Mixture Manifold Networks: A Computationally Efficient Baseline for Inverse Modeling Article Swipe
Gregory P. Spell
,
Simiao Ren
,
Leslie M. Collins
,
Jordan M. Malof
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1609/aaai.v37i8.26178
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1609/aaai.v37i8.26178
We propose and show the efficacy of a new method to address generic inverse problems. Inverse modeling is the task whereby one seeks to determine the hidden parameters of a natural system that produce a given set of observed measurements. Recent work has shown impressive results using deep learning, but we note that there is a trade-off between model performance and computational time. For some applications, the computational time at inference for the best performing inverse modeling method may be overly prohibitive to its use. In seeking a faster, high-performing model, we present a new method that leverages multiple manifolds as a mixture of backward (e.g., inverse) models in a forward-backward model architecture. These multiple backwards models all share a common forward model, and their training is mitigated by generating training examples from the forward model. The proposed method thus has two innovations: 1) the multiple Manifold Mixture Network (MMN) architecture, and 2) the training procedure involving augmenting backward model training data using the forward model. We demonstrate the advantages of our method by comparing to several baselines on four benchmark inverse problems, and we furthermore provide analysis to motivate its design.
Related Topics
Concepts
Computer science
Benchmark (surveying)
Inverse
Inference
Set (abstract data type)
Baseline (sea)
Inverse problem
Manifold (fluid mechanics)
Algorithm
Task (project management)
Artificial intelligence
Machine learning
Mathematics
Engineering
Geometry
Geology
Oceanography
Mechanical engineering
Geodesy
Geography
Systems engineering
Mathematical analysis
Programming language
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1609/aaai.v37i8.26178
- https://ojs.aaai.org/index.php/AAAI/article/download/26178/25950
- OA Status
- diamond
- Cited By
- 1
- References
- 31
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4382317963
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4382317963Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1609/aaai.v37i8.26178Digital Object Identifier
- Title
-
Mixture Manifold Networks: A Computationally Efficient Baseline for Inverse ModelingWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-06-26Full publication date if available
- Authors
-
Gregory P. Spell, Simiao Ren, Leslie M. Collins, Jordan M. MalofList of authors in order
- Landing page
-
https://doi.org/10.1609/aaai.v37i8.26178Publisher landing page
- PDF URL
-
https://ojs.aaai.org/index.php/AAAI/article/download/26178/25950Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
diamondOpen access status per OpenAlex
- OA URL
-
https://ojs.aaai.org/index.php/AAAI/article/download/26178/25950Direct OA link when available
- Concepts
-
Computer science, Benchmark (surveying), Inverse, Inference, Set (abstract data type), Baseline (sea), Inverse problem, Manifold (fluid mechanics), Algorithm, Task (project management), Artificial intelligence, Machine learning, Mathematics, Engineering, Geometry, Geology, Oceanography, Mechanical engineering, Geodesy, Geography, Systems engineering, Mathematical analysis, Programming languageTop 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)
-
31Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4382317963 |
|---|---|
| doi | https://doi.org/10.1609/aaai.v37i8.26178 |
| ids.doi | https://doi.org/10.1609/aaai.v37i8.26178 |
| ids.openalex | https://openalex.org/W4382317963 |
| fwci | 0.14420839 |
| type | article |
| title | Mixture Manifold Networks: A Computationally Efficient Baseline for Inverse Modeling |
| biblio.issue | 8 |
| biblio.volume | 37 |
| biblio.last_page | 9881 |
| biblio.first_page | 9874 |
| topics[0].id | https://openalex.org/T12814 |
| topics[0].field.id | https://openalex.org/fields/17 |
| topics[0].field.display_name | Computer Science |
| topics[0].score | 0.9901999831199646 |
| 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 | Gaussian Processes and Bayesian Inference |
| 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 | 0.9818000197410583 |
| 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/T10320 |
| topics[2].field.id | https://openalex.org/fields/17 |
| topics[2].field.display_name | Computer Science |
| topics[2].score | 0.9688000082969666 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/1702 |
| topics[2].subfield.display_name | Artificial Intelligence |
| topics[2].display_name | Neural Networks and Applications |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C41008148 |
| concepts[0].level | 0 |
| concepts[0].score | 0.7120108604431152 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[0].display_name | Computer science |
| concepts[1].id | https://openalex.org/C185798385 |
| concepts[1].level | 2 |
| concepts[1].score | 0.6946007013320923 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q1161707 |
| concepts[1].display_name | Benchmark (surveying) |
| concepts[2].id | https://openalex.org/C207467116 |
| concepts[2].level | 2 |
| concepts[2].score | 0.6668161749839783 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q4385666 |
| concepts[2].display_name | Inverse |
| concepts[3].id | https://openalex.org/C2776214188 |
| concepts[3].level | 2 |
| concepts[3].score | 0.5891349911689758 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q408386 |
| concepts[3].display_name | Inference |
| concepts[4].id | https://openalex.org/C177264268 |
| concepts[4].level | 2 |
| concepts[4].score | 0.48895275592803955 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q1514741 |
| concepts[4].display_name | Set (abstract data type) |
| concepts[5].id | https://openalex.org/C12725497 |
| concepts[5].level | 2 |
| concepts[5].score | 0.47602397203445435 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q810247 |
| concepts[5].display_name | Baseline (sea) |
| concepts[6].id | https://openalex.org/C135252773 |
| concepts[6].level | 2 |
| concepts[6].score | 0.4709680378437042 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q1567213 |
| concepts[6].display_name | Inverse problem |
| concepts[7].id | https://openalex.org/C529865628 |
| concepts[7].level | 2 |
| concepts[7].score | 0.4661836326122284 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q1790740 |
| concepts[7].display_name | Manifold (fluid mechanics) |
| concepts[8].id | https://openalex.org/C11413529 |
| concepts[8].level | 1 |
| concepts[8].score | 0.4376413822174072 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q8366 |
| concepts[8].display_name | Algorithm |
| concepts[9].id | https://openalex.org/C2780451532 |
| concepts[9].level | 2 |
| concepts[9].score | 0.4339873194694519 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q759676 |
| concepts[9].display_name | Task (project management) |
| concepts[10].id | https://openalex.org/C154945302 |
| concepts[10].level | 1 |
| concepts[10].score | 0.3992840349674225 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q11660 |
| concepts[10].display_name | Artificial intelligence |
| concepts[11].id | https://openalex.org/C119857082 |
| concepts[11].level | 1 |
| concepts[11].score | 0.38577479124069214 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q2539 |
| concepts[11].display_name | Machine learning |
| concepts[12].id | https://openalex.org/C33923547 |
| concepts[12].level | 0 |
| concepts[12].score | 0.2093389630317688 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[12].display_name | Mathematics |
| concepts[13].id | https://openalex.org/C127413603 |
| concepts[13].level | 0 |
| concepts[13].score | 0.0967068076133728 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q11023 |
| concepts[13].display_name | Engineering |
| concepts[14].id | https://openalex.org/C2524010 |
| concepts[14].level | 1 |
| concepts[14].score | 0.0 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q8087 |
| concepts[14].display_name | Geometry |
| concepts[15].id | https://openalex.org/C127313418 |
| concepts[15].level | 0 |
| concepts[15].score | 0.0 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q1069 |
| concepts[15].display_name | Geology |
| concepts[16].id | https://openalex.org/C111368507 |
| concepts[16].level | 1 |
| concepts[16].score | 0.0 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q43518 |
| concepts[16].display_name | Oceanography |
| concepts[17].id | https://openalex.org/C78519656 |
| concepts[17].level | 1 |
| concepts[17].score | 0.0 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q101333 |
| concepts[17].display_name | Mechanical engineering |
| concepts[18].id | https://openalex.org/C13280743 |
| concepts[18].level | 1 |
| concepts[18].score | 0.0 |
| concepts[18].wikidata | https://www.wikidata.org/wiki/Q131089 |
| concepts[18].display_name | Geodesy |
| concepts[19].id | https://openalex.org/C205649164 |
| concepts[19].level | 0 |
| concepts[19].score | 0.0 |
| concepts[19].wikidata | https://www.wikidata.org/wiki/Q1071 |
| concepts[19].display_name | Geography |
| concepts[20].id | https://openalex.org/C201995342 |
| concepts[20].level | 1 |
| concepts[20].score | 0.0 |
| concepts[20].wikidata | https://www.wikidata.org/wiki/Q682496 |
| concepts[20].display_name | Systems engineering |
| concepts[21].id | https://openalex.org/C134306372 |
| concepts[21].level | 1 |
| concepts[21].score | 0.0 |
| concepts[21].wikidata | https://www.wikidata.org/wiki/Q7754 |
| concepts[21].display_name | Mathematical analysis |
| concepts[22].id | https://openalex.org/C199360897 |
| concepts[22].level | 1 |
| concepts[22].score | 0.0 |
| concepts[22].wikidata | https://www.wikidata.org/wiki/Q9143 |
| concepts[22].display_name | Programming language |
| keywords[0].id | https://openalex.org/keywords/computer-science |
| keywords[0].score | 0.7120108604431152 |
| keywords[0].display_name | Computer science |
| keywords[1].id | https://openalex.org/keywords/benchmark |
| keywords[1].score | 0.6946007013320923 |
| keywords[1].display_name | Benchmark (surveying) |
| keywords[2].id | https://openalex.org/keywords/inverse |
| keywords[2].score | 0.6668161749839783 |
| keywords[2].display_name | Inverse |
| keywords[3].id | https://openalex.org/keywords/inference |
| keywords[3].score | 0.5891349911689758 |
| keywords[3].display_name | Inference |
| keywords[4].id | https://openalex.org/keywords/set |
| keywords[4].score | 0.48895275592803955 |
| keywords[4].display_name | Set (abstract data type) |
| keywords[5].id | https://openalex.org/keywords/baseline |
| keywords[5].score | 0.47602397203445435 |
| keywords[5].display_name | Baseline (sea) |
| keywords[6].id | https://openalex.org/keywords/inverse-problem |
| keywords[6].score | 0.4709680378437042 |
| keywords[6].display_name | Inverse problem |
| keywords[7].id | https://openalex.org/keywords/manifold |
| keywords[7].score | 0.4661836326122284 |
| keywords[7].display_name | Manifold (fluid mechanics) |
| keywords[8].id | https://openalex.org/keywords/algorithm |
| keywords[8].score | 0.4376413822174072 |
| keywords[8].display_name | Algorithm |
| keywords[9].id | https://openalex.org/keywords/task |
| keywords[9].score | 0.4339873194694519 |
| keywords[9].display_name | Task (project management) |
| keywords[10].id | https://openalex.org/keywords/artificial-intelligence |
| keywords[10].score | 0.3992840349674225 |
| keywords[10].display_name | Artificial intelligence |
| keywords[11].id | https://openalex.org/keywords/machine-learning |
| keywords[11].score | 0.38577479124069214 |
| keywords[11].display_name | Machine learning |
| keywords[12].id | https://openalex.org/keywords/mathematics |
| keywords[12].score | 0.2093389630317688 |
| keywords[12].display_name | Mathematics |
| keywords[13].id | https://openalex.org/keywords/engineering |
| keywords[13].score | 0.0967068076133728 |
| keywords[13].display_name | Engineering |
| language | en |
| locations[0].id | doi:10.1609/aaai.v37i8.26178 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4210191458 |
| locations[0].source.issn | 2159-5399, 2374-3468 |
| locations[0].source.type | conference |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | 2159-5399 |
| locations[0].source.is_core | False |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | Proceedings of the AAAI Conference on Artificial Intelligence |
| locations[0].source.host_organization | https://openalex.org/P4310320058 |
| locations[0].source.host_organization_name | Association for the Advancement of Artificial Intelligence |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310320058 |
| locations[0].source.host_organization_lineage_names | Association for the Advancement of Artificial Intelligence |
| locations[0].license | |
| locations[0].pdf_url | https://ojs.aaai.org/index.php/AAAI/article/download/26178/25950 |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | Proceedings of the AAAI Conference on Artificial Intelligence |
| locations[0].landing_page_url | https://doi.org/10.1609/aaai.v37i8.26178 |
| indexed_in | crossref |
| authorships[0].author.id | https://openalex.org/A5072522626 |
| authorships[0].author.orcid | |
| authorships[0].author.display_name | Gregory P. Spell |
| authorships[0].countries | US |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I170897317 |
| authorships[0].affiliations[0].raw_affiliation_string | Duke University |
| authorships[0].institutions[0].id | https://openalex.org/I170897317 |
| authorships[0].institutions[0].ror | https://ror.org/00py81415 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I170897317 |
| authorships[0].institutions[0].country_code | US |
| authorships[0].institutions[0].display_name | Duke University |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Gregory P. Spell |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | Duke University |
| authorships[1].author.id | https://openalex.org/A5048895233 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-7113-9208 |
| authorships[1].author.display_name | Simiao Ren |
| authorships[1].countries | US |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I170897317 |
| authorships[1].affiliations[0].raw_affiliation_string | Duke University |
| authorships[1].institutions[0].id | https://openalex.org/I170897317 |
| authorships[1].institutions[0].ror | https://ror.org/00py81415 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I170897317 |
| authorships[1].institutions[0].country_code | US |
| authorships[1].institutions[0].display_name | Duke University |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Simiao Ren |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | Duke University |
| authorships[2].author.id | https://openalex.org/A5004578492 |
| authorships[2].author.orcid | https://orcid.org/0000-0002-9043-6531 |
| authorships[2].author.display_name | Leslie M. Collins |
| authorships[2].countries | US |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I170897317 |
| authorships[2].affiliations[0].raw_affiliation_string | Duke University |
| authorships[2].institutions[0].id | https://openalex.org/I170897317 |
| authorships[2].institutions[0].ror | https://ror.org/00py81415 |
| authorships[2].institutions[0].type | education |
| authorships[2].institutions[0].lineage | https://openalex.org/I170897317 |
| authorships[2].institutions[0].country_code | US |
| authorships[2].institutions[0].display_name | Duke University |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Leslie M. Collins |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | Duke University |
| authorships[3].author.id | https://openalex.org/A5007239332 |
| authorships[3].author.orcid | https://orcid.org/0000-0002-7851-4920 |
| authorships[3].author.display_name | Jordan M. Malof |
| authorships[3].countries | US |
| authorships[3].affiliations[0].institution_ids | https://openalex.org/I6750721 |
| authorships[3].affiliations[0].raw_affiliation_string | University of Montana |
| authorships[3].institutions[0].id | https://openalex.org/I6750721 |
| authorships[3].institutions[0].ror | https://ror.org/0078xmk34 |
| authorships[3].institutions[0].type | education |
| authorships[3].institutions[0].lineage | https://openalex.org/I6750721 |
| authorships[3].institutions[0].country_code | US |
| authorships[3].institutions[0].display_name | University of Montana |
| authorships[3].author_position | last |
| authorships[3].raw_author_name | Jordan M. Malof |
| authorships[3].is_corresponding | False |
| authorships[3].raw_affiliation_strings | University of Montana |
| has_content.pdf | True |
| has_content.grobid_xml | True |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://ojs.aaai.org/index.php/AAAI/article/download/26178/25950 |
| open_access.oa_status | diamond |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Mixture Manifold Networks: A Computationally Efficient Baseline for Inverse Modeling |
| has_fulltext | True |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T12814 |
| primary_topic.field.id | https://openalex.org/fields/17 |
| primary_topic.field.display_name | Computer Science |
| primary_topic.score | 0.9901999831199646 |
| 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 | Gaussian Processes and Bayesian Inference |
| related_works | https://openalex.org/W2383111961, https://openalex.org/W2365952365, https://openalex.org/W2352448290, https://openalex.org/W2380820513, https://openalex.org/W2913146933, https://openalex.org/W2372385138, https://openalex.org/W2331917905, https://openalex.org/W3155039083, https://openalex.org/W1543136835, https://openalex.org/W1970914699 |
| cited_by_count | 1 |
| counts_by_year[0].year | 2024 |
| counts_by_year[0].cited_by_count | 1 |
| locations_count | 1 |
| best_oa_location.id | doi:10.1609/aaai.v37i8.26178 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4210191458 |
| best_oa_location.source.issn | 2159-5399, 2374-3468 |
| best_oa_location.source.type | conference |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | 2159-5399 |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | Proceedings of the AAAI Conference on Artificial Intelligence |
| best_oa_location.source.host_organization | https://openalex.org/P4310320058 |
| best_oa_location.source.host_organization_name | Association for the Advancement of Artificial Intelligence |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310320058 |
| best_oa_location.source.host_organization_lineage_names | Association for the Advancement of Artificial Intelligence |
| best_oa_location.license | |
| best_oa_location.pdf_url | https://ojs.aaai.org/index.php/AAAI/article/download/26178/25950 |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | Proceedings of the AAAI Conference on Artificial Intelligence |
| best_oa_location.landing_page_url | https://doi.org/10.1609/aaai.v37i8.26178 |
| primary_location.id | doi:10.1609/aaai.v37i8.26178 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4210191458 |
| primary_location.source.issn | 2159-5399, 2374-3468 |
| primary_location.source.type | conference |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | 2159-5399 |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | Proceedings of the AAAI Conference on Artificial Intelligence |
| primary_location.source.host_organization | https://openalex.org/P4310320058 |
| primary_location.source.host_organization_name | Association for the Advancement of Artificial Intelligence |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310320058 |
| primary_location.source.host_organization_lineage_names | Association for the Advancement of Artificial Intelligence |
| primary_location.license | |
| primary_location.pdf_url | https://ojs.aaai.org/index.php/AAAI/article/download/26178/25950 |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | Proceedings of the AAAI Conference on Artificial Intelligence |
| primary_location.landing_page_url | https://doi.org/10.1609/aaai.v37i8.26178 |
| publication_date | 2023-06-26 |
| publication_year | 2023 |
| referenced_works | https://openalex.org/W2887540873, https://openalex.org/W6634652361, https://openalex.org/W6634817459, https://openalex.org/W3135261467, https://openalex.org/W3113300316, https://openalex.org/W2148801469, https://openalex.org/W2043968544, https://openalex.org/W3168693657, https://openalex.org/W3125097811, https://openalex.org/W2766162919, https://openalex.org/W3015290768, https://openalex.org/W2974878544, https://openalex.org/W2775280502, https://openalex.org/W4214611600, https://openalex.org/W3089336059, https://openalex.org/W6718379498, https://openalex.org/W6632491856, https://openalex.org/W6635848118, https://openalex.org/W3016069476, https://openalex.org/W1959608418, https://openalex.org/W4287240322, https://openalex.org/W4289694518, https://openalex.org/W4320341657, https://openalex.org/W2503676979, https://openalex.org/W1579853615, https://openalex.org/W4240796046, https://openalex.org/W2963373786, https://openalex.org/W1598311721, https://openalex.org/W3129644058, https://openalex.org/W2286699414, https://openalex.org/W1540100713 |
| referenced_works_count | 31 |
| abstract_inverted_index.a | 7, 29, 34, 55, 87, 93, 101, 109, 119 |
| abstract_inverted_index.1) | 143 |
| abstract_inverted_index.2) | 152 |
| abstract_inverted_index.In | 85 |
| abstract_inverted_index.We | 0, 166 |
| abstract_inverted_index.as | 100 |
| abstract_inverted_index.at | 69 |
| abstract_inverted_index.be | 79 |
| abstract_inverted_index.by | 128, 173 |
| abstract_inverted_index.in | 108 |
| abstract_inverted_index.is | 17, 54, 126 |
| abstract_inverted_index.of | 6, 28, 37, 103, 170 |
| abstract_inverted_index.on | 178 |
| abstract_inverted_index.to | 10, 23, 82, 175, 188 |
| abstract_inverted_index.we | 50, 91, 184 |
| abstract_inverted_index.For | 63 |
| abstract_inverted_index.The | 136 |
| abstract_inverted_index.all | 117 |
| abstract_inverted_index.and | 2, 60, 123, 151, 183 |
| abstract_inverted_index.but | 49 |
| abstract_inverted_index.for | 71 |
| abstract_inverted_index.has | 42, 140 |
| abstract_inverted_index.its | 83, 190 |
| abstract_inverted_index.may | 78 |
| abstract_inverted_index.new | 8, 94 |
| abstract_inverted_index.one | 21 |
| abstract_inverted_index.our | 171 |
| abstract_inverted_index.set | 36 |
| abstract_inverted_index.the | 4, 18, 25, 66, 72, 133, 144, 153, 163, 168 |
| abstract_inverted_index.two | 141 |
| abstract_inverted_index.best | 73 |
| abstract_inverted_index.data | 161 |
| abstract_inverted_index.deep | 47 |
| abstract_inverted_index.four | 179 |
| abstract_inverted_index.from | 132 |
| abstract_inverted_index.note | 51 |
| abstract_inverted_index.show | 3 |
| abstract_inverted_index.some | 64 |
| abstract_inverted_index.task | 19 |
| abstract_inverted_index.that | 32, 52, 96 |
| abstract_inverted_index.thus | 139 |
| abstract_inverted_index.time | 68 |
| abstract_inverted_index.use. | 84 |
| abstract_inverted_index.work | 41 |
| abstract_inverted_index.(MMN) | 149 |
| abstract_inverted_index.These | 113 |
| abstract_inverted_index.given | 35 |
| abstract_inverted_index.model | 58, 111, 159 |
| abstract_inverted_index.seeks | 22 |
| abstract_inverted_index.share | 118 |
| abstract_inverted_index.shown | 43 |
| abstract_inverted_index.their | 124 |
| abstract_inverted_index.there | 53 |
| abstract_inverted_index.time. | 62 |
| abstract_inverted_index.using | 46, 162 |
| abstract_inverted_index.(e.g., | 105 |
| abstract_inverted_index.Recent | 40 |
| abstract_inverted_index.common | 120 |
| abstract_inverted_index.hidden | 26 |
| abstract_inverted_index.method | 9, 77, 95, 138, 172 |
| abstract_inverted_index.model, | 90, 122 |
| abstract_inverted_index.model. | 135, 165 |
| abstract_inverted_index.models | 107, 116 |
| abstract_inverted_index.overly | 80 |
| abstract_inverted_index.system | 31 |
| abstract_inverted_index.Inverse | 15 |
| abstract_inverted_index.Mixture | 147 |
| abstract_inverted_index.Network | 148 |
| abstract_inverted_index.address | 11 |
| abstract_inverted_index.between | 57 |
| abstract_inverted_index.design. | 191 |
| abstract_inverted_index.faster, | 88 |
| abstract_inverted_index.forward | 121, 134, 164 |
| abstract_inverted_index.generic | 12 |
| abstract_inverted_index.inverse | 13, 75, 181 |
| abstract_inverted_index.mixture | 102 |
| abstract_inverted_index.natural | 30 |
| abstract_inverted_index.present | 92 |
| abstract_inverted_index.produce | 33 |
| abstract_inverted_index.propose | 1 |
| abstract_inverted_index.provide | 186 |
| abstract_inverted_index.results | 45 |
| abstract_inverted_index.seeking | 86 |
| abstract_inverted_index.several | 176 |
| abstract_inverted_index.whereby | 20 |
| abstract_inverted_index.Manifold | 146 |
| abstract_inverted_index.analysis | 187 |
| abstract_inverted_index.backward | 104, 158 |
| abstract_inverted_index.efficacy | 5 |
| abstract_inverted_index.examples | 131 |
| abstract_inverted_index.inverse) | 106 |
| abstract_inverted_index.modeling | 16, 76 |
| abstract_inverted_index.motivate | 189 |
| abstract_inverted_index.multiple | 98, 114, 145 |
| abstract_inverted_index.observed | 38 |
| abstract_inverted_index.proposed | 137 |
| abstract_inverted_index.training | 125, 130, 154, 160 |
| abstract_inverted_index.backwards | 115 |
| abstract_inverted_index.baselines | 177 |
| abstract_inverted_index.benchmark | 180 |
| abstract_inverted_index.comparing | 174 |
| abstract_inverted_index.determine | 24 |
| abstract_inverted_index.inference | 70 |
| abstract_inverted_index.involving | 156 |
| abstract_inverted_index.learning, | 48 |
| abstract_inverted_index.leverages | 97 |
| abstract_inverted_index.manifolds | 99 |
| abstract_inverted_index.mitigated | 127 |
| abstract_inverted_index.problems, | 182 |
| abstract_inverted_index.problems. | 14 |
| abstract_inverted_index.procedure | 155 |
| abstract_inverted_index.trade-off | 56 |
| abstract_inverted_index.advantages | 169 |
| abstract_inverted_index.augmenting | 157 |
| abstract_inverted_index.generating | 129 |
| abstract_inverted_index.impressive | 44 |
| abstract_inverted_index.parameters | 27 |
| abstract_inverted_index.performing | 74 |
| abstract_inverted_index.demonstrate | 167 |
| abstract_inverted_index.furthermore | 185 |
| abstract_inverted_index.performance | 59 |
| abstract_inverted_index.prohibitive | 81 |
| abstract_inverted_index.innovations: | 142 |
| abstract_inverted_index.applications, | 65 |
| abstract_inverted_index.architecture, | 150 |
| abstract_inverted_index.architecture. | 112 |
| abstract_inverted_index.computational | 61, 67 |
| abstract_inverted_index.measurements. | 39 |
| abstract_inverted_index.high-performing | 89 |
| abstract_inverted_index.forward-backward | 110 |
| cited_by_percentile_year.max | 94 |
| cited_by_percentile_year.min | 90 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile.value | 0.28295987 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |