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Mathematical Machine Learning - Publications by Date

inJournal
2024 Journal Open Access
Johannes Müller and Guido Montúfar

Geometry and convergence of natural policy gradient methods

In: Information geometry, 7 (2024) 1, pp. 485-523
inJournal
2023 Repository Open Access
Jing An and Lexing Ying

Combining resampling and reweighting for faithful stochastic optimization

In: Communications in mathematical sciences, 21 (2023) 6, pp. 1569-1588
inJournal
2023 Repository Open Access
Jing An, Christopher Henderson and Lenya Ryzhik

Quantitative steepness, semi-FKPP reactions, and pushmi-pullyu fronts

In: Archive for rational mechanics and analysis, 247 (2023) 5, p. 88
Preprint
2023 Repository Open Access
Marie-Charlotte Brandenburg and Chiara Meroni

Intersection bodies of polytopes : translations and convexity

inJournal
2023 Repository Open Access
Marie-Charlotte Brandenburg, Sophia Elia and Leon Zhang

Multivariate volume, Ehrhart, and \(h*\)-polynomials of polytropes

In: Journal of symbolic computation, 114 (2023), pp. 209-230
Preprint
2023 Repository Open Access
Marie-Charlotte Brandenburg, Jesús A. De Loera and Chiara Meroni

The best ways to slice a polytope

Academic
2023 Repository Open Access
Marie-Charlotte Brandenburg

Tropical positivity and semialgebraic sets from polytopes

Dissertation, Universität Leipzig, 2023
inJournal
2023 Repository Open Access
Mareike Dressler, Marina Garrote-López, Guido Montúfar, Kemal Rose and Johannes Müller

Algebraic optimization of sequential decision problems

In: Journal of symbolic computation, (2023)
inJournal
2023 Journal Open Access
Hui Jin and Guido Montúfar

Implicit bias of gradient descent for mean squared error regression with wide neural networks

In: Journal of machine learning research, 24 (2023), p. 137
Preprint
2023 Repository Open Access
Kedar Karhadkar, Michael Murray, Hanna Tseran and Guido Montúfar

Mildly overparameterized ReLU networks have a favorable loss landscape

Preprint
2023 Repository Open Access
Kathlén Kohn, Guido Montúfar, Vahid Shahverdi and Matthew Trager

Function space and critical points of linear convolutional networks

inBook
2023 Repository Open Access
Thomas Merkh and Guido Montúfar

Stochastic feedforward neural networks : universal approximation

In: Mathematical aspects of deep learning / Philipp Grohs... (eds.)
Cambridge : Cambridge University Press, 2023. - pp. 267-313
Preprint
2023 Repository Open Access
Johannes Müller and Marius Zeinhofer

Achieving high accuracy with PINNs via energy natural gradients

inJournal
2023 Repository Open Access
Johannes Rauh, Pradeep Kumar Banerjee, Eckehard Olbrich, Guido Montúfar and Jürgen Jost

Continuity and additivity properties of information decompositions

In: International journal of approximate reasoning, 161 (2023), p. 108979
Academic
2023 Repository Open Access
Hanna Tseran

Expected complexity and gradients of deep maxout neural networks and implications to parameter initialization

Dissertation, Universität Leipzig, 2023
Preprint
2023 Repository Open Access
Hanna Tseran and Guido Montúfar

Expected gradients of maxout networks and consequences to parameter initialization

inJournal
2023 Repository Open Access
Xuebin Zheng, Bingxin Zhou, Ming Li, Yu Guang Wang and Junbin Gao

MathNet : Haar-like wavelet multiresolution analysis for graph representation learning

In: Knowledge-based systems, 273 (2023), p. 110609
inBook
2022 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

In: 2022 58th Annual Allerton Conference on communication, control, and computing : 27-30 Sept. 2022
Piscataway, N.J. : IEEE, 2022. - p. 9929363
Preprint
2022 Repository Open Access
Benjamin Bowman and Guido Montúfar

Implicit bias of MSE gradient optimization in underparameterized neural networks

Preprint
2022 Repository Open Access
Benjamin Bowman and Guido Montúfar

Spectral bias outside the training set for deep networks in the kernel regime

inJournal
2022 Journal 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), p. 49
Preprint
2022 Repository 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

Preprint
2022 Repository Open Access
Kedar Karhadkar, Pradeep Kumar Banerjee and Guido Montúfar

FoSR : first-order spectral rewiring for addressing oversquashing in GNNs

inJournal
2022 Journal 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, pp. 368-406
inBook
2022 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. - pp. 619-651
(Proceedings of machine learning research ; 145)
inJournal
2022 Journal Open Access
Guido Montúfar and Yu Guang Wang

Distributed learning via filtered hyperinterpolation on manifolds

In: Foundations of computational mathematics, 22 (2022) 4, pp. 1219-1271
inJournal
2022 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

In: SIAM journal on applied algebra and geometry, 6 (2022) 4, pp. 618-649
inBook
2022 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. - pp. 215-230
(Proceedings of machine learning research ; 190)
inBook
2022 Repository 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. - pp. 231-240
(Proceedings of machine learning research ; 190)
Preprint
2022 Repository Open Access
Johannes Müller and Guido Montúfar

Solving infinite-horizon POMDPs with memoryless stochastic policies in state-action space

inBook
2022 Repository Open Access
Johannes Müller and Guido Montúfar

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. - pp. 1-45
Preprint
2022 Repository Open Access
Michael Murray, Hui Jin, Benjamin Bowman and Guido Montúfar

Characterizing the spectrum of the NTK via a power series expansion

Preprint
2022 Repository Open Access
Yang-Wen Sun, Katerina Papagiannouli and Vladimir Spokoiny

High dimensional change-point detection: a complete graph approach

inBook
2022 Repository Open Access
Renata Turkeš, Guido Montúfar and Nina Otter

On the effectiveness of persistent homology

In: Advances in neural information processing systems 35 : NeurIPS 2022 ; annual conference on neural information processing systems 2022
[S. L.] : NeurIPS, 2022. - pp. 35432-35448
inJournal
2022 Journal Open Access
Jesse van Oostrum, Johannes Müller and Nihat Ay

Invariance properties of the natural gradient in overparametrised systems

In: Information geometry, (2022)
inJournal
2022 Journal 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

In: npj precision oncology, 6 (2022) 1, p. 45
inJournal
2022 Journal 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), p. 18
inJournal
2021 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), pp. 3-22
Preprint
2021 Repository Open Access
Jing An, Christopher Henderson and Lenya Ryzhik

Pushed, pulled and pushmi-pullyu fronts of the Burgers-FKPP equation

inBook
2021 Repository 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. - pp. 676-681
inBook
2021 Repository 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. - pp. 1-15
inBook
2021 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.)
[S. L.] : NeurIPS, 2021. - pp. 2625-2640
inBook
2021 Journal 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. - pp. 1026-1037
(Proceedings of machine learning research ; 139)
inJournal
2021 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), pp. 855-873
Preprint
2021 Repository Open Access
Hui Jin, Pradeep Kumar Banerjee and Guido Montúfar

Learning curves for Gaussian process regression with power-law priors and targets

Preprint
2021 Repository Open Access
Dohyun Kwon, Yeoneung Kim, Guido Montúfar and Insoon Yang

Training Wasserstein GANs without gradient penalties

inBook
2021
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. - pp. 419-431
(Studies in systems, decision and control ; 325)
inBook
2021 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. - pp. 524-533
(Lecture notes in computer science ; 12829)
inJournal
2021 Repository 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, pp. 634-659
inJournal
2021 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, p. 124011
Preprint
2021 Repository Open Access
Quynh Nguyen

A note on connectivity of sublevel sets in deep learning

inBook
2021 Journal 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. - pp. 8056-8062
(Proceedings of machine learning research ; 139)
inBook
2021 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. - pp. 8119-8129
(Proceedings of machine learning research ; 139)
inBook
2021 Repository 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.)
[S. L.] : NeurIPS, 2021. - pp. 20956-20969
inBook
2021 Repository 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.)
[S. L.] : NeurIPS, 2021. - pp. 28995-29008
inBook
2021 Journal 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. - pp. 12761-12771
(Proceedings of machine learning research ; 139)
Preprint
2020 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

Preprint
2020 Repository Open Access
Michael Arbel, Arthur Gretton, Wuchen Li and Guido Montúfar

A Pytorch implementation of the KWNG estimator [Computer code]

inBook
2020 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. - pp. 1-31
Preprint
2020 Repository Open Access
Pradeep Kumar Banerjee, Johannes Rauh and Guido Montúfar

computeUI [Computer code]

inBook
2020 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. - pp. 1-8
Academic
2020
Pradeep Kumar Banerjee

Unique information and the Blackwell order

Dissertation, Universität Leipzig, 2020
inBook
2020 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. - pp. 364-381
(Lecture notes in computer science ; 11989)
inBook
2020 Journal 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. - pp. 2751-2760
(Proceedings of machine learning research ; 119)
Preprint
2020 Repository Open Access
Yonatan Dukler, Wuchen Li, Alex Tong Lin and Guido Montúfar

Wasserstein of Wasserstein loss for generative models - WWGAN [Computer code]

inJournal
2020 Repository Open Access
Wuchen Li and Guido Montúfar

Ricci curvature for parametric statistics via optimal transport

In: Information geometry, 3 (2020) 1, pp. 89-117
inBook
2020 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: 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.)
[S. L.] : NeurIPS, 2020. - pp. 16421-16433
inJournal
2020 Journal Open Access
Thomas Merkh and Guido Montúfar

Factorized mutual information maximization

In: Kybernetika, 56 (2020) 5, pp. 948-978
inBook
2020 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
[S. L.] : NeurIPS, 2020.
inBook
2020 Repository 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
[S. L.] : ICLR, 2020.
inBook
2020 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
[S. L.] : ICLR, 2020.
inBook
2020 Repository 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.)
[S. L.] : NeurIPS, 2020. - pp. 11961-11972
Preprint
2020 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

inBook
2020 Journal 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. - pp. 9952-9962
(Proceedings of machine learning research ; 119)
inBook
2019 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. - pp. 362-365
inBook
2019 Journal 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. - pp. 1716-1725
(Proceedings of machine learning research ; 97)
inBook
2019 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
[S. L.] : NeurIPS, 2019.
inBook
2019 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. - pp. 705-714
(Lecture notes in computer science ; 11712)
Preprint
2019 Repository Open Access
Anton Mallasto, Guido Montúfar and Augusto Gerolin

How well do WGANs estimate the Wasserstein metric?

inBook
2019 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
[S. L.] : ICLR, 2019.
inBook
2019 Repository Open Access
Johannes Rauh, Pradeep Kumar Banerjee, Eckehard Olbrich and Jürgen Jost

Unique information and secret key decompositions

In: IEEE international symposium on information theory (ISIT) from July 7 to 12, 2019 ; Paris, France
Piscataway, NY : IEEE, 2019. - pp. 3042-3046
inBook
2018 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. - pp. 141-145
inJournal
2018 Repository Open Access
Wuchen Li and Guido Montúfar

Natural gradient via optimal transport

In: Information geometry, 1 (2018) 2, pp. 181-214
inBook
2018 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. - pp. 75-115
(Springer proceedings in mathematics and statistics ; 252)
inJournal
2018 Journal Open Access
Anna Seigal and Guido Montúfar

Mixtures and products in two graphical models

In: Journal of algebraic statistics, 9 (2018) 1, pp. 1-20