A Geometric Theory for Binary Classification of Finite Datasets by DNNs with Relu Activations
Sign Up to like & getrecommendations! Published in 2024 at "Neural Processing Letters"
DOI: 10.1007/s11063-024-11612-1
Abstract: In this paper we investigate deep neural networks for binary classification of datasets from geometric perspective in order to understand the working mechanism of deep neural networks. First, we establish a geometrical result on injectivity… read more here.
Keywords: classification; geometric theory; hidden layers; theory binary ... See more keywords
An Ergodic Theory of Binary Operations—Part II: Applications to Polarization
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DOI: 10.1109/tit.2016.2617958
Abstract: An open problem in polarization theory is to determine the binary operations that always lead to polarization (in the general multilevel sense) when they are used in Arıkan style constructions. This paper, which is presented… read more here.
Keywords: binary operations; part; theory; polarization ... See more keywords
An Algorithmic Reduction Theory for Binary Codes: LLL and More
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Information Theory"
DOI: 10.1109/tit.2022.3143620
Abstract: In this article, we propose an adaptation of the algorithmic reduction theory of lattices to binary codes. This includes the celebrated LLL algorithm (Lenstra, Lenstra, Lovasz, 1982), as well as adaptations of associated algorithms such… read more here.
Keywords: binary codes; theory; theory binary; reduction theory ... See more keywords
Assembly Theory of Binary Messages
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DOI: 10.3390/math12101600
Abstract: Using assembly theory, we investigate the assembly pathways of binary strings (bitstrings) of length N formed by joining bits present in the assembly pool and the bitstrings that entered the pool as a result of… read more here.
Keywords: length; problem; assembly index; theory binary ... See more keywords