Mathematical Machine Learning

Head:
Guido Montúfar (Email)

Phone:
+49 (0) 341 - 9959 - 880

Fax:
+49 (0) 341 - 9959 - 658

Address:
Inselstr. 22
04103 Leipzig

Institute publications of the group

Mareike Dressler ; Marina Garrote-López ; Guido Montúfar ; Kemal Rose and Johannes Müller: Algebraic optimization of sequential decision problems
Repository Open Access

Yanan Wang ; Yu Guang Wang ; Changyuan Hu ; Ming Li ; Yanan Fan ; Nina Otter ; Ikuan Sam ; Hongquan Gou ; Yiqun Hu ; Terry Kwok ; John Zalcberg ; Alex Boussioutas ; Roger J. Daly ; Guido Montúfar ; Pietro Lió ; Dakang Xu ; Geoffrey I. Webb and Jiangning Song: Cell graph neural networks enable the digital staging of tumor microenvironment and precise prediction of patient survival in gastric cancer
Journal Open Access

Michael Murray ; Hui Jin ; Benjamin Bowman and Guido Montúfar: Characterizing the spectrum of the NTK via a power series expansion
Repository Open Access

Paul Görlach ; Yue Ren and Leon Zhang: Computing zero-dimensional tropical varieties via projections
In: Computational complexity, 31 (2022) 1, 5
Bibtex MIS-Preprint: 79/2019 DOI: 10.1007/s00037-022-00222-9 ARXIV: https://arxiv.org/abs/1908.03486 CODE: https://mathrepo.mis.mpg.de/tropicalProjections
Journal Open Access

Johannes Rauh ; Pradeep Kumar Banerjee ; Eckehard Olbrich ; Guido Montúfar and Jürgen Jost: Continuity and additivity properties of information decompositions
Repository Open Access

Alex Tong Lin ; Mark J. Debord ; Katia Estabridis ; Gary Hewer ; Guido Montúfar and Stanley Osher: Decentralized multi-agents by imitations of a centralized controller
In: 2nd annual conference on mathematical and scientific machine learning : 16-19 August 2021, virtual conference
[s. l.] : PMLR, 2022. - P. 619-651
(Proceedings of machine learning research ; 145)
Bibtex ARXIV: https://arxiv.org/abs/1902.02311 LINK: https://proceedings.mlr.press/v145/lin22a.html
Repository Open Access

Yuebin Zheng ; Bingxin Zhou ; Yu Guang Wang and Xiaosheng Zhuang: Decimated framelet system on graphs and fast \(G\)-framelet transforms
In: Journal of machine learning research, 23 (2022), 18
Bibtex ARXIV: https://arxiv.org/abs/2012.06922 LINK: http://jmlr.org/papers/v23/20-1402.html
Journal Open Access

Guido Montúfar and Yu Guang Wang: Distributed learning via filtered hyperinterpolation on manifolds
In: Foundations of computational mathematics, 22 (2022) 4, p. 1219-1271
Bibtex MIS-Preprint: 79/2020 DOI: 10.1007/s10208-021-09529-5 ARXIV: https://arxiv.org/abs/2007.09392
Journal Open Access

Laura Escobar ; Patricio Gallardo ; Javier González-Anaya ; José L. Gonzáles ; Guido Montúfar and Alejandro H. Morales: Enumeration of max-pooling responses with generalized permutohedra
Repository Open Access

Johannes Müller and Marius Zeinhofer: Error estimates for the Deep Ritz Method with boundary penalty
In: 3rd annual conference on mathematical and scientific machine learning : 15-17 August 2022, Peking University, Beijing, China
[s. l.] : PMLR, 2022. - P. 215-230
(Proceedings of machine learning research ; 190)
Bibtex ARXIV: https://arxiv.org/abs/2103.01007 LINK: https://proceedings.mlr.press/v190/muller22a.html
Repository Open Access

Guido Montúfar ; Pradeep Kumar Banerjee and Kedar Karhadkar: FoSR : first-order spectral rewiring for addressing oversquashing in GNNs
Repository Open Access

Johannes Müller and Guido Montúfar: Geometry and convergence of natural policy gradient methods
Repository Open Access

Kathlén Kohn ; Thomas Merkh ; Guido Montúfar and Matthew Trager: Geometry of linear convolutional networks
In: SIAM journal on applied algebra and geometry, 6 (2022) 3, p. 368-406
Bibtex DOI: 10.1137/21M1441183 ARXIV: https://arxiv.org/abs/2108.01538
Journal Open Access

Yang-Wen Sun ; Katerina Papagiannouli and Vladimir Spokoiny: High dimensional change-point detection: a complete graph approach
Repository Open Access

Benjamin Bowman and Guido Montúfar: Implicit bias of MSE gradient optimization in underparameterized neural networks
Repository Open Access

Jesse van Oostrum ; Johannes Müller and Nihat Ay: Invariance properties of the natural gradient in overparametrised systems
In: Information geometry, Vol. not yet known, pp. not yet known
Bibtex DOI: 10.1007/s41884-022-00067-9 ARXIV: https://arxiv.org/abs/2206.15273
Journal Open Access

Johannes Müller and Marius Zeinhofer: Notes on exact boundary values in residual minimisation
In: 3rd annual conference on mathematical and scientific machine learning : 15-17 August 2022, Peking University, Beijing, China
[s. l.] : PMLR, 2022. - P. 231-240
(Proceedings of machine learning research ; 190)
Bibtex ARXIV: https://arxiv.org/abs/2105.02550 LINK: https://proceedings.mlr.press/v190/muller22b.html
Repository Open Access

Renata Turkeš ; Guido Montúfar and Nina Otter: On the effectiveness of persistent homology
Repository Open Access

Pradeep Kumar Banerjee ; Kedar Karhadkar ; Yu Guang Wang ; Uri Alon and Guido Montúfar: Oversquashing in GNNs through the lens of information contraction and graph expansion
Repository Open Access

Jing An ; Christopher Henderson and Lenya Ryzhik: Quantitative steepness, semi-FKPP reactions, and pushmi-pullyu fronts
Repository Open Access

Johannes Müller and Guido Montúfar: Solving infinite-horizon POMDPs with memoryless stochastic policies in state-action space
Repository Open Access

Benjamin Bowman and Guido Montúfar: Spectral bias outside the training set for deep networks in the kernel regime
Repository Open Access

Guido Montúfar and Johannes Müller: The geometry of memoryless stochastic policy optimization in infinite-horizon POMDPs
In: ICLR 2022 : Tenth international conference on learning representations ; 25th April 2022
[s. l.] : ICLR, 2022
Bibtex MIS-Preprint: 22/2021 ARXIV: https://arxiv.org/abs/2110.07409 LINK: https://openreview.net/forum?id=A05I5IvrdL-
Repository Open Access

Patrick W. Dondl ; Johannes Müller and Marius Zeinhofer: Uniform convergence guarantees for the deep ritz method for nonlinear problems
In: Advances in continuous and discrete models : theory and modern applications, 2022 (2022), 49
Bibtex DOI: 10.1186/s13662-022-03722-8 ARXIV: https://arxiv.org/abs/2111.05637
Journal Open Access

Quynh Nguyen: A note on connectivity of sublevel sets in deep learning
Repository Open Access

Alex Tong Lin ; Guido Montúfar and Stanley Osher: A top-down approach to attain decentralized multi-agents
In: Handbook of reinforcement learning and control / Kyriakos G. Vamvoudakis... (eds.)
Cham : Springer, 2021. - P. 419-431
(Studies in systems, decision and control ; 325)
Bibtex DOI: 10.1007/978-3-030-60990-0_14

Kathlén Kohn ; Ragni Piene ; Kristian Ranestad ; Felix Rydell ; Boris Shapiro ; Rainer Sinn ; Miruna-Stefana Sorea and Simon Telen: Adjoints and canonical forms of polypols
Repository Open Access

Jing An and Lexing Ying: Combining resampling and reweighting for faithful stochastic optimization
Repository Open Access

Paul Görlach ; Yue Ren and Jeff Sommars: Detecting tropical defects of polynomial equations
In: Journal of algebraic combinatorics, 53 (2021) 1, p. 31-47
Bibtex DOI: 10.1007/s10801-019-00916-4 ARXIV: https://arxiv.org/abs/1809.03350 CODE: https://mathrepo.mis.mpg.de/tropicalBases
Journal Open Access

Shao-bo Lin ; Yu Guang Wang and Ding-Xuan Zhou: Distributed filtered hyperinterpolation for noisy data on the sphere
In: SIAM journal on numerical analysis, 59 (2021) 2, p. 634-659
Bibtex DOI: 10.1137/19M1281095 ARXIV: https://arxiv.org/abs/1910.02434 LINK: https://www.researchgate.net/publication/349953493
Repository Open Access

Vo V. Anh ; Andriy Olenko and Yu Guang Wang: Fractional stochastic partial differential equation for random tangent fields on the sphere
In: Theory of probability and mathematical statistics, 104 (2021), p. 3-22
Bibtex DOI: 10.1090/tpms/1142 ARXIV: https://arxiv.org/abs/2107.03717
Repository Open Access

Xuebin Zheng ; Bingxin Zhou ; Junbin Gao ; Yu Guang Wang ; Pietro Lió ; Ming Li and Guido Montúfar: How framelets enhance graph neural networks
In: ICML 2021 : Proceedings of the 38th international conference on machine learning ; 18-24 July 2021
[s. l.] : PMLR, 2021. - P. 12761-12771
(Proceedings of machine learning research ; 139)
Bibtex ARXIV: https://arxiv.org/abs/2102.06986 LINK: https://proceedings.mlr.press/v139/zheng21c.html
Journal Open Access

Pradeep Kumar Banerjee and Guido Montúfar: Information complexity and generalization bounds
In: IEEE international symposium on information theory (ISIT) from 12 - 20 July 2021 ; Melbourne, Victoria, Australia
Piscataway, NY : IEEE, 2021. - P. 676-681
Bibtex DOI: 10.1109/ISIT45174.2021.9517960 ARXIV: https://arxiv.org/abs/2105.01747
Repository Open Access

Kathlén Kohn and James Mathews: Isotropic and coisotropic subvarieties of Grassmannians
In: Advances in mathematics, 377 (2021), 107492
Bibtex DOI: 10.1016/j.aim.2020.107492 ARXIV: https://arxiv.org/abs/1901.06584
Repository Open Access

Hui Jin ; Pradeep Kumar Banerjee and Guido Montúfar: Learning curves for Gaussian process regression with power-law priors and targets
Repository Open Access

Yuhan Jiang ; Kathlén Kohn and Rosa Winter: Linear spaces of symmetric matrices with non-maximal maximum likelihood degree
In: Le Matematiche, 76 (2021) 2, p. 461-481
Bibtex DOI: 10.4418/2021.76.2.11 ARXIV: https://arxiv.org/abs/2012.00145
Journal Open Access

Xuebin Zheng ; Bingxin Zhou ; Ming Li ; Yu Guang Wang and Junbin Gao: MathNet : Haar-like wavelet multiresolution-analysis for graph representation and learning
Repository Open Access

Stefan Dye ; Kathlén Kohn ; Felix Rydell and Rainer Sinn: Maximum likelihood estimation for nets of conics
In: Le Matematiche, 76 (2021) 2, p. 399-414
Bibtex DOI: 10.4418/2021.76.2.7 ARXIV: https://arxiv.org/abs/2011.08989
Journal Open Access

Hanna Tseran and Guido Montúfar: On the expected complexity of maxout networks
In: Advances in neural information processing systems 34 : NeurIPS 2021 ; annual conference on neural information processing systems 2021, December 6-14, 2021, virtual / Marc'Aurelio Ranzato (ed.)
2021. - P. 28995-29008
Bibtex MIS-Preprint: 18/2021 ARXIV: https://arxiv.org/abs/2107.00379 LINK: https://proceedings.neurips.cc/paper/2021/hash/f2c3b258e9cd8ba16e18f319b3c88c66-Abstract.html
Repository Open Access

Quynh Nguyen: On the proof of global convergence of gradient descent for deep ReLU networks with linear widths
In: ICML 2021 : Proceedings of the 38th international conference on machine learning ; 18-24 July 2021
[s. l.] : PMLR, 2021. - P. 8056-8062
(Proceedings of machine learning research ; 139)
Bibtex ARXIV: https://arxiv.org/abs/2101.09612 LINK: http://proceedings.mlr.press/v139/nguyen21a.html
Journal Open Access

Pradeep Kumar Banerjee and Guido Montúfar: PAC-bayes and information complexity
In: ICLR 2021 workshop on neural compression : from information theory to applications
[s. l.] : ICLR, 2021. - P. 1-15
Bibtex MIS-Preprint: 21/2021 LINK: https://openreview.net/forum?id=LPw-isa6Ngb
Repository Open Access

Zheng Ma ; Junyu Xuan ; Yu Guang Wang ; Ming Li and Pietro Lió: Path integral based convolution and pooling for graph neural networks
In: Journal of statistical mechanics, 2021 (2021) 12, 124011
Bibtex DOI: 10.1088/1742-5468/ac3ae4 ARXIV: https://arxiv.org/abs/2006.16811
Repository Open Access

Jing An ; Christopher Henderson and Lenya Ryzhik: Pushed, pulled and pushmi-pullyu fronts of the Burgers-FKPP equation
Repository Open Access

Guido Montúfar ; Yue Ren and Leon Zhang: Sharp bounds for the number of regions of maxout networks and vertices of Minkowski sums
Repository Open Access

Carlos Améndola ; Lukas Gustafsson ; Kathlén Kohn ; Orlando Marigliano and Anna Seigal: The maximum likelihood degree of linear spaces of symmetric matrices
In: Le Matematiche, 76 (2021) 2, p. 535-557
Bibtex DOI: 10.4418/2021.76.2.15 ARXIV: https://arxiv.org/abs/2012.00198
Journal Open Access

Quynh Nguyen ; Marco Mondelli and Guido Montúfar: Tight bounds on the smallest eigenvalue of the neural tangent kernel for deep ReLU networks
In: ICML 2021 : Proceedings of the 38th international conference on machine learning ; 18-24 July 2021
[s. l.] : PMLR, 2021. - P. 8119-8129
(Proceedings of machine learning research ; 139)
Bibtex ARXIV: https://arxiv.org/abs/2012.11654 LINK: https://proceedings.mlr.press/v139/nguyen21g.html
Journal Open Access

Dohyun Kwon ; Yeoneung Kim ; Guido Montúfar and Insoon Yang: Training Wasserstein GANs without gradient penalties
Repository Open Access

Marvin Anas Hahn ; Hannah Markwig ; Yue Ren and Ilya Tyomkin: Tropicalized quartics and canonical embeddings for tropical curves of genus 3
In: International mathematics research notices, 2021 (2021) 12, p. 8946-8976
Bibtex MIS-Preprint: 20/2018 DOI: 10.1093/imrn/rnz084 ARXIV: https://arxiv.org/abs/1802.02440 CODE: https://mathrepo.mis.mpg.de/tropicalModifications
Repository Open Access

Türkü Ozlüm Celik ; Asgar Jamneshan ; Guido Montúfar ; Bernd Sturmfels and Lorenzo Venturello: Wasserstein distance to independence models
In: Journal of symbolic computation, 104 (2021), p. 855-873
Bibtex DOI: 10.1016/j.jsc.2020.10.005 ARXIV: https://arxiv.org/abs/2003.06725
Repository Open Access

Alex Tong Lin ; Wuchen Li ; Stanley Osher and Guido Montúfar: Wasserstein proximal of GANs
In: Geometric science of information : 5th international conference, GSI 2021, Paris, France, July 21-23, 2021, proceedings / Frank Nielsen... (eds.)
Cham : Springer, 2021. - P. 524-533
(Lecture notes in computer science ; 12829)
Bibtex MIS-Preprint: 88/2018 DOI: 10.1007/978-3-030-80209-7_57 ARXIV: https://arxiv.org/abs/2102.06862 LINK: https://www.researchgate.net/publication/331976172
Repository Open Access

Christian Bodnar ; Fabrizio Frasca ; Nina Otter ; Yu Guang Wang ; Pietro Lió ; Guido Montúfar and Michael Bronstein: Weisfeiler and Lehman go cellular : CW networks
In: Advances in neural information processing systems 34 : NeurIPS 2021 ; annual conference on neural information processing systems 2021, December 6-14, 2021, virtual / Marc'Aurelio Ranzato (ed.)
2021. - P. 2625-2640
Bibtex ARXIV: https://arxiv.org/abs/2106.12575 LINK: https://proceedings.neurips.cc/paper/2021/hash/157792e4abb490f99dbd738483e0d2d4-Abstract.html
Repository Open Access

Christian Bodnar ; Fabrizio Frasca ; Yu Guang Wang ; Nina Otter ; Guido Montúfar ; Pietro Lió and Michael Bronstein: Weisfeiler and Lehman go topological : message passing simplicial networks
In: ICML 2021 : Proceedings of the 38th international conference on machine learning ; 18-24 July 2021
[s. l.] : PMLR, 2021. - P. 1026-1037
(Proceedings of machine learning research ; 139)
Bibtex ARXIV: https://arxiv.org/abs/2103.03212 LINK: https://proceedings.mlr.press/v139/bodnar21a.html
Journal Open Access

Quynh Nguyen ; Pierre Brechet and Marco Mondelli: When are solutions connected in deep networks?
In: Advances in neural information processing systems 34 : NeurIPS 2021 ; annual conference on neural information processing systems 2021, December 6-14, 2021, virtual / Marc'Aurelio Ranzato (ed.)
2021. - P. 20956-20969
Bibtex ARXIV: https://arxiv.org/abs/2102.09671 LINK: https://proceedings.neurips.cc/paper/2021/hash/af5baf594e9197b43c9f26f17b205e5b-Abstract.html
Repository Open Access

Michael Arbel ; Arthur Gretton ; Wuchen Li and Guido Montúfar: A Pytorch implementation of the KWNG estimator [Computer code]
Repository Open Access

Guido Montúfar ; Nina Otter and Yu Guang Wang: Can neural networks learn persistent homology features?
In: NeurIPS 2020 : Workshop on topological data analysis and beyond ; 11 December 2020
2020
Bibtex ARXIV: https://arxiv.org/abs/2011.14688 LINK: https://openreview.net/forum?id=pqpXM1Wjsxe
Repository Open Access

Pradeep Kumar Banerjee ; Johannes Rauh and Guido Montúfar: computeUI [Computer code]
Repository Open Access

Thomas Markwig and Yue Ren: Computing tropical varieties over fields with valuation
In: Foundations of computational mathematics, 20 (2020) 4, p. 783-800
Bibtex DOI: 10.1007/s10208-019-09430-2 ARXIV: https://arxiv.org/abs/1612.01762
Journal Open Access

Nidhi Kaihnsa ; Yue Ren ; Mohab Safey El Din and Johannes W. R. Martini: Cooperativity, absolute interaction, and algebraic optimization
In: Journal of mathematical biology, 81 (2020) 4/5, p. 1169-1191
Bibtex MIS-Preprint: 57/2019 DOI: 10.1007/s00285-020-01540-8 ARXIV: https://arxiv.org/abs/1906.10006
Journal Open Access

Johannes Müller and Marius Zeinhofer: Deep Ritz revisited
In: ICLR 2020 workshop on integration of deep neural models and differential equations : Millennium Hall, Addis Ababa, Ethiopia ; 26th April 2020
2020
Bibtex ARXIV: https://arxiv.org/abs/1912.03937 LINK: https://openreview.net/group?id=ICLR.cc/2020/Workshop/DeepDiffEq
Repository Open Access

Thomas Merkh and Guido Montúfar: Factorized mutual information maximization
Journal Open Access

Quynh Nguyen and Marco Mondelli: Global convergence of deep networks with one wide layer followed by pyramidal topology
In: Advances in neural information processing systems 33 : NeurIPS 2020 ; annual conference on neural information processing systems 2020, December 6-12, 2020, virtual / Hugo Larochelle (ed.)
2020. - P. 11961-11972
Bibtex ARXIV: https://arxiv.org/abs/2002.07867 LINK: https://proceedings.neurips.cc/paper/2020/hash/8abfe8ac9ec214d68541fcb888c0b4c3-Abstract.html
Repository Open Access

Yu Guang Wang ; Ming Li ; Zheng Ma ; Guido Montúfar ; Xiaosheng Zhuang and Yanan Fan: Haar graph pooling
In: ICML 2020 : Proceedings of the 37th international conference on machine learning ; 13-18 July 2020
[s. l.] : PMLR, 2020. - P. 9952-9962
(Proceedings of machine learning research ; 119)
Bibtex MIS-Preprint: 72/2020 ARXIV: https://arxiv.org/abs/1909.11580 LINK: http://proceedings.mlr.press/v119/wang20m.html CODE: https://github.com/YuGuangWang/HaarPool
Journal Open Access

Hui Jin and Guido Montúfar: Implicit bias of gradient descent for mean squared error regression with wide neural networks
Repository Open Access

Michael Arbel ; Arthur Gretton ; Wuchen Li and Guido Montúfar: Kernelized Wasserstein natural gradient
In: ICLR 2020 : Eighth international conference on learning representations ; Millennium Hall, Addis Ababa, Ethiopia ; 26th-30th April 2020
[s. l.] : ICLR, 2020. - P. 1-31
Bibtex ARXIV: https://arxiv.org/abs/1910.09652 LINK: https://openreview.net/pdf?id=Hklz71rYvS CODE: https://github.com/MichaelArbel/KWNG
Repository Open Access

Kathlén Kohn ; Boris Shapiro and Bernd Sturmfels: Moment varieties of measures on polytopes
In: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 21 (2020), p. 739-770
Bibtex MIS-Preprint: 50/2018 DOI: 10.2422/2036-2145.201808_003 ARXIV: https://arxiv.org/abs/1807.10258
Repository Open Access

Sho Sonoda ; Ming Li ; Feilong Cao ; Changqin Huang and Yu Guang Wang: On the approximation lower bound for neural nets with random weights
Repository Open Access

Johannes Müller: On the space-time expressivity of ResNets
In: ICLR 2020 workshop on integration of deep neural models and differential equations : Millennium Hall, Addis Ababa, Ethiopia ; 26th April 2020
2020
Bibtex ARXIV: https://arxiv.org/abs/1910.09599 LINK: https://openreview.net/group?id=ICLR.cc/2020/Workshop/DeepDiffEq
Repository Open Access

Türkü Ozlüm Celik ; Asgar Jamneshan ; Guido Montúfar ; Bernd Sturmfels and Lorenzo Venturello: Optimal transport to a variety
In: Mathematical aspects of computer and information sciences : 8th international conference, MACIS 2019, Gebze-Istanbul, Turkey, November 13-15, 2019 ; revised selected papers / Daniel Slamanig... (eds.)
Cham : Springer, 2020. - P. 364-381
(Lecture notes in computer science ; 11989)
Bibtex MIS-Preprint: 7/2021 DOI: 10.1007/978-3-030-43120-4_29 ARXIV: https://arxiv.org/abs/1909.11716
Repository Open Access

Yonatan Dukler ; Quanquan Gu and Guido Montúfar: Optimization theory for ReLU neural networks trained with normalization layers
In: ICML 2020 : Proceedings of the 37th international conference on machine learning ; 13-18 July 2020
[s. l.] : PMLR, 2020. - P. 2751-2760
(Proceedings of machine learning research ; 119)
Bibtex MIS-Preprint: 64/2020 ARXIV: https://arxiv.org/abs/2006.06878 LINK: http://proceedings.mlr.press/v119/dukler20a.html
Journal Open Access

Zheng Ma ; Junyu Xuan ; Yu Guang Wang ; Ming Li and Pietro Lió: Path integral based convolution and pooling for graph neural networks
In: Advances in neural information processing systems 33 : NeurIPS 2020 ; annual conference on neural information processing systems 2020, December 6-12, 2020, virtual / Hugo Larochelle (ed.)
2020. - P. 16421-16433
Bibtex ARXIV: https://arxiv.org/abs/2006.16811 LINK: https://proceedings.neurips.cc/paper/2020/hash/be53d253d6bc3258a8160556dda3e9b2-Abstract.html
Repository Open Access

Timothy Duff ; Kathlén Kohn ; Anton Leykin and Tomas Pajdla: PL\(_{1}\)P - point-line minimal problems under partial visibility in three views
In: Computer vision - ECCV 2020 ; 16th european conference, Glasgow, UK, August 23-28, 2020 ; proceedings, Part XXVI / Andrea Vedaldi... (eds.)
Cham : Springer, 2020. - P. 175-192
(Lecture notes in computer science ; 12371)
Bibtex DOI: 10.1007/978-3-030-58574-7_11 ARXIV: https://arxiv.org/abs/2003.05015
Repository Open Access

Vo V. Anh ; Hung T. Nguyen ; Ashley Craig ; Yvonne Tran and Yu Guang Wang: Power-law scaling of brain wave activity associated with mental fatigue
Repository Open Access

Wuchen Li and Guido Montúfar: Ricci curvature for parametric statistics via optimal transport
In: Information geometry, 3 (2020) 1, p. 89-117
Bibtex DOI: 10.1007/s41884-020-00026-2 ARXIV: https://arxiv.org/abs/1807.07095
Repository Open Access

Pradeep Kumar Banerjee and Guido Montúfar: The variational deficiency bottleneck
In: Proceedings of the international joint conference on neural networks 2020 (IJCNN)
Piscataway, NJ : IEEE Operations Center, 2020. - P. 1-8
Bibtex DOI: 10.1109/IJCNN48605.2020.9206900 ARXIV: https://arxiv.org/abs/1810.11677 LINK: https://www.researchgate.net/publication/328213639
Repository Open Access

Yonatan Dukler ; Wuchen Li ; Alex Tong Lin and Guido Montúfar: Wasserstein of Wasserstein loss for generative models - WWGAN [Computer code]
Repository Open Access

Nihat Ay ; Johannes Rauh and Guido Montúfar: A continuity result for optimal memoryless planning in POMDPs
In: RLDM 2019 : 4th multidisciplinary conference on reinforcement learning and decision making ; July 7-10, 2019 ; Montréal, Canada
Montréal, Canada : University, 2019. - P. 362-365
Bibtex MIS-Preprint: 5/2021 LINK: http://rldm.org/papers/extendedabstracts.pdf#page=362
Repository Open Access

Wuchen Li ; Alex Tong Lin and Guido Montúfar: Affine natural proximal learning
In: Geometric science of information : 4th international conference, GSI 2019, Toulouse, France, August 27-29, 2019, proceedings / Frank Nielsen... (eds.)
Cham : Springer, 2019. - P. 705-714
(Lecture notes in computer science ; 11712)
Bibtex MIS-Preprint: 6/2021 DOI: 10.1007/978-3-030-26980-7_73 LINK: https://www.researchgate.net/publication/331162910
Repository Open Access

Yue Ren: Computing zero-dimensional tropical varieties [In: Tropical geometry : new directions ; 22 September - 28 September 2019 ; report no. 21/2019]
In: Oberwolfach reports, 16 (2019) 2, p. 1276-1277
Bibtex DOI: 10.4171/OWR/2019/21 LINK: https://publications.mfo.de/handle/mfo/3754
Repository Open Access

Yue Ren ; Johannes W. R. Martini and Jacinta Torres: Decoupled molecules with binding polynomials of bidegree \((n,2)\)
In: Journal of mathematical biology, 78 (2019) 4, p. 879-898
Bibtex MIS-Preprint: 75/2017 DOI: 10.1007/s00285-018-1295-x ARXIV: https://arxiv.org/abs/1711.06865 CODE: https://mathrepo.mis.mpg.de/ligands
Journal Open Access

Anton Mallasto ; Guido Montúfar and Augusto Gerolin: How well do WGANs estimate the Wasserstein metric?
Repository Open Access

Thomas Merkh and Guido Montúfar: Stochastic feedforward neural networks : universal approximation
Repository Open Access

Guido Montúfar ; Johannes Rauh and Nihat Ay: Task-agnostic constraining in average reward POMDPs
In: Task-agnostic reinforcement learning : workshop at ICLR, 06 May 2019, New Orleans
2019
Bibtex MIS-Preprint: 9/2021 LINK: https://tarl2019.github.io/assets/papers/montufar2019taskagnostic.pdf
Repository Open Access

Anders Jensen ; Yue Ren and Hans Schönemann: The gfanlib interface in Singular and its applications
In: Journal of software for algebra and geometry, 9 (2019) 1, p. 81-87
Bibtex DOI: 10.2140/jsag.2019.9.81
Journal Open Access

Türkü Ozlüm Celik ; Avinash Kulkarni ; Yue Ren and Mahsa Sayyary Namin: Tritangents and their space sextics
In: Journal of algebra, 538 (2019), p. 290-311
Bibtex MIS-Preprint: 39/2018 DOI: 10.1016/j.jalgebra.2019.07.037 ARXIV: https://arxiv.org/abs/1805.11702
Repository Open Access

Alex Tong Lin ; Yonatan Dukler ; Wuchen Li and Guido Montúfar: Wasserstein diffusion Tikhonov regularization
In: NeurIPS 2019 : Workshop on optimal transport and machine learning ; Vancouver, December 13 2019
2019
Bibtex ARXIV: https://arxiv.org/abs/1909.06860 LINK: https://sites.google.com/view/otml2019/home
Repository Open Access

Yonatan Dukler ; Wuchen Li ; Alex Tong Lin and Guido Montúfar: Wasserstein of Wasserstein loss for learning generative models
In: Proceedings of the 36th international conference on machine learning, 9-15 June 2019, Long Beach, California, USA / Kamalika Chaudhuri (ed.)
Long Beach, California : PMLR, 2019. - P. 1716-1725
(Proceedings of machine learning research ; 97)
Bibtex MIS-Preprint: 13/2019 LINK: http://proceedings.mlr.press/v97/dukler19a.html CODE: https://github.com/dukleryoni/WWGAN
Journal Open Access

Kathlén Kohn ; Bernd Sturmfels and Matthew Trager: Changing views on curves and surfaces
In: Acta mathematica Vietnamica, 43 (2018) 1, p. 1-29
Bibtex MIS-Preprint: 39/2017 DOI: 10.1007/s40306-017-0240-1 ARXIV: https://arxiv.org/abs/1707.01877
Repository Open Access

Pradeep Kumar Banerjee ; Johannes Rauh and Guido Montúfar: Computing the unique information
In: IEEE international symposium on information theory (ISIT) from June 17 to 22, 2018 at the Talisa Hotel in Vail, Colorado, USA
Piscataway, NY : IEEE, 2018. - P. 141-145
Bibtex MIS-Preprint: 73/2017 DOI: 10.1109/ISIT.2018.8437757 ARXIV: https://arxiv.org/abs/1709.07487 CODE: https://github.com/infodeco/computeUI
Repository Open Access

Tommy Hofmann and Yue Ren: Computing tropical points and tropical links
In: Discrete and computational geometry, 60 (2018) 3, p. 627-645
Bibtex DOI: 10.1007/s00454-018-0023-z ARXIV: https://arxiv.org/abs/1611.02878
Journal Open Access

Guido Montúfar: Illustration of maxout layer upper bound [Suppl. to: On the number of linear regions of deep neural networks]
Repository Open Access

Anna Seigal and Guido Montúfar: Mixtures and products in two graphical models
In: Journal of algebraic statistics, 9 (2018) 1, p. 1-20
Bibtex DOI: 10.18409/jas.v9i1.90 ARXIV: https://arxiv.org/abs/1709.05276
Journal Open Access

Wuchen Li and Guido Montúfar: Natural gradient via optimal transport
In: Information geometry, 1 (2018) 2, p. 181-214
Bibtex DOI: 10.1007/s41884-018-0015-3 ARXIV: https://arxiv.org/abs/1803.07033
Repository Open Access

Avinash Kulkarni ; Yue Ren ; Mahsa Sayyary Namin and Bernd Sturmfels: Real space sextics and their tritangents
In: ISSAC '18 proceedings of the 43rd international symposium on symbolic and algebraic computation ; New York, USA, July 16-19, 2018
New York : ACM, 2018. - P. 247-254
Bibtex MIS-Preprint: 81/2017 DOI: 10.1145/3208976.3208977 ARXIV: https://arxiv.org/abs/1712.06274 CODE: https://mathrepo.mis.mpg.de/spaceSexticCurves
Repository Open Access

Guido Montúfar: Restricted Boltzmann machines : introduction and review
In: Information geometry and its applications : on the occasion of Shun-ichi Amari's 80th Birthday, IGAIA IV Liblice, Czech Republic, June 2016 / Nihat Ay... (eds.)
Cham : Springer, 2018. - P. 75-115
(Springer proceedings in mathematics and statistics ; 252)
Bibtex MIS-Preprint: 87/2018 DOI: 10.1007/978-3-319-97798-0_4 ARXIV: https://arxiv.org/abs/1806.07066
Repository Open Access

Guido Montúfar ; Johannes Rauh and Nihat Ay: Uncertainty and stochasticity of optimal policies
In: Proceedings of the 11th workshop on uncertainty processing WUPES '18, June 6-9, 2018 / Václav Kratochvíl (ed.)
Praha : MatfyzPress, 2018. - P. 133-140
Bibtex MIS-Preprint: 8/2021 LINK: http://wupes.utia.cas.cz/proceedings/proceedings.pdf
Repository Open Access
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