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This paper addresses the problem of resolving errors under uncertainty in a rule-based system. A new approach has been developed that reformulates this problem as a neural-network learning problem. The strength and the fundamental…

Artificial Intelligence · Computer Science 2013-04-10 Li-Min Fu

The histogram is an analysis tool in widespread use within many sciences, with high energy physics as a prime example. However, there exists an inherent bias in the choice of binning for the histogram, with different choices potentially…

Data Analysis, Statistics and Probability · Physics 2014-05-21 Abram Krislock , Nathan Krislock

In Nature Machine Intelligence 4, 367 (2022), Schuetz et al provide a scheme to employ graph neural networks (GNN) as a heuristic to solve a variety of classical, NP-hard combinatorial optimization problems. It describes how the network is…

Disordered Systems and Neural Networks · Physics 2023-01-03 Stefan Boettcher

There are a number of ways to procedurally generate interesting three-dimensional shapes, and a method where a cellular neural network is combined with a mesh growth algorithm is presented here. The aim is to create a shape from a genetic…

Neural and Evolutionary Computing · Computer Science 2016-03-30 Hugo Martay

Algorithms have been fundamental to recent global technological advances and, in particular, they have been the cornerstone of technical advances in one field rapidly being applied to another. We argue that algorithms possess fundamentally…

Machine Learning · Computer Science 2021-08-09 Petar Veličković , Charles Blundell

We describe a linear-time algorithm that finds a planar drawing of every graph of a simple line or pseudoline arrangement within a grid of area O(n^{7/6}). No known input causes our algorithm to use area \Omega(n^{1+\epsilon}) for any…

Computational Geometry · Computer Science 2015-07-16 David Eppstein

This paper does not describe a working system. Instead, it presents a single idea about representation which allows advances made by several different groups to be combined into an imaginary system called GLOM. The advances include…

Computer Vision and Pattern Recognition · Computer Science 2021-02-26 Geoffrey Hinton

Many NLP applications can be framed as a graph-to-sequence learning problem. Previous work proposing neural architectures on this setting obtained promising results compared to grammar-based approaches but still rely on linearisation…

Computation and Language · Computer Science 2018-06-27 Daniel Beck , Gholamreza Haffari , Trevor Cohn

Learning a well-informed heuristic function for hard task planning domains is an elusive problem. Although there are known neural network architectures to represent such heuristic knowledge, it is not obvious what concrete information is…

Artificial Intelligence · Computer Science 2021-12-06 Leah Chrestien , Tomas Pevny , Antonin Komenda , Stefan Edelkamp

Neural networks have become ubiquitous tools for solving signal and image processing problems, and they often outperform standard approaches. Nevertheless, training neural networks is a challenging task in many applications. The prevalent…

Optimization and Control · Mathematics 2022-10-28 Patrick L. Combettes , Jean-Christophe Pesquet , Audrey Repetti

The problem of finding the densest subgraph in a given graph has several applications in graph mining, particularly in areas like social network analysis, protein and gene analyses etc. Depending on the application, finding dense subgraphs…

Data Structures and Algorithms · Computer Science 2019-11-07 Naga V. C. Gudapati , Enrico Malaguti , Michele Monaci

We propose a new kind of sliding-block puzzle, called Gourds, where the objective is to rearrange 1 x 2 pieces on a hexagonal grid board of 2n + 1 cells with n pieces, using sliding, turning and pivoting moves. This puzzle has a single…

Data Structures and Algorithms · Computer Science 2020-11-03 Joep Hamersma , Marc van Kreveld , Yushi Uno , Tom C. van der Zanden

Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated…

Symbolic Computation · Computer Science 2019-12-04 Guillaume Lample , François Charton

We present probabilistic neural programs, a framework for program induction that permits flexible specification of both a computational model and inference algorithm while simultaneously enabling the use of deep neural networks.…

Neural and Evolutionary Computing · Computer Science 2016-12-05 Kenton W. Murray , Jayant Krishnamurthy

Homomorphism is a key mapping technique between graphs that preserves their structure. Given a graph and a pattern, the subgraph homomorphism problem involves finding a mapping from the pattern to the graph, ensuring that adjacent vertices…

Artificial Intelligence · Computer Science 2025-12-18 Shuyang Guo , Wenjin Xie , Ping Lu , Ting Deng , Richong Zhang , Jianxin Li , Xiangping Huang , Zhongyi Liu

Neural Algorithmic Reasoning (NAR) research has demonstrated that graph neural networks (GNNs) could learn to execute classical algorithms. However, most previous approaches have always used a recurrent architecture, where each iteration of…

Machine Learning · Computer Science 2024-10-22 Dobrik Georgiev , JJ Wilson , Davide Buffelli , Pietro Liò

This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…

Numerical Analysis · Mathematics 2023-03-07 Yiqi Gu , Michael K. Ng

Two major difficulties in using default logics are their intractability and the problem of selecting among multiple extensions. We propose an approach to these problems based on integrating nommonotonic reasoning with plausible reasoning…

Artificial Intelligence · Computer Science 2013-04-08 Piero P. Bonissone , David A. Cyrluk , James W. Goodwin , Jonathan Stillman

We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…

Numerical Analysis · Mathematics 2024-12-20 Kailai Xu , Eric Darve

A large amount of research on Convolutional Neural Networks has focused on flat Classification in the multi-class domain. In the real world, many problems are naturally expressed as problems of hierarchical classification, in which the…

Computer Vision and Pattern Recognition · Computer Science 2020-05-19 Riccardo La Grassa , Ignazio Gallo , Nicola Landro