For all the experiments in the paper, we used three different random seeds (0, 1, 2) and reported the average errors (and standard deviations). A.1 Baseline details We referred to the official implementations of the baselines. We use the reported best hyperparameters from their paper or code. We further tuned hyperparameters if there exists a hyperparameter selection guideline. Here, we provide additional details of the baseline implementations, including hyperparameters.

Test-time adaptation (TTA) is an emerging paradigm that addresses distributional shifts between training and testing phases without additional data acquisition or labeling cost; only unlabeled test data streams are used for continual model adaptation. Previous TTA schemes assume that the test samples are independent and identically distributed (i.i.d.), even though they are often temporally correlated (non-i.i.d.) in application scenarios, e.g., autonomous driving. We discover that most existing TTA methods fail dramatically under such scenarios. Motivated by this, we present a new test-time adaptation scheme that is robust against non-i.i.d.

Neural Collapse refers to the remarkable structural properties characterizing the geometry of class embeddings and classifier weights, found by deep nets when trained beyond zero training error. However, this characterization only holds for balanced data. Here we thus ask whether it can be made invariant to class imbalances. Towards this end, we adopt the unconstrained-features model (UFM), a recent theoretical model for studying neural collapse, and introduce Simplex-Encoded-Labels Interpolation (SELI) as an invariant characterization of the neural collapse phenomenon. We prove for the UFM with cross-entropy loss and vanishing regularization that, irrespective of class imbalances, the embeddings and classifiers always interpolate a simplexencoded label matrix and that their individual geometries are determined by the SVD factors of this same label matrix. We then present extensive experiments on synthetic and real datasets that confirm convergence to the SELI geometry. However, we caution that convergence worsens with increasing imbalances. We theoretically support this finding by showing that unlike the balanced case, when minorities are present, ridge-regularization plays a critical role in tweaking the geometry. This defines new questions and motivates further investigations into the impact of class imbalances on the rates at which first-order methods converge to their preferred solutions.

Reinforcement learning from human feedback (RLHF) provides a principled framework for aligning AI systems with human preference data. For various reasons, e.g., personal bias, context ambiguity, lack of training, etc, human annotators may give incorrect or inconsistent preference labels.

Recent works have presented methods to identify if individual text sequences were members of the model's training data, known as membership inference attacks (MIAs). We demonstrate that the apparent success of these MIAs is confounded by selecting non-members (text sequences not used for training) belonging to a different distribution from the members (e.g., temporally shifted recent Wikipedia articles compared with ones used to train the model). This distribution shift makes membership inference appear successful. However, most MIA methods perform no better than random guessing when discriminating between members and non-members from the same distribution (e.g., in this case, the same period of time). Even when MIAs work, we find that different MIAs succeed at inferring membership of samples from different distributions. Instead, we propose a new dataset inference method to accurately identify the datasets used to train large language models.