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15 Jul 2023: Read more about these breakthroughs in SIAM News! Short video summariesavailable on YouTube:. ... 2] Antun, V., M. J. Colbrook, and A. C. Hansen. "Proving existence is not enough: Mathematical paradoxes unravel the limits of neural networks in artificial

28 Nov 2023: Theorem 3.4 (Worst case optimality bounds). Under Assumptions 1 and 2, the following holds. ... Antun et al. in [9] and N. M. Gottschling etal. in [55].

15 Jul 2023: e2107151119. [2] Antun, V., M. J. Colbrook, and A. C. Hansen. "Proving existence is not enough: Mathematical paradoxes unravel the limits of neural networks in artificial intelligence." SIAM News 55.4 ... References. , V., M. J. Colbrook, and A. C. Hansen

15 Jul 2023: Not Enough: : Mathematical Paradoxes Unravel the Limits of Neural Networks in Artificial Intelligence,” SIAM News, May 2022.• Choi, “Some AI Systems May Be Impossible to Compute,” IEEE Spectrum, March 2022. ... 2] Antun, V., M. J. Colbrook, and A.

18 Dec 2023: K̂[[v]]2. )). with probability at least p. 4. CONNECTION TO PREVIOUS WORK. ... See also the work by Beck &Teboulle [9] and Wright, Nowak & Figueiredo [55], and the references therein, as well as [2, 14, 54].However, while these algorithms are capable of

18 Dec 2023: Remark 1.4 (Condition and GHA). Condition numbers are well-known to often provide sufficient conditions forthe existence of trustworthy algorithms in optimisation [16, 19, 53, 55–58]. ... In optimisation J.Renegar has pioneered the theory of condition

21 Feb 2023: newly established Solvability Complexity Index (SCI) hierarchy[11–13, 49, 51–53, 55, 57, 59, 95, 96]. ... Recent results establishing the SCI hierarchy [11–13, 49, 51–53, 55, 57, 59, 95, 96]reveal that the computational spectral problem becomes