2024-06-30-caro24a.md

title	section	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Information-theoretic generalization bounds for learning from quantum data	Original Papers	Learning tasks play an increasingly prominent role in quantum information and computation. They range from fundamental problems such as state discrimination and metrology over the framework of quantum probably approximately correct (PAC) learning, to the recently proposed shadow variants of state tomography. However, the many directions of quantum learning theory have so far evolved separately. We propose a mathematical formalism for describing quantum learning by training on classical-quantum data and then testing how well the learned hypothesis generalizes to new data. In this framework, we prove bounds on the expected generalization error of a quantum learner in terms of classical and quantum information-theoretic quantities measuring how strongly the learner’s hypothesis depends on the data seen during training. To achieve this, we use tools from quantum optimal transport and quantum concentration inequalities to establish non-commutative versions of decoupling lemmas that underlie classical information-theoretic generalization bounds. Our framework encompasses and gives intuitive generalization bounds for a variety of quantum learning scenarios such as quantum state discrimination, PAC learning quantum states, quantum parameter estimation, and quantumly PAC learning classical functions. Thereby, our work lays a foundation for a unifying quantum information-theoretic perspective on quantum learning.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	caro24a	0	Information-theoretic generalization bounds for learning from quantum data	775	839	775-839	775	false	Caro, Matthias C. and Gur, Tom and Rouz{\'e}, Cambyse and Stilck Fran\c{c}a, Daniel and Subramanian, Sathyawageeswar	given family Matthias C. Caro given family Tom Gur given family Cambyse Rouzé given family Daniel Stilck França given family Sathyawageeswar Subramanian	2024-06-30		Proceedings of Thirty Seventh Conference on Learning Theory	247	inproceedings	date-parts 2024 6 30	https://proceedings.mlr.press/v247/caro24a/caro24a.pdf