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Teaching requires distilling a rich category distribution into a small set of informative exemplars. Although prior work shows that humans consider both representativeness and diversity when teaching, the computational principles underlying…

Machine Learning · Computer Science 2026-02-04 Fanxiao Wani Qiu , Oscar Leong , Alexander LaTourrette

Deep neural networks have demonstrated remarkable performance in many data-driven and prediction-oriented applications, and sometimes even perform better than humans. However, their most significant drawback is the lack of interpretability,…

Machine Learning · Computer Science 2023-02-22 Jiahui Li , Kun Kuang , Lin Li , Long Chen , Songyang Zhang , Jian Shao , Jun Xiao

We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of propagation of waves and their nonlinear interactions, we…

Analysis of PDEs · Mathematics 2018-11-12 Gunther Uhlmann , Yiran Wang

Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods…

Machine Learning · Computer Science 2024-06-25 Rüdiger Brecht , Dmytro R. Popovych , Alex Bihlo , Roman O. Popovych

Transformers are effective and efficient at modeling complex relationships and learning patterns from structured data in many applications. The main aim of this paper is to propose and design NLAFormer, which is a transformer-based…

Numerical Analysis · Mathematics 2025-08-28 Zhantao Ma , Yihang Gao , Michael K. Ng

Foundation models have demonstrated remarkable generalization, data efficiency, and robustness properties across various domains. In this paper, we explore the feasibility of foundation models for applications in the control domain. The…

Machine Learning · Computer Science 2024-12-18 Martin Ziegler , Andres Felipe Posada-Moreno , Friedrich Solowjow , Sebastian Trimpe

Existing work on understanding deep learning often employs measures that compress all data-dependent information into a few numbers. In this work, we adopt a perspective based on the role of individual examples. We introduce a measure of…

Machine Learning · Computer Science 2021-06-21 Robert J. N. Baldock , Hartmut Maennel , Behnam Neyshabur

Deep learning has demonstrated the power of detailed modeling of complex high-order (multivariate) interactions in data. For some learning tasks there is power in learning models that are not only Deep but also Broad. By Broad, we mean…

Machine Learning · Computer Science 2015-09-07 Nayyar A. Zaidi , Geoffrey I. Webb , Mark J. Carman , Francois Petitjean

In this paper, we study the ability of large language models to learn specific mathematical rules such as distributivity or simplifying equations. We present an empirical analysis of their ability to generalize these rules, as well as to…

Computation and Language · Computer Science 2024-10-28 Antoine Gorceix , Bastien Le Chenadec , Ahmad Rammal , Nelson Vadori , Manuela Veloso

Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and…

Signal Processing · Electrical Eng. & Systems 2022-09-13 Nir Shlezinger , Jay Whang , Yonina C. Eldar , Alexandros G. Dimakis

Typical deep learning approaches to modeling high-dimensional data often result in complex models that do not easily reveal a new understanding of the data. Research in the deep learning field is very actively pursuing new methods to…

Machine Learning · Computer Science 2022-05-16 Charles Anderson , Jason Stock , David Anderson

Representation learning is the foundation for the recent success of neural network models. However, the distributed representations generated by neural networks are far from ideal. Due to their highly entangled nature, they are di cult to…

Machine Learning · Computer Science 2016-02-09 William Whitney

Mixture models arise in many regression problems, but most methods have seen limited adoption partly due to these algorithms' highly-tailored and model-specific nature. On the other hand, transformers are flexible, neural sequence models…

Machine Learning · Computer Science 2023-11-15 Reese Pathak , Rajat Sen , Weihao Kong , Abhimanyu Das

Continual learning is the ability to acquire new knowledge without forgetting the previously learned one, assuming no further access to past training data. Neural network approximators trained with gradient descent are known to fail in this…

Machine Learning · Computer Science 2021-11-05 Rodrigue Siry

Machine Learning (ML) models are very effective in many learning tasks, due to the capability to extract meaningful information from large data sets. Nevertheless, there are learning problems that cannot be easily solved relying on pure…

Machine Learning · Computer Science 2021-01-29 Andrea Borghesi , Federico Baldo , Michele Lombardi , Michela Milano

In this paper we present a technique to train neural network models on small amounts of data. Current methods for training neural networks on small amounts of rich data typically rely on strategies such as fine-tuning a pre-trained neural…

Machine Learning · Computer Science 2016-11-08 Ark Anderson , Kyle Shaffer , Artem Yankov , Court D. Corley , Nathan O. Hodas

It is well known that deep generative models have a rich latent space, and that it is possible to smoothly manipulate their outputs by traversing this latent space. Recently, architectures have emerged that allow for more complex…

Machine Learning · Computer Science 2019-12-06 Andrew Gambardella , Atılım Güneş Baydin , Philip H. S. Torr

The recent literature on deep learning offers new tools to learn a rich probability distribution over high dimensional data such as images or sounds. In this work we investigate the possibility of learning the prior distribution over neural…

Machine Learning · Statistics 2017-12-19 Alexandre Lacoste , Thomas Boquet , Negar Rostamzadeh , Boris Oreshkin , Wonchang Chung , David Krueger

Transformers have achieved great success across a wide range of applications, yet the theoretical foundations underlying their success remain largely unexplored. To demystify the strong capacities of transformers applied to versatile…

Machine Learning · Computer Science 2026-03-25 Chenyang Zhang , Qingyue Zhao , Quanquan Gu , Yuan Cao

Data transformations (e.g. rotations, reflections, and cropping) play an important role in self-supervised learning. Typically, images are transformed into different views, and neural networks trained on tasks involving these views produce…

Machine Learning · Computer Science 2022-02-04 Chen Qiu , Timo Pfrommer , Marius Kloft , Stephan Mandt , Maja Rudolph