Neural network integral representations with the ReLU activation function
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Abstract (arXiv)
In this effort, we derive a formula for the integral representation of a shallow neural network with the ReLU activation function. We assume that the outer weighs admit a finite L1-norm with respect to Lebesgue measure on the sphere. For univariate target functions we further provide a closed-form formula for all possible representations. Additionally, in this case our formula allows one to explicitly solve the least L1-norm neural network representation for a given function.
Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Oct 2019.
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Citing papers per year: 2021: 2; 2022: 1; 2023: 1; 2024: 3; 2025: 0; 2026: 1.
8 papers.
- 2021Characterization of the Variation Spaces Corresponding to Shallow Neural Networkscited by 48
- 2024Neural Control Variates with Automatic Integrationcited by 5
- 2024Approximation with Random Shallow ReLU Networks with Applications to Model Reference Adaptive Controlcited by 4
- 2021Integral representations of shallow neural network with Rectified Power Unit activation functioncited by 2
- 2024Nonuniform random feature models using derivative informationcited by 2
- 2022Towards Global Neural Network Abstractions with Locally-Exact Reconstructioncited by 0
- 2023Function Approximation with Randomly Initialized Neural Networks for Approximate Model Reference Adaptive Controlcited by 0
- 2026Explicit integral representations and quantitative bounds for two-layer ReLU networkscited by 0
- 2026Explicit integral representations and quantitative bounds for two-layer ReLU networks25 Apr 2026
- 2024Nonuniform random feature models using derivative information3 Oct 2024
- 2024Neural Control Variates with Automatic Integration23 Sep 2024
- 2024Approximation with Random Shallow ReLU Networks with Applications to Model Reference Adaptive Control25 Mar 2024
- 2023Function Approximation with Randomly Initialized Neural Networks for Approximate Model Reference Adaptive Control28 Mar 2023
- 2022Towards Global Neural Network Abstractions with Locally-Exact Reconstruction21 Oct 2022
- 2021Integral representations of shallow neural network with Rectified Power Unit activation function20 Dec 2021
- 2021Characterization of the Variation Spaces Corresponding to Shallow Neural Networks28 Jun 2021