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The remarkable success of the Transformer model in Natural Language Processing (NLP) is increasingly capturing the attention of vision researchers in contemporary times. The Vision Transformer (ViT) model effectively models long-range dependencies while utilizing a self-attention mechanism by converting image information into meaningful representations. Moreover, the parallelism property of ViT ensures better scalability and model generalization compared to Recurrent Neural Networks (RNN). However, developing robust ViT models for high-risk vision applications, such as self-driving cars, is critical. Deterministic ViT models are susceptible to noise and adversarial attacks and incapable of yielding a level of confidence in output predictions. Quantifying the confidence (or uncertainty) level in the decision is highly important in such real-world applications. In this work, we introduce a probabilistic framework for ViT to quantify the level of uncertainty in the model's decision. We approximate the posterior distribution of network parameters using variational inference. While progressing through non-linear layers, the first-order Taylor approximation was deployed. The developed framework propagates the mean and covariance of the posterior distribution through layers of the probabilistic ViT model and quantifies uncertainty at the output predictions. Quantifying uncertainty aids in providing warning signals to real-world applications in case of noisy situations. Experimental results from extensive simulation conducted on numerous benchmark datasets (e.g., MNIST and Fashion-MNIST) for image classification tasks exhibit 1) higher accuracy of proposed probabilistic ViT under noise or adversarial attacks compared to the deterministic ViT. 2) Self-evaluation through uncertainty becomes notably pronounced as noise levels escalate. Simulations were conducted at the Texas Advanced Computing Center (TACC) on the Lonestar6 supercomputer node. With the help of this vital resource, we completed all the experiments within a reasonable period. 

Synthetic aperture radar (SAR) image classification is a challenging problem due to the complex imaging mechanism as well as the random speckle noise, which affects radar image interpretation. Recently, convolutional neural networks (CNNs) have been shown to outperform previous state-of-the-art techniques in computer vision tasks owing to their ability to learn relevant features from the data. However, CNNs in particular and neural networks, in general, lack uncertainty quantification and can be easily deceived by adversarial attacks. This paper proposes Bayes-SAR Net, a Bayesian CNN that can perform robust SAR image classification while quantifying the uncertainty or confidence of the network in its decision. Bayes-SAR Net propagates the first two moments (mean and covariance) of the approximate posterior distribution of the network parameters given the data and obtains a predictive mean and covariance of the classification output. Experiments, using the benchmark datasets Flevoland and Oberpfaffenhofen, show superior performance and robustness to Gaussian noise and adversarial attacks, as compared to the SAR-Net homologue. Bayes-SAR Net achieves a test accuracy that is around 10% higher in the case of adversarial perturbation (levels > 0.05).