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Related papers: Data Complexity Estimates for Operator Learning

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A large set of signals can sometimes be described sparsely using a dictionary, that is, every element can be represented as a linear combination of few elements from the dictionary. Algorithms for various signal processing applications,…

Machine Learning · Statistics 2013-02-06 Daniel Vainsencher , Shie Mannor , Alfred M. Bruckstein

The goal of a learning algorithm is to receive a training data set as input and provide a hypothesis that can generalize to all possible data points from a domain set. The hypothesis is chosen from hypothesis classes with potentially…

Machine Learning · Statistics 2023-03-29 Soosan Beheshti , Mahdi Shamsi

Social and real-world considerations such as robustness, fairness, social welfare and multi-agent tradeoffs have given rise to multi-distribution learning paradigms, such as collaborative learning, group distributionally robust…

Machine Learning · Computer Science 2024-04-04 Nika Haghtalab , Michael I. Jordan , Eric Zhao

This paper establishes convergence rates for learning elliptic pseudo-differential operators, a fundamental operator class in partial differential equations and mathematical physics. In a wavelet-Galerkin framework, we formulate learning…

Statistics Theory · Mathematics 2026-01-09 Jiaheng Chen , Daniel Sanz-Alonso

Data efficiency, despite being an attractive characteristic, is often challenging to measure and optimize for in task-oriented semantic parsing; unlike exact match, it can require both model- and domain-specific setups, which have,…

Computation and Language · Computer Science 2021-07-13 Shrey Desai , Akshat Shrivastava , Justin Rill , Brian Moran , Safiyyah Saleem , Alexander Zotov , Ahmed Aly

Neural operators aim to approximate the solution operator of a system of differential equations purely from data. They have shown immense success in modeling complex dynamical systems across various domains. However, the occurrence of…

Machine Learning · Computer Science 2025-04-01 Christopher Bülte , Philipp Scholl , Gitta Kutyniok

We establish sample complexity results for stochastic optimization over the integers, especially with a view to understand the complexity with respect to the corresponding continuous optimization problem. We show that integer optimization…

Machine Learning · Computer Science 2026-05-11 Hongyu Cheng , Yinghao Zheng , Marco Molinaro , Amitabh Basu

Although deep learning based approximation algorithms have been applied very successfully to numerous problems, at the moment the reasons for their performance are not entirely understood from a mathematical point of view. Recently,…

Machine Learning · Computer Science 2023-04-13 Arnulf Jentzen , Adrian Riekert

Consider a regression problem where the learner is given a large collection of $d$-dimensional data points, but can only query a small subset of the real-valued labels. How many queries are needed to obtain a $1+\epsilon$ relative error…

Machine Learning · Computer Science 2021-06-29 Xue Chen , Michał Dereziński

Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…

Machine Learning · Computer Science 2025-12-22 Xinyue Yu , Hayden Schaeffer

In training neural networks, it is common practice to use partial gradients computed over batches, mostly very small subsets of the training set. This approach is motivated by the argument that such a partial gradient is close to the true…

Machine Learning · Computer Science 2024-11-25 Jan Spörer , Bernhard Bermeitinger , Tomas Hrycej , Niklas Limacher , Siegfried Handschuh

Learned Bloom Filters, i.e., models induced from data via machine learning techniques and solving the approximate set membership problem, have recently been introduced with the aim of enhancing the performance of standard Bloom Filters,…

Machine Learning · Computer Science 2022-11-29 Dario Malchiodi , Davide Raimondi , Giacomo Fumagalli , Raffaele Giancarlo , Marco Frasca

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…

Machine Learning · Computer Science 2025-12-23 Edoardo Calvello , Nikola B. Kovachki , Matthew E. Levine , Andrew M. Stuart

Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral layer that leverages a discretization-convergent representation…

Machine Learning · Computer Science 2024-03-06 Robert Joseph George , Jiawei Zhao , Jean Kossaifi , Zongyi Li , Anima Anandkumar

The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems, e.g., via extended dynamic mode decomposition. Despite its popularity, convergence results and, in particular, error bounds are…

Optimization and Control · Mathematics 2022-02-16 Feliks Nüske , Sebastian Peitz , Friedrich Philipp , Manuel Schaller , Karl Worthmann

Traditional statistical analysis requires that the analysis process and data are independent. By contrast, the new field of adaptive data analysis hopes to understand and provide algorithms and accuracy guarantees for research as it is…

Machine Learning · Computer Science 2017-03-22 Sam Elder

Compression has been a critical lens to understand the success of Transformers. In the past, we have typically taken the target distribution as a criterion to evaluate a model's compression performance. Nevertheless,it often remains…

Machine Learning · Computer Science 2025-04-29 Ruifeng Ren , Yong Liu

For four decades statistical physics has been providing a framework to analyse neural networks. A long-standing question remained on its capacity to tackle deep learning models capturing rich feature learning effects, thus going beyond the…

Machine Learning · Statistics 2025-12-15 Jean Barbier , Francesco Camilli , Minh-Toan Nguyen , Mauro Pastore , Rudy Skerk

Recent research demonstrated that training large language models involves memorization of a significant fraction of training data. Such memorization can lead to privacy violations when training on sensitive user data and thus motivates the…

Machine Learning · Computer Science 2025-10-29 Vitaly Feldman , Guy Kornowski , Xin Lyu

We formalize the problem of machine unlearning as design of efficient unlearning algorithms corresponding to learning algorithms which perform a selection of adaptive queries from structured query classes. We give efficient unlearning…

Machine Learning · Computer Science 2023-07-24 Enayat Ullah , Raman Arora
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