Theory-to-Practice Gap for Neural Networks and Neural Operators
Fuente:
arXiv
Saved in:
| Main Authors: | Grohs, Philipp, Lanthaler, Samuel, Trautner, Margaret |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Similar Items
Discretization Error of Fourier Neural Operators
by: Lanthaler, Samuel, et al.
Published: (2024)
by: Lanthaler, Samuel, et al.
Published: (2024)
Approximation by Steklov Neural Network Operators
by: Karaman, S. N., et al.
Published: (2024)
by: Karaman, S. N., et al.
Published: (2024)
Operator Learning of Lipschitz Operators: An Information-Theoretic Perspective
by: Lanthaler, Samuel
Published: (2024)
by: Lanthaler, Samuel
Published: (2024)
Parseval Convolution Operators and Neural Networks
by: Unser, Michael, et al.
Published: (2024)
by: Unser, Michael, et al.
Published: (2024)
Convergence Analysis of Max-Min Exponential Neural Network Operators in Orlicz Space
by: Pradhan, Satyaranjan, et al.
Published: (2025)
by: Pradhan, Satyaranjan, et al.
Published: (2025)
Non-Asymptotic Stability and Consistency Guarantees for Physics-Informed Neural Networks via Coercive Operator Analysis
by: Katende, Ronald
Published: (2025)
by: Katende, Ronald
Published: (2025)
The Function Representation of Artificial Neural Network
by: Ma, Zhongkui
Published: (2019)
by: Ma, Zhongkui
Published: (2019)
Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation
by: Hao, Nicole
Published: (2026)
by: Hao, Nicole
Published: (2026)
How Analysis Can Teach Us the Optimal Way to Design Neural Operators
by: Le, Vu-Anh, et al.
Published: (2024)
by: Le, Vu-Anh, et al.
Published: (2024)
Horizon Activation Mapping for Neural Networks in Time Series Forecasting
by: Hans, Krupakar, et al.
Published: (2026)
by: Hans, Krupakar, et al.
Published: (2026)
Controlled Learning of Pointwise Nonlinearities in Neural-Network-Like Architectures
by: Unser, Michael, et al.
Published: (2024)
by: Unser, Michael, et al.
Published: (2024)
The Parametric Complexity of Operator Learning
by: Lanthaler, Samuel, et al.
Published: (2023)
by: Lanthaler, Samuel, et al.
Published: (2023)
Stable Learning Using Spiking Neural Networks Equipped With Affine Encoders and Decoders
by: Neuman, A. Martina, et al.
Published: (2024)
by: Neuman, A. Martina, et al.
Published: (2024)
Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning
by: Berner, Julius, et al.
Published: (2025)
by: Berner, Julius, et al.
Published: (2025)
Neural networks in non-metric spaces
by: Galimberti, Luca
Published: (2024)
by: Galimberti, Luca
Published: (2024)
Neural Hilbert Ladders: Multi-Layer Neural Networks in Function Space
by: Chen, Zhengdao
Published: (2023)
by: Chen, Zhengdao
Published: (2023)
Merging Memory and Space: A State Space Neural Operator
by: Koren, Nodens, et al.
Published: (2025)
by: Koren, Nodens, et al.
Published: (2025)
Data Complexity Estimates for Operator Learning
by: Kovachki, Nikola B., et al.
Published: (2024)
by: Kovachki, Nikola B., et al.
Published: (2024)
Nonlocality and Nonlinearity Implies Universality in Operator Learning
by: Lanthaler, Samuel, et al.
Published: (2023)
by: Lanthaler, Samuel, et al.
Published: (2023)
Neural reproducing kernel Banach spaces and representer theorems for deep networks
by: Bartolucci, Francesca, et al.
Published: (2024)
by: Bartolucci, Francesca, et al.
Published: (2024)
Why High-rank Neural Networks Generalize?: An Algebraic Framework with RKHSs
by: Hashimoto, Yuka, et al.
Published: (2025)
by: Hashimoto, Yuka, et al.
Published: (2025)
Kantorovich--Kernel Neural Operators: Approximation Theory, Asymptotics, and Neural Network Interpretation
by: He, Tian-Xiao
Published: (2026)
by: He, Tian-Xiao
Published: (2026)
Operator Learning: Algorithms and Analysis
by: Kovachki, Nikola B., et al.
Published: (2024)
by: Kovachki, Nikola B., et al.
Published: (2024)
Sparse-Aware Neural Networks for Nonlinear Functionals: Mitigating the Exponential Dependence on Dimension
by: Li, Jianfei, et al.
Published: (2026)
by: Li, Jianfei, et al.
Published: (2026)
Bridging Smoothness and Approximation: Theoretical Insights into Over-Smoothing in Graph Neural Networks
by: Yang, Guangrui, et al.
Published: (2024)
by: Yang, Guangrui, et al.
Published: (2024)
Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees
by: Mukherjee, Amartya, et al.
Published: (2026)
by: Mukherjee, Amartya, et al.
Published: (2026)
Noncommutative $C^*$-algebra Net: Learning Neural Networks with Powerful Product Structure in $C^*$-algebra
by: Hataya, Ryuichiro, et al.
Published: (2023)
by: Hataya, Ryuichiro, et al.
Published: (2023)
Upper Approximation Bounds for Neural Oscillators
by: Huang, Zifeng, et al.
Published: (2025)
by: Huang, Zifeng, et al.
Published: (2025)
Langevin Monte-Carlo Provably Learns Depth Two Neural Nets at Any Size and Data
by: Kumar, Dibyakanti, et al.
Published: (2025)
by: Kumar, Dibyakanti, et al.
Published: (2025)
Pointwise Generalization in Deep Neural Networks
by: Li, Shaojie, et al.
Published: (2026)
by: Li, Shaojie, et al.
Published: (2026)
Understanding Transfer Learning via Mean-field Analysis
by: Aminian, Gholamali, et al.
Published: (2024)
by: Aminian, Gholamali, et al.
Published: (2024)
A Fractional Fox H-Function Kernel for Support Vector Machines: Robust Classification via Weighted Transmutation Operators
by: Dorrego, Gustavo
Published: (2026)
by: Dorrego, Gustavo
Published: (2026)
Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels
by: Yang, Jia-Qi, et al.
Published: (2025)
by: Yang, Jia-Qi, et al.
Published: (2025)
Featured Reproducing Kernel Banach Spaces for Learning and Neural Networks
by: de la Higuera, Isabel, et al.
Published: (2026)
by: de la Higuera, Isabel, et al.
Published: (2026)
Fitting Auditory Filterbanks with Multiresolution Neural Networks
by: Lostanlen, Vincent, et al.
Published: (2023)
by: Lostanlen, Vincent, et al.
Published: (2023)
A Probabilistic Framework for Solving High-Frequency Helmholtz Equations via Diffusion Models
by: Zou, Yicheng, et al.
Published: (2026)
by: Zou, Yicheng, et al.
Published: (2026)
A Multiplicative Neural Network Architecture: Locality and Regularity of Approximation
by: Choi, Hee-Sun, et al.
Published: (2026)
by: Choi, Hee-Sun, et al.
Published: (2026)
Learning Operators with Stochastic Gradient Descent in General Hilbert Spaces
by: Shi, Lei, et al.
Published: (2024)
by: Shi, Lei, et al.
Published: (2024)
A Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning
by: Yang, Jia-Qi, et al.
Published: (2025)
by: Yang, Jia-Qi, et al.
Published: (2025)
Approximation by Neural Network Sampling Operators in Mixed Lebesgue Spaces
by: Dey, Arpan Kumar, et al.
Published: (2025)
by: Dey, Arpan Kumar, et al.
Published: (2025)
Similar Items
-
Discretization Error of Fourier Neural Operators
by: Lanthaler, Samuel, et al.
Published: (2024) -
Approximation by Steklov Neural Network Operators
by: Karaman, S. N., et al.
Published: (2024) -
Operator Learning of Lipschitz Operators: An Information-Theoretic Perspective
by: Lanthaler, Samuel
Published: (2024) -
Parseval Convolution Operators and Neural Networks
by: Unser, Michael, et al.
Published: (2024) -
Convergence Analysis of Max-Min Exponential Neural Network Operators in Orlicz Space
by: Pradhan, Satyaranjan, et al.
Published: (2025)