001 Writhe-Based Polymer Link Classification Using Machine Learning arXiv Paper Jack Beda, Djordje Mihajlovic et al. Jul 22 002 Low-dimensional topology of deep neural networks arXiv Paper Jun Ren, Lek-Heng Lim Jun 30 003 The Two-Hump Problem: Bridging the Difficulty Gap in Mathematical Reinforcement Learning arXiv Paper Lucas Fagan, Michele Tarquini et al. Jun 19 004 Minimal surfaces, Knots, and Neural Networks arXiv Paper Tancredi Schettini Gherardini, Marco Usula May 25 005 Towards Symmetry-sensitive Pose Estimation: A Rotation Representation for Symmetric Object Classes arXiv Paper A. Kriegler, Csaba Beleznai et al. Apr 20 006 RL unknotter, hard unknots and unknotting number arXiv Paper Anne Dranowski et al. Mar 9 007 Shortcut learning in geometric knot classification arXiv Paper Djordje Mihajlovic, Davide Michieletto Feb 19 008 First Proof arXiv Paper Mohammed Abouzaid et al. Feb 5 009 Mapper-GIN: Lightweight Structural Graph Abstraction for Corrupted 3D Point Cloud Classification arXiv Paper Jeongbin You et al. Feb 5 010 Understanding and Improving UMAP with Geometric and Topological Priors: The JORC-UMAP Algorithm arXiv Paper Xiaobin Li et al. Jan 23 011 The N-5 Scaling Law: Topological Dimensionality Reduction in the Optimal Design of Fully-actuated Multirotors arXiv Paper A. Franchi Dec 29, 2025 012 On knot detection via picture recognition arXiv Paper Anne Dranowski et al. Oct 6, 2025 013 On detection probabilities of link invariants arXiv Paper Tuomas Kelomäki et al. Sep 6, 2025 014 Towards Geometry Problem Solving in the Large Model Era: A Survey arXiv Paper Yurui Zhao et al. Jun 3, 2025 015 EuLearn: A 3D database for learning Euler characteristics arXiv Paper Pablo Su'arez-Serrato, Rodrigo Fritz et al. May 18, 2025 016 Triangulating PL functions and the existence of efficient ReLU DNNs arXiv Paper Danny Calegari May 11, 2025 017 Geometric Meta-Learning via Coupled Ricci Flow: Unifying Knowledge Representation and Quantum Entanglement arXiv Paper Ming Lei, C. Baehr Mar 25, 2025 018 Big data comparison of quantum invariants arXiv Paper Daniel Tubbenhauer et al. Mar 20, 2025 019 Colored Jones Polynomials and the Volume Conjecture arXiv Paper Mark Hughes et al. Feb 25, 2025 020 On the Learnability of Knot Invariants: Representation, Predictability, and Neural Similarity arXiv Paper Audrey Lindsay et al. Feb 17, 2025 021 Low rank matrix completion and realization of graphs: results and problems arXiv Paper S. Dzhenzher et al. Jan 10, 2025 022 Topology-Aware 3D Gaussian Splatting: Leveraging Persistent Homology for Optimized Structural Integrity arXiv Paper Tianqi Shen, Shaohua Liu et al. Dec 21, 2024 023 GeLoRA: Geometric Adaptive Ranks For Efficient LoRA Fine-tuning arXiv Paper Abdessalam Ed-dib, Z. Datbayev et al. Dec 12, 2024 024 Emergent Structure in Multi-agent Systems Using Geometric Embeddings arXiv Paper Dimitria Silveria, Kléber Cabral et al. Nov 17, 2024 025 Towards the methodology for solving the minimum enclosing ball and related problems arXiv Paper Michael N. Vrahatis Oct 14, 2024 026 Bi-Filtration and Stability of TDA Mapper for Point Cloud Data arXiv Paper Wako Bungula et al. Sep 25, 2024 027 The unknotting number, hard unknot diagrams, and reinforcement learning arXiv Paper Taylor Applebaum, Sam Blackwell et al. Sep 13, 2024 028 What makes math problems hard for reinforcement learning: a case study arXiv Paper Ali Shehper, Anibal M. Medina-Mardones et al. Aug 27, 2024 029 Topological Representational Similarity Analysis in Brains and Beyond arXiv Paper Baihan Lin Aug 21, 2024 030 Porosity and topological properties of triply periodic minimal surfaces arXiv Paper Sergei Ermolenko et al. Jun 23, 2024 031 Learning BPS Spectra and the Gap Conjecture arXiv Paper Sergei Gukov et al. May 16, 2024 032 Learning 3-Manifold Triangulations arXiv Paper Francesco Costantino et al. May 15, 2024 033 Learning bridge numbers of knots arXiv Paper Hanh Vo, Puttipong Pongtanapaisan et al. Apr 29, 2024 034 Equivalent Environments and Covering Spaces for Robots arXiv Paper Vadim Weinstein, Steven M. LaValle Feb 28, 2024 035 Towards the mathematical foundation of the minimum enclosing ball and related problems arXiv Paper Michael N. Vrahatis Jan 9, 2024 036 Adaptive Hierarchical Origami Metastructures arXiv Paper Yanbin Li et al. Nov 29, 2023 037 Metric Space Magnitude for Evaluating the Diversity of Latent Representations arXiv Paper Katharina Limbeck, Rayna Andreeva et al. Nov 27, 2023 038 GeoTop: Advancing Image Classification with Geometric-Topological Analysis arXiv Paper Mariem Abaach, I. Morilla Nov 8, 2023 039 Estimating the Coverage Measure and the Area Explored by a Line-Sweep Sensor on the Plane arXiv Paper Maria Costa Vianna, Éric Goubault et al. Sep 7, 2023 040 Minimum Width for Deep, Narrow MLP: A Diffeomorphism Approach arXiv Paper Geonho Hwang Aug 30, 2023 041 Machine learning discovers invariants of braids and flat braids arXiv Paper A. Lisitsa, Mateo Salles et al. Jul 22, 2023 042 Neural Polytopes arXiv Paper Koji Hashimoto et al. Jul 3, 2023 043 Low-Resource White-Box Semantic Segmentation of Supporting Towers on 3D Point Clouds via Signature Shape Identification arXiv Paper Diogo Mateus Lavado, Cláudia Soares et al. Jun 13, 2023 044 Hidden symmetries of ReLU networks arXiv Paper J. Elisenda Grigsby, Kathryn Lindsey et al. Jun 9, 2023 045 Geometric deep learning approach to knot theory arXiv Paper Lennart Jaretzki May 26, 2023 046 Graph Neural Networks and 3-Dimensional Topology arXiv Paper Song Jin Ri, Pavel Putrov May 10, 2023 047 Metric Space Magnitude and Generalisation in Neural Networks arXiv Paper Rayna Andreeva, Katharina Limbeck et al. May 9, 2023 048 Searching for ribbons with machine learning arXiv Paper S. Gukov, James Halverson et al. Apr 18, 2023 049 Average degree of the essential variety arXiv Paper Paul Breiding, Samantha Fairchild et al. Dec 3, 2022 050 PatchGT: Transformer over Non-trainable Clusters for Learning Graph Representations arXiv Paper Han Gao, Xu Han et al. Nov 26, 2022 051 Deep Neural Networks as the Semi-classical Limit of Topological Quantum Neural Networks: The problem of generalisation arXiv Paper Antonino Marcianò, Emanuele Zappala et al. Oct 25, 2022 052 Functional dimension of feedforward ReLU neural networks arXiv Paper J. E. Grigsby, Kathryn A. Lindsey et al. Sep 8, 2022 053 Generative Thermal Design Through Boundary Representation and Multi-Agent Cooperative Environment arXiv Paper Hadi Keramati et al. Aug 16, 2022 054 Understanding Deep Learning using Topological Dynamical Systems, Index Theory, and Homology arXiv Paper Bill Basener Jul 25, 2022 055 Optimization of the Shape of a Hydrokinetic Turbine's Draft Tube and Hub Assembly Using Design-by-Morphing with Bayesian Optimization arXiv Paper Haris Moazam Sheikh et al. Jul 23, 2022 056 Braid-based architecture search arXiv Paper Olga Lukyanova, Оleg V. Nikitin et al. Jul 8, 2022 057 An application of neural networks to a problem in knot theory and group theory (untangling braids) arXiv Paper A. Lisitsa, Mateo Salles et al. Jun 10, 2022 058 Geodesic Properties of a Generalized Wasserstein Embedding for Time Series Analysis arXiv Paper Shiying Li et al. Jun 4, 2022 059 Local and global topological complexity measures OF ReLU neural network functions arXiv Paper J. E. Grigsby, Kathryn A. Lindsey et al. Apr 12, 2022 060 Geometric and Topological Inference for Deep Representations of Complex Networks arXiv Paper Baihan Lin Mar 10, 2022