constructive mathematics, realizability, computability
propositions as types, proofs as programs, computational trinitarianism
Machine learning is a branch of computer science which devises algorithms to learn from data so as to perform tasks without being explicitly programmed to do so. Notable approaches include neural networks, support vector machines and Bayesian networks.
Textbook accounts:
Sumio Watanabe, Algebraic geometry and statistical learning theory, CRC Press (2009) [doi:10.1017/CBO9780511800474]
Sumio Watanabe, Mathematical theory of Bayesian statistics, Cambridge University Press (2018) [ISBN:9780367734817, pdf]
Shai Shalev-Shwartz, Shai Ben-David, Understanding machine learning: from theory to algorithms, Cambridge University Press (2014) [doi:10.1017/CBO9781107298019]
Ian Goodfellow, Y. Bengio, A. Courville, Deep learning, MIT Press (2016) [web, pdf, ISBN:9780262035613]
See also:
Expository review:
On transformers and large language models (LLM):
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Łukasz Kaiser, Illia Polosukhin, Attention is all you need, in Advances in Neural Information Processing Systems 30 (NIPS 2017) pdf
Michael R. Douglas, Large language models, arXiv:2307.05782
With regards to kernel methods:
Thomas Hofmann, Bernhard Schölkopf, Alexander J. Smola, Kernel methods in machine learning, Annals of Statistics 2008, Vol. 36, No. 3, 1171-1220 (arXiv:math/0701907)
Julien Mairal, Jean-Philippe Vert, Machine Learning with Kernel Methods, 2017 (pdf, pdf)
Hông Vân Lê, Supervised learning with probabilistic morphisms and kernel mean embeddings, arXiv:2305.06348
Proposal for applications of category theory to machine learning:
The following framework claims to relate to homotopy type theory
On a definition of artificial general intelligence
S. Legg, M. Hutter, Universal intelligence: a definition of machine intelligence, Minds & Machines 17, 391–444 (2007) doi
M. Hutter, Universal artificial intelligence: sequential decisions based on algorithmic probability, Springer 2005; book presentation pdf
Shane Legg, Machine super intelligence, PhD thesis, 2008 pdf
In view of quantum computation (ie. quantum machine learning):
Diego Ristè, Marcus P. da Silva, Colm A. Ryan, Andrew W. Cross, Antonio D. Córcoles, John A. Smolin, Jay M. Gambetta, Jerry M. Chow & Blake R. Johnson,
Demonstration of quantum advantage in machine learning, npj Quantum Information volume 3, Article number: 16 (2017) (doi:10.1038/s41534-017-0017-3)
Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, Seth Lloyd, Quantum Machine Learning, Nature 549 (2017) 195–202 (doi:10.1038/nature23474)
EurekaAlert, Quantum Machine Learning 14-Sep-2017
Iris Cong, Soonwon Choi, Mikhail D. Lukin, Quantum convolutional neural networks, Nature Physics volume 15, pages 1273–1278 (2019) (doi:10.1038/s41567-019-0648-8)
Yunchao Liu, Srinivasan Arunachalam, Kristan Temme, A rigorous and robust quantum speed-up in supervised machine learning (arXiv:2010.02174)
Melanie Swan, Renato P dos Santos, Frank Witte, Between Science and Economics, Volume 2: Quantum Computing Physics, Blockchains, and Deep Learning Smart Networks, World Scientific 2020 (doi:10.1142/q0243)
Stefano Mangini, Francesco Tacchino, Dario Gerace, Daniele Bajoni, Chiara Macchiavello, Quantum computing models for artificial neural networks, EPL (Europhysics Letters) 134(1), 10002 (2021) (arXiv:2102.03879)
review:
and with emphasis on classically controlled NISQ-computes:
John Preskill, Section 6.5 of: Quantum Computing in the NISQ era and beyond, Quantum 2018-08-06, volume 2, page 79 (arXiv:1801.00862, doi:10.22331/q-2018-08-06-79)
Kosuke Mitarai, Makoto Negoro, Masahiro Kitagawa, Keisuke Fujii, Quantum Circuit Learning, Phys. Rev. A 98, 032309 (2018) (arXiv:1803.00745)
Marcello Benedetti, Erika Lloyd, Stefan Sack, Mattia Fiorentini, Parameterized quantum circuits as machine learning models, Quantum Science and Technology 4, 043001 (2019) (arXiv:1906.07682)
Marco Radic, Quantum-enhanced Machine Learning in the NISQ era, 2019 (pdf, pdf)
Dario Gerace, Quantum Machine Learning on NISQ hardware,, talk at INT online program on “Scientific Quantum Computing and Simulation on Near-Term Devices” 2020 (pdf, pdf)
Andrea Mari, Thomas R. Bromley, Josh Izaac, Maria Schuld, Nathan Killoran, Transfer learning in hybrid classical-quantum neural networks, Quantum 4, 340 (2020) (arXiv:1912.08278)
Lucas Munds, Quantum Machine Learning: A Roadmap for NISQ Era and Beyond, Oct 17, 2020
Tirthajyoti Sarkar, TensorFlow Quantum: Marrying machine learning with quantum computing, Mar 11, 2020
QunaSys, Tech Blog, Quantum machine learning of quantum data with NISQ devices (Feb 15 2021)
TensorFlow.org (Google), Quantum Machine Learning
Critical discussion:
“We present this as a challenge to the community and argue that until the viability of QCNNs for [not classically simulable] datasets can be demonstrated there is no reason to believe QCNNs will be useful. […] Hence we boldly claim: There is currently no evidence that QCNNs will work on classically non-trivial tasks, and their place in the upper echelon of promising QML architectures should be seriously revised.”
There are or will be innumerable applications. Here are some:
To mathematical structures in algebraic geometry, representation theory, number theory and combinatorics:
reviewed in:
To the conformal bootstrap:
(…)
Last revised on September 2, 2024 at 13:29:09. See the history of this page for a list of all contributions to it.