Develop a predictive mechanistic theory of robustness

Develop a mechanistic theory or diagnostic that predicts in advance when a given Oscillatory Predictive Learning configuration will be robust to adversarial perturbations.

Background

The experiments show that robustness depends sensitively on architectural and dynamical choices, particularly oscillator dimension, integration steps, randomness, and predictive-pretraining settings. However, the reported hyperparameter sweeps identify robust and non-robust configurations empirically rather than providing a principled criterion for predicting robustness before training or evaluation.

A predictive theory or diagnostic would help explain the narrow robust regime observed for OPL and guide the design of configurations beyond the CIFAR-10 and CIFAR-100 experiments.

References

Although the contrast between the $N{=}2$ and $N{=}4$ regimes suggests that oscillatory dynamics matter, we do not yet provide a mechanistic theory or diagnostic that predicts in advance when a given configuration will be robust.

— Neither Adversarial Training Nor Purification: Emergent Adversarial Robustness from Oscillatory Predictive Learning  (2609.08683 - Habibi et al., 8 Sep 2026) in Section "Discussion, Trade-offs, and Limitations," paragraph "Limitations"