English
Related papers

Related papers: The Inverse Function Fallacy: On Sign Determinatio…

200 papers

We describe students revising the mathematical form of physics equations to match the physical situation they are describing, even though their revision violates physical laws. In an unfamiliar air resistance problem, a majority of students…

Physics Education · Physics 2015-05-13 Kate Hayes , Michael C. Wittmann

We state the problem of inverse reinforcement learning in terms of preference elicitation, resulting in a principled (Bayesian) statistical formulation. This generalises previous work on Bayesian inverse reinforcement learning and allows us…

Machine Learning · Statistics 2011-06-30 Constantin Rothkopf , Christos Dimitrakakis

In reverse mathematics, is is possible to have a curious situation where we know that an implication does not reverse, but appear to have no information on on how to weaken the assumption while preserving the conclusion. A main cause of…

Logic · Mathematics 2012-12-03 Henry Towsner

Humans can often quickly and efficiently solve complex new learning tasks given only a small set of examples. In contrast, modern artificially intelligent systems often require thousands or millions of observations in order to solve even…

Machine Learning · Computer Science 2025-05-08 Christian Raymond

Sign changes in sums of arithmetic functions and their inverses are a subtle topic with room to grow new results. Suppose that $S_f(x) := \sum_{n \leq x} f(n)$ is the summatory function of some arithmetic function $f$ such that $f(1) \neq…

Number Theory · Mathematics 2026-03-10 Maxie Dion Schmidt

Contrastive learning is a popular form of self-supervised learning that encourages augmentations (views) of the same input to have more similar representations compared to augmentations of different inputs. Recent attempts to theoretically…

Machine Learning · Computer Science 2022-03-01 Nikunj Saunshi , Jordan Ash , Surbhi Goel , Dipendra Misra , Cyril Zhang , Sanjeev Arora , Sham Kakade , Akshay Krishnamurthy

Solving inverse problems requires the knowledge of the forward operator, but accurate models can be computationally expensive and hence cheaper variants that do not compromise the reconstruction quality are desired. This chapter reviews…

Numerical Analysis · Mathematics 2024-03-19 Simon Arridge , Andreas Hauptmann , Yury Korolev

The property of conformal predictors to guarantee the required accuracy rate makes this framework attractive in various practical applications. However, this property is achieved at a price of reduction in precision. In the case of…

Machine Learning · Computer Science 2021-08-13 Marharyta Aleksandrova , Oleg Chertov

In deep learning, classification tasks are formalized as optimization problems often solved via the minimization of the cross-entropy. However, recent advancements in the design of objective functions allow the usage of the $f$-divergence…

Machine Learning · Computer Science 2024-05-17 Nicola Novello , Andrea M. Tonello

Standard regression techniques, while powerful, are often constrained by predefined, differentiable loss functions such as mean squared error. These functions may not fully capture the desired behavior of a system, especially when dealing…

Machine Learning · Computer Science 2025-08-04 Yongchao Huang

We consider the problem of decision-making with side information and unbounded loss functions. Inspired by probably approximately correct learning model, we use a slightly different model that incorporates the notion of side information in…

Machine Learning · Computer Science 2007-07-13 Majid Fozunbal , Ton Kalker

In this paper we investigate the solution of inverse problems with neural network ansatz functions with generalized decision functions. The relevant observation for this work is that such functions can approximate typical test cases, such…

Numerical Analysis · Mathematics 2024-01-19 Leon Frischauf , Otmar Scherzer , Cong Shi

This work introduces a new inversion formula for analytical functions. It is simple, generally applicable and straightforward to use both in hand calculations and for symbolic machine processing. It is easier to apply than the traditional…

General Mathematics · Mathematics 2017-12-07 Henrik Stenlund

Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…

Numerical Analysis · Mathematics 2020-06-09 Markus Haltmeier , Linh V. Nguyen

Function approximation from input and output data pairs constitutes a fundamental problem in supervised learning. Deep neural networks are currently the most popular method for learning to mimic the input-output relationship of a general…

Machine Learning · Computer Science 2019-12-09 Nikos Kargas , Nicholas D. Sidiropoulos

This paper discusses a system that accelerates reinforcement learning by using transfer from related tasks. Without such transfer, even if two tasks are very similar at some abstract level, an extensive re-learning effort is required. The…

Artificial Intelligence · Computer Science 2011-06-10 C. Drummond

We study the problem of inverse reinforcement learning (IRL), where the learning agent recovers a reward function using expert demonstrations. Most of the existing IRL techniques make the often unrealistic assumption that the agent has…

Machine Learning · Computer Science 2021-12-20 Franck Djeumou , Murat Cubuktepe , Craig Lennon , Ufuk Topcu

We present improved algorithms for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithms are much more accurate than the famous fast inverse square root algorithm and have the same or…

Numerical Analysis · Computer Science 2018-02-22 Cezary J. Walczyk , Leonid V. Moroz , Jan L. Cieśliński

Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-form expression necessitates surrogate modeling to guide the…

Numerical Analysis · Mathematics 2025-09-16 Qi Sun , Shengyan Li , Bowen Zheng , Lili Ju , Xuejun Xu

Inverse reinforcement learning methods aim to retrieve the reward function of a Markov decision process based on a dataset of expert demonstrations. The commonplace scarcity and heterogeneous sources of such demonstrations can lead to the…

Machine Learning · Computer Science 2024-09-13 Ivan Ovinnikov , Eugene Bykovets , Joachim M. Buhmann