Memorization capacity of deep ReLU neural networks characterized by width and depth
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917329628037120 |
|---|---|
| author | Yang, Xin Yang, Yunfei |
| author_facet | Yang, Xin Yang, Yunfei |
| contents | 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 $δ$ 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 $W^2L^2= \mathcal{O}(N\log(δ^{-1}))$, that can memorize any $N$ data samples. We also prove that any such networks should also satisfy the lower bound $W^2L^2=Ω(N \log(δ^{-1}))$, which implies that our construction is optimal up to logarithmic factors when $δ^{-1}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09589 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Memorization capacity of deep ReLU neural networks characterized by width and depth Yang, Xin Yang, Yunfei Machine Learning Numerical Analysis 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 $δ$ 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 $W^2L^2= \mathcal{O}(N\log(δ^{-1}))$, that can memorize any $N$ data samples. We also prove that any such networks should also satisfy the lower bound $W^2L^2=Ω(N \log(δ^{-1}))$, which implies that our construction is optimal up to logarithmic factors when $δ^{-1}$ 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. |
| title | Memorization capacity of deep ReLU neural networks characterized by width and depth |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2603.09589 |