Robust exponential binary pattern storage in Little-Hopfield networks
| Title: | Robust exponential binary pattern storage in Little-Hopfield networks |
|---|---|
| Authors: | Hillar, Christopher, Tran, Ngoc, Koepsell, Kilian |
| Publication Year: | 2012 |
| Collection: | Mathematics Quantitative Biology |
| Subject Terms: | Quantitative Biology - Neurons and Cognition, Mathematics - Combinatorics, Mathematics - Dynamical Systems |
| More Details: | The Little-Hopfield network is an auto-associative computational model of neural memory storage and retrieval. This model is known to robustly store collections of randomly generated binary patterns as stable-states of the network dynamics. However, the number of binary memories so storable scales linearly in the number of neurons, and it has been a long-standing open problem whether robust exponential storage of binary patterns was possible in such a network memory model. In this note, we design simple families of Little-Hopfield networks that provably solve this problem affirmatively. As a byproduct, we produce a set of novel (nonlinear) binary codes with an efficient, highly parallelizable denoising mechanism. Comment: This paper has been withdrawn by the authors. preliminary early draft unsuitable for viewing and attribution, instead, see: arXiv:1411.4625 |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/1206.2081 |
| Accession Number: | edsarx.1206.2081 |
| Database: | arXiv |
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| Items | – Name: Title Label: Title Group: Ti Data: Robust exponential binary pattern storage in Little-Hopfield networks – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Hillar%2C+Christopher%22">Hillar, Christopher</searchLink><br /><searchLink fieldCode="AR" term="%22Tran%2C+Ngoc%22">Tran, Ngoc</searchLink><br /><searchLink fieldCode="AR" term="%22Koepsell%2C+Kilian%22">Koepsell, Kilian</searchLink> – Name: DatePubCY Label: Publication Year Group: Date Data: 2012 – Name: Subset Label: Collection Group: HoldingsInfo Data: Mathematics<br />Quantitative Biology – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Quantitative+Biology+-+Neurons+and+Cognition%22">Quantitative Biology - Neurons and Cognition</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+-+Combinatorics%22">Mathematics - Combinatorics</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+-+Dynamical+Systems%22">Mathematics - Dynamical Systems</searchLink> – Name: Abstract Label: Description Group: Ab Data: The Little-Hopfield network is an auto-associative computational model of neural memory storage and retrieval. This model is known to robustly store collections of randomly generated binary patterns as stable-states of the network dynamics. However, the number of binary memories so storable scales linearly in the number of neurons, and it has been a long-standing open problem whether robust exponential storage of binary patterns was possible in such a network memory model. In this note, we design simple families of Little-Hopfield networks that provably solve this problem affirmatively. As a byproduct, we produce a set of novel (nonlinear) binary codes with an efficient, highly parallelizable denoising mechanism.<br />Comment: This paper has been withdrawn by the authors. preliminary early draft unsuitable for viewing and attribution, instead, see: arXiv:1411.4625 – Name: TypeDocument Label: Document Type Group: TypDoc Data: Working Paper – Name: URL Label: Access URL Group: URL Data: <link linkTarget="URL" linkTerm="http://arxiv.org/abs/1206.2081" linkWindow="_blank">http://arxiv.org/abs/1206.2081</link> – Name: AN Label: Accession Number Group: ID Data: edsarx.1206.2081 |
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| RecordInfo | BibRecord: BibEntity: Subjects: – SubjectFull: Quantitative Biology - Neurons and Cognition Type: general – SubjectFull: Mathematics - Combinatorics Type: general – SubjectFull: Mathematics - Dynamical Systems Type: general Titles: – TitleFull: Robust exponential binary pattern storage in Little-Hopfield networks Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Hillar, Christopher – PersonEntity: Name: NameFull: Tran, Ngoc – PersonEntity: Name: NameFull: Koepsell, Kilian IsPartOfRelationships: – BibEntity: Dates: – D: 10 M: 06 Type: published Y: 2012 |
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