Generalization and Memorization along the Learning Trajectory of Neural Language Models: A Geometric Account of Categorization

Memorization has been proposed as a mechanism to explain how language models fit the tail of their training distributions, but its training dynamics are not understood well. In this work, we take a fine-grained look at memorization by decomposing the loss trajectory of memorized sequences over training and model parameters. Across the Pythia family, we study memorization of duplicated training sequences (recitation) and rare ones (recollection). We find that memorization in both cases is characterized by sequence-level gradient alignment, though recitation suffers from misalignment with other training influences which causes forgetting, explaining the necessity for higher duplication of these examples. We further show that the lower model layers are the most involved in memorization and forgetting. Predicting memorization, our decomposition improves over a cross-entropy baseline, especially in larger models and early in training. Intervening on a small set of highly influential parameters we are able to ablate memorization in the final model. Together, these findings advance our understanding of how memorization develops during training and offer insights for predicting and intervening on it.

While unlearning seeks to negate undesired capabilities acquired through learning, little research has examined how the way models learn shapes their subsequent unlearning. In this paper, we investigate this connection from the perspectives of memorization and generalization, the two most representative yet competing strategies that models employ during training. We first classify memorization- and generalization-heavy models using grokking in modular addition and compare their responses to unlearning, showing that the latter suffer greater retain damage, i.e., a larger performance drop on the retain set. Furthermore, we conduct a finer-grained analysis by introducing bucketed modular addition, in which the respective contributions of the two strategies can be explicitly controlled across the memorization-generalization spectrum. In this setup, we reaffirm that the same trend persists and is nearly monotonic. We further demonstrate that this relationship also holds in LLM unlearning across verbatim and factual recall settings. Finally, we provide two practical insights for developing better unlearning methods, highlighting the importance of accounting for learning dynamics in unlearning.

A fruitful approach towards understanding generalization in machine learning involves characterizing how models separate generalizable structure from idiosyncratic or even corrupted features of training data. Fisher information has emerged as a diagnostic tool for this separation, leveraging loss geometry to distinguish generalization from memorization. Here we investigate this connection in vision models trained on CIFAR-10 with controlled noise that can be learned only through memorization. We show that projecting model weights onto the top Fisher eigenvectors decouples general task performance from noisy sample memorization, and we investigate how this decoupling presents differentially across layers. We show that the same phenomena are present in small transformers trained to solve a synthetic in-context learning task, and are reproduced in closed form in a simple, analytically solvable linear model. Our results reveal that Fisher information captures aspects of the geometric structure underlying how neural networks allocate capacity between generalization and memorization.