Many deployed learning systems must update models on streaming data under memory constraints. The default strategy, sequential fine-tuning on each new phase, is architecture-agnostic but often suffers catastrophic forgetting when later phases correspond to different sub-populations or tasks. Replay with a finite buffer is a simple alternative, yet its behaviour across generative and predictive objectives is not well understood. We present a unified study of stateful replay for streaming autoencoding, time series forecasting, and classification. We view both sequential fine-tuning and replay as stochastic gradient methods for an ideal joint objective, and use a gradient alignment analysis to show when mixing current and historical samples should reduce forgetting. We then evaluate a single replay mechanism on six streaming scenarios built from Rotated MNIST, ElectricityLoadDiagrams 2011-2014, and Airlines delay data, using matched training budgets and three seeds. On heterogeneous multi task streams, replay reduces average forgetting by a factor of two to three, while on benign time based streams both methods perform similarly. These results position stateful replay as a strong and simple baseline for continual learning in streaming environments.

Understanding the inner workings of machine learning models like Transformers is vital for their safe and ethical use. This paper presents an in-depth analysis of a one-layer Transformer model trained for n-digit integer addition. We reveal that the model divides the task into parallel, digit-specific streams and employs distinct algorithms for different digit positions. Our study also finds that the model starts calculations late but executes them rapidly. A rare use case with high loss is identified and explained. Overall, the model's algorithm is explained in detail. These findings are validated through rigorous testing and mathematical modeling, contributing to the broader works in Mechanistic Interpretability, AI safety, and alignment. Our approach opens the door for analyzing more complex tasks and multi-layer Transformer models.

Unlike its intercept, a linear classifier's weight vector cannot be tuned by a simple grid search. Hence, this paper proposes weight vector tuning of a generic binary linear classifier through the parameterization of a decomposition of the discriminant by a scalar which controls the trade-off between conflicting informative and noisy terms. By varying this parameter, the original weight vector is modified in a meaningful way. Applying this method to a number of linear classifiers under a variety of data dimensionality and sample size settings reveals that the classification performance loss due to non-optimal native hyperparameters can be compensated for by weight vector tuning. This yields computational savings as the proposed tuning method reduces to tuning a scalar compared to tuning the native hyperparameter, which may involve repeated weight vector generation along with its burden of optimization, dimensionality reduction, etc., depending on the classifier. It is also found that weight vector tuning significantly improves the performance of Linear Discriminant Analysis (LDA) under high estimation noise. Proceeding from this second finding, an asymptotic study of the misclassification probability of the parameterized LDA classifier in the growth regime where the data dimensionality and sample size are comparable is conducted. Using random matrix theory, the misclassification probability is shown to converge to a quantity that is a function of the true statistics of the data. Additionally, an estimator of the misclassification probability is derived. Finally, computationally efficient tuning of the parameter using this estimator is demonstrated on real data. Alouni, and T. Y. Al-Naffouri are with the Electrical and Computer Engineering Program, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia; emails: {lama.niyazi,

In the absence of explicit regularization, Kernel "Ridgeless" Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still generalize well on test data. We isolate a phenomenon of implicit regularization for minimum-norm interpolated solutions which is due to a combination of high dimensionality of the input data, curvature of the kernel function, and favorable geometric properties of the data such as an eigenvalue decay of the empirical covariance and kernel matrices. In addition to deriving a data-dependent upper bound on the out-of-sample error, we present experimental evidence suggesting that the phenomenon occurs in the MNIST dataset.