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Contrasts laziness with the barren plateau concept, which is linked to loss-function flatness during gradient descent. Uses neural tangent kernel theory to explain noiseless overparameterized regimes: complicated landscapes can still yield quantum laziness without barren plateaus. Incorporates intuitive noise models and shows noise resilience of variational quantum algorithms in overparameterized settings, reformulating barren-plateau precision statements.","Mach. Learn.: Sci. Technol. 5 (2024) 015058 [https://doi.org/10.1088/2632-2153/ad35a3](https://doi.org/10.1088/2632-2153/ad35a3)  \nPAPER  \nLaziness, barren plateau, and noises in machine learning  \nOPEN ACCESS  \nJunyu Liu1,2,3,4,5, ∗􀁂, Zexi Lin1 and Liang Jiang1  \nR5ECEMIaVyED2023 1 Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL 60637, United States of America  \n2 Department of Computer Science, The University of Chicago, Chicago, IL 60637, United States of America R5EVISEDDecember 2023 34 KadqBraaindofCfoC,enHrporrThCoueoreticrt 523 PhysChiccgso,,ThILe6Univ0615e, rsity of ChiUnited Statceagos of, CAhmiceagorica, IL 60637, United States of America ACCEPTED FOR PUBLICATION 5 SeQure, Chicago, IL 60615, United States of America  \n19 March 2024 ∗  \nAuthor to whom any correspondence should be addressed.  \nPUBLISHED  \n[2 April 2024](2 April 2024 E-mail: junyuliu@uchicago.edu)[ E-mail: junyuliu@uchicago.edu](2 April 2024 E-mail: junyuliu@uchicago.edu), zexil@uchicago.edu and liangjiang@uchicago.edu  \n   Keywords: quantum machine learning, machine learning theory, quantum algorithms Original Content from  \nthis work may be used Supplementary material for this article is available online under the terms of the  \nCreative Commons  \nAttribution 4 .0 licence. ~~ ~~  \nAbstract  \nAny further distribution  \nof this work must We define laziness to describe a large suppression of variational parameter updates for neural maintain attribution to  \nthe author(s) and the title networks, classical or quantum. In the quantum case, the suppression is exponential in the number ofcithe worktion and, jouDOrInal of qubits for randomized variational quantum circuits. We discuss the difference between laziness  \n and barren plateau in quantum machine learning created by quantum physicists in McClean et al  (2018 Nat. Commun. 9 1–6) for the flatness of the loss function landscape during gradient descent.  \nWe address a novel theoretical understanding of those two phenomena in light of the theory of neural tangent kernels. For noiseless quantum circuits, without the measurement noise, the loss function landscape is complicated in the overparametrized regime with a large number of trainable variational angles. Instead, around a random starting point in optimization, there are large numbers of local minima that are good enough and could minimize the mean square loss function, where we still have quantum laziness, but we do not have barren plateaus. However, the complicated landscape is not visible within a limited number of iterations, and low precision in quantum control and quantum sensing. Moreover, we look at the effect of noises during optimization by assuming intuitive noise models, and show that variational quantum algorithms are noise-resilient in the overparametrization regime. Our work precisely reformulates the quantum barren plateau statement towards a precision statement and justifies the statement in certain noise models, injects new hope toward near-term variational quantum algorithms, and provides theoretical connections toward classical machine learning. Our paper provides conceptual perspectives about quantum barren plateaus, together with discussions about the gradient descent dynamics in Liu et al (2023 Phys. Rev. Lett. 130 150601) .  \n1. Barren plateau, laziness and noise  \nVariational quantum circuits [1–6] can be used to optimize cost function measured on quantum computers. Specifically, these cost functions can be used for machine learning tasks [7–14] . In this case variational quantum circuits are addressed as quantum neural networks.  \nHowever, a generically designed variational quantum ansatz may not be applicable to real problems. Specifically, a problem so-called barren plateau has been widely discussed in the variational quantum algorithm community, which is believed to be one of the primary problems of quantum machine learning [15] . The argument is given as follows. A typical gradient descent a","cbCaido73byXFkxm","https://ap.wps.com/l/cbCaido73byXFkxm","pdf",774988,1,21,"English","en",105,"# Barren plateau, laziness and noise\n## Variational quantum circuits and quantum neural networks\n## Gradient descent dynamics and suppressed derivatives\n## Noise-resilience and theoretical connections","[{\"question\":\"What does the paper define as “laziness” in machine learning?\",\"answer\":\"“Laziness” describes a large suppression of variational parameter updates in neural networks, with exponential suppression in the quantum case for randomized variational quantum circuits.\"},{\"question\":\"How does the paper distinguish laziness from barren plateau?\",\"answer\":\"It contrasts laziness with the barren plateau phenomenon that is associated with flat loss-function landscapes during gradient descent, and analyzes both using neural tangent kernel theory.\"},{\"question\":\"What is the paper’s conclusion about noise in variational quantum algorithms?\",\"answer\":\"Using intuitive noise models, the paper shows variational quantum algorithms are noise-resilient in the overparameterized regime, and reformulates barren-plateau claims into precision statements under certain noise assumptions.\"}]","Laziness, barren plateau, and noises in machine learning | 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does the paper define as “laziness” in machine learning?","Question",{"text":75,"@type":76},"“Laziness” describes a large suppression of variational parameter updates in neural networks, with exponential suppression in the quantum case for randomized variational quantum circuits.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the paper distinguish laziness from barren plateau?",{"text":80,"@type":76},"It contrasts laziness with the barren plateau phenomenon that is associated with flat loss-function landscapes during gradient descent, and analyzes both using neural tangent kernel theory.",{"name":82,"@type":73,"acceptedAnswer":83},"What is the paper’s conclusion about noise in variational quantum algorithms?",{"text":84,"@type":76},"Using intuitive noise models, the paper shows variational quantum algorithms are noise-resilient in the overparameterized regime, and reformulates barren-plateau claims into precision statements under certain noise 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