Munich Center for Mathematical Philosophy (MCMP)

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Zoom Talk: Tom Sterkenburg (MCMP) und Gemma de Las Cuevas (Innsbruck)

Meeting-ID: 9443 3194 088

21.04.2021 16:00  – 18:00 

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Universality and undecidability in physics and machine learning

Gemma de las Cuevas (Innsbruck): The unbearable lightness of universality and undecidability

Why is it so easy to generate complexity? I will suggest that this is due to the phenomenon of universality — essentially every non-trivial system is universal, and thus able to explore all
complexity in its domain. We understand universality in spin models, automata and neural networks. I will a present a framework for universality, and will also talk about the other side of the coin, namely undecidability. I will also present an exploration of self-reference and negation (i.e. undecidability) in the brain-computer analogy.

Tom Sterkenburg (MCMP): The unbearable lightness of undecidability in machine learning

Ben-David et al. (Nature Mach. Intel., 2019) construct a machine learning problem such that the question of its learnability is independent of the standard axioms of set theory. In my talk, I will investigate whether we should be disturbed. I distinguish two possible interpretations of the results' interest and accompanying questions: (1) there is a particular and particularly interesting learnability problem that is undecidable (question: is this problem really interesting?), and (2) there *are* undecidable problems in machine learning (question: is this disturbing/surprising?). Following earlier criticisms, including by the authors themselves, the answer to the first question is rather *no*. Towards an answer to the second question, I investigate whether we cannot already exhibit undecidability in a much more straightforward way.