The Cost of Robustness: Tighter Bounds on Parameter Complexity for Robust Memorization in ReLU Nets
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911237085855744 |
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| author | Kim, Yujun Moon, Chaewon Yun, Chulhee |
| author_facet | Kim, Yujun Moon, Chaewon Yun, Chulhee |
| contents | We study the parameter complexity of robust memorization for $\mathrm{ReLU}$ networks: the number of parameters required to interpolate any given dataset with $ε$-separation between differently labeled points, while ensuring predictions remain consistent within a $μ$-ball around each training sample. We establish upper and lower bounds on the parameter count as a function of the robustness ratio $ρ= μ/ ε$. Unlike prior work, we provide a fine-grained analysis across the entire range $ρ\in (0,1)$ and obtain tighter upper and lower bounds that improve upon existing results. Our findings reveal that the parameter complexity of robust memorization matches that of non-robust memorization when $ρ$ is small, but grows with increasing $ρ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24643 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Cost of Robustness: Tighter Bounds on Parameter Complexity for Robust Memorization in ReLU Nets Kim, Yujun Moon, Chaewon Yun, Chulhee Machine Learning Artificial Intelligence We study the parameter complexity of robust memorization for $\mathrm{ReLU}$ networks: the number of parameters required to interpolate any given dataset with $ε$-separation between differently labeled points, while ensuring predictions remain consistent within a $μ$-ball around each training sample. We establish upper and lower bounds on the parameter count as a function of the robustness ratio $ρ= μ/ ε$. Unlike prior work, we provide a fine-grained analysis across the entire range $ρ\in (0,1)$ and obtain tighter upper and lower bounds that improve upon existing results. Our findings reveal that the parameter complexity of robust memorization matches that of non-robust memorization when $ρ$ is small, but grows with increasing $ρ$. |
| title | The Cost of Robustness: Tighter Bounds on Parameter Complexity for Robust Memorization in ReLU Nets |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2510.24643 |