The emergence of vision-language foundation models, such as CLIP, has revolutionized image-text representation, enabling a broad range of applications via prompt learning. Despite its promise, real-world datasets often contain noisy labels that can degrade prompt learning performance. In this paper, we demonstrate that using mean absolute error (MAE) loss in prompt learning, named PromptMAE, significantly enhances robustness against noisy labels while maintaining high accuracy. Though MAE is straightforward and recognized for its robustness, it is rarely used in noisy-label learning due to its slow convergence and poor performance outside prompt learning scenarios. To elucidate the robustness of PromptMAE, we leverage feature learning theory to show that MAE can suppress the influence of noisy samples, thereby improving the signal-to-noise ratio and enhancing overall robustness. Additionally, we introduce PromptOT, a prompt-based optimal transport data purification method to enhance the robustness further. PromptOT employs text features in vision-language models as prototypes to construct an optimal transportation matrix. This matrix effectively partitions datasets into clean and noisy subsets, allowing for the application of cross-entropy loss to the clean subset and MAE loss to the noisy subset. Our Noise-Label Prompt Learning method, named NLPrompt, offers a simple and efficient approach that leverages the expressive representations and precise alignment capabilities of vision-language models for robust prompt learning. We validate NLPrompt through extensive experiments across various noise settings, demonstrating significant performance improvements.

Integrating pretrained vision-language foundation models like CLIP into federated learning has attracted significant attention for enhancing generalization across diverse tasks. Typically, federated learning of vision-language models employs prompt learning to reduce communication and computational costs, i.e., prompt-based federated learning. However, there is limited theoretical analysis to understand the performance of prompt-based federated learning. In this work, we construct a theoretical analysis framework for prompt-based federated learning via feature learning theory. Specifically, we monitor the evolution of signal learning and noise memorization in prompt-based federated learning, demonstrating that performance can be assessed by the ratio of task-relevant to task-irrelevant coefficients. Furthermore, we draw an analogy between income and risk in portfolio optimization and the task-relevant and task-irrelevant terms in feature learning. Leveraging inspiration from portfolio optimization that combining two independent assets will maintain the income while reducing the risk, we introduce two prompts: global prompt and local prompt to construct a prompt portfolio to balance the generalization and personalization. Consequently, we showed the performance advantage of the prompt portfolio and derived the optimal mixing coefficient. These theoretical claims have been further supported by empirical experiments.

Machine learning methods suffer from test-time performance degeneration when faced with out-of-distribution (OoD) data whose distribution is not necessarily the same as training data distribution. Although a plethora of algorithms have been proposed to mitigate this issue, it has been demonstrated that achieving better performance than ERM simultaneously on different types of distributional shift datasets is challenging for existing approaches. Besides, it is unknown how and to what extent these methods work on any OoD datum without theoretical guarantees. In this paper, we propose a certifiable out-of-distribution generalization method that provides provable OoD generalization performance guarantees via a functional optimization framework leveraging random distributions and max-margin learning for each input datum. With this approach, the proposed algorithmic scheme can provide certified accuracy for each input datum's prediction on the semantic space and achieves better performance simultaneously on OoD datasets dominated by correlation shifts or diversity shifts. Our code is available at https://github.com/ZlatanWilliams/StochasticDisturbanceLearning.