Representations embedded in the hyperbolic space have demonstrated significant improvements over their Euclidean counterparts across a variety of datasets, including images [1], natural languages [2], and complex tabular data such as single-cell sequencing [3]. On the other hand, learning and optimization on hyperbolic spaces are typically more involved than that on Euclidean spaces. Problems that are convex in Euclidean spaces become constrained non-convex problems in hyperbolic spaces. The hyperbolic Support Vector Machine (HSVM), as explored in recent studies [4, 5], exemplifies such challenges by presenting as a non-convex constrained programming problem that has been solved predominantly based on projected gradient descent. Attempts have been made to alleviate its non-convex nature through reparametrization [6] or developing a hyperbolic perceptron algorithm that converges to a separator with finetuning using adversarial samples to approximate the large-margin solution [7].

With the introduction of machine learning in high-stakes decision making, ensuring algorithmic fairness has become an increasingly important problem to solve. In response to this, many mathematical definitions of fairness have been proposed, and a variety of optimisation techniques have been developed, all designed to maximise a defined notion of fairness. However, fair solutions are reliant on the quality of the training data, and can be highly sensitive to noise. Recent studies have shown that robustness (the ability for a model to perform well on unseen data) plays a significant role in the type of strategy that should be used when approaching a new problem and, hence, measuring the robustness of these strategies has become a fundamental problem. In this work, we therefore propose a new criterion to measure the robustness of various fairness optimisation strategies - the robustness ratio. We conduct multiple extensive experiments on five bench mark fairness data sets using three of the most popular fairness strategies with respect to four of the most popular definitions of fairness. Our experiments empirically show that fairness methods that rely on threshold optimisation are very sensitive to noise in all the evaluated data sets, despite mostly outperforming other methods. This is in contrast to the other two methods, which are less fair for low noise scenarios but fairer for high noise ones. To the best of our knowledge, we are the first to quantitatively evaluate the robustness of fairness optimisation strategies. This can potentially can serve as a guideline in choosing the most suitable fairness strategy for various data sets.

The surge in multimodal AI's success has sparked concerns over data privacy in vision-and-language tasks. While CLIP has revolutionized multimodal learning through joint training on images and text, its potential to unintentionally disclose sensitive information necessitates the integration of privacy-preserving mechanisms. We introduce a differentially private adaptation of the Contrastive Language-Image Pretraining (CLIP) model that effectively addresses privacy concerns while retaining accuracy. Our proposed method, Dp-CLIP, is rigorously evaluated on benchmark datasets encompassing diverse vision-and-language tasks such as image classification and visual question answering. We demonstrate that our approach retains performance on par with the standard non-private CLIP model. Furthermore, we analyze our proposed algorithm under linear representation settings. We derive the convergence rate of our algorithm and show a trade-off between utility and privacy when gradients are clipped per-batch and the loss function does not satisfy smoothness conditions assumed in the literature for the analysis of DP-SGD.

Deep neural networks are widely known to be vulnerable to adversarial examples, especially showing significantly poor performance on adversarial examples generated under the white-box setting. However, most white-box attack methods rely heavily on the target model and quickly get stuck in local optima, resulting in poor adversarial transferability. The momentum-based methods and their variants are proposed to escape the local optima for better transferability. In this work, we notice that the transferability of adversarial examples generated by the iterative fast gradient sign method (I-FGSM) exhibits a decreasing trend when increasing the number of iterations. Motivated by this finding, we argue that the information of adversarial perturbations near the benign sample, especially the direction, benefits more on the transferability. Thus, we propose a novel strategy, which uses the Scheduled step size and the Dual example (SD), to fully utilize the adversarial information near the benign sample. Our proposed strategy can be easily integrated with existing adversarial attack methods for better adversarial transferability. Empirical evaluations on the standard ImageNet dataset demonstrate that our proposed method can significantly enhance the transferability of existing adversarial attacks.