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

We study the parameter complexity of robust memorization for ReLU networks: the number of parameters required to interpolate any dataset with $\epsilon$ -separation between differently labeled points, while ensuring predictions remain consistent within a $\mu$ -ball around each training example. 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 $\rho$ .

In 3rd Workshop on High-dimensional Learning Dynamics (HiLD), International Conference on Machine Learning 2025