Persistent Homology

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5 papers in the last four weeks, up 67% on the four weeks before. 0.0% of all new papers.

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Exact Topological Compliance: Generating Persistence-Equivalent Graphs
Oct 13, 2026Mattie Ji, Indradyumna Roy, Vikas GargConstrained Generative Modeling Persistent Homology
University of Pennsylvania · Equal Contributions. · Aalto University +1
Persistence Positional Encoding: A Minimal Transformer Recipe for Persistence Diagrams
Oct 13, 2026Eunwoo Heo, Ganghyun Kim, Jaejun YooTopological Representation Learning Persistent Homology
Graduate School of Artificial Intelligence, Ulsan National Institute of Science and Technology
GPU-Accelerated Computation of Persistent Homology for Topological Analysis of Image Data
Oct 7, 2026Fan Wang, Hubert Wagner, Rezaul Chowdhury +1Persistent Homology Topological Data Analysis
Department of Computer Science, Stony Brook University, Stony Brook, NY 11794 USA · Department of Mathematics, University of Florida, Gainesville, FL 32611 USA · Department of Biomedical Informatics, Stony Brook University, Stony Brook, NY 11794 USA
The sublevel Flood bifiltration: towards scalable 2-parameter persistent homology
Oct 4, 2026Mattéo Clémot, Julie Digne, Julien TiernyPersistent Homology Topological Data Analysis
Université Lyon 1 · CNRS, Université Lyon 1 · CNRS, Sorbonne Université
A differentiability framework for zigzag persistent homology via linear interpolation
Sep 30, 2026Enrico Maria Ferrari, Clemens Bannwart, Matteo BiagettiPersistent Homology
Area Science Park, Trieste, Italy · Politecnico di Torino, Torino, Italy
Sparse cubical complexes for efficient topology-preservation in image data
Sep 29, 2026Alexander H. Berger, Marco Fontana, Daniel Rueckert +3Image Segmentation Topology-Preserving Image Segmentation
Weill Cornell Medicine, New York, USA · Technical University of Munich, Munich, Germany · Department of Computing, Imperial College London, UK +3
LandscapeSHAP: Which Persistent Homology Class Gets the Credit?
Sep 25, 2026Nikola MilićevićShapley Value Attribution Topological Data Analysis
Sierpiński--Knopp Wasserstein Distance for Persistence Diagrams and Applications to 2-Wasserstein Approximation
Sep 1, 2026Sebastien Tchitchek, Julien TiernyPersistent Homology Wasserstein Distance
CNRS and Sorbonne Université
Persistent Cross Entropy
Aug 25, 2026Sijin Yeom, Jae-Hun JungPersistent Homology
Artificial Intelligence Graduate School, Pohang University of Science and Technology, Pohang, Korea · Department of Mathematics, Pohang University of Science and Technology, Pohang, Korea
Persistent Magnitude Homology for Quantitative Equational Theories
Aug 21, 2026Luciano MelodiaPersistent Homology
Friedrich-Alexander Universität Erlangen-Nürnberg, Germany
Topology of a Smile: Persistent Homology in Dental Imaging
Aug 14, 2026Leon Dahlmeier, Sara Kališnik, Albert Mehl +1Medical Image Classification Persistent Homology
Department of Mathematics, ETH Zürich, Zürich, Switzerland · Department of Mathematics, PSU, Pennsylvania, United States · Department of Computerized Dentistry, Clinic of Conservative and Preventive Dentistry, University of Zürich, Zürich, Switzerland +1
Stochastic Dynamics on Persistence Diagram Space via Reinforcement Learning
Aug 6, 2026Farzana NasrinRL for Generative Models Persistent Homology
Department of Mathematics, University of Tennessee, Knoxville, TN -37916, USA
Voronoi Histograms for Adaptive Vectorization of Expected Persistence Diagrams
Jul 29, 2026Kaifeng Zhang, Kai Ming TingPersistent Homology
School of Artificial Intelligence Nanjing University, China
Denoising 3D images: robustness of persistent homology measures
Jul 27, 2026Ebru Dagdelen, Aakash Karlekar, Manav Arora +4Noise Robustness Persistent Homology
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA
Calibrated Alzheimer's Conversion Risk in Mild Cognitive Impairment: Persistent Homology of Clinical Trajectories with Conformal Guarantees
Jul 20, 2026Navin BondadeClinical Outcome Prediction Alzheimer's Disease Classification
Institute of Health Informatics, University College London
PHINN-EEG: Topological Time-Series Analysis of Dream-State EEG -- Dynamic Betti Curves for Dream Content Classification and Topology-Conditioned Neural Signal Synthesis
Jul 10, 2026Ren Takahashi, Emre Yusuf, Jayabrata BhaduriEEG Decoding Persistent Homology
Mugen.Codes (DBA of CapaCloud Corp, Wyoming)
Complexity of Normalized Persistence Problems for Topological Data Analysis and Local Hamiltonians
Jul 3, 2026Dominic Lowe, M. S. Kim, Roberto Bondesan +1Spectral Methods Persistent Homology
Blackett Laboratory, Imperial College London, SW7 2AZ, United Kingdom · Department of Computing, Imperial College London, SW7 2AZ, United Kingdom · Yukawa Institute for Theoretical Physics & The Hakubi Center, Kyoto University, Japan
TopoAgent: An Agentic Framework for Automated Topology Learning in Medical Imaging
Jun 29, 2026Guangyu Meng, Pengfei Gu, Xueyang Li +3Medical Image Analysis Persistent Homology
Dept. of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN, USA · Dept. of Computer Science, The University of Texas Rio Grande Valley, Edinburg, TX, USA
Topological summaries of fingerprint ridge patterns carry identity information
Jun 20, 2026Chad M. Topaz, Niny Arcila-Maya, Elizabeth Munch +2Biometric Identification Persistent Homology
Williams College, Williamstown, MA 01267 · QSIDE Institute, Williamstown, MA 01267 · University of Colorado Boulder, Boulder, CO 80309 +3
PHINN: Persistent Homology Inspired Neural Network for Rare-Event Time Series Generation
Jun 13, 2026Emre Yusuf, Ren Takahashi, Jayabrata BhaduriTime Series Generation Flow-Based Generative Modeling
Defense.Codes (a DBA of CapaCloud Corp
From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Features
Jun 10, 2026Juliette Murris, Bernadette Stolz, Karsten BorgwardtTwo-Sample Testing Persistent Homology
Department of Machine Learning and Systems Biology, Max Planck Institute of Biochemistry, Martinsried, Germany
Symmetric Divergence and Normalized Similarity: A Unified Topological Framework for Representation Analysis
Jun 4, 2026Yan Wang, Tianyang HuRepresentational Similarity Analysis Neural Representation Geometry
School of Data Science The Chinese University of Hong Kong, Shenzhen
$p$ -adic Bi-Filtrations for Topological Machine Learning on Genomic Sequences
Jun 4, 2026Tirtharaj Dash, Gunja SachdevaGenomics Persistent Homology
Department of CS & IS, BITS Pilani, K K Birla Goa Campus, Zuarinagar, Goa 403726, India. · Department of Mathematics, BITS Pilani, K K Birla Goa Campus, Zuarinagar, Goa 403726, India.
Fast Cubical Persistent Homology on 2D and 3D Images via Union-Find, Pruning, and Lookup Tables
Jun 3, 2026Titouan Le Breton, Karol Szustakowski, Marie PiraudPersistent Homology Topological Data Analysis
1Helmholtz AI, Helmholtz Munich, Neuherberg, Germany · 2École des Ponts ParisTech, ENS Paris-Saclay · Institute of AI for Health, Helmholtz Munich, Neuherberg, Germany
Learning Topological Representations of Protein Structure and Dynamics
Jun 2, 2026Dominik Geng, Florian Graf, Martin Uray +1Generative Modeling Persistent Homology
University of Salzburg, Austria · Josef Ressel Centre for Intelligent and Secure Industrial Automation, University of Applied Sciences, Salzburg, Austria
PFlow-T: A Persistence-Driven Forward Process for Topology-Controlled Generation
May 17, 2026Snigdha Chandan KhilarGenerative Modeling Persistent Homology
Independent Researcher
ToMAToMP: Robust and Multi-Parameter Topological Clustering
May 14, 2026Ludo Andrianirina, Mathieu CarrièreClustering Persistent Homology
DataShape, Centre Inria d’Université Côte d’Azur, Sophia-Antipolis, France
Towards Scalable Persistence-Based Topological Optimization
May 9, 2026Abderrahim Bendahi, Alexandre Duplessis, Arnaud FickingerPersistent Homology Topological Data Analysis
ENS Ulm, PSL Paris, France · UC Berkeley Berkeley, CA, USA
A Closed-Form Adaptive-Landmark Kernel for Certified Point-Cloud and Graph Classification
May 5, 2026Sushovan Majhi, Atish Mitra, Žiga Virk +1Point Cloud Classification Classification
Data Science, George Washington University, USA · Department of Mathematical Sciences, Montana Technological University, USA · Faculty of Computer and Information Science, University of Ljubljana, Slovenia +1
Global and Local Topology-Aware Attention with Persistent Homology and Euler Biases for Time-Series Forecasting
May 4, 2026Usef Faghihi, Amir SakiTime Series Forecasting Persistent Homology
Department of Mathematics and computer science · University of Quebec Trois Rivieres

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Exact Topological Compliance: Generating Persistence-Equivalent Graphs

Mattie Ji, Indradyumna Roy, Vikas Garg

University of Pennsylvania · Equal Contributions. · Aalto University+1

Constrained Generative Modeling Persistent Homology

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Persistent homology summarizes the topological evolution of a graph as persistence diagrams (PDs). Generating graphs whose topology matches a target descriptor is increasingly important, yet existing topology-aware generative models rely on soft regularization, producing graphs whose PDs may only be approximately similar. We initiate a principled investigation of the generation problem: produce graphs that realize a target PD exactly. We propose two approaches guided by the implicit local and global constraints a target PD imposes. The local approach builds degree-based PD-equivalent graphs iteratively, and we prove that every output realizes the target PD and that every degree-based PD-equivalent graph is reachable. However, as shown thereafter, local generation necessarily trades off between sample diversity and reaching infeasible states. We therefore recast generation as a global constraint satisfaction problem with a complete encoding solvable by modern constraint programming solvers. This is applicable to any vertex-based permutation equivariant filtration scheme and is minimal under the degree filtration. Experiments on four standard graph generation benchmarks confirm that both methods realize the target PD exactly. Together, our methods provide a principled treatment of strict topology-compliant graph generation. Code is available at https://github.com/Aalto-QuML/ExactCompliance.