Learning a Sparse Representation of Barron Functions with the Inverse Scale Space Flow
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Abstract (arXiv)
This paper presents a method for finding a sparse representation of Barron functions. Specifically, given an L2 function f, the inverse scale space flow is used to find a sparse measure μ minimising the L2 loss between the Barron function associated to the measure μ and the function f. The convergence properties of this method are analysed in an ideal setting and in the cases of measurement noise and sampling bias. In an ideal setting the objective decreases strictly monotone in time to a minimizer with O(1/t), and in the case of measurement noise or sampling bias the optimum is achieved up to a multiplicative or additive constant. This convergence is preserved on discretization of the parameter space, and the minimizers on increasingly fine discretizations converge to the optimum on the full parameter space.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 17 of its 44 references that are in the map. First posted on arXiv 5 Dec 2023.
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17 of 44 references.
References · 17
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5 more
- 2021Neural Architecture Search via Bregman Iterationscited by 5
- 2023Neural Hilbert Ladders: Multi-Layer Neural Networks in Function Spacecited by 5
- 2023Embeddings between Barron spaces with higher order activation functionscited by 4
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Citing papers per year: 2026: 1.
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