Robustness and Accuracy Could Be Reconcilable by (Proper) Definition (2202.10103v2)

Abstract: The trade-off between robustness and accuracy has been widely studied in the adversarial literature. Although still controversial, the prevailing view is that this trade-off is inherent, either empirically or theoretically. Thus, we dig for the origin of this trade-off in adversarial training and find that it may stem from the improperly defined robust error, which imposes an inductive bias of local invariance -- an overcorrection towards smoothness. Given this, we advocate employing local equivariance to describe the ideal behavior of a robust model, leading to a self-consistent robust error named SCORE. By definition, SCORE facilitates the reconciliation between robustness and accuracy, while still handling the worst-case uncertainty via robust optimization. By simply substituting KL divergence with variants of distance metrics, SCORE can be efficiently minimized. Empirically, our models achieve top-rank performance on RobustBench under AutoAttack. Besides, SCORE provides instructive insights for explaining the overfitting phenomenon and semantic input gradients observed on robust models. Code is available at https://github.com/P2333/SCORE.

• The paper redefines robust error by introducing SCORE, substituting local invariance with local equivariance to harmonize adversarial robustness and model accuracy.
• It employs distance metrics and convex functions to derive bounds that optimize SCORE, achieving convergence comparable to traditional methods like TRADES.
• The approach enhances sample efficiency in finite settings and opens new avenues for mitigating semantic gradient issues and overfitting in adversarial training.

Robustness-Accuracy Trade-off and Self-Consistent Robust Error

In the field of adversarial robustness, the trade-off between robustness and accuracy has been extensively explored, predominantly with the assertion that such a trade-off is inherently embedded both empirically and theoretically. This paper by Pang et al. addresses the core issue of this trade-off, proposing that the crux lies within the improperly defined robust error in adversarial training. The authors argue that the prominent robust error models emphasize local invariance excessively, leading to smoothness overcorrection, which may compromise model accuracy. To counteract such deficiency, the researchers put forward the Self-COnsistent Robust Error (SCORE)—a framework designed to harmonize robustness and accuracy using local equivariance, thereby fostering a model that adheres to robust optimization principles while managing worst-case uncertainties.

Key Insights and Contributions

The paper starts by revisiting traditional definitions of robust error, such as those formulated by Madry et al., and highlights the proclivity towards inductive biases that impose local invariance, often leading to over-smoothed model behaviors. The introduction of SCORE redefines the robust error by substituting local invariance with equivariance. This change enables the robust model to converge more closely to the data distribution, effectively aligning robustness and accuracy.

To optimize SCORE practically, the authors explore the replacement of KL divergence with distance metrics, which furnish upper and lower bounds aiding efficient optimization. Significant observations include:

• Bounding Mechanism: The bounds ascertain that optimizing traditional robust errors can guide the optimization of SCORE, keeping revisions within practical limits.
• Monotonic Function Utilization: By employing monotonically increasing convex functions over distance metrics, more efficient and effective learning paths are forged.
• Equivalent Parameter Space: The paper indicates an equivalence between distance-metric-based robust errors and traditional methods like TRADES, maintaining comparable learning surfaces in optimizations.

Implications and Future Directions

The implications of SCORE are multifaceted:

1. Theoretical Consistency: The method suggests evolving robustness definitions in research to better align functionality with expected outcomes, altering theoretical underpinnings to accommodate equivariance over invariance.
2. Enhanced Sample Efficiency: In finite-sample scenarios, SCORE's alignment with robust optimization principles leverages improved model training even under sample constraints.
3. Semantic Gradients and Overfitting: The insights into semantic gradients and overfitting phenomena open avenues for further exploration into generative characteristics in adversarial training.

Future developments in AI, particularly in adversarial training, could benefit from SCORE's alignment methodologies, which promise consistency and reliability in model performance across diverse adversarial landscapes. Current pragmatic applications under high-dimensional attack scenarios already demonstrate empirical improvement, positioning SCORE as a valuable reference point for ongoing machine learning advancements.

Conclusion

This paper by Pang et al. enriches the understanding of adversarial robustness by not merely juxtaposing robustness and accuracy but redefining foundational error metrics to reconcile the two. By transforming the essence of robust error definitions to nurture equivariance, SCORE demonstrates potential pathways to overcome inherent adversarial training dilemmas, guiding future AI systems toward enhanced, mutually inclusive performance metrics. As AI continues to evolve, the SCORE framework offers a compelling direction for both theoretical and empirical explorations.