Topology

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Topological Data Analysis

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Persistent Homology

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Topological Deep Learning

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269 papers

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Non-negative Matrix Factorisation with Topological Regularisation
Jun 16, 2026Matias de Jong van Lier, Shizuo Kaji, Keunsu KimNonnegative Matrix Factorization Persistent Homology
Analytic Torsion and Spectral Gap Capture Persistent-Laplacian Performance
Jun 15, 2026Jernej Grlj, Aaron D. LaudaPersistent Homology Graph Laplacians
Automated Digital Twin Construction for Highway Scenarios Using LiDAR Point Clouds and OpenStreetMap
Jun 15, 2026Yongqi Zhao, Dong Bi, Paul Kovacevic +4Lane Geometry Lidar
Topological Flow Matching
Jun 14, 2026Kacper Wyrwal, İsmail İlkan Ceylan, Alexander TongTopological Data Analysis Brain Magnetic Resonance Imaging
PHINN: Persistent Homology Inspired Neural Network for Rare-Event Time Series Generation
Jun 13, 2026Emre Yusuf, Ren Takahashi, Jayabrata BhaduriSynthetic Time Series Generative Models
NetCause: Counterfactual Learning for Root Cause Analysis in Large-Scale Networks
Jun 11, 2026Fabien Chraim, Jian Zhang, Dominik Janzing +3Root Cause Analysis Causal Graph
Effects of Social Interactions in Self-Organising Railway Traffic Management
Jun 11, 2026Fabio Oddi, Federico Naldini, Leo D'Amato +3Complex Networks Long-Horizon Forecasting
From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Features
Jun 10, 2026Juliette Murris, Bernadette Stolz, Karsten BorgwardtPersistent Homology Topological Data Analysis
Topological Neural Operators
Jun 8, 2026Lennart Bastian, Samuel Leventhal, Mustafa Hajij +1Neural Operators Topological Data Analysis
Detecting Differences Is Not Understanding Structure: Large Language Models Fail at Graph Isomorphism
Jun 8, 2026Kumar Thushalika, Sukumar Kishanthan, Asela HevapathigeLarge Language Model Performance Reasoning Benchmark
PRISM: Topology-Aware Cross-Modal Imputation for Modality-Deficient Federated Graph Learning
Jun 8, 2026Zekai Chen, Miao Zhang, Jiayang Xing +4Federated Graph Learning Missing Modalities
Improved Convergence Analysis of Topology Dependence in Decentralized SGD
Jun 8, 2026Yuki Takezawa, Anastasia Koloskova, Sebastian U. StichConvergence Analysis Stochastic Gradient Descent
Byzantine Cheap Talk: Adversarial Resilience and Topology Effects in LLM Coordination Games
Jun 5, 2026Aya El Mir, Martin Takáč, Salem LahlouMulti-Agent Large Language Model Byzantine Attacks
Constructing VAE Latent Spaces with Prescribed Topology
Jun 5, 2026Jilles S. van Hulst, Jakub M. Tomczak, W. P. M. H. Heemels +1Variational Autoencoder Manifolds
AMD-FCG: An Enhanced Function Call Graph Dataset with Integrated Topological Features for Malware Detection and Classification
Jun 5, 2026Parthajit Borah, Sakshi Singh, D. K. Bhattacharyya +1Malware Detection Generalist Graph Anomaly Detection
Symmetric Divergence and Normalized Similarity: A Unified Topological Framework for Representation Analysis
Jun 4, 2026Yan Wang, Tianyang HuTopological Data Analysis Semantic Similarity Metrics
Tight list replicability bounds via a novel sphere covering theorem
Jun 4, 2026Ari Blondal, Hamed Hatami, Pooya Hatami +2Repetition Reproducibility
$p$ -adic Bi-Filtrations for Topological Machine Learning on Genomic Sequences
Jun 4, 2026Tirtharaj Dash, Gunja SachdevaGenomics Topological Deep Learning
MS-DKC: A Dataset Knowledge Card Framework for Designing and Adapting Medical Image Segmentation Models
Jun 4, 2026Tariq M. Khan, Syed Saud Naqvi, Thantrira Porntaveetus +4Medical Image Segmentation Medical Imaging
Multi-Task Crack Foundation Model for Engineering-Reliable Crack Representation and Topology Preservation in Civil Infrastructure
Jun 4, 2026Blessing Agyei Kyem, Joshua Kofi Asamoah, Eugene Denteh +1Wireless Foundation Models Topological Data Analysis
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 Cubifygs
Exploring the Topology and Memory of Consensus: How LLM Agents Agree, Fragment, or Settle When Forming Conventions
Jun 2, 2026Aliakbar Mehdizadeh, Martin HilbertMulti-Agent Coordination Agent Memory
Learning Topological Representations for Molecular Dynamics
Jun 2, 2026Dominik Geng, Florian Graf, Martin Uray +1Molecular Dynamics Protein
Learning Coherent Representations: A Topological Approach to Interpretability
Jun 1, 2026Sigurd Gaukstad, Melvin Vaupel, Valdemar Kargård Olsen +2Model Interpretability Representation Learning
GloResNet: A lightweight 3D CNN with global topological features for preterm brain injury prediction
Jun 1, 2026Boyu Yuan, Jiamiao Lu, Weichuan Zhang +5Magnetic Resonance Imaging Topological Deep Learning
Topological texture analysis of microscopy images of dynamic casein gelation and its relation to rheological properties
Jun 1, 2026Zahra Tabatabaei, Diana Soto Aguilar, Jose C. Bonilla +2Topological Data Analysis Porous Media
Dynamic Trust-Aware Sparse Communication Topology for LLM-Based Multi-Agent Consensus
Jun 1, 2026Wanshuang Gou, Zihan LiuMulti-Agent Debate Communication
PlatonicNav: Unveiling Semantic Correspondence in Navigation with Platonic Topological Maps
Jun 1, 2026Junlin Long, Zeyu Zhang, Xu Deng +5Vision-Language Navigation Object Goal Navigation
Bridging Topology and Deep Representation Learning: A TDA-ViT Fusion Model for Four-Class Brain Tumor Classification
May 30, 2026Faisal AhmedBrain Tumor Classification Medical Imaging
Learning Transfers: Kan Extensions for Neural Invariants
May 30, 2026Luciano MelodiaTransfer Learning Invariance
Real-Time Physics Simulation with Dynamic Mesh-Gaussian Reconstructions
May 30, 2026Adrian Ramlal, John S. ZelekPhysics Simulation Topological Data Analysis
Topology-Aware State Abstraction with Tangle Cores for Markov Decision Processes
May 29, 2026Ibne Farabi Shihab, Sanjeda Akter, Anuj SharmaMarkov Decision Processes Topological Data Analysis
The Sword, Shield, and Achilles' Heel: Characterizing the Linguistic Inductive Bias of Large Language Models for Spatial Reasoning in Navigation Planning
May 29, 2026Xudong Zhang, Jian Yang, Shengkai Wang +5Large Language Model Planning Spatial Reasoning
DiffoR: A Unified Continuous Generative Framework for Universal Ordinal Regression
May 29, 2026Hongxu Ma, Lin Wang, Chenghou Jin +6Generative Models Topological Data Analysis
A Topological Characterization of Graph Neural Networks via Stochastic Block Model Embeddings on the n-Sphere
May 29, 2026Gopal AnantharamanGraph Neural Networks Message Passing Neural Networks
Evolutionary Refinement of Generative Graph Topologies: A Hybrid WGAN-GA Approach
May 27, 2026James Sargant, Seyedeh Ava Razi Razavi, Renata Dividino +1Genetic Algorithms Topological Data Analysis
Accelerating Robot Path Planning via Connectivity-Preserving Region Proposal Network
May 27, 2026Zhanzheng Ma, Cancan Zhao, Shuai Zhang +1Robot Planning Segmentation Model
EdgeFlow: Edge-Map Augmented VLM-Based Flowchart Processing for Industrial Requirements Engineering
May 26, 2026Zhifei Dou, Shabnam Hassani, Ou WeiDiagrams Ava-Vlm
Curve Skeletonization in Continuous domain for Meshes and Point Clouds
May 25, 2026Jai Bardhan, Ramya Hebbalaguppe, Aravind UdupaSkeletonization Statistical Shape Model
TopoAlign: Topology-Aware Visual Representation Alignment
May 25, 2026Xinyuan Yan, Rita Sevastjanova, Mennatallah El-Assady +1Topological Data Analysis Visual Representations
MARVEL: Universal Murray's Law-informed Vessel Tree Segmentation and Topology Estimation
May 25, 2026Yi Zhou, Thiara Sana Ahmed, Jacqueline Chua +7Retinal Vessel Segmentation Topological Data Analysis
RoboHitch: Learning Visual Affordance from Disordered Keypoints for Hitch Knots Tying
May 23, 2026Jiahui Zuo, Boyang Zhang, Fumin ZhangKnots Generalizable Robotic Manipulations
Any-Dimensional Invariant Universality
May 22, 2026Shengtai Yao, Eitan Levin, Mateo DíazUniversality Metric Spaces
Resilience Characterization of AI-Native Wireless Receivers via Persistent Homology
May 21, 2026Christo Kurisummoottil Thomas, Emilio Calvanese StrinatiChannel Modeling Resilience
PhylaFlow: Hybrid Flow Matching in Billera-Holmes-Vogtmann Tree Space for Phylogenetic Inference
May 21, 2026Yasha Ektefaie, Leo Cui, Shrey Jain +2Phylogenetic Trees Conditional Flow Matching
SciAtlas: A Large-Scale Knowledge Graph for Automated Scientific Research
May 20, 2026Shuofei Qiao, Yunxiang Wei, Jiazheng Fan +8Knowledge Graphs Scientific Discovery
Causely: A Causal Intelligence Layer for Enterprise AI A Benchmark Study on SRE and Reliability Workflows
May 18, 2026Dhairya Dalal, Endre Sara, Ben Yemini +2Root Cause Analysis Causal Reasoning
Prism: Structural Symmetry Scanning via Duality-Constrained Laplacian Projection
May 18, 2026Jiatong XieComplex Networks Graph Laplacians
Topological Data Analysis combined with Machine Learning for Predicting Permeability of Porous Media
May 17, 2026Ebru Dagdelen, Catherin Neena Lalu, Aakash Karlekar +5Porous Media Topological Data Analysis
PFlow-T: A Persistence-Driven Forward Process for Topology-Controlled Generation
May 17, 2026Snigdha Chandan KhilarDiscrete Diffusion Model Persistent Homology
Heterogeneous Information-Bottleneck Coordination Graphs for Multi-Agent Reinforcement Learning
May 17, 2026Wei Duan, Junyu Xuan, En Yu +2Multi-Agent Reinforcement Learning Coordination
Topo-GS: Continuous Volumetric Embedding of High-Dimensional Data via Topological Gaussian Splatting
May 16, 2026João Paulo Gois, Luis Gustavo NonatoVolume Topological Data Analysis
Beyond Point-Wise Matching: Structural Representation Alignment for Accelerating Diffusion Transformers
May 16, 2026Shaodong Xu, Zhendong Wang, Litong Gong +4Multimodal Diffusion Transformers Feature Matching
Encoding Robust Topological Signatures for Hyperdimensional Computing
May 16, 2026Arpan KusariTopological Deep Learning Topological Data Analysis
PAGER: Bridging the Semantic-Execution Gap in Point-Precise Geometric GUI Control
May 15, 2026Jingxuan Wei, Xi Bai, Shan Liu +8Graphical User Interface Topological Data Analysis
Preserving Topology Privacy of Network Systems by Feedback: Conditions and Distributed Design
May 15, 2026Yushan Li, Jiabao He, Julien M. Hendrickx +1Topological Data Analysis Networked Systems
TopoEvo: A Topology-Aware Self-Evolving Multi-Agent Framework for Root Cause Analysis in Microservices
May 15, 2026Junle Wang, Xingchuang Liao, Wenjun WuRoot Cause Analysis Microservices
Automatic Construction of a Legal Citation Graph from 100 Million Ukrainian Court Decisions: Large-Scale Extraction, Topological Analysis, and Ontology-Driven Clustering
May 14, 2026Volodymyr OvcharovLegal Domain Citations
TopoPrimer: The Missing Topological Context in Forecasting Models
May 14, 2026Zara Zetlin, Kayhan Moharreri, Maria SafiTime Series Topological Data Analysis
ToMAToMP: Robust and Multi-Parameter Topological Clustering
May 14, 2026Ludo Andrianirina, Mathieu CarrièreImage Clustering Persistent Homology

Jun 16, 2026 · cs.LGJ/K move · Enter open · S save

Non-negative Matrix Factorisation with Topological Regularisation

Matias de Jong van Lier, Shizuo Kaji, Keunsu Kim

Recursive Inc. · Tokyo, 150-0002, Japan · Graduate School of Science · Kyoto University · Kyoto, 606-8502, Japan

We investigate the learning of interpretable bases in non-negative matrix factorisation (NMF) by regularising the topology of the learned basis functions. Our approach is motivated by the observation that many data modalities can be viewed as non-negative functions on a structured domain, where the quality of a basis is intrinsically linked to its topology. However, naive methods for incorporating the topology of the support are often hindered by discreteness and threshold dependence, rendering them unsuitable for continuous optimisation. We address these challenges by employing persistent homology as a stable, threshold-free topological quantifier and by designing topological scores that integrate into the NMF objective as regularisers. The resulting framework encompasses spatially coherent image components, periodic time-series structures, and clique-like graph signals within a unified modelling language.

Nonnegative Matrix Factorization Persistent Homology Regularization Techniques Graph Representation Learning

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