promise of making us all healthier, wealthier, and happier by reducing the need for human labour and by vastly increasing our scientific and technological progress.Since the inception of the AI research field in the mid-twentieth century, a range of practical and theoretical approaches have been investigated. This chapter will discuss universal artificial intelligence (UAI) as a unifying framework and foundational theory for many (most?) of these approaches. The development of a foundational theory has been pivotal for many other research fields. Well-known examples include the development of Zermelo-Fraenkel set theory (ZFC) for mathematics, Turingmachines for computer science, evolution for biology, and decision and game theory for economics and the social sciences. Successful foundational theories give a precise, coherent understanding of the field, and offer a common language for communicating research. As most research studies focus on one narrow question, it is essential that the value of each isolated result can be appreciated in light of a broader framework or goal formulation. UAI offers several benefits to AI research beyond the general advantages of foundational theories just mentioned. Substantial attention has recently been called to the safety of autonomous AI systems [10]. A highly intelligent autonomous system may cause substantial unintended harm if constructed carelessly. The trustworthiness of autonomous agents may be much improved if their design is grounded in a formal theory (such as UAI) that allows formal verification of their behavioural properties. Unsafe designs can be ruled out at an early stage, and adequate attention can be given to crucial design choices.

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Section: Fig 23mentioning

confidence: 99%

Universal Artificial Intelligence

Hutter

2018

Foundations of Trusted Autonomy

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“…Some theorems on this idea have already been published in a conference paper[4], which unfortunately contained several mistakes.…”

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A theory of incremental compression

Franz,

Antonenko,

Soletskyi

2019

Preprint

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The ability to find short representations, i.e. to compress data, is crucial for many intelligent systems. We present a theory of incremental compression showing that arbitrary data strings, that can be described by a set of features, can be compressed by searching for those features incrementally, which results in a partition of the information content of the string into a complete set of pairwise independent pieces. The description length of this partition turns out to be close to optimal in terms of the Kolmogorov complexity of the string. At the same time, the incremental nature of our method constitutes a major step toward faster compression compared to non-incremental versions of universal search, while still staying general. We further show that our concept of a feature is closely related to Martin-Löf randomness tests, thereby formalizing the meaning of "property" for computable objects.

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