F3arwin Site

$$\theta_t+1 = \theta_t - \eta \nabla_\theta \frac1 \sum \delta \in \mathcalP \textadv L(f \theta(x+\delta), y)$$

[5] Su, J., Vargas, D. V., & Sakurai, K. (2018). One pixel attack for fooling deep neural networks. IEEE Transactions on Evolutionary Computation .

f3arwin significantly outperforms prior genetic attacks due to adaptive mutation and SBX crossover, which preserves high-fitness perturbation structures. Compared to Square Attack, f3arwin requires 11% fewer queries for a similar ASR. On VGG-16 (unseen during attack generation), f3arwin perturbations crafted on ResNet-50 achieved 68.3% ASR, vs. 51.2% for Square Attack and 59.7% for standard genetic attack. This suggests that evolutionary perturbations capture more model-agnostic features. 5.3 Defensive Robustness | Defense Method | Clean Acc. | Robust Acc. (PGD) | Robust Acc. (f3arwin attack) | |----------------|------------|------------------|-------------------------------| | Standard | 92.1% | 0.3% | 0.1% | | PGD-AT | 88.4% | 51.2% | 43.5% | | TRADES | 87.9% | 53.1% | 46.2% | | f3arwin defense | 89.2% | 54.8% | 58.9% | f3arwin

[6] Zhang, H., Yu, Y., Jiao, J., Xing, E. P., Ghaoui, L. E., & Jordan, M. I. (2019). Theoretically principled trade-off between robustness and accuracy. ICML .

(1) f3arwin requires more computational time than PGD-AT for large models (≈3× training slowdown due to population evaluation). (2) The attack may fail on models with extremely non-smooth decision boundaries where crossover becomes destructive. (3) For very high-dimensional inputs (e.g., 224×224×3), the perturbation search space remains challenging without dimensionality reduction. $$\theta_t+1 = \theta_t - \eta \nabla_\theta \frac1 \sum

[2] Goodfellow, I. J., Shlens, J., & Szegedy, C. (2015). Explaining and harnessing adversarial examples. ICLR .

$$F(\delta) = \underbrace\mathbbI[f_\theta(x+\delta) \neq y] \cdot (1 - \textsoftmax(f_\theta(x+\delta)) y) \textMisclassification confidence - \lambda \cdot \frac\epsilon \sqrtd$$ One pixel attack for fooling deep neural networks

f3arwin defense yields against its own evolutionary attack compared to PGD-AT, and also generalizes better to PGD (54.8% vs 51.2%). This demonstrates that co-evolving attacks and defenses leads to a more balanced robustness. 5.4 Query Efficiency over Generations f3arwin converges to successful adversarial examples in a median of 38 generations (≈ 2280 queries) compared to 68 generations for standard genetic attack. The adaptive mutation rate prevents premature convergence and reduces wasted queries on low-fitness regions. 6. Discussion Why does evolution help robustness? Standard adversarial training uses a fixed attack method, creating a "gradient-aligned" robust region. Evolutionary attacks explore non-gradient directions, revealing vulnerabilities that gradient-based methods miss. f3arwin defense then closes these gaps, producing a model robust to a wider class of perturbations.