{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T15:12:40Z","timestamp":1783437160686,"version":"3.54.6"},"reference-count":254,"publisher":"IOP Publishing","issue":"3","license":[{"start":{"date-parts":[[2025,8,1]],"date-time":"2025-08-01T00:00:00Z","timestamp":1754006400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,8,1]],"date-time":"2025-08-01T00:00:00Z","timestamp":1754006400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"National Science Foundation","award":["2134241"],"award-info":[{"award-number":["2134241"]}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"crossref","award":["R01NS119468"],"award-info":[{"award-number":["R01NS119468"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000936","name":"Gordon and Betty Moore Foundation","doi-asserted-by":"crossref","award":["2919.02"],"award-info":[{"award-number":["2919.02"]}],"id":[{"id":"10.13039\/100000936","id-type":"DOI","asserted-by":"crossref"}]},{"name":"University of California Santa Barbara Chancellor\u2019s Fellowship"},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"crossref","award":["587432"],"award-info":[{"award-number":["587432"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]},{"name":"European Research Council","award":["786854"],"award-info":[{"award-number":["786854"]}]},{"DOI":"10.13039\/100014989","name":"Chan Zuckerberg Initiative","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100014989","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"crossref","award":["ANR-23-IACL-0001"],"award-info":[{"award-number":["ANR-23-IACL-0001"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2025,9,30]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently non-Euclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.<\/jats:p>","DOI":"10.1088\/2632-2153\/adf375","type":"journal-article","created":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T22:51:57Z","timestamp":1753311117000},"page":"031002","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["Beyond Euclid: an illustrated guide to modern machine learning with geometric, topological, and algebraic structures"],"prefix":"10.1088","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1674-4218","authenticated-orcid":true,"given":"Mathilde","family":"Papillon","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1957-7067","authenticated-orcid":true,"given":"Sophia","family":"Sanborn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-8096-574X","authenticated-orcid":false,"given":"Johan","family":"Mathe","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-7156-9884","authenticated-orcid":false,"given":"Louisa","family":"Cornelis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-5081-4983","authenticated-orcid":true,"given":"Abby","family":"Bertics","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Domas","family":"Buracas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hansen","family":"J Lillemark","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4363-5615","authenticated-orcid":false,"given":"Christian","family":"Shewmake","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0921-0162","authenticated-orcid":false,"given":"Fatih","family":"Dinc","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6617-7664","authenticated-orcid":true,"given":"Xavier","family":"Pennec","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1200-9024","authenticated-orcid":true,"given":"Nina","family":"Miolane","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2025,8,1]]},"reference":[{"key":"mlstadf375bib1","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1038\/s41551-023-01106-1","article-title":"Dynamical flexible inference of nonlinear latent factors and structures in neural population activity","volume":"8","author":"Abbaspourazad","year":"2024","journal-title":"Nat. Biomed. Eng."},{"key":"mlstadf375bib2","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1038\/s41586-024-07487-w","article-title":"Accurate structure prediction of biomolecular interactions with alphafold 3","volume":"630","author":"Abramson","year":"2024","journal-title":"Nature"},{"key":"mlstadf375bib3","doi-asserted-by":"publisher","first-page":"2401","DOI":"10.1109\/TKDE.2020.3006475","article-title":"Role-based graph embeddings","volume":"34","author":"Ahmed","year":"2022","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"mlstadf375bib4","article-title":"Principal subbundles for dimension reduction","author":"Akh\u00f8j","year":"2023"},{"key":"mlstadf375bib5","article-title":"Gaussian processes on cellular complexes","author":"Alain","year":"2024"},{"key":"mlstadf375bib6","first-page":"pp 16384","article-title":"Noether networks: meta-learning useful conserved quantities","volume":"vol 34","author":"Alet","year":"2021"},{"key":"mlstadf375bib7","first-page":"pp 44","article-title":"Fusing structural and functional mris using graph convolutional networks for autism classification","volume":"vol 121","author":"Arya","year":"2020"},{"key":"mlstadf375bib8","article-title":"Cross-sectional t1-weighted MRI of a healthy human brain produced at a ultra high-field mr of 7 tesla","author":"Asnaebsa","year":"2022"},{"key":"mlstadf375bib9","article-title":"Neural machine translation by jointly learning to align and translate","author":"Bahdanau","year":"2015"},{"key":"mlstadf375bib10","article-title":"Attending to topological spaces: the cellular transformer","author":"Ballester","year":"2024"},{"key":"mlstadf375bib11","first-page":"pp 719","author":"Banerjee","year":"2015"},{"key":"mlstadf375bib12","doi-asserted-by":"publisher","DOI":"10.5281\/zenodo.593816","article-title":"pyriemann\/pyriemann: v0.5","author":"Barachant","year":"2023","unstructured":"Barachant A et al 2023 pyriemann\/pyriemann: v0.5 10.5281\/zenodo.593816 (Accessed 15 March 2024)"},{"key":"mlstadf375bib13","article-title":"E(n) equivariant topological neural networks","author":"Battiloro","year":"2025"},{"key":"mlstadf375bib14","doi-asserted-by":"publisher","first-page":"2453","DOI":"10.1038\/s41467-022-29939-5","article-title":"E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials","volume":"13","author":"Batzner","year":"2022","journal-title":"Nat. Commun."},{"key":"mlstadf375bib15","article-title":"Fast, expressive se(n) equivariant networks through weight-sharing in position-orientation space","author":"Bekkers","year":"2024"},{"key":"mlstadf375bib16","article-title":"Visualizing riemannian data with RIE-SNE","author":"Bergsson","year":"2024"},{"key":"mlstadf375bib17","article-title":"Simplex2vec embeddings for community detection in simplicial complexes","author":"Billings","year":"2019"},{"key":"mlstadf375bib18","first-page":"pp 382","article-title":"Bayesian pca","author":"Bishop","year":"1998"},{"key":"mlstadf375bib19","article-title":"Invariant slot attention: object discovery with slot-centric reference frames","author":"Biza","year":"2023"},{"key":"mlstadf375bib20","article-title":"Topological deep learning: graphs, complexes, sheaves","author":"Bodnar","year":"2022"},{"key":"mlstadf375bib21","first-page":"pp 1026","article-title":"Weisfeiler and lehman go topological: message passing simplicial networks","volume":"vol 139","author":"Bodnar","year":"2021"},{"key":"mlstadf375bib22","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1109\/TMI.2007.911474","article-title":"Geometric variability of the scoliotic spine using statistics on articulated shape models","volume":"27","author":"Boisvert","year":"2008","journal-title":"IEEE Trans. Med. Imaging"},{"key":"mlstadf375bib23","first-page":"pp 12426","article-title":"Mat\u00e9rn Gaussian processes on Riemannian manifolds","volume":"vol 33","author":"Borovitskiy","year":"2020"},{"key":"mlstadf375bib24","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1093\/biomet\/55.1.119","article-title":"A bayesian approach to some outlier problems","volume":"55","author":"Box","year":"1968","journal-title":"Biometrika"},{"key":"mlstadf375bib25","article-title":"Geometric and physical quantities improve e(3) equivariant message passing","author":"Brandstetter","year":"2022"},{"key":"mlstadf375bib26","article-title":"Does equivariance matter at scale?","author":"Brehmer","year":"2024"},{"key":"mlstadf375bib27","article-title":"Geometric algebra transformer","author":"Brehmer","year":"2023"},{"key":"mlstadf375bib28","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"mlstadf375bib29","article-title":"Geometric deep learning: grids, groups, graphs, geodesics, and gauges","author":"Bronstein","year":"2021"},{"key":"mlstadf375bib30","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1109\/MSP.2017.2693418","article-title":"Geometric deep learning: going beyond euclidean data","volume":"34","author":"Bronstein","year":"2017","journal-title":"IEEE Signal Process. Mag."},{"key":"mlstadf375bib31","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2022.104950","article-title":"Graph-valued regression: prediction of unlabelled networks in a non-euclidean graph space","volume":"190","author":"Calissano","year":"2022","journal-title":"J. Multivariate Anal."},{"key":"mlstadf375bib32","first-page":"pp 891","article-title":"Grarep: Learning graph representations with global structural information","author":"Cao","year":"2015"},{"key":"mlstadf375bib33","article-title":"A program to build E(N)-equivariant steerable CNNs","author":"Cesa","year":"2022"},{"key":"mlstadf375bib34","doi-asserted-by":"publisher","first-page":"799","DOI":"10.1109\/TPAMI.2020.3003846","article-title":"Manifoldnet: a deep neural network for manifold-valued data with applications","volume":"44","author":"Chakraborty","year":"2020","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"mlstadf375bib35","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1109\/34.899944","article-title":"A unified model for probabilistic principal surfaces","volume":"23","author":"Chang","year":"2001","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"mlstadf375bib36","author":"Chernov","year":"2010"},{"key":"mlstadf375bib37","article-title":"Equivariant convolutional networks","author":"Cohen","year":"2021"},{"key":"mlstadf375bib38","article-title":"Spherical CNNs","author":"Cohen","year":"2018"},{"key":"mlstadf375bib39","article-title":"A general theory of equivariant cnns on homogeneous spaces","volume":"vol 32","author":"Cohen","year":"2019b"},{"key":"mlstadf375bib40","article-title":"Steerable CNNs","author":"Cohen","year":"2017"},{"key":"mlstadf375bib41","first-page":"pp 1321","article-title":"Gauge equivariant convolutional networks and the icosahedral cnn","author":"Cohen","year":"2019a"},{"key":"mlstadf375bib42","first-page":"pp 2990","article-title":"Group equivariant convolutional networks","volume":"vol 48","author":"Cohen","year":"2016"},{"key":"mlstadf375bib43","doi-asserted-by":"publisher","first-page":"2363","DOI":"10.1093\/mnras\/stac2010","article-title":"Translation and rotation equivariant normalizing flow (trenf) for optimal cosmological analysis","volume":"516","author":"Dai","year":"2022","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"mlstadf375bib44","doi-asserted-by":"publisher","first-page":"708","DOI":"10.1016\/j.cag.2012.02.016","article-title":"Efficient construction of the Cech complex","volume":"36","author":"Dantchev","year":"2012","journal-title":"Comput. Graph."},{"key":"mlstadf375bib45","first-page":"pp 856","article-title":"Hyperspherical variational auto-encoders","volume":"vol 2","author":"Davidson","year":"2018"},{"key":"mlstadf375bib46","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/s11263-010-0367-1","article-title":"Population shape regression from random design data","volume":"90","author":"Davis","year":"2010","journal-title":"Int. J. Comput. Vis."},{"key":"mlstadf375bib47","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1038\/s42254-023-00569-0","article-title":"Graph neural networks at the large hadron collider","volume":"5","author":"DeZoort","year":"2023","journal-title":"Nat. Rev. Phys."},{"key":"mlstadf375bib48","article-title":"Latent computing by biological neural networks: a dynamical systems framework","author":"Dinc","year":"2025"},{"key":"mlstadf375bib49","doi-asserted-by":"crossref","DOI":"10.18653\/v1\/2020.emnlp-main.399","article-title":"Be more with less: hypergraph attention networks for inductive text classification","author":"Ding","year":"2020"},{"key":"mlstadf375bib50","article-title":"An image is worth 16x16 words: transformers for image recognition at scale","author":"Dosovitskiy","year":"2021"},{"key":"mlstadf375bib51","article-title":"Simplicial neural networks","author":"Ebli","year":"2020"},{"key":"mlstadf375bib52","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1145\/174462.156635","article-title":"Three-dimensional alpha shapes","volume":"13","author":"Edelsbrunner","year":"1994","journal-title":"ACM Trans. Graph."},{"key":"mlstadf375bib53","first-page":"pp 9071","article-title":"E(n) equivariant message passing simplicial networks","author":"Eijkelboom","year":"2023"},{"key":"mlstadf375bib54","doi-asserted-by":"publisher","first-page":"134826","DOI":"10.1109\/ACCESS.2021.3116304","article-title":"Point transformer","volume":"9","author":"Engel","year":"2020","journal-title":"IEEE Access"},{"key":"mlstadf375bib55","first-page":"pp 1","article-title":"Explorations in homeomorphic variational auto-encoding","author":"Falorsi","year":"2018"},{"key":"mlstadf375bib56","doi-asserted-by":"publisher","first-page":"4125","DOI":"10.1109\/TPAMI.2021.3059313","article-title":"Heterogeneous hypergraph variational autoencoder for link prediction","volume":"44","author":"Fan","year":"2022","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"mlstadf375bib57","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1214\/aos\/1176349022","article-title":"Local linear regression smoothers and their minimax efficiencies","volume":"21","author":"Fan","year":"1993","journal-title":"Ann. Stat."},{"key":"mlstadf375bib58","first-page":"pp 593","article-title":"L2 norm regularized feature kernel regression for graph data","author":"Fei","year":"2009"},{"key":"mlstadf375bib59","article-title":"Fast graph representation learning with PyTorch Geometric","author":"Fey","year":"2019"},{"key":"mlstadf375bib60","first-page":"pp 3318","article-title":"A practical method for constructing equivariant multilayer perceptrons for arbitrary matrix groups","volume":"vol 139","author":"Finzi","year":"2021"},{"key":"mlstadf375bib61","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1111\/j.1469-1809.1936.tb02137.x","article-title":"The use of multiple measurements in taxonomic problems","volume":"7","author":"Fisher","year":"1936","journal-title":"Ann. Eugen."},{"key":"mlstadf375bib62","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1016\/j.sigpro.2005.12.018","article-title":"Riemannian geometry for the statistical analysis of diffusion tensor data","volume":"87","author":"Fletcher","year":"2007","journal-title":"Signal Process."},{"key":"mlstadf375bib63","doi-asserted-by":"publisher","first-page":"995","DOI":"10.1109\/TMI.2004.831793","article-title":"Principal geodesic analysis for the study of nonlinear statistics of shape","volume":"23","author":"Fletcher","year":"2004","journal-title":"IEEE Trans. Med. Imaging"},{"key":"mlstadf375bib64","first-page":"pp 75","article-title":"Geodesic regression on riemannian manifolds","author":"Fletcher","year":"2011"},{"key":"mlstadf375bib65","article-title":"Learning discrete structures for graph neural networks","author":"Franceschi","year":"2019"},{"key":"mlstadf375bib66","article-title":"A growing neural gas network learns topologies","volume":"vol 7","author":"Fritzke","year":"1994"},{"key":"mlstadf375bib67","article-title":"Se(3)-transformers: 3D roto-translation equivariant attention networks","author":"Fuchs","year":"2020"},{"key":"mlstadf375bib68","article-title":"Invariant embedding for graph classification","author":"Galland","year":"2019"},{"key":"mlstadf375bib69","doi-asserted-by":"publisher","first-page":"3181","DOI":"10.1109\/TPAMI.2022.3182052","article-title":"Hgnn+: general hypergraph neural networks","volume":"45","author":"Gao","year":"2022","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"mlstadf375bib70","doi-asserted-by":"publisher","first-page":"bbab159","DOI":"10.1093\/bib\/bbab159","article-title":"Utilizing graph machine learning within drug discovery and development","volume":"22","author":"Gaudelet","year":"2021","journal-title":"Brief. Bioinf."},{"key":"mlstadf375bib71","article-title":"Position: Categorical deep learning is an algebraic theory of all architectures","author":"Gavranovi\u0107","year":"2024"},{"key":"mlstadf375bib72","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1007\/s00220-011-1313-y","article-title":"Invariant higher-order variational problems","volume":"309","author":"Gay-Balmaz","year":"2011","journal-title":"Commun. Math. Phys."},{"key":"mlstadf375bib73","article-title":"Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules","volume":"vol 32","author":"Gebauer","year":"2019"},{"key":"mlstadf375bib74","doi-asserted-by":"publisher","DOI":"10.5281\/zenodo.3724963","article-title":"Euclidean neural networks: e3nn","author":"Geiger","year":"2022","unstructured":"Geiger M et al 2022 Euclidean neural networks: e3nn 10.5281\/zenodo.3724963 (Accessed 15 March 2024)"},{"key":"mlstadf375bib75","first-page":"242","article-title":"Application de la m\u00e9thode des moindres carr\u00e9s \u00e0 l\u2019interpolation des suites","volume":"6","author":"Gergonne","year":"1815","journal-title":"Ann. Math. Pures Appl."},{"key":"mlstadf375bib76","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1093\/pan\/mpq009","article-title":"Circular data in political science and how to handle it","volume":"18","author":"Gill","year":"2010","journal-title":"Polit. Anal."},{"key":"mlstadf375bib77","first-page":"pp 1263","article-title":"Neural message passing for quantum chemistry","volume":"vol 70","author":"Gilmer","year":"2017"},{"key":"mlstadf375bib78","doi-asserted-by":"crossref","DOI":"10.1109\/IJCNN54540.2023.10191530","article-title":"Cell attention networks","author":"Giusti","year":"2023"},{"key":"mlstadf375bib79","doi-asserted-by":"publisher","first-page":"540","DOI":"10.1038\/s41598-023-27565-9","article-title":"Generative hypergraph models and spectral embedding","volume":"13","author":"Gong","year":"2023","journal-title":"Sci. Rep."},{"key":"mlstadf375bib80","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1038\/nature20101","article-title":"Hybrid computing using a neural network with dynamic external memory","volume":"538","author":"Graves","year":"2016","journal-title":"Nature"},{"key":"mlstadf375bib81","article-title":"Neural turing machines","author":"Graves","year":"2014"},{"key":"mlstadf375bib82","first-page":"pp 855","article-title":"node2vec: scalable feature learning for networks","author":"Grover","year":"2016"},{"key":"mlstadf375bib83","article-title":"AutoGL: a library for automated graph learning","author":"Guan","year":"2021"},{"key":"mlstadf375bib84","first-page":"pp 1076","article-title":"Reconstruction using witness complexes","author":"Guibas","year":"2007"},{"key":"mlstadf375bib85","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1561\/2200000098","article-title":"Introduction to riemannian geometry and geometric statistics: from basic theory to implementation with geomstats","volume":"16","author":"Guigui","year":"2023","journal-title":"Found. Trends\u00ae Mach. Learn."},{"key":"mlstadf375bib86","article-title":"Hyperbolic attention networks","author":"Gulcehre","year":"2019"},{"key":"mlstadf375bib87","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/s41095-021-0229-5","article-title":"Pct: Point cloud transformer","volume":"7","author":"Guo","year":"2021","journal-title":"Comput. Vis. Media"},{"key":"mlstadf375bib88","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1080\/02664763.2019.1669541","article-title":"Statistical regression analysis of functional and shape data","volume":"47","author":"Guo","year":"2019","journal-title":"J. Appl. Stat."},{"key":"mlstadf375bib89","article-title":"k-simplex2vec: a simplicial extension of node2vec. Spotlight","author":"Hacker","year":"2020"},{"key":"mlstadf375bib90","doi-asserted-by":"crossref","DOI":"10.25080\/TCWV9851","article-title":"Exploring network structure, dynamics and function using networkx","author":"Hagberg","year":"2008"},{"key":"mlstadf375bib91","article-title":"Topological deep learning: going beyond graph data","author":"Hajij","year":"2023"},{"key":"mlstadf375bib92","first-page":"1","article-title":"Topox: a suite of python packages for machine learning on topological domains","volume":"25","author":"Hajij","year":"2024","journal-title":"J. Mach. Learn. Res."},{"key":"mlstadf375bib93","article-title":"Cell complex neural networks","author":"Hajij","year":"2020a"},{"key":"mlstadf375bib94","article-title":"Cell complex neural networks","author":"Hajij","year":"2020b"},{"key":"mlstadf375bib95","article-title":"Simplicial complex representation learning","author":"Hajij","year":"2022"},{"key":"mlstadf375bib96","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1080\/01621459.1973.10481352","article-title":"Polynomial regression from a bayesian approach","volume":"68","author":"Halpern","year":"1973","journal-title":"J. Am. Stat. Assoc."},{"key":"mlstadf375bib97","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-030-59719-1_60","article-title":"Nonlinear regression on manifolds for shape analysis using intrinsic b\u00e9zier splines","author":"Hanik","year":"2020"},{"key":"mlstadf375bib98","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1080\/01621459.1989.10478797","article-title":"Principal curves","volume":"84","author":"Hastie","year":"1989","journal-title":"J. Am. Stat. Assoc."},{"key":"mlstadf375bib99","doi-asserted-by":"publisher","first-page":"1915","DOI":"10.1109\/TPAMI.2015.2496166","article-title":"Principal curves on riemannian manifolds","volume":"38","author":"Hauberg","year":"2016","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"mlstadf375bib100","first-page":"pp 27331","article-title":"Gauge equivariant transformer","volume":"vol 34","author":"He","year":"2021"},{"key":"mlstadf375bib101","doi-asserted-by":"publisher","DOI":"10.3389\/frai.2021.681108","article-title":"A survey of topological machine learning methods","volume":"4","author":"Hensel","year":"2021","journal-title":"Front. Artif. Intell."},{"key":"mlstadf375bib102","first-page":"pp 583","article-title":"Message passing neural networks for hypergraphs","author":"Heydari","year":"2022"},{"key":"mlstadf375bib103","first-page":"pp 1","article-title":"Polynomial regression on riemannian manifolds","author":"Hinkle","year":"2012a"},{"key":"mlstadf375bib104","first-page":"pp 1","article-title":"Polynomial regression on riemannian manifolds","author":"Hinkle","year":"2012b"},{"key":"mlstadf375bib105","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1016\/j.sigpro.2015.10.004","article-title":"Hypergraph regularized autoencoder for image-based 3d human pose recovery","volume":"124","author":"Hong","year":"2016","journal-title":"Signal Process."},{"key":"mlstadf375bib106","first-page":"pp 8867","article-title":"Equivariant diffusion for molecule generation in 3D","volume":"vol 162","author":"Hoogeboom","year":"2022"},{"key":"mlstadf375bib107","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/s10115-012-0609-3","article-title":"High-dimensional clustering: a clique-based hypergraph partitioning framework","volume":"39","author":"Hu","year":"2014","journal-title":"Knowl. Inf. Syst."},{"key":"mlstadf375bib108","first-page":"pp 2036","article-title":"A riemannian network for spd matrix learning","author":"Huang","year":"2017"},{"key":"mlstadf375bib109","first-page":"1","article-title":"Intrinsic shape analysis: geodesic pca for riemannian manifolds modulo isometric lie group actions","volume":"20","author":"Huckemann","year":"2010","journal-title":"Stat. Sin."},{"key":"mlstadf375bib110","article-title":"Lietransformer: equivariant self-attention for lie groups","author":"Hutchinson","year":"2021"},{"key":"mlstadf375bib111","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10463-023-00884-4","article-title":"Identifiability of latent-variable and structural-equation models: from linear to nonlinear","volume":"76","author":"Hyv\u00e4rinen","year":"2024","journal-title":"Ann. Inst. Stat. Math."},{"key":"mlstadf375bib112","article-title":"Manifold gplvms for discovering non-euclidean latent structure in neural data","author":"Jensen","year":"2020"},{"key":"mlstadf375bib113","first-page":"pp 11305","article-title":"Semi-supervised learning with graph learning-convolutional networks","author":"Jiang","year":"2019a"},{"key":"mlstadf375bib114","doi-asserted-by":"crossref","DOI":"10.24963\/ijcai.2019\/366","article-title":"Dynamic hypergraph neural networks","author":"Jiang","year":"2019b"},{"key":"mlstadf375bib115","doi-asserted-by":"publisher","first-page":"1543","DOI":"10.3982\/ECTA14605","article-title":"Fixed-effect regressions on network data","volume":"87","author":"Jochmans","year":"2019","journal-title":"Econometrica"},{"key":"mlstadf375bib116","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1080\/01621459.1978.10480062","article-title":"Some angular-linear distributions and related regression models","volume":"73","author":"Johnson","year":"1978","journal-title":"J. Am. Stat. Assoc."},{"key":"mlstadf375bib117","first-page":"pp 3183","article-title":"Molecular hypergraph grammar with its application to molecular optimization","volume":"vol 97","author":"Kajino","year":"2019"},{"key":"mlstadf375bib118","doi-asserted-by":"publisher","first-page":"4843","DOI":"10.1109\/TPAMI.2024.3357801","article-title":"Probabilistic principal curves on riemannian manifolds","volume":"46","author":"Kang","year":"2024","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"mlstadf375bib119","doi-asserted-by":"publisher","first-page":"1606","DOI":"10.1109\/TPAMI.2022.3170249","article-title":"Differentiable graph module (dgm) for graph convolutional networks","volume":"45","author":"Kazi","year":"2023","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"mlstadf375bib120","article-title":"Auto-encoding variational bayes","author":"Kingma","year":"2014"},{"key":"mlstadf375bib121","article-title":"Variational graph auto-encoders","author":"Kipf","year":"2016"},{"key":"mlstadf375bib122","article-title":"Semi-supervised classification with graph convolutional networks","author":"Kipf","year":"2017"},{"key":"mlstadf375bib123","first-page":"pp 2688","article-title":"Neural relational inference for interacting systems","author":"Kipf","year":"2018"},{"key":"mlstadf375bib124","article-title":"Geoopt: Riemannian optimization in pytorch","author":"Kochurov","year":"2020"},{"key":"mlstadf375bib125","first-page":"p 31","article-title":"Clebsch\u2013gordan nets: a fully fourier space spherical convolutional neural network","author":"Kondor","year":"2018"},{"key":"mlstadf375bib126","first-page":"pp 2747","article-title":"On the generalization of equivariance and convolution in neural networks to the action of compact groups","author":"Kondor","year":"2018"},{"key":"mlstadf375bib127","doi-asserted-by":"publisher","first-page":"123433","DOI":"10.1109\/ACCESS.2023.3329952","article-title":"Multi-manifold attention for vision transformers","volume":"11","author":"Konstantinidis","year":"2023","journal-title":"IEEE Access"},{"key":"mlstadf375bib128","doi-asserted-by":"publisher","first-page":"432","DOI":"10.1198\/jcgs.2011.09203","article-title":"Nonparametric regression on a graph","volume":"20","author":"Kovac","year":"2011","journal-title":"J. Comput. Graph. Stat."},{"key":"mlstadf375bib129","first-page":"1","article-title":"Neural operator: learning maps between function spaces with applications to pdes","volume":"24","author":"Kovachki","year":"2023","journal-title":"J. Mach. Learn. Res."},{"key":"mlstadf375bib130","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1145\/3065386","article-title":"Imagenet classification with deep convolutional neural networks","volume":"60","author":"Krizhevsky","year":"2012","journal-title":"Commun. ACM"},{"key":"mlstadf375bib131","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-59050-9_5","article-title":"Stochastic development regression on non-linear manifolds","author":"K\u00fchnel","year":"2017"},{"key":"mlstadf375bib132","article-title":"Steerable transformers","author":"Kundu","year":"2024"},{"key":"mlstadf375bib133","doi-asserted-by":"publisher","first-page":"5162","DOI":"10.21105\/joss.05162","article-title":"Xgi: A python package for higher-order interaction networks","volume":"8","author":"Landry","year":"2023","journal-title":"J. Open Source Softw."},{"key":"mlstadf375bib134","first-page":"pp 329","article-title":"Gaussian process latent variable models for visualisation of high dimensional data","author":"Lawrence","year":"2003"},{"key":"mlstadf375bib135","doi-asserted-by":"publisher","first-page":"685","DOI":"10.1016\/j.jmva.2019.05.008","article-title":"Quantization and clustering on riemannian manifolds with an application to air traffic analysis","volume":"173","author":"Le Brigant","year":"2019","journal-title":"J. Multivariate Anal."},{"key":"mlstadf375bib136","doi-asserted-by":"publisher","first-page":"2278","DOI":"10.1109\/5.726791","article-title":"Gradient-based learning applied to document recognition","volume":"86","author":"LeCun","year":"1998","journal-title":"Proc. IEEE"},{"key":"mlstadf375bib137","first-page":"pp 3744","article-title":"Set transformer: a framework for attention-based permutation-invariant neural networks","volume":"vol 97","author":"Lee","year":"2019"},{"key":"mlstadf375bib138","first-page":"pp 3192","article-title":"Sgat: simplicial graph attention network","author":"Lee","year":"2022"},{"key":"mlstadf375bib139","author":"Legendre","year":"1806"},{"key":"mlstadf375bib140","doi-asserted-by":"publisher","first-page":"1353","DOI":"10.1038\/s41551-022-00942-x","article-title":"Graph representation learning in biomedicine and healthcare","volume":"6","author":"Li","year":"2022a","journal-title":"Nat. Biomed. Eng."},{"key":"mlstadf375bib141","article-title":"Probabilistic relational PCA","volume":"vol 22","author":"Li","year":"2009"},{"key":"mlstadf375bib142","first-page":"pp 6190","article-title":"Geodesic self-attention for 3d point clouds","volume":"vol 35","author":"Li","year":"2022b"},{"key":"mlstadf375bib143","doi-asserted-by":"publisher","first-page":"1261","DOI":"10.1080\/01621459.2016.1208615","article-title":"Extrinsic local regression on manifold-valued data","volume":"112","author":"Lin","year":"2017","journal-title":"J. Am. Stat. Assoc."},{"key":"mlstadf375bib144","article-title":"Clifford group equivariant simplicial message passing networks","author":"Liu","year":"2024"},{"key":"mlstadf375bib145","first-page":"1","article-title":"Dig: a turnkey library for diving into graph deep learning research","volume":"22","author":"Liu","year":"2021","journal-title":"J. Mach. Learn. Res."},{"key":"mlstadf375bib146","doi-asserted-by":"publisher","first-page":"452","DOI":"10.1109\/TIP.2016.2621671","article-title":"Elastic net hypergraph learning for image clustering and semi-supervised classification","volume":"26","author":"Liu","year":"2017","journal-title":"Trans. Img. Process."},{"key":"mlstadf375bib147","first-page":"pp 11525","article-title":"Object-centric learning with slot attention","volume":"vol 33","author":"Locatello","year":"2020"},{"key":"mlstadf375bib148","first-page":"pp 19","article-title":"Ames: a differentiable embedding space selection framework for latent graph inference","volume":"vol 228","author":"Lu","year":"2023"},{"key":"mlstadf375bib149","article-title":"An autoregressive flow model for 3d molecular geometry generation from scratch","author":"Luo","year":"2022"},{"key":"mlstadf375bib150","first-page":"25","article-title":"Fitting smooth paths on Riemannian manifolds","volume":"6","author":"Machado","year":"2006","journal-title":"Int. J. Appl. Math. Stat."},{"key":"mlstadf375bib151","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/s10883-010-9080-1","article-title":"Higher-order smoothing splines versus least squares problems on Riemannian manifolds","volume":"16","author":"Machado","year":"2010","journal-title":"J. Dyn. Control Syst."},{"key":"mlstadf375bib152","article-title":"Simplicial representation learning with neural k-forms","author":"Maggs","year":"2024"},{"key":"mlstadf375bib153","first-page":"pp 12","author":"Maignant","year":"2023"},{"key":"mlstadf375bib154","first-page":"5580","article-title":"Wrapped Gaussian process regression on Riemannian manifolds","author":"Mallasto","year":"2018"},{"key":"mlstadf375bib155","article-title":"Scattering networks on the sphere for scalable and rotationally equivariant spherical CNNs","author":"McEwen","year":"2022"},{"key":"mlstadf375bib156","doi-asserted-by":"publisher","first-page":"861","DOI":"10.21105\/joss.00861","article-title":"UMAP: uniform manifold approximation and projection","volume":"3","author":"McInnes","year":"2018","journal-title":"J. Open Source Softw."},{"key":"mlstadf375bib157","doi-asserted-by":"publisher","first-page":"1436","DOI":"10.1214\/009053606000000281","article-title":"High-dimensional graphs and variable selection with the Lasso","volume":"34","author":"Meinshausen","year":"2006","journal-title":"Ann. Stat."},{"key":"mlstadf375bib158","article-title":"Efficient estimation of word representations in vector space","author":"Mikolov","year":"2013"},{"key":"mlstadf375bib159","article-title":"Toroidal autoencoder","author":"Mikulski","year":"2019"},{"key":"mlstadf375bib160","first-page":"1","article-title":"Geomstats: a python package for Riemannian geometry in machine learning","volume":"21","author":"Miolane","year":"2020","journal-title":"J. Mach. Learn. Res."},{"key":"mlstadf375bib161","first-page":"pp 14503","article-title":"Learning weighted submanifolds with variational autoencoders and Riemannian variational autoencoders","author":"Miolane","year":"2020"},{"key":"mlstadf375bib162","article-title":"The geometrickernels package: Heat and mat\u00e9rn kernels for geometric learning on manifolds, meshes, and graphs","author":"Mostowsky","year":"2024"},{"key":"mlstadf375bib163","first-page":"pp 215","article-title":"A map estimation algorithm for Bayesian polynomial regression on riemannian manifolds","author":"Muralidharan","year":"2017"},{"key":"mlstadf375bib164","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1137\/1109020","article-title":"On estimating regression","volume":"9","author":"Nadaraya","year":"1964","journal-title":"Theory Probab. Appl."},{"key":"mlstadf375bib165","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1080\/01621459.2017.1389739","article-title":"Bayesian graphical regression","volume":"114","author":"Ni","year":"2018","journal-title":"J. Am. Stat. Assoc."},{"key":"mlstadf375bib166","first-page":"pp 6341","article-title":"Poincar\u00e9 embeddings for learning hierarchical representations","author":"Nickel","year":"2017"},{"key":"mlstadf375bib167","doi-asserted-by":"publisher","first-page":"424","DOI":"10.1080\/01621459.2013.849199","article-title":"Principal flows","volume":"109","author":"Panaretos","year":"2014","journal-title":"J. Am. Stat. Assoc."},{"key":"mlstadf375bib168","article-title":"Architectures of topological deep learning: a survey on topological neural networks","author":"Papillon","year":"2024"},{"key":"mlstadf375bib169","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1080\/14786440109462720","article-title":"Liii. on lines and planes of closest fit to systems of points in space","volume":"2","author":"Pearson","year":"1901","journal-title":"London, Edinburgh Dublin Phil. Mag. J. Sci."},{"key":"mlstadf375bib170","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1080\/10485250500504828","article-title":"Non-parametric regression estimation on closed riemannian manifolds","volume":"18","author":"Pelletier","year":"2006","journal-title":"J. Nonpar. Stat."},{"key":"mlstadf375bib171","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/s10851-006-6228-4","article-title":"Intrinsic statistics on riemannian manifolds: basic tools for geometric measurements","volume":"25","author":"Pennec","year":"2006","journal-title":"J. Math. Imaging Vis."},{"key":"mlstadf375bib172","doi-asserted-by":"publisher","first-page":"2711","DOI":"10.1214\/17-AOS1636","article-title":"Barycentric subspace analysis on manifolds","volume":"46","author":"Pennec","year":"2018","journal-title":"Ann. Stat."},{"key":"mlstadf375bib173","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/s11263-005-3222-z","article-title":"A riemannian framework for tensor computing","volume":"66","author":"Pennec","year":"2006","journal-title":"Int. J. Comput. Vis."},{"key":"mlstadf375bib174","author":"Pennec","year":"2019"},{"key":"mlstadf375bib175","first-page":"pp 701","article-title":"Deepwalk: online learning of social representations","author":"Perozzi","year":"2014"},{"key":"mlstadf375bib176","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1214\/17-AOS1624","article-title":"Fr\u00e9chet regression for random objects with euclidean predictors","volume":"47","author":"Petersen","year":"2016","journal-title":"Ann. Stat."},{"key":"mlstadf375bib177","article-title":"Learning mesh-based simulation with graph networks","author":"Pfaff","year":"2021"},{"key":"mlstadf375bib178","first-page":"pp 17403","article-title":"Disentangling by subspace diffusion","volume":"vol 33","author":"Pfau","year":"2020"},{"key":"mlstadf375bib179","article-title":"Gaussian processes on hypergraphs","author":"Pinder","year":"2021"},{"key":"mlstadf375bib180","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1023\/A:1026313132218","article-title":"Deformable m-reps for 3d medical image segmentation","volume":"55","author":"Pizer","year":"2003","journal-title":"Int. J. Comput. Vis."},{"key":"mlstadf375bib181","doi-asserted-by":"publisher","first-page":"6016","DOI":"10.21105\/joss.06016","article-title":"Hypernetx: a python package for modeling complex network data as hypergraphs","volume":"9","author":"Praggastis","year":"2024","journal-title":"J. Open Source Softw."},{"key":"mlstadf375bib182","article-title":"Pointnet: deep learning on point sets for 3d classification and segmentation","author":"Qi","year":"2017a"},{"key":"mlstadf375bib183","first-page":"pp 5105","article-title":"Pointnet++: deep hierarchical feature learning on point sets in a metric space","author":"Qi","year":"2017b"},{"key":"mlstadf375bib184","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1038\/s41591-021-01614-0","article-title":"AI in health and medicine","volume":"28","author":"Rajpurkar","year":"2022","journal-title":"Nat. Med."},{"key":"mlstadf375bib185","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1021\/acs.jcim.4c01001","article-title":"Coarsenconf: equivariant coarsening with aggregated attention for molecular conformer generation","volume":"65","author":"Reidenbach","year":"2025","journal-title":"J. Chem. Inf. Modeling"},{"key":"mlstadf375bib186","first-page":"pp 8852","article-title":"Signal processing on cell complexes","author":"Roddenberry","year":"2022"},{"key":"mlstadf375bib187","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1186\/s12859-015-0694-x","article-title":"A simplicial complex-based approach to unmixing tumor progression data","volume":"16","author":"Roman","year":"2015","journal-title":"BMC Bioinform."},{"key":"mlstadf375bib188","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1037\/h0042519","article-title":"The perceptron: a probabilistic model for information storage and organization in the brain","volume":"65","author":"Rosenblatt","year":"1958","journal-title":"Psychol. Rev."},{"key":"mlstadf375bib189","doi-asserted-by":"publisher","first-page":"2323","DOI":"10.1126\/science.290.5500.2323","article-title":"Nonlinear dimensionality reduction by locally linear embedding","volume":"290","author":"Roweis","year":"2000","journal-title":"Science"},{"key":"mlstadf375bib190","first-page":"pp 99","article-title":"Fast sequence-based embedding with diffusion graphs","author":"Rozemberczki","year":"2018"},{"key":"mlstadf375bib191","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1038\/323533a0","article-title":"Learning representations by back-propagating errors","volume":"323","author":"Rumelhart","year":"1986","journal-title":"Nature"},{"key":"mlstadf375bib192","first-page":"pp 371","article-title":"The principal components analysis of a graph and its relationships to spectral clustering","volume":"vol 3201","author":"Saerens","year":"2004"},{"key":"mlstadf375bib193","first-page":"pp 578","article-title":"Partial least squares regression for graph mining","author":"Saigo","year":"2008"},{"key":"mlstadf375bib194","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/s10994-008-5089-z","article-title":"gboost: a mathematical programming approach to graph classification and regression","volume":"75","author":"Saigo","year":"2009","journal-title":"Mach. Learn."},{"key":"mlstadf375bib195","first-page":"pp 8459","article-title":"Learning to simulate complex physics with graph networks","author":"Sanchez-Gonzalez","year":"2020"},{"key":"mlstadf375bib196","first-page":"pp 9323","article-title":"E(n) equivariant graph neural networks","author":"Satorras","year":"2021a"},{"key":"mlstadf375bib197","first-page":"pp 9323","article-title":"E(n) equivariant graph neural networks","volume":"vol 139","author":"Satorras","year":"2021b"},{"key":"mlstadf375bib198","doi-asserted-by":"publisher","first-page":"2369","DOI":"10.1093\/mnras\/stab530","article-title":"Fanaroff\u2013riley classification of radio galaxies using group-equivariant convolutional neural networks","volume":"503","author":"Scaife","year":"2021","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"mlstadf375bib199","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1137\/18M1201019","article-title":"Random walks on simplicial complexes and the normalized hodge 1-laplacian","volume":"62","author":"Schaub","year":"2020","journal-title":"SIAM Rev."},{"key":"mlstadf375bib200","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41586-023-06031-6","article-title":"Learnable latent embeddings for joint behavioural and neural analysis","volume":"617","author":"Schneider","year":"2023","journal-title":"Nature"},{"key":"mlstadf375bib201","doi-asserted-by":"publisher","first-page":"4679","DOI":"10.1214\/22-EJS2056","article-title":"Nonparametric regression in nonstandard spaces","volume":"16","author":"Sch\u00f6tz","year":"2022","journal-title":"Electron. J. Stat."},{"key":"mlstadf375bib202","first-page":"pp 992","article-title":"Schnet: a continuous-filter convolutional neural network for modeling quantum interactions","author":"Sch\u00fctt","year":"2017"},{"key":"mlstadf375bib203","doi-asserted-by":"publisher","first-page":"e373","DOI":"10.1002\/sta4.373","article-title":"Non-parametric regression for networks","volume":"10","author":"Severn","year":"2021","journal-title":"Stat"},{"key":"mlstadf375bib204","first-page":"pp 75012","article-title":"Transformers represent belief state geometry in their residual stream","volume":"vol 37","author":"Shai","year":"2024"},{"key":"mlstadf375bib205","first-page":"pp 192","author":"Shi","year":"2009"},{"key":"mlstadf375bib206","article-title":"Topological estimation using witness complexes","author":"Silva","year":"2004"},{"key":"mlstadf375bib207","article-title":"Symmetry-aware actor-critic for 3d molecular design","author":"Simm","year":"2021"},{"key":"mlstadf375bib208","first-page":"pp 412","article-title":"Graphvae: towards generation of small graphs using variational autoencoders","author":"Simonovsky","year":"2018"},{"key":"mlstadf375bib209","article-title":"Topological methods for the analysis of high dimensional data sets and 3D object recognition","author":"Singh","year":"2007"},{"key":"mlstadf375bib210","first-page":"pp 76","article-title":"Horizontal dimensionality reduction and iterated frame bundle development","author":"Sommer","year":"2013"},{"key":"mlstadf375bib211","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/s10444-013-9308-1","article-title":"Optimization over geodesics for exact principal geodesic analysis","volume":"40","author":"Sommer","year":"2014","journal-title":"Adv. Comput. Math."},{"key":"mlstadf375bib212","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1111\/j.1467-8659.2008.01141.x","article-title":"Manifold-valued thin-plate splines with applications in computer graphics","volume":"27","author":"Steinke","year":"2008","journal-title":"Comput. Graph. Forum"},{"key":"mlstadf375bib213","doi-asserted-by":"publisher","first-page":"688","DOI":"10.1016\/j.cell.2020.01.021","article-title":"A deep learning approach to antibiotic discovery","volume":"180","author":"Stokes","year":"2020","journal-title":"Cell"},{"key":"mlstadf375bib214","first-page":"pp 817","article-title":"Relational learning via latent social dimensions","author":"Tang","year":"2009"},{"key":"mlstadf375bib215","article-title":"Topobench: a framework for benchmarking topological deep learning","author":"Telyatnikov","year":"2024"},{"key":"mlstadf375bib216","doi-asserted-by":"publisher","first-page":"2319","DOI":"10.1126\/science.290.5500.2319","article-title":"A global geometric framework for nonlinear dimensionality reduction","volume":"290","author":"Tenenbaum","year":"2000","journal-title":"Science"},{"key":"mlstadf375bib217","article-title":"Tensor field networks: rotation-and translation-equivariant neural networks for 3D point clouds","author":"Thomas","year":"2018"},{"key":"mlstadf375bib218","doi-asserted-by":"publisher","first-page":"611","DOI":"10.1111\/1467-9868.00196","article-title":"Probabilistic principal component analysis","volume":"61","author":"Tipping","year":"1999","journal-title":"J. R. Stat. Soc. B"},{"key":"mlstadf375bib219","article-title":"Understanding over-squashing and bottlenecks on graphs via curvature","author":"Topping","year":"2022"},{"key":"mlstadf375bib220","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1016\/0031-3203(80)90066-7","article-title":"The relative neighbourhood graph of a finite planar set","volume":"12","author":"Toussaint","year":"1980","journal-title":"Pattern Recognit."},{"key":"mlstadf375bib221","first-page":"1","article-title":"Pymanopt: a python toolbox for optimization on manifolds using automatic differentiation","volume":"17","author":"Townsend","year":"2016","journal-title":"J. Mach. Learn. Res."},{"key":"mlstadf375bib222","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1016\/j.patrec.2017.11.008","article-title":"Random forest regression for manifold-valued responses","volume":"101","author":"Tsagkrasoulis","year":"2018","journal-title":"Pattern Recognit. Lett."},{"key":"mlstadf375bib223","first-page":"pp 919","article-title":"Entire regularization paths for graph data","author":"Tsuda","year":"2007"},{"key":"mlstadf375bib224","doi-asserted-by":"publisher","first-page":"2634","DOI":"10.1080\/01621459.2023.2270750","article-title":"Latent space modeling of hypergraph data","volume":"119","author":"Turnbull","year":"2023","journal-title":"J. Am. Stat. Assoc."},{"key":"mlstadf375bib225","first-page":"2579","article-title":"Visualizing data using {t-sne}","volume":"9","author":"van der Maaten","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"mlstadf375bib226","first-page":"pp 6000","article-title":"Attention is all you need","author":"Vaswani","year":"2017"},{"key":"mlstadf375bib227","article-title":"Graph attention networks","author":"Velickovi\u0107","year":"2018"},{"key":"mlstadf375bib228","doi-asserted-by":"publisher","first-page":"698","DOI":"10.1109\/TSIPN.2019.2936358","article-title":"Predicting graph signals using kernel regression where the input signal is agnostic to a graph","volume":"5","author":"Venkitaraman","year":"2019","journal-title":"IEEE Trans. Signal Inf. Process. Netw."},{"key":"mlstadf375bib229","doi-asserted-by":"publisher","first-page":"454","DOI":"10.1007\/BF01447877","article-title":"\u00dcber den h\u00f6heren zusammenhang kompakter r\u00e4ume und eine klasse von zusammenhangstreuen abbildungen","volume":"97","author":"Vietoris","year":"1927","journal-title":"Math. Ann."},{"key":"mlstadf375bib230","first-page":"pp 560","article-title":"Midi: mixed graph and 3D denoising diffusion for molecule generation","author":"Vignac","year":"2023"},{"key":"mlstadf375bib231","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1038\/s41586-023-06221-2","article-title":"Scientific discovery in the age of artificial intelligence","volume":"620","author":"Wang","year":"2023","journal-title":"Nature"},{"key":"mlstadf375bib232","doi-asserted-by":"publisher","first-page":"3043","DOI":"10.1038\/s41467-022-30706-9","article-title":"Full reconstruction of simplicial complexes from binary contagion and ising data","volume":"13","author":"Wang","year":"2022","journal-title":"Nat. Commun."},{"key":"mlstadf375bib233","first-page":"pp 3478","article-title":"Graph embedding via diffusion-wavelets-based node feature distribution characterization","author":"Wang","year":"2021"},{"key":"mlstadf375bib234","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1214\/ECP.v20-4193","article-title":"Height and diameter of brownian tree","volume":"20","author":"Wang","year":"2015","journal-title":"Electr. Commun. Probab."},{"key":"mlstadf375bib235","article-title":"Deep graph library: a graph-centric, highly-performant package for graph neural networks","author":"Wang","year":"2019"},{"key":"mlstadf375bib236","doi-asserted-by":"publisher","first-page":"2564","DOI":"10.1109\/TKDE.2015.2415497","article-title":"Visual classification by \u21131-hypergraph modeling","volume":"27","author":"Wang","year":"2015","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"mlstadf375bib237","author":"Weiler","year":"2025"},{"key":"mlstadf375bib238","first-page":"pp 514","article-title":"Gaussian processes for regression","author":"Williams","year":"1995"},{"key":"mlstadf375bib239","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3535101","article-title":"Graph neural networks in recommender systems: a survey","volume":"55","author":"Wu","year":"2022","journal-title":"ACM Comput. Surv."},{"key":"mlstadf375bib240","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1109\/TNNLS.2020.2978386","article-title":"A comprehensive survey on graph neural networks","volume":"32","author":"Wu","year":"2021","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"mlstadf375bib241","article-title":"Geometric latent diffusion models for 3d molecule generation","author":"Xu","year":"2023"},{"key":"mlstadf375bib242","article-title":"Geodiff: a geometric diffusion model for molecular conformation generation","author":"Xu","year":"2022"},{"key":"mlstadf375bib243","doi-asserted-by":"publisher","first-page":"876","DOI":"10.1214\/15-AOS1390","article-title":"Bayesian manifold regression","volume":"44","author":"Yang","year":"2016","journal-title":"Ann. Stat."},{"key":"mlstadf375bib244","doi-asserted-by":"publisher","first-page":"3262","DOI":"10.1109\/TIP.2012.2190083","article-title":"Adaptive hypergraph learning and its application in image classification","volume":"21","author":"Yu","year":"2012","journal-title":"IEEE Trans. Image Process."},{"key":"mlstadf375bib245","article-title":"Purple iris flower (iris tingitana \u00d7 iris xiphium)","author":"Yunakov","year":"2011"},{"key":"mlstadf375bib246","first-page":"pp 3394","article-title":"Deep sets","author":"Zaheer","year":"2017"},{"key":"mlstadf375bib247","doi-asserted-by":"publisher","first-page":"824","DOI":"10.1111\/biom.13335","article-title":"Bayesian compositional regression with structured priors for microbiome feature selection","volume":"77","author":"Zhang","year":"2020","journal-title":"Biometrics"},{"key":"mlstadf375bib248","first-page":"pp 1178","article-title":"Probabilistic principal geodesic analysis","volume":"vol 1","author":"Zhang","year":"2013"},{"key":"mlstadf375bib249","article-title":"D-vae: a variational autoencoder for directed acyclic graphs","author":"Zhang","year":"2019"},{"key":"mlstadf375bib250","article-title":"Learning with hypergraphs: clustering, classification and embedding","volume":"vol 19","author":"Zhou","year":"2006"},{"key":"mlstadf375bib251","first-page":"pp 5745","article-title":"On the continuity of rotation representations in neural networks","author":"Zhou","year":"2019"},{"key":"mlstadf375bib252","first-page":"320","article-title":"Network regression with graph laplacians","volume":"23","author":"Zhou","year":"2022","journal-title":"J. Mach. Learn. Res."},{"key":"mlstadf375bib253","doi-asserted-by":"publisher","first-page":"517","DOI":"10.1007\/s11280-017-0514-5","article-title":"Low-rank hypergraph feature selection for multi-output regression","volume":"22","author":"Zhu","year":"2019","journal-title":"World Wide Web"},{"key":"mlstadf375bib254","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/j.cag.2010.03.007","article-title":"Fast construction of the vietoris-rips complex","volume":"34","author":"Zomorodian","year":"2010","journal-title":"Comput. Graph."}],"container-title":["Machine Learning: Science and Technology"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adf375","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adf375\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adf375","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adf375\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adf375\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adf375\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adf375\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adf375\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,1]],"date-time":"2025-08-01T12:51:41Z","timestamp":1754052701000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/adf375"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,1]]},"references-count":254,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,8,1]]},"published-print":{"date-parts":[[2025,9,30]]}},"URL":"https:\/\/doi.org\/10.1088\/2632-2153\/adf375","relation":{},"ISSN":["2632-2153"],"issn-type":[{"value":"2632-2153","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,1]]},"assertion":[{"value":"Beyond Euclid: an illustrated guide to modern machine learning with geometric, topological, and algebraic structures","name":"article_title","label":"Article Title"},{"value":"Machine Learning: Science and Technology","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2025 The Author(s). Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2024-09-26","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-07-23","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-08-01","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}