--- _id: '9249' abstract: - lang: eng text: Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In this paper, we describe a new coordinate system where every 3-integer coordinates grid point corresponds to a rhombic dodecahedron centroid. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. We also present the characterization of 3D digital lines and study it as the intersection of multiple digital planes. Characterization of 3D digital sphere with relevant topological features is proposed as well along with the 48-symmetry appearing in the new coordinate system. acknowledgement: "This work has been partially supported by the European Research Council (ERC) under\r\nthe European Union’s Horizon 2020 research and innovation programme, grant no. 788183, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), grant no. I 02979-N35. " article_processing_charge: No article_type: original author: - first_name: Ranita full_name: Biswas, Ranita id: 3C2B033E-F248-11E8-B48F-1D18A9856A87 last_name: Biswas orcid: 0000-0002-5372-7890 - first_name: Gaëlle full_name: Largeteau-Skapin, Gaëlle last_name: Largeteau-Skapin - first_name: Rita full_name: Zrour, Rita last_name: Zrour - first_name: Eric full_name: Andres, Eric last_name: Andres citation: ama: Biswas R, Largeteau-Skapin G, Zrour R, Andres E. Digital objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications. 2020;4(1):143-158. doi:10.1515/mathm-2020-0106 apa: Biswas, R., Largeteau-Skapin, G., Zrour, R., & Andres, E. (2020). Digital objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications. De Gruyter. https://doi.org/10.1515/mathm-2020-0106 chicago: Biswas, Ranita, Gaëlle Largeteau-Skapin, Rita Zrour, and Eric Andres. “Digital Objects in Rhombic Dodecahedron Grid.” Mathematical Morphology - Theory and Applications. De Gruyter, 2020. https://doi.org/10.1515/mathm-2020-0106. ieee: R. Biswas, G. Largeteau-Skapin, R. Zrour, and E. Andres, “Digital objects in rhombic dodecahedron grid,” Mathematical Morphology - Theory and Applications, vol. 4, no. 1. De Gruyter, pp. 143–158, 2020. ista: Biswas R, Largeteau-Skapin G, Zrour R, Andres E. 2020. Digital objects in rhombic dodecahedron grid. Mathematical Morphology - Theory and Applications. 4(1), 143–158. mla: Biswas, Ranita, et al. “Digital Objects in Rhombic Dodecahedron Grid.” Mathematical Morphology - Theory and Applications, vol. 4, no. 1, De Gruyter, 2020, pp. 143–58, doi:10.1515/mathm-2020-0106. short: R. Biswas, G. Largeteau-Skapin, R. Zrour, E. Andres, Mathematical Morphology - Theory and Applications 4 (2020) 143–158. date_created: 2021-03-16T08:55:19Z date_published: 2020-11-17T00:00:00Z date_updated: 2021-03-22T09:01:50Z day: '17' ddc: - '510' department: - _id: HeEd doi: 10.1515/mathm-2020-0106 ec_funded: 1 file: - access_level: open_access checksum: 4a1043fa0548a725d464017fe2483ce0 content_type: application/pdf creator: dernst date_created: 2021-03-22T08:56:37Z date_updated: 2021-03-22T08:56:37Z file_id: '9272' file_name: 2020_MathMorpholTheoryAppl_Biswas.pdf file_size: 3668725 relation: main_file success: 1 file_date_updated: 2021-03-22T08:56:37Z has_accepted_license: '1' intvolume: ' 4' issue: '1' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 143-158 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Mathematical Morphology - Theory and Applications publication_identifier: issn: - 2353-3390 publication_status: published publisher: De Gruyter quality_controlled: '1' status: public title: Digital objects in rhombic dodecahedron grid tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 4 year: '2020' ... --- _id: '9299' abstract: - lang: eng text: We call a multigraph non-homotopic if it can be drawn in the plane in such a way that no two edges connecting the same pair of vertices can be continuously transformed into each other without passing through a vertex, and no loop can be shrunk to its end-vertex in the same way. It is easy to see that a non-homotopic multigraph on n>1 vertices can have arbitrarily many edges. We prove that the number of crossings between the edges of a non-homotopic multigraph with n vertices and m>4n edges is larger than cm2n for some constant c>0 , and that this bound is tight up to a polylogarithmic factor. We also show that the lower bound is not asymptotically sharp as n is fixed and m⟶∞ . acknowledgement: Supported by the National Research, Development and Innovation Office, NKFIH, KKP-133864, K-131529, K-116769, K-132696, by the Higher Educational Institutional Excellence Program 2019 NKFIH-1158-6/2019, the Austrian Science Fund (FWF), grant Z 342-N31, by the Ministry of Education and Science of the Russian Federation MegaGrant No. 075-15-2019-1926, and by the ERC Synergy Grant “Dynasnet” No. 810115. A full version can be found at https://arxiv.org/abs/2006.14908. article_processing_charge: No author: - first_name: János full_name: Pach, János id: E62E3130-B088-11EA-B919-BF823C25FEA4 last_name: Pach - first_name: Gábor full_name: Tardos, Gábor last_name: Tardos - first_name: Géza full_name: Tóth, Géza last_name: Tóth citation: ama: 'Pach J, Tardos G, Tóth G. Crossings between non-homotopic edges. In: 28th International Symposium on Graph Drawing and Network Visualization. Vol 12590. LNCS. Springer Nature; 2020:359-371. doi:10.1007/978-3-030-68766-3_28' apa: 'Pach, J., Tardos, G., & Tóth, G. (2020). Crossings between non-homotopic edges. In 28th International Symposium on Graph Drawing and Network Visualization (Vol. 12590, pp. 359–371). Virtual, Online: Springer Nature. https://doi.org/10.1007/978-3-030-68766-3_28' chicago: Pach, János, Gábor Tardos, and Géza Tóth. “Crossings between Non-Homotopic Edges.” In 28th International Symposium on Graph Drawing and Network Visualization, 12590:359–71. LNCS. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-68766-3_28. ieee: J. Pach, G. Tardos, and G. Tóth, “Crossings between non-homotopic edges,” in 28th International Symposium on Graph Drawing and Network Visualization, Virtual, Online, 2020, vol. 12590, pp. 359–371. ista: 'Pach J, Tardos G, Tóth G. 2020. Crossings between non-homotopic edges. 28th International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network VisualizationLNCS vol. 12590, 359–371.' mla: Pach, János, et al. “Crossings between Non-Homotopic Edges.” 28th International Symposium on Graph Drawing and Network Visualization, vol. 12590, Springer Nature, 2020, pp. 359–71, doi:10.1007/978-3-030-68766-3_28. short: J. Pach, G. Tardos, G. Tóth, in:, 28th International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2020, pp. 359–371. conference: end_date: 2020-09-18 location: Virtual, Online name: 'GD: Graph Drawing and Network Visualization' start_date: 2020-09-16 date_created: 2021-03-28T22:01:44Z date_published: 2020-09-20T00:00:00Z date_updated: 2021-04-06T11:32:32Z day: '20' department: - _id: HeEd doi: 10.1007/978-3-030-68766-3_28 external_id: arxiv: - '2006.14908' intvolume: ' 12590' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2006.14908 month: '09' oa: 1 oa_version: Preprint page: 359-371 project: - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: The Wittgenstein Prize publication: 28th International Symposium on Graph Drawing and Network Visualization publication_identifier: eissn: - 1611-3349 isbn: - '9783030687656' issn: - 0302-9743 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' series_title: LNCS status: public title: Crossings between non-homotopic edges type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 12590 year: '2020' ... --- _id: '9632' abstract: - lang: eng text: "Second-order information, in the form of Hessian- or Inverse-Hessian-vector products, is a fundamental tool for solving optimization problems. Recently, there has been significant interest in utilizing this information in the context of deep\r\nneural networks; however, relatively little is known about the quality of existing approximations in this context. Our work examines this question, identifies issues with existing approaches, and proposes a method called WoodFisher to compute a faithful and efficient estimate of the inverse Hessian. Our main application is to neural network compression, where we build on the classic Optimal Brain Damage/Surgeon framework. We demonstrate that WoodFisher significantly outperforms popular state-of-the-art methods for oneshot pruning. Further, even when iterative, gradual pruning is allowed, our method results in a gain in test accuracy over the state-of-the-art approaches, for standard image classification datasets such as ImageNet ILSVRC. We examine how our method can be extended to take into account first-order information, as well as\r\nillustrate its ability to automatically set layer-wise pruning thresholds and perform compression in the limited-data regime. The code is available at the following link, https://github.com/IST-DASLab/WoodFisher." acknowledgement: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 805223 ScaleML). Also, we would like to thank Alexander Shevchenko, Alexandra Peste, and other members of the group for fruitful discussions. article_processing_charge: No author: - first_name: Sidak Pal full_name: Singh, Sidak Pal id: DD138E24-D89D-11E9-9DC0-DEF6E5697425 last_name: Singh - first_name: Dan-Adrian full_name: Alistarh, Dan-Adrian id: 4A899BFC-F248-11E8-B48F-1D18A9856A87 last_name: Alistarh orcid: 0000-0003-3650-940X citation: ama: 'Singh SP, Alistarh D-A. WoodFisher: Efficient second-order approximation for neural network compression. In: Advances in Neural Information Processing Systems. Vol 33. Curran Associates; 2020:18098-18109.' apa: 'Singh, S. P., & Alistarh, D.-A. (2020). WoodFisher: Efficient second-order approximation for neural network compression. In Advances in Neural Information Processing Systems (Vol. 33, pp. 18098–18109). Vancouver, Canada: Curran Associates.' chicago: 'Singh, Sidak Pal, and Dan-Adrian Alistarh. “WoodFisher: Efficient Second-Order Approximation for Neural Network Compression.” In Advances in Neural Information Processing Systems, 33:18098–109. Curran Associates, 2020.' ieee: 'S. P. Singh and D.-A. Alistarh, “WoodFisher: Efficient second-order approximation for neural network compression,” in Advances in Neural Information Processing Systems, Vancouver, Canada, 2020, vol. 33, pp. 18098–18109.' ista: 'Singh SP, Alistarh D-A. 2020. WoodFisher: Efficient second-order approximation for neural network compression. Advances in Neural Information Processing Systems. NeurIPS: Conference on Neural Information Processing Systems vol. 33, 18098–18109.' mla: 'Singh, Sidak Pal, and Dan-Adrian Alistarh. “WoodFisher: Efficient Second-Order Approximation for Neural Network Compression.” Advances in Neural Information Processing Systems, vol. 33, Curran Associates, 2020, pp. 18098–109.' short: S.P. Singh, D.-A. Alistarh, in:, Advances in Neural Information Processing Systems, Curran Associates, 2020, pp. 18098–18109. conference: end_date: 2020-12-12 location: Vancouver, Canada name: 'NeurIPS: Conference on Neural Information Processing Systems' start_date: 2020-12-06 date_created: 2021-07-04T22:01:26Z date_published: 2020-12-06T00:00:00Z date_updated: 2023-02-23T14:03:06Z day: '06' department: - _id: DaAl - _id: ToHe ec_funded: 1 external_id: arxiv: - '2004.14340' intvolume: ' 33' language: - iso: eng main_file_link: - open_access: '1' url: https://proceedings.neurips.cc/paper/2020/hash/d1ff1ec86b62cd5f3903ff19c3a326b2-Abstract.html month: '12' oa: 1 oa_version: Published Version page: 18098-18109 project: - _id: 268A44D6-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '805223' name: Elastic Coordination for Scalable Machine Learning publication: Advances in Neural Information Processing Systems publication_identifier: isbn: - '9781713829546' issn: - '10495258' publication_status: published publisher: Curran Associates quality_controlled: '1' scopus_import: '1' status: public title: 'WoodFisher: Efficient second-order approximation for neural network compression' type: conference user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf volume: 33 year: '2020' ... --- _id: '9630' abstract: - lang: eng text: Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory needed for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context. acknowledgement: This research is partially supported by the Office of Naval Research, through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF). article_processing_charge: Yes article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Ziga full_name: Virk, Ziga id: 2E36B656-F248-11E8-B48F-1D18A9856A87 last_name: Virk - first_name: Hubert full_name: Wagner, Hubert id: 379CA8B8-F248-11E8-B48F-1D18A9856A87 last_name: Wagner citation: ama: Edelsbrunner H, Virk Z, Wagner H. Topological data analysis in information space. Journal of Computational Geometry. 2020;11(2):162-182. doi:10.20382/jocg.v11i2a7 apa: Edelsbrunner, H., Virk, Z., & Wagner, H. (2020). Topological data analysis in information space. Journal of Computational Geometry. Carleton University. https://doi.org/10.20382/jocg.v11i2a7 chicago: Edelsbrunner, Herbert, Ziga Virk, and Hubert Wagner. “Topological Data Analysis in Information Space.” Journal of Computational Geometry. Carleton University, 2020. https://doi.org/10.20382/jocg.v11i2a7. ieee: H. Edelsbrunner, Z. Virk, and H. Wagner, “Topological data analysis in information space,” Journal of Computational Geometry, vol. 11, no. 2. Carleton University, pp. 162–182, 2020. ista: Edelsbrunner H, Virk Z, Wagner H. 2020. Topological data analysis in information space. Journal of Computational Geometry. 11(2), 162–182. mla: Edelsbrunner, Herbert, et al. “Topological Data Analysis in Information Space.” Journal of Computational Geometry, vol. 11, no. 2, Carleton University, 2020, pp. 162–82, doi:10.20382/jocg.v11i2a7. short: H. Edelsbrunner, Z. Virk, H. Wagner, Journal of Computational Geometry 11 (2020) 162–182. date_created: 2021-07-04T22:01:26Z date_published: 2020-12-14T00:00:00Z date_updated: 2021-08-11T12:26:34Z day: '14' ddc: - '510' - '000' department: - _id: HeEd doi: 10.20382/jocg.v11i2a7 file: - access_level: open_access checksum: f02d0b2b3838e7891a6c417fc34ffdcd content_type: application/pdf creator: asandaue date_created: 2021-08-11T11:55:11Z date_updated: 2021-08-11T11:55:11Z file_id: '9882' file_name: 2020_JournalOfComputationalGeometry_Edelsbrunner.pdf file_size: 1449234 relation: main_file success: 1 file_date_updated: 2021-08-11T11:55:11Z has_accepted_license: '1' intvolume: ' 11' issue: '2' language: - iso: eng license: https://creativecommons.org/licenses/by/3.0/ month: '12' oa: 1 oa_version: Published Version page: 162-182 project: - _id: 0aa4bc98-070f-11eb-9043-e6fff9c6a316 grant_number: I4887 name: Discretization in Geometry and Dynamics publication: Journal of Computational Geometry publication_identifier: eissn: - 1920180X publication_status: published publisher: Carleton University quality_controlled: '1' scopus_import: '1' status: public title: Topological data analysis in information space tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode name: Creative Commons Attribution 3.0 Unported (CC BY 3.0) short: CC BY (3.0) type: journal_article user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf volume: 11 year: '2020' ... --- _id: '9631' abstract: - lang: eng text: The ability to leverage large-scale hardware parallelism has been one of the key enablers of the accelerated recent progress in machine learning. Consequently, there has been considerable effort invested into developing efficient parallel variants of classic machine learning algorithms. However, despite the wealth of knowledge on parallelization, some classic machine learning algorithms often prove hard to parallelize efficiently while maintaining convergence. In this paper, we focus on efficient parallel algorithms for the key machine learning task of inference on graphical models, in particular on the fundamental belief propagation algorithm. We address the challenge of efficiently parallelizing this classic paradigm by showing how to leverage scalable relaxed schedulers in this context. We present an extensive empirical study, showing that our approach outperforms previous parallel belief propagation implementations both in terms of scalability and in terms of wall-clock convergence time, on a range of practical applications. acknowledgement: "We thank Marco Mondelli for discussions related to LDPC decoding, and Giorgi Nadiradze for discussions on analysis of relaxed schedulers. This project has received funding from the European Research Council (ERC) under the European\r\nUnion’s Horizon 2020 research and innovation programme (grant agreement No 805223 ScaleML)." article_processing_charge: No author: - first_name: Vitaly full_name: Aksenov, Vitaly last_name: Aksenov - first_name: Dan-Adrian full_name: Alistarh, Dan-Adrian id: 4A899BFC-F248-11E8-B48F-1D18A9856A87 last_name: Alistarh orcid: 0000-0003-3650-940X - first_name: Janne full_name: Korhonen, Janne id: C5402D42-15BC-11E9-A202-CA2BE6697425 last_name: Korhonen citation: ama: 'Aksenov V, Alistarh D-A, Korhonen J. Scalable belief propagation via relaxed scheduling. In: Advances in Neural Information Processing Systems. Vol 33. Curran Associates; 2020:22361-22372.' apa: 'Aksenov, V., Alistarh, D.-A., & Korhonen, J. (2020). Scalable belief propagation via relaxed scheduling. In Advances in Neural Information Processing Systems (Vol. 33, pp. 22361–22372). Vancouver, Canada: Curran Associates.' chicago: Aksenov, Vitaly, Dan-Adrian Alistarh, and Janne Korhonen. “Scalable Belief Propagation via Relaxed Scheduling.” In Advances in Neural Information Processing Systems, 33:22361–72. Curran Associates, 2020. ieee: V. Aksenov, D.-A. Alistarh, and J. Korhonen, “Scalable belief propagation via relaxed scheduling,” in Advances in Neural Information Processing Systems, Vancouver, Canada, 2020, vol. 33, pp. 22361–22372. ista: 'Aksenov V, Alistarh D-A, Korhonen J. 2020. Scalable belief propagation via relaxed scheduling. Advances in Neural Information Processing Systems. NeurIPS: Conference on Neural Information Processing Systems vol. 33, 22361–22372.' mla: Aksenov, Vitaly, et al. “Scalable Belief Propagation via Relaxed Scheduling.” Advances in Neural Information Processing Systems, vol. 33, Curran Associates, 2020, pp. 22361–72. short: V. Aksenov, D.-A. Alistarh, J. Korhonen, in:, Advances in Neural Information Processing Systems, Curran Associates, 2020, pp. 22361–22372. conference: end_date: 2020-12-12 location: Vancouver, Canada name: 'NeurIPS: Conference on Neural Information Processing Systems' start_date: 2020-12-06 date_created: 2021-07-04T22:01:26Z date_published: 2020-12-06T00:00:00Z date_updated: 2023-02-23T14:03:03Z day: '06' department: - _id: DaAl ec_funded: 1 external_id: arxiv: - '2002.11505' intvolume: ' 33' language: - iso: eng main_file_link: - open_access: '1' url: https://proceedings.neurips.cc/paper/2020/hash/fdb2c3bab9d0701c4a050a4d8d782c7f-Abstract.html month: '12' oa: 1 oa_version: Published Version page: 22361-22372 project: - _id: 268A44D6-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '805223' name: Elastic Coordination for Scalable Machine Learning publication: Advances in Neural Information Processing Systems publication_identifier: isbn: - '9781713829546' issn: - '10495258' publication_status: published publisher: Curran Associates quality_controlled: '1' scopus_import: '1' status: public title: Scalable belief propagation via relaxed scheduling type: conference user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf volume: 33 year: '2020' ...