001 Representation Geometry as a Diagnostic for Out-of-Distribution Robustness arXiv Paper Ali Zia et al. Feb 3 002 Universality of shallow and deep neural networks on non-Euclidean spaces arXiv Paper V. Ismailov Feb 3 003 Dimensionality reduction and width of deep neural networks based on topological degree theory arXiv Paper Xiao-Song Yang Nov 10, 2025 004 Typed Topological Structures Of Datasets arXiv Paper Wanjun Hu Aug 19, 2025 005 New universal operator approximation theorem for encoder-decoder architectures arXiv Paper Janek Gödeke, Pascal Fernsel Mar 31, 2025 006 Safe and Efficient Social Navigation through Explainable Safety Regions Based on Topological Features arXiv Paper Victor Toscano-Duran et al. Feb 14, 2025 007 Is magnitude 'generically continuous' for finite metric spaces? arXiv Paper Hirokazu Katsumasa et al. Jan 15, 2025 008 Deep Learning 2.0: Artificial Neurons That Matter -- Reject Correlation, Embrace Orthogonality arXiv Paper Taha Bouhsine Nov 12, 2024 009 Bi-Filtration and Stability of TDA Mapper for Point Cloud Data arXiv Paper Wako Bungula et al. Sep 25, 2024 010 Topology-enhanced machine learning model (Top-ML) for anticancer peptide prediction arXiv Paper J. Tan, Junjie Wee et al. Jul 12, 2024 011 On the Theoretical Expressive Power and the Design Space of Higher-Order Graph Transformers arXiv Paper Cai Zhou, Rose Yu et al. Apr 4, 2024 012 Equivalent Environments and Covering Spaces for Robots arXiv Paper Vadim Weinstein, Steven M. LaValle Feb 28, 2024 013 A Motion Planning Algorithm in a Figure Eight Track arXiv Paper Cristian Jardon, B. L. Sheppard et al. Feb 22, 2024 014 Conway's law, revised from a mathematical viewpoint arXiv Paper Shigeki Matsutani et al. Nov 17, 2023 015 The Shape of Learning: Anisotropy and Intrinsic Dimensions in Transformer-Based Models arXiv Paper Anton Razzhigaev et al. Nov 10, 2023 016 Human Semantic Segmentation using Millimeter-Wave Radar Sparse Point Clouds arXiv Paper Pengfei Song, Luoyu Mei et al. Apr 27, 2023 017 Shape is (almost) all!: Persistent homology features (PHFs) are an information rich input for efficient molecular machine learning arXiv Paper E. Gale Apr 15, 2023 018 A Primer on Topological Data Analysis to Support Image Analysis Tasks in Environmental Science arXiv Paper Lander Ver Hoef et al. Jul 21, 2022 019 Fixed Points of Cone Mapping with the Application to Neural Networks arXiv Paper G. Gabor, Krzysztof Rykaczewski Jul 20, 2022 020 The language of pre-topology in knowledge spaces arXiv Paper Fucai Lin et al. Nov 29, 2021 021 Intrinsic Dimension, Persistent Homology and Generalization in Neural Networks arXiv Paper Tolga Birdal, Aaron Lou et al. Nov 25, 2021 022 A Topological-Framework to Improve Analysis of Machine Learning Model Performance arXiv Paper Henry Kvinge, Colby Wight et al. Jul 9, 2021 023 Digital homotopy relations and digital homology theories arXiv Paper P. Christopher Staecker Jun 2, 2021 024 Universal Approximation Theorems for Differentiable Geometric Deep Learning arXiv Paper Anastasis Kratsios, Leonie Papon Jan 13, 2021 025 Support vector machines and Radon's theorem arXiv Paper Henry Adams, Brittany Carr et al. Nov 1, 2020 026 Fuzzy Simplicial Networks: A Topology-Inspired Model to Improve Task Generalization in Few-shot Learning arXiv Paper Henry Kvinge, Zachary New et al. Sep 23, 2020 027 On Frink's type metrization of weighted graphs arXiv Paper María Florencia Acosta et al. Aug 2, 2020 028 Non-Euclidean Universal Approximation arXiv Paper Anastasis Kratsios, Ievgen Bilokopytov Jun 3, 2020 029 Conley's fundamental theorem for a class of hybrid systems arXiv Paper Matthew D. Kvalheim et al. May 7, 2020 030 A (Simplified) Supreme Being Necessarily Exists, says the Computer: Computationally Explored Variants of Gödel's Ontological Argument arXiv Paper Christoph Benzmüller Jan 14, 2020 031 Computer-supported Analysis of Positive Properties, Ultrafilters and Modal Collapse in Variants of Gödel's Ontological Argument arXiv Paper Christoph Benzmüller et al. Oct 20, 2019 032 Strong homotopy of digitally continuous functions arXiv Paper P. Christopher Staecker Mar 2, 2019 033 Logarithmic mathematical morphology: a new framework adaptive to illumination changes arXiv Paper Guillaume Noyel Jun 8, 2018 034 Robots That Do Not Avoid Obstacles arXiv Paper Kyriakos Papadopoulos et al. Jan 2, 2018 035 A Converse to Banach's Fixed Point Theorem and its CLS Completeness arXiv Paper Constantinos Daskalakis et al. Feb 23, 2017 036 Persistence Lenses: Segmentation, Simplification, Vectorization, Scale Space and Fractal Analysis of Images arXiv Paper Martin Brooks Apr 25, 2016 037 Homotopy relations for digital images arXiv Paper Laurence Boxer et al. Sep 22, 2015 038 Connectivity Preserving Multivalued Functions in Digital Topology arXiv Paper Laurence Boxer et al. Apr 9, 2015 039 Remarks on pointed digital homotopy arXiv Paper Laurence Boxer et al. Mar 10, 2015 040 Some enumerations of binary digital images arXiv Paper P. Christopher Staecker Feb 22, 2015 041 Homotopy equivalence of finite digital images arXiv Paper Jason Haarmann et al. Aug 11, 2014 042 Covering with Excess One: Seeing the Topology arXiv Paper Han Wang Dec 28, 2013 043 A notion of continuity in discrete spaces and applications arXiv Paper Valerio Capraro Oct 8, 2012 044 Piecewise Linear Topology, Evolutionary Algorithms, and Optimization Problems arXiv Paper Andrew Clark Jun 28, 2012 045 Lyapunov exponent evaluation of a digital watermarking scheme proven to be secure arXiv Paper Jacques M. Bahi et al. Mar 3, 2012 046 Chaotic iterations for steganography: Stego-security and topological-security arXiv Paper Nicolas Friot et al. Dec 16, 2011 047 Chaotic iterations versus Spread-spectrum: topological-security and stego-security arXiv Paper Christophe Guyeux et al. Dec 16, 2011 048 Building a Chaotic Proved Neural Network arXiv Paper J. Bahi, C. Guyeux et al. Jan 23, 2011 049 Quasi-metrics, Similarities and Searches: aspects of geometry of protein datasets arXiv Paper Aleksandar Stojmirovic Oct 30, 2008