Variational Autoencoders: A Harmonic Perspective Article Swipe
Alexander Camuto
,
Matthew Willetts
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2105.14866
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2105.14866
In this work we study Variational Autoencoders (VAEs) from the perspective of harmonic analysis. By viewing a VAE's latent space as a Gaussian Space, a variety of measure space, we derive a series of results that show that the encoder variance of a VAE controls the frequency content of the functions parameterised by the VAE encoder and decoder neural networks. In particular we demonstrate that larger encoder variances reduce the high frequency content of these functions. Our analysis allows us to show that increasing this variance effectively induces a soft Lipschitz constraint on the decoder network of a VAE, which is a core contributor to the adversarial robustness of VAEs. We further demonstrate that adding Gaussian noise to the input of a VAE allows us to more finely control the frequency content and the Lipschitz constant of the VAE encoder networks. To support our theoretical analysis we run experiments with VAEs with small fully-connected neural networks and with larger convolutional networks, demonstrating empirically that our theory holds for a variety of neural network architectures.
Related Topics
Concepts
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2105.14866
- https://arxiv.org/pdf/2105.14866
- OA Status
- green
- Cited By
- 1
- References
- 33
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W3169645411
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W3169645411Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2105.14866Digital Object Identifier
- Title
-
Variational Autoencoders: A Harmonic PerspectiveWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2021Year of publication
- Publication date
-
2021-05-31Full publication date if available
- Authors
-
Alexander Camuto, Matthew WillettsList of authors in order
- Landing page
-
https://arxiv.org/abs/2105.14866Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2105.14866Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2105.14866Direct OA link when available
- Concepts
-
Computer science, Encoder, Robustness (evolution), Gaussian, Perspective (graphical), Artificial neural network, Convolutional neural network, Artificial intelligence, Algorithm, Pattern recognition (psychology), Gene, Quantum mechanics, Physics, Operating system, Biochemistry, ChemistryTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
-
2024: 1Per-year citation counts (last 5 years)
- References (count)
-
33Number of works referenced by this work
- Related works (count)
-
20Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W3169645411 |
|---|---|
| doi | https://doi.org/10.48550/arxiv.2105.14866 |
| ids.doi | https://doi.org/10.48550/arxiv.2105.14866 |
| ids.mag | 3169645411 |
| ids.openalex | https://openalex.org/W3169645411 |
| fwci | 0.14110358 |
| type | preprint |
| title | Variational Autoencoders: A Harmonic Perspective |
| awards[0].id | https://openalex.org/G4500485203 |
| awards[0].funder_id | https://openalex.org/F4320334627 |
| awards[0].display_name | |
| awards[0].funder_award_id | EP/N510129/1 |
| awards[0].funder_display_name | Engineering and Physical Sciences Research Council |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T11689 |
| topics[0].field.id | https://openalex.org/fields/17 |
| topics[0].field.display_name | Computer Science |
| topics[0].score | 0.9986000061035156 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1702 |
| topics[0].subfield.display_name | Artificial Intelligence |
| topics[0].display_name | Adversarial Robustness in Machine Learning |
| topics[1].id | https://openalex.org/T10775 |
| topics[1].field.id | https://openalex.org/fields/17 |
| topics[1].field.display_name | Computer Science |
| topics[1].score | 0.9961000084877014 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/1707 |
| topics[1].subfield.display_name | Computer Vision and Pattern Recognition |
| topics[1].display_name | Generative Adversarial Networks and Image Synthesis |
| topics[2].id | https://openalex.org/T11206 |
| topics[2].field.id | https://openalex.org/fields/31 |
| topics[2].field.display_name | Physics and Astronomy |
| topics[2].score | 0.9950000047683716 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/3109 |
| topics[2].subfield.display_name | Statistical and Nonlinear Physics |
| topics[2].display_name | Model Reduction and Neural Networks |
| funders[0].id | https://openalex.org/F4320334627 |
| funders[0].ror | https://ror.org/0439y7842 |
| funders[0].display_name | Engineering and Physical Sciences Research Council |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C41008148 |
| concepts[0].level | 0 |
| concepts[0].score | 0.7006841897964478 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[0].display_name | Computer science |
| concepts[1].id | https://openalex.org/C118505674 |
| concepts[1].level | 2 |
| concepts[1].score | 0.6502406597137451 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q42586063 |
| concepts[1].display_name | Encoder |
| concepts[2].id | https://openalex.org/C63479239 |
| concepts[2].level | 3 |
| concepts[2].score | 0.5396007299423218 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q7353546 |
| concepts[2].display_name | Robustness (evolution) |
| concepts[3].id | https://openalex.org/C163716315 |
| concepts[3].level | 2 |
| concepts[3].score | 0.5223777890205383 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q901177 |
| concepts[3].display_name | Gaussian |
| concepts[4].id | https://openalex.org/C12713177 |
| concepts[4].level | 2 |
| concepts[4].score | 0.517449676990509 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q1900281 |
| concepts[4].display_name | Perspective (graphical) |
| concepts[5].id | https://openalex.org/C50644808 |
| concepts[5].level | 2 |
| concepts[5].score | 0.46822306513786316 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q192776 |
| concepts[5].display_name | Artificial neural network |
| concepts[6].id | https://openalex.org/C81363708 |
| concepts[6].level | 2 |
| concepts[6].score | 0.4653428792953491 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q17084460 |
| concepts[6].display_name | Convolutional neural network |
| concepts[7].id | https://openalex.org/C154945302 |
| concepts[7].level | 1 |
| concepts[7].score | 0.459911048412323 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q11660 |
| concepts[7].display_name | Artificial intelligence |
| concepts[8].id | https://openalex.org/C11413529 |
| concepts[8].level | 1 |
| concepts[8].score | 0.4219541847705841 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q8366 |
| concepts[8].display_name | Algorithm |
| concepts[9].id | https://openalex.org/C153180895 |
| concepts[9].level | 2 |
| concepts[9].score | 0.41690582036972046 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q7148389 |
| concepts[9].display_name | Pattern recognition (psychology) |
| concepts[10].id | https://openalex.org/C104317684 |
| concepts[10].level | 2 |
| concepts[10].score | 0.0 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q7187 |
| concepts[10].display_name | Gene |
| concepts[11].id | https://openalex.org/C62520636 |
| concepts[11].level | 1 |
| concepts[11].score | 0.0 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q944 |
| concepts[11].display_name | Quantum mechanics |
| concepts[12].id | https://openalex.org/C121332964 |
| concepts[12].level | 0 |
| concepts[12].score | 0.0 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[12].display_name | Physics |
| concepts[13].id | https://openalex.org/C111919701 |
| concepts[13].level | 1 |
| concepts[13].score | 0.0 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q9135 |
| concepts[13].display_name | Operating system |
| concepts[14].id | https://openalex.org/C55493867 |
| concepts[14].level | 1 |
| concepts[14].score | 0.0 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q7094 |
| concepts[14].display_name | Biochemistry |
| concepts[15].id | https://openalex.org/C185592680 |
| concepts[15].level | 0 |
| concepts[15].score | 0.0 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q2329 |
| concepts[15].display_name | Chemistry |
| keywords[0].id | https://openalex.org/keywords/computer-science |
| keywords[0].score | 0.7006841897964478 |
| keywords[0].display_name | Computer science |
| keywords[1].id | https://openalex.org/keywords/encoder |
| keywords[1].score | 0.6502406597137451 |
| keywords[1].display_name | Encoder |
| keywords[2].id | https://openalex.org/keywords/robustness |
| keywords[2].score | 0.5396007299423218 |
| keywords[2].display_name | Robustness (evolution) |
| keywords[3].id | https://openalex.org/keywords/gaussian |
| keywords[3].score | 0.5223777890205383 |
| keywords[3].display_name | Gaussian |
| keywords[4].id | https://openalex.org/keywords/perspective |
| keywords[4].score | 0.517449676990509 |
| keywords[4].display_name | Perspective (graphical) |
| keywords[5].id | https://openalex.org/keywords/artificial-neural-network |
| keywords[5].score | 0.46822306513786316 |
| keywords[5].display_name | Artificial neural network |
| keywords[6].id | https://openalex.org/keywords/convolutional-neural-network |
| keywords[6].score | 0.4653428792953491 |
| keywords[6].display_name | Convolutional neural network |
| keywords[7].id | https://openalex.org/keywords/artificial-intelligence |
| keywords[7].score | 0.459911048412323 |
| keywords[7].display_name | Artificial intelligence |
| keywords[8].id | https://openalex.org/keywords/algorithm |
| keywords[8].score | 0.4219541847705841 |
| keywords[8].display_name | Algorithm |
| keywords[9].id | https://openalex.org/keywords/pattern-recognition |
| keywords[9].score | 0.41690582036972046 |
| keywords[9].display_name | Pattern recognition (psychology) |
| language | en |
| locations[0].id | pmh:oai:arXiv.org:2105.14866 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4306400194 |
| locations[0].source.issn | |
| locations[0].source.type | repository |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | |
| locations[0].source.is_core | False |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | arXiv (Cornell University) |
| locations[0].source.host_organization | https://openalex.org/I205783295 |
| locations[0].source.host_organization_name | Cornell University |
| locations[0].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[0].license | |
| locations[0].pdf_url | https://arxiv.org/pdf/2105.14866 |
| locations[0].version | submittedVersion |
| locations[0].raw_type | text |
| locations[0].license_id | |
| locations[0].is_accepted | False |
| locations[0].is_published | False |
| locations[0].raw_source_name | |
| locations[0].landing_page_url | http://arxiv.org/abs/2105.14866 |
| locations[1].id | mag:3169645411 |
| locations[1].is_oa | True |
| locations[1].source.id | https://openalex.org/S4306400194 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | True |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | arXiv (Cornell University) |
| locations[1].source.host_organization | https://openalex.org/I205783295 |
| locations[1].source.host_organization_name | Cornell University |
| locations[1].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[1].license | |
| locations[1].pdf_url | |
| locations[1].version | submittedVersion |
| locations[1].raw_type | |
| locations[1].license_id | |
| locations[1].is_accepted | False |
| locations[1].is_published | False |
| locations[1].raw_source_name | arXiv (Cornell University) |
| locations[1].landing_page_url | https://arxiv.org/pdf/2105.14866.pdf |
| locations[2].id | doi:10.48550/arxiv.2105.14866 |
| locations[2].is_oa | True |
| locations[2].source.id | https://openalex.org/S4306400194 |
| locations[2].source.issn | |
| locations[2].source.type | repository |
| locations[2].source.is_oa | True |
| locations[2].source.issn_l | |
| locations[2].source.is_core | False |
| locations[2].source.is_in_doaj | False |
| locations[2].source.display_name | arXiv (Cornell University) |
| locations[2].source.host_organization | https://openalex.org/I205783295 |
| locations[2].source.host_organization_name | Cornell University |
| locations[2].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[2].license | cc-by |
| locations[2].pdf_url | |
| locations[2].version | |
| locations[2].raw_type | article-journal |
| locations[2].license_id | https://openalex.org/licenses/cc-by |
| locations[2].is_accepted | False |
| locations[2].is_published | |
| locations[2].raw_source_name | |
| locations[2].landing_page_url | https://doi.org/10.48550/arxiv.2105.14866 |
| indexed_in | arxiv, datacite |
| authorships[0].author.id | https://openalex.org/A5075596560 |
| authorships[0].author.orcid | |
| authorships[0].author.display_name | Alexander Camuto |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Alexander Camuto |
| authorships[0].is_corresponding | False |
| authorships[1].author.id | https://openalex.org/A5019067441 |
| authorships[1].author.orcid | https://orcid.org/0000-0001-6585-3950 |
| authorships[1].author.display_name | Matthew Willetts |
| authorships[1].author_position | last |
| authorships[1].raw_author_name | Matthew Willetts |
| authorships[1].is_corresponding | False |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://arxiv.org/pdf/2105.14866 |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Variational Autoencoders: A Harmonic Perspective |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T06:51:31.235846 |
| primary_topic.id | https://openalex.org/T11689 |
| primary_topic.field.id | https://openalex.org/fields/17 |
| primary_topic.field.display_name | Computer Science |
| primary_topic.score | 0.9986000061035156 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1702 |
| primary_topic.subfield.display_name | Artificial Intelligence |
| primary_topic.display_name | Adversarial Robustness in Machine Learning |
| related_works | https://openalex.org/W2913529100, https://openalex.org/W2949649636, https://openalex.org/W3117416243, https://openalex.org/W2883813744, https://openalex.org/W2898043227, https://openalex.org/W2921269048, https://openalex.org/W2559626456, https://openalex.org/W2945791915, https://openalex.org/W2979843248, https://openalex.org/W2624978294, https://openalex.org/W2765934517, https://openalex.org/W3181674477, https://openalex.org/W3111317448, https://openalex.org/W3003552232, https://openalex.org/W3035827960, https://openalex.org/W3104688295, https://openalex.org/W852785498, https://openalex.org/W3177150392, https://openalex.org/W3202410655, https://openalex.org/W3007099473 |
| cited_by_count | 1 |
| counts_by_year[0].year | 2024 |
| counts_by_year[0].cited_by_count | 1 |
| locations_count | 3 |
| best_oa_location.id | pmh:oai:arXiv.org:2105.14866 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4306400194 |
| best_oa_location.source.issn | |
| best_oa_location.source.type | repository |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | arXiv (Cornell University) |
| best_oa_location.source.host_organization | https://openalex.org/I205783295 |
| best_oa_location.source.host_organization_name | Cornell University |
| best_oa_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| best_oa_location.license | |
| best_oa_location.pdf_url | https://arxiv.org/pdf/2105.14866 |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | text |
| best_oa_location.license_id | |
| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | |
| best_oa_location.landing_page_url | http://arxiv.org/abs/2105.14866 |
| primary_location.id | pmh:oai:arXiv.org:2105.14866 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4306400194 |
| primary_location.source.issn | |
| primary_location.source.type | repository |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | arXiv (Cornell University) |
| primary_location.source.host_organization | https://openalex.org/I205783295 |
| primary_location.source.host_organization_name | Cornell University |
| primary_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| primary_location.license | |
| primary_location.pdf_url | https://arxiv.org/pdf/2105.14866 |
| primary_location.version | submittedVersion |
| primary_location.raw_type | text |
| primary_location.license_id | |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | |
| primary_location.landing_page_url | http://arxiv.org/abs/2105.14866 |
| publication_date | 2021-05-31 |
| publication_year | 2021 |
| referenced_works | https://openalex.org/W2796892552, https://openalex.org/W2808614141, https://openalex.org/W2963540169, https://openalex.org/W3133199143, https://openalex.org/W3099628018, https://openalex.org/W3159654895, https://openalex.org/W2996461983, https://openalex.org/W1794737594, https://openalex.org/W2124647067, https://openalex.org/W1959608418, https://openalex.org/W2962964508, https://openalex.org/W2964127395, https://openalex.org/W2962897886, https://openalex.org/W3014079140, https://openalex.org/W2964160479, https://openalex.org/W2044618041, https://openalex.org/W2962695743, https://openalex.org/W3129544566, https://openalex.org/W2964122153, https://openalex.org/W3006277800, https://openalex.org/W2146596719, https://openalex.org/W2576042238, https://openalex.org/W2950048339, https://openalex.org/W2971028215, https://openalex.org/W1988115241, https://openalex.org/W2949416428, https://openalex.org/W3172760977, https://openalex.org/W3009708360, https://openalex.org/W2963556353, https://openalex.org/W2111406701, https://openalex.org/W2970620827, https://openalex.org/W3159681767, https://openalex.org/W2951682695 |
| referenced_works_count | 33 |
| abstract_inverted_index.a | 16, 21, 24, 31, 42, 88, 97, 101, 121, 168 |
| abstract_inverted_index.By | 14 |
| abstract_inverted_index.In | 0, 60 |
| abstract_inverted_index.To | 141 |
| abstract_inverted_index.We | 110 |
| abstract_inverted_index.as | 20 |
| abstract_inverted_index.by | 52 |
| abstract_inverted_index.is | 100 |
| abstract_inverted_index.of | 11, 26, 33, 41, 48, 73, 96, 108, 120, 136, 170 |
| abstract_inverted_index.on | 92 |
| abstract_inverted_index.to | 80, 104, 117, 125 |
| abstract_inverted_index.us | 79, 124 |
| abstract_inverted_index.we | 3, 29, 62, 146 |
| abstract_inverted_index.Our | 76 |
| abstract_inverted_index.VAE | 43, 54, 122, 138 |
| abstract_inverted_index.and | 56, 132, 156 |
| abstract_inverted_index.for | 167 |
| abstract_inverted_index.our | 143, 164 |
| abstract_inverted_index.run | 147 |
| abstract_inverted_index.the | 9, 38, 45, 49, 53, 69, 93, 105, 118, 129, 133, 137 |
| abstract_inverted_index.VAE, | 98 |
| abstract_inverted_index.VAEs | 150 |
| abstract_inverted_index.core | 102 |
| abstract_inverted_index.from | 8 |
| abstract_inverted_index.high | 70 |
| abstract_inverted_index.more | 126 |
| abstract_inverted_index.show | 36, 81 |
| abstract_inverted_index.soft | 89 |
| abstract_inverted_index.that | 35, 37, 64, 82, 113, 163 |
| abstract_inverted_index.this | 1, 84 |
| abstract_inverted_index.with | 149, 151, 157 |
| abstract_inverted_index.work | 2 |
| abstract_inverted_index.VAE's | 17 |
| abstract_inverted_index.VAEs. | 109 |
| abstract_inverted_index.holds | 166 |
| abstract_inverted_index.input | 119 |
| abstract_inverted_index.noise | 116 |
| abstract_inverted_index.small | 152 |
| abstract_inverted_index.space | 19 |
| abstract_inverted_index.study | 4 |
| abstract_inverted_index.these | 74 |
| abstract_inverted_index.which | 99 |
| abstract_inverted_index.(VAEs) | 7 |
| abstract_inverted_index.Space, | 23 |
| abstract_inverted_index.adding | 114 |
| abstract_inverted_index.allows | 78, 123 |
| abstract_inverted_index.derive | 30 |
| abstract_inverted_index.finely | 127 |
| abstract_inverted_index.larger | 65, 158 |
| abstract_inverted_index.latent | 18 |
| abstract_inverted_index.neural | 58, 154, 171 |
| abstract_inverted_index.reduce | 68 |
| abstract_inverted_index.series | 32 |
| abstract_inverted_index.space, | 28 |
| abstract_inverted_index.theory | 165 |
| abstract_inverted_index.content | 47, 72, 131 |
| abstract_inverted_index.control | 128 |
| abstract_inverted_index.decoder | 57, 94 |
| abstract_inverted_index.encoder | 39, 55, 66, 139 |
| abstract_inverted_index.further | 111 |
| abstract_inverted_index.induces | 87 |
| abstract_inverted_index.measure | 27 |
| abstract_inverted_index.network | 95, 172 |
| abstract_inverted_index.results | 34 |
| abstract_inverted_index.support | 142 |
| abstract_inverted_index.variety | 25, 169 |
| abstract_inverted_index.viewing | 15 |
| abstract_inverted_index.Gaussian | 22, 115 |
| abstract_inverted_index.analysis | 77, 145 |
| abstract_inverted_index.constant | 135 |
| abstract_inverted_index.controls | 44 |
| abstract_inverted_index.harmonic | 12 |
| abstract_inverted_index.networks | 155 |
| abstract_inverted_index.variance | 40, 85 |
| abstract_inverted_index.Lipschitz | 90, 134 |
| abstract_inverted_index.analysis. | 13 |
| abstract_inverted_index.frequency | 46, 71, 130 |
| abstract_inverted_index.functions | 50 |
| abstract_inverted_index.networks, | 160 |
| abstract_inverted_index.networks. | 59, 140 |
| abstract_inverted_index.variances | 67 |
| abstract_inverted_index.constraint | 91 |
| abstract_inverted_index.functions. | 75 |
| abstract_inverted_index.increasing | 83 |
| abstract_inverted_index.particular | 61 |
| abstract_inverted_index.robustness | 107 |
| abstract_inverted_index.Variational | 5 |
| abstract_inverted_index.adversarial | 106 |
| abstract_inverted_index.contributor | 103 |
| abstract_inverted_index.demonstrate | 63, 112 |
| abstract_inverted_index.effectively | 86 |
| abstract_inverted_index.empirically | 162 |
| abstract_inverted_index.experiments | 148 |
| abstract_inverted_index.perspective | 10 |
| abstract_inverted_index.theoretical | 144 |
| abstract_inverted_index.Autoencoders | 6 |
| abstract_inverted_index.convolutional | 159 |
| abstract_inverted_index.demonstrating | 161 |
| abstract_inverted_index.parameterised | 51 |
| abstract_inverted_index.architectures. | 173 |
| abstract_inverted_index.fully-connected | 153 |
| cited_by_percentile_year.max | 94 |
| cited_by_percentile_year.min | 90 |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.53395562 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |