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We argue how AI can assist mathematics in three ways: theorem-proving, conjecture formulation, and language processing. Inspired by initial experiments in geometry and theoretical physics in 2017, we summarize how this emerging field has…

History and Overview · Mathematics 2025-11-24 Yang-Hui He

Deep learning is computationally intensive, with significant efforts focused on reducing arithmetic complexity, particularly regarding energy consumption dominated by data movement. While existing literature emphasizes inference, training…

Machine Learning · Statistics 2025-06-09 Van Minh Nguyen , Cristian Ocampo , Aymen Askri , Louis Leconte , Ba-Hien Tran

Deep neural networks ("deep learning") have emerged as a technology of choice to tackle problems in natural language processing, computer vision, speech recognition and gameplay, and in just a few years has led to superhuman level…

Computational Physics · Physics 2020-05-05 Rama K. Vasudevan , Maxim Ziatdinov , Lukas Vlcek , Sergei V. Kalinin

People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…

Computational Complexity · Computer Science 2008-07-08 Mark Burgin

Deep learning has been shown to achieve impressive results in several tasks where a large amount of training data is available. However, deep learning solely focuses on the accuracy of the predictions, neglecting the reasoning process…

Artificial Intelligence · Computer Science 2020-02-07 Giuseppe Marra , Michelangelo Diligenti , Francesco Giannini , Marco Gori , Marco Maggini

Over the last decades, a class of important mathematical results have required an ever increasing amount of human effort to carry out. For some, the help of computers is now indispensable. We analyze the implications of this trend towards…

Mathematical Software · Computer Science 2019-10-23 Jacques Carette , William M. Farmer , Michael Kohlhase , Florian Rabe

Explainable reinforcement learning allows artificial agents to explain their behavior in a human-like manner aiming at non-expert end-users. An efficient alternative of creating explanations is to use an introspection-based method that…

Machine Learning · Computer Science 2021-08-23 Angel Ayala , Francisco Cruz , Bruno Fernandes , Richard Dazeley

This paper will discuss the role of an artificially-intelligent computer system as critique-based, implicit-organizational, and an inherently necessary device, deployed in synchrony with parallel governmental policy, as a genuine means of…

Artificial Intelligence · Computer Science 2020-02-27 Christopher A. Tucker

Neural algorithmic reasoning aims to capture computations with neural networks by training models to imitate the execution of classical algorithms. While common architectures are expressive enough to contain the correct model in the weight…

Machine Learning · Computer Science 2025-08-14 Gleb Rodionov , Liudmila Prokhorenkova

Over the past few years, deep learning techniques have achieved tremendous success in many visual understanding tasks such as object detection, image segmentation, and caption generation. Despite this thriving in computer vision and natural…

Computer Vision and Pattern Recognition · Computer Science 2019-03-26 Anh Nguyen

The successes of Artificial Intelligence in recent years in areas such as image analysis, natural language understanding and strategy games have sparked interest from the world of finance. Specifically, there are high expectations, and…

Artificial Intelligence · Computer Science 2021-08-30 Remo Pareschi , Federico Zappone

Recent advances in computing have changed not only the nature of mathematical computation, but mathematical proof and inquiry itself. While artificial intelligence and formalized mathematics have been the major topics of this conversation,…

Databases · Computer Science 2024-04-12 Steven Clontz

These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…

Data Analysis, Statistics and Probability · Physics 2016-09-08 Ariel Caticha

In this review, we explore the historical development and future prospects of artificial intelligence (AI) and deep learning in astronomy. We trace the evolution of connectionism in astronomy through its three waves, from the early use of…

Instrumentation and Methods for Astrophysics · Physics 2023-06-01 Michael J. Smith , James E. Geach

Deep learning is increasingly being used in high-stake decision making applications that affect individual lives. However, deep learning models might exhibit algorithmic discrimination behaviors with respect to protected groups, potentially…

Machine Learning · Computer Science 2020-03-20 Mengnan Du , Fan Yang , Na Zou , Xia Hu

Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains…

Machine Learning · Computer Science 2020-03-27 Maithra Raghu , Eric Schmidt

Remarkable success of modern image-based AI methods and the resulting interest in their applications in critical decision-making processes has led to a surge in efforts to make such intelligent systems transparent and explainable. The need…

Artificial Intelligence · Computer Science 2020-11-30 Adriano Lucieri , Muhammad Naseer Bajwa , Andreas Dengel , Sheraz Ahmed

Despite significant achievements and current interest in machine learning and artificial intelligence, the quest for a theory of intelligence, allowing general and efficient problem solving, has done little progress. This work tries to…

Artificial Intelligence · Computer Science 2020-12-18 Abel Torres Montoya

When there exists uncertainty, AI machines are designed to make decisions so as to reach the best expected outcomes. Expectations are based on true facts about the objective environment the machines interact with, and those facts can be…

Machine Learning · Computer Science 2024-07-09 Jinsook Kim

If you want to tell people the truth, make them laugh, otherwise they'll kill you. (source unclear) Machine learning and deep learning are the technologies of the day for developing intelligent automatic systems. However, a key hurdle for…

Machine Learning · Computer Science 2019-01-08 Fayyaz Minhas , Amina Asif , Asa Ben-Hur