Automatic Perturbation Analysis for Scalable Certified Robustness and Beyond (2002.12920v3)

Abstract: Linear relaxation based perturbation analysis (LiRPA) for neural networks, which computes provable linear bounds of output neurons given a certain amount of input perturbation, has become a core component in robustness verification and certified defense. The majority of LiRPA-based methods focus on simple feed-forward networks and need particular manual derivations and implementations when extended to other architectures. In this paper, we develop an automatic framework to enable perturbation analysis on any neural network structures, by generalizing existing LiRPA algorithms such as CROWN to operate on general computational graphs. The flexibility, differentiability and ease of use of our framework allow us to obtain state-of-the-art results on LiRPA based certified defense on fairly complicated networks like DenseNet, ResNeXt and Transformer that are not supported by prior works. Our framework also enables loss fusion, a technique that significantly reduces the computational complexity of LiRPA for certified defense. For the first time, we demonstrate LiRPA based certified defense on Tiny ImageNet and Downscaled ImageNet where previous approaches cannot scale to due to the relatively large number of classes. Our work also yields an open-source library for the community to apply LiRPA to areas beyond certified defense without much LiRPA expertise, e.g., we create a neural network with a probably flat optimization landscape by applying LiRPA to network parameters. Our opensource library is available at https://github.com/KaidiXu/auto_LiRPA.

• The paper introduces an automated framework that generalizes LiRPA by employing forward and backward bound propagation across various neural architectures.
• The paper integrates a loss fusion technique and dynamic programming to enhance scalability and extend robustness analysis to NLP tasks.
• The paper demonstrates that the approach achieves improved certified robustness and efficiency across datasets like CIFAR-10, Tiny ImageNet, and SST-2.

Automatic Perturbation Analysis for Scalable Certified Robustness and Beyond

The paper "Automatic Perturbation Analysis for Scalable Certified Robustness and Beyond" presents an advanced methodology designed to extend the applicability of Linear Relaxation-based Perturbation Analysis (LiRPA) by automating perturbation analysis in diverse neural network architectures. This work targets robustness verification and certified defense mechanisms by implementing automatic differentiation methodologies analogous to backpropagation, but aimed at determining bounds rather than gradients.

Key Contributions and Methodologies

1. Automatic Generalization of LiRPA: The paper meticulously describes a framework for automatically applying perturbation analysis across any neural network model. By leveraging a generalized approach applicable to any computational graph, this method provides a seamless solution for previously unsupported architectures like DenseNet, ResNeXt, and Transformer networks. This innovation positions the approach as a comprehensive tool, facilitating perturbation analysis without the need for specialized LiRPA expertise.
2. Forward and Backward Bound Propagation: This framework capitalizes on forward and backward modes of LiRPA for conducting perturbation analyses. The forward mode propagates bounds based on the independent nodes, whereas the backward mode focuses on dependent nodes, recursively extending the bounds in a manner akin to gradient computations in backpropagation.
3. Loss Fusion Technique: A significant novelty introduced is the loss fusion technique, which enhances scalability. This method integrates the computation of robust loss directly, effectively bypassing the computational challenges posed by large output layers—especially pertinent in datasets with numerous classes, like Tiny ImageNet.
4. Dynamic Programming for NLP Applications: Addressing non-traditional perturbations, the authors extend their framework to handle semantic perturbations like synonym-based word substitutions in NLP tasks. This capability is supported by a dynamic programming approach, notoriously efficient for such discrete settings, which reflects the versatility of their method beyond typical $\ell_p$ perturbations.
5. Scalability and Efficiency: The open-source library initially rolled out by the authors as part of this work significantly lowers the barrier for employing LiRPA in various scenarios beyond certified defense, reinforcing its use in non-robustness related inquiries, such as flatness analysis in optimization landscapes.

Experimental Analysis

Through several experimental setups, including CIFAR-10, Tiny-ImageNet, and SST-2 datasets, the framework demonstrated a marked ability to improve both efficiency and certified robustness metrics of complex network models. Notably, the utilization of loss fusion considerably expedited the training processes, achieving times close to standard training routines while maintaining verifiable robustness standards.

Implications and Future Directions

The findings from this research hold profound implications for the development of more generalized, flexible adversarial defense systems that can be easily applied across a range of existing network models without necessitating custom LiRPA adjustments. The framework’s ability to scale efficiently, encompassed with robust evaluation mechanisms, paves the way for more widespread application in safety-critical industries, such as autonomous driving and secure communications.

In terms of future developments, exploring additional perturbation settings within the same automatic framework presents a viable pathway. Further refinement of the computational graph propagation strategies could closely align execution times with those of simpler, non-defensive training regimes, therefore broadening the practical utility of these techniques in real-time deployment scenarios.

In summary, this paper significantly scales the promise of certified defense architectures by introducing a highly adaptable and efficient perturbation analysis framework. The synthesis of LiRPA with automatic differentiation stylings renders this approach readily applicable to both verification tasks and broader explorations within AI, enhancing resiliency and interpretability across machine learning models.