# Error bounds for deep ReLU networks using the Kolmogorov--Arnold superposition theorem

arXiv: https://arxiv.org/abs/1906.11945 · HTML: https://mlsanity.com/paper/1906.11945/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2019.

## Built on by (most cited first, 30 of 49)

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- [KAC: Kolmogorov-Arnold Classifier for Continual Learning](https://mlsanity.com/paper/2503.21076/) (2025)
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## Abstract (arXiv)

We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks, for which the curse of the dimensionality is lessened. Our theorem is based on a constructive proof of the Kolmogorov--Arnold superposition theorem, and on a subset of multivariate continuous functions whose outer superposition functions can be efficiently approximated by deep ReLU networks.