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Editors: Guillermo Bernardez Gil, Mitchell Black, Alexander Cloninger, Timothy Doster, Tegan Emerson, Ińes Garcı́a-Rodondo, Chester Holtz, Mit Kotak, Henry Kvinge, Gal Mishne, Mathilde Papillon, Alison Pouplin, Katie Rainey, Bastian Rieck, Lev Telyatnikov, Eric Yeats, Qingsong Wang, Yusu Wang, Jeremy Wayland
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1st Conference on Topology, Algebra, and Geometry in Data Science (TAG-DS 2025): Preface
Guillermo Bernardez Gil, Mitchell Black, Alexander Cloninger, Timothy Doster, Tegan Emerson, Ińes Garcı́a-Rodondo, Chester Holtz, Mit Kotak, Henry Kvinge, Gal Mishne, Mathilde Papillon, Alison Pouplin, Katie Rainey, Bastian Rieck, Lev Telyatnikov, Eric Yeats, Qingsong Wang, Yusu Wang, Jeremy Wayland; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:1-3
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Topological Deep Learning Challenge 2025: Expanding the Data Landscape
Guillermo Bernárdez, Lev Telyatnikov, Mathilde Papillon, Marco Montagna, Raffael Theiler, Louisa Cornelis, Johan Mathe, Miquel Ferriol, Pavlo Vasylenko, Jan-Willem Van Looy, Lucia Testa, Bruno Neri, Donatella Genovese, Melanie Weber, Amaury Wei, Alessio Devoto, Alexander Weers, Robert Jankowski, Loris Cino, David Leko, Michael Banf, Jonas Müller, Thomas Grapentin, Taejin Paik, Abhijeet Dutta, Hugo Walter, Thomas Vaitses Fontanari, Ali Ghasemi, Dario Loi, Haitz Sáez de Ocáriz Borde, Gabriela Aguilar-Argüello, Giovanni B. da Rosa, Théo Saulus, Eric Rubiel Dolores-Cuenca, Leonardo Di Nino, Pierrick Leroy, Mario Edoardo Pandolfo, Andrea Cavallo, Yu Qin, Pavel Snopov, Amirreza Akbari, Ixchel Meza-Chávez, Louis Van Langendonck, Jared Able, Maria Yuffa Meshcheryakova, Henry Tsay, Luka Benić, Dominik Filipiak, Patrick Liu, Huidong Liang, Alexsandro Santos da Rosa Jr., Tiziana Cattai, Henrique M. Borges, Enrico Grimaldi, Manuel Lecha, Claudio Battiloro, Xuan-Chen Liu, Raj Deshpande, Graham Johnson, Igor Morgunov, Hugo Micheron, Rémi Devaux, Antoine Jardin, Tegan Emerson, Olga Fink, Nina Miolane; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:4-14
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LR-RaNN: Lipschitz Regularized Randomized Neural Networks for System Identification
; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:15-29
Peeling metric spaces of strict negative type
Steve Huntsman; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:30-44
Bilevel Optimization for Hyperparameter Learning in Supporting Vector Machines
Lei Huang, Jiawang Nie, Jiajia Wang, Suhan Zhong; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:45-55
Topological Preservation in Temporal Link Prediction
Marco Campos, Casey Doyle, Daniel Krofcheck, Sarah Simpson, Michael Xi, William Ott, Henry Adams; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:56-78
Neural Local Wasserstein Regression
Inga Girshfeld, Xiaohui Chen; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:79-89
Learning Polynomial Activation Functions for Deep Neural Networks
Linghao Zhang, Jiawang Nie, Tingting Tang; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:90-99
Kernel Mean Embeddings of \texttt[CLS] Tokens in ViTs
Mason Faldet; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:100-113
Which Way from B to A: The role of embedding geometry in image interpolation for Stable Diffusion
Nicholas Karris, Luke Durell, Javier Flores, Tegan Emerson; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:114-125
Advancing Local Clustering on Graphs via Compressive Sensing: Semi-supervised and Unsupervised Methods
Zhaiming Shen, Sung Ha Kang; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:126-146
Quasi Zigzag Persistence: A Topological Framework for Analyzing Time-Varying Data
Tamal K. Dey, Shreyas N. Samaga; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:147-165
Scratching the Surface: Reflections of Training Data Properties in Early CNN Filters
Grayson Jorgenson, Cassie Heine, Robin Cosbey, Abby Reynolds, Davis Brown, Henry Kvinge, Timothy Doster, Tegan Emerson; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:166-175
Looping back: Circular nodes revisited with novel applications in the radio frequency domain
Tim Marrinan, Bill Kay, Audun Myers, Rachel Wofford, Tegan Emerson; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:176-190
HAGGLE: Get a better deal using a Hierarchical Autoencoder for Graph Generation and Latent-space Expressivity
Audun Myers, Stephen J. Young, Tegan Emerson; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:191-202
Multi-View Graph Learning with Graph-Tuple
Shiyu Chen, Ningyuan (Teresa) Huang, Soledad Villar; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:203-216
Symmetry-Aware Graph Metanetwork Autoencoders: Model Merging through Parameter Canonicalization
Odysseas Boufalis, Jorge Carrasco-Pollo, Joshua Rosenthal, Eduardo Terres-Caballero, Alejandro Garcı́a-Castellanos; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:217-235
DYMAG: Rethinking Message Passing Using Dynamical-systems-based Waveforms
Dhananjay Bhaskar, Xingzhi Sun, Yanlei Zhang, Charles Xu, Arman Afrasiyabi, Siddharth Viswanath, Oluwadamilola Fasina, Guy Wolf, Michael Perlmutter, Smita Krishnaswamy; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:236-268
LINSCAN - A Linearity Based Clustering Algorithm
Andrew Dennehy, Xiaoyu Zou, Shabnam J. Semnani, Yuri Fialko, Alexander Cloninger; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:269-286
Topological Signatures of ReLU Neural Network Activation Patterns
Vicente Bosca, Tatum Rask, Sunia Tanweer, Andrew R. Tawfeek, Branden Stone; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:287-301
Can Neural Networks Learn Small Algebraic Worlds? An Investigation Into the Group-theoretic Structures Learned By Narrow Models Trained To Predict Group Operations
Henry Kvinge, Andrew Aguilar, Nayda Farnsworth, Grace O’Brien, Robert Jasper, Sarah Scullen, Helen Jenne; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:302-312
A Model of Flocking Using Sheaves
Joseph Geisz; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:313-337
Robust Hyperspectral Anomaly Detection via Bootstrap Sampling-based Subspace Modeling in the Signed Cumulative Distribution Transform Domain
Abu Hasnat Mohammad Rubaiyat, Jordan Vincent, Colin Olson; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:338-348
Precision Matrix based Feature Learning Mechanism for Subspace Clustering Task
Haohan Zou, Alexander Cloninger; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:349-361
Self-Organizing Maps for the Reconstruction of Images in Pixel Permuted Image Stacks
Connor Price, David Kott, Chris Peterson, Michael Kirby; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:362-374
On Predicting Material Fracture from Persistence Homology: Or, Which Topological Features Are Informative Covariates?
James Amarel, Nicolas Hengartner, Robyn Miller, Benjamin Migliori, Daniel Hope, Emily Casleton, Alexei Skurikhin, Earl Lawrence, Gerd J. Kunde; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:375-388
Interpreting deep neural networks trained on elementary $p$ groups reveals algorithmic structure
Gavin McCracken, Arthur Ayestas Hilgert, Sihui Wei, Gabriela Moisescu-Pareja, Zhaoyue Wang, Jonathan Love; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:389-402
Comparative Analysis in Pre-image Algorithms of Kernel PCA
Wojciech Czaja, Canran Ji; Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:403-413
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