- The paper presents YOPO, which leverages the maximal principle to reduce computational complexity in adversarial training.
- It adapts optimal control theory to perform a single propagation per update, backed by rigorous theoretical proofs.
- Empirical results on MNIST and CIFAR-10 show that YOPO achieves robust performance with significantly reduced training times.
You Only Propagate Once: Accelerating Adversarial Training via Maximal Principle
This manuscript proposes a novel methodology for improving the efficiency of adversarial training, a critical component in developing robust neural networks. The approach leverages the Maximum Principle of optimal control theory to accelerate adversarial training by reducing the computational complexity involved. The authors introduce the You Only Propagate Once (YOPO) method, which aims to minimize the iterative forward-backward propagation in adversarial training strategies, such as Projected Gradient Descent (PGD).
Problem Context and Theoretical Foundation
Adversarial training, especially with methods like PGD, typically involves significant computational costs due to multiple forward and backward passes through the network. This paper builds on the premise of conventional Pontryagin Maximum Principle (PMP) to derive a new form applicable to adversarial training. The authors meticulously prove the associated theorems to establish theoretical backing for the YOPO method.
The paper provides a rigorous proof of the maximal principle tailored for adversarial networks, drawing on the convexity of function sets in parameter space—a critical but reasonably attainable assumption in this context. This framework is applied to derive the Hamiltonian for each network layer, which dictates the optimal adversarial perturbation strategy.
Empirical Evaluation and Results
The paper's empirical section provides a comprehensive evaluation of the YOPO method on MNIST and CIFAR-10 datasets. For MNIST, YOPO-5-10 is shown to achieve performance on par with PGD-40, maintaining a trade-off between clean data accuracy and robustness under attack (96.27% for PGD-40 attack, 93.56% for CW attack).
For CIFAR-10, the YOPO-5-3 configuration outperforms equivalent PGD configurations in terms of robustness against adversarial attacks, achieving 44.72% under PGD-20 attack and 59.77% under CW attack. Notably, the computational efficiency is significantly improved, with training time reduced to approximately 71 minutes compared to 390 minutes for PGD-10.
The method is further extended to the TRADES framework, where TRADES-YOPO-3-4 achieves better robustness than TRADES-10 with lower computational requirements.
Implications and Future Directions
The YOPO approach represents a substantial advancement in reducing the computational load of adversarial training, which could facilitate the adoption of adversarial defenses in resource-constrained environments. The authors’ results suggest that efficient training can be achieved without significantly compromising on robustness.
While the results are promising, the paper opens avenues for future research, including the exploration of YOPO in conjunction with other adversarial training frameworks and its adaptation to larger and more complex datasets. Additionally, examining the impact of different neural architectures on YOPO's performance would provide deeper insights into the robustness and efficiency trade-offs.
Overall, the paper offers a significant contribution to the field, advancing our understanding of adversarial training and paving the way for more efficient implementations. As AI continued to be deployed in more diverse and populous fields, improving computational efficiency without sacrificing robustness will remain a key challenge.