Robustness of deep learning classification to adversarial input on GPUs: asynchronous parallel accumulation is a source of vulnerability

The ability of machine learning (ML) classification models to resist small, targeted input perturbations - known as adversarial attacks - is a key measure of their safety and reliability. We show that floating-point non associativity (FPNA) coupled with asynchronous parallel programming on GPUs is sufficient to result in misclassification, without any perturbation to the input. Additionally, we show this misclassification is particularly significant for inputs close to the decision boundary and that standard adversarial robustness results may be overestimated up to 4.6% when not considering machine-level details. We first study a linear classifier, before focusing on standard Graph Neural Network (GNN) architectures and datasets. We present a novel black-box attack using Bayesian optimization to determine external workloads that bias the output of reductions on GPUs and reliably lead to misclassification. Motivated by these results, we present a new learnable permutation (LP) gradient-based approach, to learn floating point operation orderings that lead to misclassifications, making the assumption that any reduction or permutation ordering is possible. This LP approach provides a worst-case estimate in a computationally efficient manner, avoiding the need to run identical experiments tens of thousands of times over a potentially large set of possible GPU states or architectures. Finally, we investigate parallel reduction ordering across different GPU architectures for a reduction under three conditions: (1) executing external background workloads, (2) utilizing multi-GPU virtualization, and (3) applying power capping. Our results demonstrate that parallel reduction ordering varies significantly across architectures under the first two conditions. The results and methods developed here can help to include machine-level considerations into adversarial robustness assessments.