Adv-BNN: Improved Adversarial Defense through Robust Bayesian Neural Network (1810.01279v2)

Abstract: We present a new algorithm to train a robust neural network against adversarial attacks. Our algorithm is motivated by the following two ideas. First, although recent work has demonstrated that fusing randomness can improve the robustness of neural networks (Liu 2017), we noticed that adding noise blindly to all the layers is not the optimal way to incorporate randomness. Instead, we model randomness under the framework of Bayesian Neural Network (BNN) to formally learn the posterior distribution of models in a scalable way. Second, we formulate the mini-max problem in BNN to learn the best model distribution under adversarial attacks, leading to an adversarial-trained Bayesian neural net. Experiment results demonstrate that the proposed algorithm achieves state-of-the-art performance under strong attacks. On CIFAR-10 with VGG network, our model leads to 14\% accuracy improvement compared with adversarial training (Madry 2017) and random self-ensemble (Liu 2017) under PGD attack with $0.035$ distortion, and the gap becomes even larger on a subset of ImageNet.

• The paper introduces Adv-BNN, which combines Bayesian inference with adversarial training to improve network robustness against adversarial attacks.
• It employs stochastic weight modeling by treating neural network weights as random variables within a min-max optimization framework.
• Experimental results demonstrate a 14% accuracy improvement on CIFAR-10 under PGD attacks, highlighting its potential for secure AI applications.

Overview of Adv-BNN: Improved Adversarial Defense through Robust Bayesian Neural Network

The paper introduces a novel approach named Adv-BNN, which seeks to enhance the robustness of neural networks against adversarial attacks. The rationale behind this method is founded upon two primary principles: integrating stochasticity through Bayesian Neural Networks (BNNs) and optimizing the network parameters within a min-max framework designed specifically for adversarial settings.

Deep neural networks are known for their susceptibility to adversarial attacks, where slight perturbations, often imperceptible to human observers, can deceive models into making incorrect predictions. Defending against such vulnerabilities is crucial, especially in domains where security and reliability are paramount.

Methodology

The Adv-BNN approach blends adversarial training with the benefits of Bayesian inference, a strategy not extensively explored at this scale prior to this paper. In essence, the method operates by treating network weights as stochastic variables, thereby turning every layer into a probabilistic entity governed by a distribution. This contrasts with typical BNN applications where randomness is usually relegated to inputs or specific hidden layers.

Key aspects of the methodology include:

• Stochastic Weight Modelling: Rather than uniformly applying noise to all layers, weights are treated as random variables characterized by learned distributions, thereby embedding stochasticity throughout the network architecture.
• Adversarial Training Integration: The authors propose a mini-max optimization framework to combine adversarial training with Bayesian inference. This involves iteratively solving for adversarial examples while simultaneously refining the weight distributions using their proposed method.
• Robustness Evaluation: Existing adversarial examples generated through established techniques (such as PGD attacks) were used to validate the effectiveness of this defense approach.

Experimental Results

Empirical validations were conducted on the CIFAR-10, STL10, and ImageNet143 datasets. The Adv-BNN demonstrated a significant improvement in accuracy, notably achieving a 14% lift under PGD attacks compared to state-of-the-art methods like adversarial training and Random Self-Ensemble on the CIFAR-10 dataset.

The results underscore the capability of Adv-BNN to mitigate the impact of adversarial perturbations more effectively than current defense strategies. The algorithm consistently outperformed its counterparts across various levels of attack intensity, indicating robustness to high-dimensional adversarial challenges.

Implications and Future Developments

The integration of Bayesian inference with adversarial training signifies a promising trajectory for developing resilient machine learning models. By optimizing model distributions in adversarial contexts, Adv-BNN not only fortifies defense but also opens pathways for more refined techniques wherein randomness can be utilized to counteract adversarial intricacies.

From a practical standpoint, Adv-BNN could be leveraged in applications demanding high-security assurance, such as autonomous driving, healthcare diagnostics, and financial forecasting systems. The scalability demonstrated across diverse datasets implies potential adaptability to even larger, more complex models.

Theoretically, the success of Adv-BNN prompts further exploration into the interplay between stochastic modeling and adversarial robustness. This could stimulate advancements in uncertainty quantification, potentially leading to innovative frameworks that simultaneously optimize for accuracy and security.

In conclusion, Adv-BNN introduces a potent defense mechanism against adversarial threats, combining Bayesian methodologies with robust optimization techniques, thereby driving forward the discourse on secure and reliable AI system development. This paper lays the groundwork for continued research into stochastic model reinforcement as a viable defense strategy in the ever-evolving landscape of AI threats.