Zobrazeno 1 - 10
of 25
pro vyhledávání: '"Kovachki, Nikola B."'
Transformers, and the attention mechanism in particular, have become ubiquitous in machine learning. Their success in modeling nonlocal, long-range correlations has led to their widespread adoption in natural language processing, computer vision, and
Externí odkaz:
http://arxiv.org/abs/2406.06486
Operator learning has emerged as a new paradigm for the data-driven approximation of nonlinear operators. Despite its empirical success, the theoretical underpinnings governing the conditions for efficient operator learning remain incomplete. The pre
Externí odkaz:
http://arxiv.org/abs/2405.15992
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of partial differ
Externí odkaz:
http://arxiv.org/abs/2402.15715
This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical inference and gene
Externí odkaz:
http://arxiv.org/abs/2302.13965
Autor:
Lim, Jae Hyun, Kovachki, Nikola B., Baptista, Ricardo, Beckham, Christopher, Azizzadenesheli, Kamyar, Kossaifi, Jean, Voleti, Vikram, Song, Jiaming, Kreis, Karsten, Kautz, Jan, Pal, Christopher, Vahdat, Arash, Anandkumar, Anima
Diffusion models have recently emerged as a powerful framework for generative modeling. They consist of a forward process that perturbs input data with Gaussian white noise and a reverse process that learns a score function to generate samples by den
Externí odkaz:
http://arxiv.org/abs/2302.07400
Publikováno v:
SIAM/ASA J. Uncertainty Quantification Vol. 11 No. 2 (2023) pp. 480-513
This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear operator. Assumi
Externí odkaz:
http://arxiv.org/abs/2108.12515
We present a novel framework for conditional sampling of probability measures, using block triangular transport maps. We develop the theoretical foundations of block triangular transport in a Banach space setting, establishing general conditions unde
Externí odkaz:
http://arxiv.org/abs/2006.06755
We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with ideas from mod
Externí odkaz:
http://arxiv.org/abs/2005.03180
Machine learning (ML) in the representation of molecular-orbital-based (MOB) features has been shown to be an accurate and transferable approach to the prediction of post-Hartree-Fock correlation energies. Previous applications of MOB-ML employed Gau
Externí odkaz:
http://arxiv.org/abs/1909.02041
Autor:
Kovachki, Nikola B., Stuart, Andrew M.
Publikováno v:
Journal of Machine Learning Research 21 (2020) 1-40
Gradient descent-based optimization methods underpin the parameter training of neural networks, and hence comprise a significant component in the impressive test results found in a number of applications. Introducing stochasticity is key to their suc
Externí odkaz:
http://arxiv.org/abs/1906.04285