Mathematical paradoxes unearth the boundaries of AI

Authors

DOI:

https://doi.org/10.25250/thescbr.brk652

Keywords:

stability and accuracy, AI and neural networks, mathematical paradoxes, | solvability complexity index hierarchy

Abstract

Instability is AI's Achilles’ heel. We show the following paradox: there are cases where stable and accurate AI exists, but it can never be trained by any algorithm. We initiate a foundations theory for when AI can be trained - such a programme will shape political and legal decision-making in the coming decades, and have a significant impact on markets for AI technologies.

Original article reference

Colbrook, M., Antun, V. & Hansen, A. The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and Smale’s 18th problem. Proceedings of the National Academy of Sciences 119, (2022)

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Published

2022-08-29

Issue

Vol. 8 No. 3 (2022)

Section

Maths, Physics & Chemistry

License

Copyright (c) 2022 Matthew Colbrook, Vegard Antun, Anders Hansen

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.