Neither Adversarial Training Nor Purification: Emergent Adversarial Robustness from Oscillatory Predictive Learning

Mohammed-Yassine Habibi, Klea Ziu, Martin Takáč, Makoto Yamada

arXiv preprint arXiv:2609.08683, 2026

Adversarial robustness
Self-supervised learning
Oscillatory neurons

Abstract

Adversarial robustness in computer vision is still largely achieved through adversarial training or test-time adversarial purification, both of which introduce significant computational overhead by generating adversarial examples during training or performing iterative denoising at test time. We study whether empirical robustness can instead emerge from architectural and representation-learning inductive biases.

We introduce Oscillatory Predictive Learning (OPL), a two-stage framework that combines Artificial Kuramoto Oscillatory Neurons (AKOrN) with predictive self-supervised pretraining using X-PhiNet. Because our default checkpoint uses randomized initial oscillator states, we compare it with other randomized adversarial defense methods that provide precise, reproducible, and strong attack protocols.

Experiments on CIFAR-10 and CIFAR-100, with additional corruption evaluation on CIFAR-10-C, demonstrate that our method achieves competitive results under the AutoAttack-rand evaluation protocol. On CIFAR-10 and CIFAR-100, OPL attains 76.63 ± 0.76 % and 50.44 % robust accuracy, respectively, under ℓ_∞, ε = 8/255, AutoAttack-rand with EoT K = 20.

Diagram of an Oscillatory Neurons Unit: a Kuramoto ODE updates the oscillator state X conditioned on the stimulus Y, and a feature extractor reads out the features — Oscillatory Neurons Unit used in the OPL encoder: the oscillator state evolves under a Kuramoto ODE conditioned on the input stimulus, and a feature extractor reads out the representation.

This paper extends our WiML @ NeurIPS 2025 workshop paper, started during my research internship at OIST.

Citation

Habibi, M.-Y., Ziu, K., Takáč, M., & Yamada, M. (2026). "Neither Adversarial Training Nor Purification: Emergent Adversarial Robustness from Oscillatory Predictive Learning." arXiv preprint arXiv:2609.08683.

@misc{habibi2026neither,
  title         = {Neither Adversarial Training Nor Purification: Emergent Adversarial Robustness from Oscillatory Predictive Learning},
  author        = {Habibi, Mohammed-Yassine and Ziu, Klea and Tak{\'a}{\v{c}}, Martin and Yamada, Makoto},
  year          = {2026},
  eprint        = {2609.08683},
  archivePrefix = {arXiv},
  primaryClass  = {cs.LG},
  url           = {https://arxiv.org/abs/2609.08683}
}