The Cost of Robustness: Tighter Bounds on Parameter Complexity for Robust Memorization in ReLU Nets

• URL: http://arxiv.org/abs/2510.24643v1
• Date: Tue, 28 Oct 2025 17:09:43 GMT
• Title: The Cost of Robustness: Tighter Bounds on Parameter Complexity for Robust Memorization in ReLU Nets
• Authors: Yujun Kim, Chaewon Moon, Chulhee Yun,
• Abstract summary: We study the parameter complexity of robust memorization for $mathrmReLU$ networks.<n>We establish upper and lower bounds on the parameter count as a function of the robustness ratio $rho = mu / epsilon$.
• Score: 22.963810255498796
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the parameter complexity of robust memorization for $\mathrm{ReLU}$ networks: the number of parameters required to interpolate any given dataset with $\epsilon$-separation between differently labeled points, while ensuring predictions remain consistent within a $\mu$-ball around each training sample. We establish upper and lower bounds on the parameter count as a function of the robustness ratio $\rho = \mu / \epsilon$. Unlike prior work, we provide a fine-grained analysis across the entire range $\rho \in (0,1)$ 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 $\rho$ is small, but grows with increasing $\rho$.

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