Robust Convolutional Neural Networks under Adversarial Noise (1511.06306v2)

Abstract: Recent studies have shown that Convolutional Neural Networks (CNNs) are vulnerable to a small perturbation of input called "adversarial examples". In this work, we propose a new feedforward CNN that improves robustness in the presence of adversarial noise. Our model uses stochastic additive noise added to the input image and to the CNN models. The proposed model operates in conjunction with a CNN trained with either standard or adversarial objective function. In particular, convolution, max-pooling, and ReLU layers are modified to benefit from the noise model. Our feedforward model is parameterized by only a mean and variance per pixel which simplifies computations and makes our method scalable to a deep architecture. From CIFAR-10 and ImageNet test, the proposed model outperforms other methods and the improvement is more evident for difficult classification tasks or stronger adversarial noise.

• The paper proposes a novel stochastic noise integration in CNN layers to improve robustness against adversarial perturbations.
• The model modifies convolution, max-pooling, and ReLU layers by incorporating Gaussian noise parameters to encode uncertainty through the network.
• Empirical evaluations on CIFAR-10 and ImageNet show that the stochastic approach outperforms traditional adversarial training methods under noisy conditions.

Evaluation of Robust Convolutional Neural Networks under Adversarial Noise

The paper "Robust Convolutional Neural Networks under Adversarial Noise" by Jonghoon Jin, Aysegul Dundar, and Eugenio Culurciello addresses the vulnerability of Convolutional Neural Networks (CNNs) to adversarial noise, a critical issue in the domain of deep learning and computer vision. The authors propose a novel feedforward CNN architecture that integrates stochastic noise models to enhance robustness against adversarial perturbations, expanding on the conventional deterministic approaches to CNN design.

Core Contributions

The principal innovation of the paper is the introduction of stochastic noise to both the input images and the CNN layers, transforming traditional deterministic processing into stochastic modeling. This stochastic model is parameterized by mean and variance for each pixel, allowing it to incorporate the probabilistic nature of noise into the decision process. The adaptation is particularly focused on altering the convolution, max-pooling, and ReLU layers to encode uncertainty, with the assumption that adversarial perturbations approximate samples from a Gaussian noise model.

Methodology

The paper rigorously details the implementation of stochastic operations across various CNN layers. For instance, each input pixel is modeled as a Gaussian random variable, and the first and second moments are computed during convolution to retain the probabilistic nature of inputs throughout the network. The max-pooling operation is adjusted to iteratively calculate the maximum of Gaussian distributions, facilitating efficient and scalable approximation to avoid excessive computational load.

Through this framework, the paper champions the propagation of pixel uncertainty throughout the network architecture, culminating in improved adversarial robustness. This propagation enables CNNs to make informed classification decisions, even when confronted with noise-induced perturbations that would typically disrupt deterministic models.

Empirical Evaluation

The researchers empirically validate their approach on CIFAR-10 and ImageNet datasets, demonstrating the model's superiority over baseline and state-of-the-art adversarial training methods. Notably, the stochastic model achieves enhanced classification accuracy under adversarial conditions. On CIFAR-10, for example, the stochastic feedforward model achieves an accuracy of 82.9% under adversarial noise intensity, surpassing traditional methods. Similar trends are observed in ImageNet, though with reported hindrances in convergence when adversarial training exceeds certain noise levels.

Implications and Future Directions

This work advances the understanding of adversarial robustness in CNNs by presenting a scalable, probabilistic CNN model that successfully elevates performance where adversarial noise is prevalent. The efficacy of the model in difficult classification tasks and its scalability suggest a promising avenue for further research in defensive architectures against adversarial attacks, particularly for applications in security-sensitive environments.

Future explorations may consider optimizing the stochastic parameters algorithmically to minimize variance-induced numerical instability and refining this approach for deployment in real-time systems. Moreover, further integration of this stochastic model with ensemble methods or hybrid models could yield robust classifiers with balanced performance under standard and adversarial conditions.

In conclusion, this paper provides a significant step forward in building resilient CNN architectures that are both scalable and effective against adversarial noise, emphasizing the potential of stochastic modeling in deep learning networks.