Computer Science > Machine Learning
arXiv:2603.09589 (cs)
[Submitted on 10 Mar 2026]
Title:Memorization capacity of deep ReLU neural networks characterized by width and depth
View a PDF of the paper titled Memorization capacity of deep ReLU neural networks characterized by width and depth, by Xin Yang and 1 other authors
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Abstract:This paper studies the memorization capacity of deep neural networks with ReLU activation. Specifically, we investigate the minimal size of such networks to memorize any $N$ data points in the unit ball with pairwise separation distance $\delta$ and discrete labels. Most prior studies characterize the memorization capacity by the number of parameters or neurons. We generalize these results by constructing neural networks, whose width $W$ and depth $L$ satisfy $W^2L^2= \mathcal{O}(N\log(\delta^{-1}))$, that can memorize any $N$ data samples. We also prove that any such networks should also satisfy the lower bound $W^2L^2=\Omega (N \log(\delta^{-1}))$, which implies that our construction is optimal up to logarithmic factors when $\delta^{-1}$ is polynomial in $N$. Hence, we explicitly characterize the trade-off between width and depth for the memorization capacity of deep neural networks in this regime.
| Subjects: | Machine Learning (cs.LG); Numerical Analysis (math.NA) |
| Cite as: | arXiv:2603.09589 [cs.LG] |
| (or arXiv:2603.09589v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2603.09589
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View a PDF of the paper titled Memorization capacity of deep ReLU neural networks characterized by width and depth, by Xin Yang and 1 other authors
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