Learning to generalize at test time

The generalization ability, which effectively applies learned knowledge from seen contexts to unfamiliar situations, is a hallmark of human intelligence but remains a significant challenge for current artificial intelligence systems. Machine learning algorithms typically rely on the assumption that training and test data share the same distributions. Consequently, when confronted with distribution shifts, they exhibit substantial performance degradation. This thesis addresses the crucial problem of enhancing generalization capabilities, specifically at test time, without access to test data during training. The thesis is structured by: 1) Generalized model-learning at training time by invariant learning with Bayesian neural networks; 2) Generalized model-learning at test time by directly adapting models to individual test samples through meta-learning and variational inference techniques, without labels and extra test information; 3) Generalized sample-learning at test time by adapting test samples to training distributions with energy-based models, avoiding model adjustment and catastrophic forgetting; 4) Generalized prompt-learning at test time for multimodal foundation models through innovative prompt-learning frameworks, including test task-specific prompt generation across any type of distribution shifts and dynamic test-time prompt tuning for online prompt update. Each of these chapters introduces innovative methods with detailed methodologies and experimental results, suggesting a comprehensive approach to improving generalization ability at test time. Finally, we further investigate 5) generalization at test time in the past and future and provide a comprehensive and systematic review of test-time adaptation to summarize the advances of generalization at test time and provide an outlook for the future development.