001 Mathematical Discovery in the Wild: AI-Guided Proofs in Banach Space Theory arXiv Paper Antonio Acuaviva, Pablo Acuaviva Jul 19 002 The VC dimension of partial concept classes via Radon's theorem arXiv Paper G. Ivanov, A. Jung et al. Jul 12 003 All you need is SAMPAT arXiv Paper Jayadeva, Ms. P. Aswani Jul 10 004 Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity arXiv Paper Julia B. Nakhleh, Robert D. Nowak Jul 6 005 Quantum Kolmogorov--Arnold representation theorem for continuous unitary-valued maps arXiv Paper Sviatoslav V. Dzhenzher Jul 3 006 Fast approximation and learning of binary classification tasks in o-minimal structures using ReLU neural networks arXiv Paper Clemens Kinn, Philipp Petersen Jun 29 007 Near-Lipschitz stability of the Kim--Milman flow map arXiv Paper Sinho Chewi et al. Jun 22 008 The Information-Theoretic Benefit of Shared Representations under Orthogonality Constraints arXiv Paper Thomas Dittrich, Oliver Potocki et al. Jun 14 009 Representation Costs in Data Science: Foundations and the Quasi-Banach Spaces of Deep Neural Networks arXiv Paper Greg Ongie, Rahul Parhi Jun 12 010 Moonshine: An Autonomous Mathematical Research Agent Centered on Conjecture Generation arXiv Paper Xiaoyang Chen, Xiang Jiang Jun 9 011 Self-Consistent Generative Paths via Admissible Random Variational Transport arXiv Paper Lei Luo, Yingzhe Zhang et al. Jun 8 012 Weighted universal approximation of differentiable maps on infinite-dimensional manifolds arXiv Paper Philipp Schmocker, Josef Teichmann Jun 8 013 Conditional Random Ordered Transport Spaces arXiv Paper Lei Luo, Jian Yang Jun 6 014 New Fractional Ambiguity Function Integrated with CNN-Based Machine Learning for Signal Classification arXiv Paper Aamir Hamid Dar, Prakhar Kumar Sonkar et al. Jun 6 015 Efficient Approximation for Encoder--Decoder Neural Operators via Variation Spaces arXiv Paper Jia-Qi Yang, Lei Shi May 31 016 Wasserstein Contraction of Coordinate Ascent Variational Inference arXiv Paper Rocco Caprio, Adrien Corenflos et al. May 28 017 Gaussian Processes with Sample Paths in Reproducing Kernel Banach Spaces arXiv Paper Toni Karvonen et al. May 27 018 A Viscosity Semigroup Framework for Stable Image Reconstruction arXiv Paper Arina Oberoi May 26 019 Any-Dimensional Invariant Universality arXiv Paper Shen Yao, Eitan Levin et al. May 22 020 Learning Orthonormal Bases for Function Spaces arXiv Paper Hamidreza Kamkari, M. Nabizadeh et al. May 19 021 Pointwise Generalization in Deep Neural Networks arXiv Paper Shaojie Li, Yunbei Xu May 18 022 Multi-Headed Transformer Architectures as Time-dependent Wasserstein Gradient Flows arXiv Paper Alex Massucco, Leonardo Del Grande et al. May 15 023 Universal Approximation of Nonlinear Operators and Their Derivatives arXiv Paper F. Feo May 14 024 Wavelet-Based Observables for Koopman Analysis: An Extended Dynamic Mode Decomposition Framework arXiv Paper Cankat Tilki, S. Gugercin May 14 025 Unified generalization analysis for physics informed neural networks arXiv Paper Yuka Hashimoto, Tomoharu Iwata May 13 026 Don't Fix the Basis -- Learn It: Spectral Representation with Adaptive Basis Learning for PDEs arXiv Paper Xuxiang Zhao, Angelica I. Avilés-Rivero May 11 027 Convergent Stochastic Training of Attention and Understanding LoRA arXiv Paper Zhengkai Sun, Dibyakanti Kumar et al. May 8 028 Structure-Preserving Reconstruction of Convex Lipschitz Functionals on Hilbert Spaces from Finite Samples arXiv Paper Anastasis Kratsios May 8 029 Grokability in five inequalities arXiv Paper P. Ivanisvili, Xinyuan Xie May 6 030 Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation arXiv Paper Nicole Hao May 4 031 Limit Properties at Critical Indices of Linear Canonical Riesz Potentials and Their Applications to Security of Multi-Image Encryption arXiv Paper Zunwei Fu et al. May 3 032 Necessary and sufficient conditions for universality of Kolmogorov-Arnold networks arXiv Paper Vugar Ismailov Apr 26 033 Duality for the Adversarial Total Variation arXiv Paper Leon Bungert, Lucas Schmitt Apr 20 034 Sparse-Aware Neural Networks for Nonlinear Functionals: Mitigating the Exponential Dependence on Dimension arXiv Paper Jianfei Li, Shuo Huang et al. Apr 8 035 Intrinsic perturbation scale for certified oracle objectives with epigraphic information arXiv Paper Karim Bounja, B. Achchab et al. Apr 7 036 Minimum Norm Interpolation via the Local Theory of Banach Spaces: The Role of $2$-Uniform Convexity arXiv Paper Gil Kur, Pierre Bizeul Mar 30 037 Kantorovich--Kernel Neural Operators: Approximation Theory, Asymptotics, and Neural Network Interpretation arXiv Paper Tian-Xiao He Mar 27 038 Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees arXiv Paper Amartya Mukherjee, Maxwell Fitzsimmons et al. Mar 19 039 A Fractional Fox H-Function Kernel for Support Vector Machines: Robust Classification via Weighted Transmutation Operators arXiv Paper Gustavo Dorrego Mar 13 040 Topological DeepONets and a generalization of the Chen-Chen operator approximation theorem arXiv Paper V. Ismailov Mar 12 041 Margin in Abstract Spaces arXiv Paper Yair Ashlagi et al. Mar 7 042 A Multiplicative Neural Network Architecture: Locality and Regularity of Approximation arXiv Paper H. Choi, Beom-Seok Han Feb 6 043 Featured Reproducing Kernel Banach Spaces for Learning and Neural Networks arXiv Paper Isabel de la Higuera, F. Herrera et al. Feb 6 044 Universal Approximation of Continuous Functionals on Compact Subsets via Linear Measurements and Scalar Nonlinearities arXiv Paper Andrey Krylov et al. Feb 3 045 Universality of shallow and deep neural networks on non-Euclidean spaces arXiv Paper V. Ismailov Feb 3 046 Use of operator defect identities in multi-channel signal plus residual-analysis via iterated products and telescoping energy-residuals: Applications to kernels in machine learning arXiv Paper Palle E. T. Jorgensen, Myung-Sin Song et al. Jan 26 047 A Mosco sufficient condition for intrinsic stability of non-unique convex Empirical Risk Minimization arXiv Paper Karim Bounja et al. Jan 25 048 On finite-dimensional encoding/decoding theorems for neural operators arXiv Paper Vinícius Luz Oliveira et al. Jan 20 049 Universal Approximation Theorem for Input-Connected Multilayer Perceptrons arXiv Paper Vugar Ismailov Jan 20 050 Manifold limit for the training of shallow graph convolutional neural networks arXiv Paper Johanna Tengler, Christoph Brune et al. Jan 9 051 Horizon Activation Mapping for Neural Networks in Time Series Forecasting arXiv Paper Hans Krupakar, V. Kandappan Jan 5 052 Learned iterative networks: An operator learning perspective arXiv Paper Andreas Hauptmann et al. Dec 9, 2025 053 Constructive Approximation under Carleman's Condition, with Applications to Smoothed Analysis arXiv Paper Frederic Koehler et al. Dec 4, 2025 054 Shorting Dynamics and Structured Kernel Regularization arXiv Paper James Tian Dec 4, 2025 055 Upper Approximation Bounds for Neural Oscillators arXiv Paper Zifeng Huang et al. Nov 30, 2025 056 A Review of Pseudospectral Optimal Control: From Theory to Flight arXiv Paper I. M. Ross et al. Nov 25, 2025 057 Generalized infinite dimensional Alpha-Procrustes based geometries arXiv Paper Salvish Goomanee et al. Nov 12, 2025 058 Infinite-Dimensional Operator/Block Kaczmarz Algorithms: Regret Bounds and $λ$-Effectiveness arXiv Paper Halyun Jeong et al. Nov 10, 2025 059 Quantitative Bounds for Sorting-Based Permutation-Invariant Embeddings arXiv Paper Nadav Dym et al. Oct 25, 2025 060 Distributionally robust approximation property of neural networks arXiv Paper Mihriban Ceylan, David J. Prömel Oct 10, 2025