Why the Maximum Second Derivative of Activations Matters for Adversarial Robustness
This work investigates the critical role of activation function curvature -- quantified by the maximum second derivative $\max|σ''|$ -- in adversarial robustness. Using the Recursive Curvature-Tunable Activation Family (RCT-AF), which enables precise control over curvature through parameters $α$ and $β$, we systematically analyze this relationship. Our study reveals a fundamental trade-off: insufficient curvature limits model expressivity, while excessive curvature amplifies the normalized Hessian diagonal norm of the loss, leading to sharper minima that hinder robust generalization. This results in a non-monotonic relationship where optimal adversarial robustness consistently occurs when...
| Authors | Yunrui Yu, Hang Su, Jun Zhu |
|---|---|
| Primary category | cs.LG |
| Published | 25 March 2026 |
| Last updated at source | 25 March 2026 |
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