Interval Methods for Seeking Fixed Points of Recurrent Neural Networks

Kubica, Bartłomiej Jacek; Hoser, Paweł; Wiliński, Artur

doi:10.1007/978-3-030-50420-5_30

Cited by 2 publications

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References 9 publications

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“…In a series of earlier papers, including [25], [26], [27], [28], the author has introduced his solver HIBA_USNE (Heuristical Interval Branch-and-prune Algorithm for Underdetermined and well-determined Systems of Nonlinear Equations) [29]. It was also used in [4] to analyze a Hopfield-like neural network.…”

Section: The Solver and Other Software Usedmentioning

confidence: 99%

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Developing an interval method for training denoising autoencoders by bounding the noise

Kubica

2023

Annals of Computer Science and Information Systems

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This paper discusses prospects of using interval methods to training denoising autoencoders. Advantages and disadvantages of using the interval approach are discussed. It is proposed to formulate the problem of training the proper neural network as a constraint-satisfaction, and not optimization, problem. Pros and cons of this approach are considered. Preliminary numerical experiments are also presented.

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Section: The Solver and Other Software Usedmentioning

confidence: 99%

“…Interval methods, while used by several authors for neural network training (see, e.g., [1], [2], [3], [4], [5], [6], [7]), have rarely been used in conjunction with AE, so far. The only known exception is the paper [8].…”

Section: Introductionmentioning

confidence: 99%

Developing an interval method for training denoising autoencoders by bounding the noise

Kubica

2023

Annals of Computer Science and Information Systems

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Algorithmic differentiation and hull-consistency enforcing using C++ template meta-programming

Kubica

2023

Numer Algor

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Algorithmic differentiation is a tool used in several branches of computational science, both in conjunction with the interval calculus, and apart of it. This paper presents the ADHC library [14] developed by the author, and identified as package “na60” by Numerical Algorithms journal. This library makes intensive use of the C++ template meta-programming, and it has several unique features. ADHC seems particularly useful for interval-related applications. The library has been used by some solvers, also developed by the author, including HIBA_USNE. The paper describes the library, presenting its features, focusing on the new ones, added in version 2.0; in particular, we describe bounding subdifferentials of non-smooth functions and computing derivatives over various datatypes. Efficiency comparison with respect to other packages is also presented. Then some examples of ADHC applications are given, involving the use of HIBA_USNE and standard benchmark problems for solving nonlinear systems. A particular emphasis is put on examples related to modern machine learning, but not limited to them. Planned extensions and possible directions for future development of ADHC are also outlined and discussed.

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Interval Methods for Seeking Fixed Points of Recurrent Neural Networks

Cited by 2 publications

References 9 publications

Developing an interval method for training denoising autoencoders by bounding the noise

Developing an interval method for training denoising autoencoders by bounding the noise

Algorithmic differentiation and hull-consistency enforcing using C++ template meta-programming

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