In this reproduction study, we revisit recent claims that self-attention implements kernel principal component analysis (KPCA) (Teo and Nguyen, 2024), positing that (i) value vectors V capture the eigenvectors of the Gram matrix of the keys, and (ii) that self-attention projects queries onto the principal component axes of the key matrix K in a feature space. Our analysis reveals three critical inconsistencies: (1) No alignment exists between learned self-attention value vectors and what is proposed in the KPCA perspective, with average similarity metrics (optimal cosine similarity ≤ 0.32, linear CKA (Centered Kernel Alignment) ≤ 0.11, kernel CKA ≤ 0.32) indicating negligible correspondence; (2) Reported decreases in reconstruction loss Jproj, arguably justifying the claim that the self-attentionminimizes the projection error of KPCA, are misinterpreted, as the quantities involved differ by orders of magnitude (∼ 10³); (3) Gram matrix eigenvalue statistics, introduced to justify that V captures the eigenvector of the gram matrix, are irreproducible without undocumented implementation-specific adjustments. Across 10 transformer architectures, we conclude that the KPCA interpretation of self-attention lacks empirical support.

In the last decade, the generalization and adaptation abilities of deep learning models were typically evaluated on fixed training and test distributions. Contrary to traditional deep learning, large language models (LLMs) are (i) even more overparameterized, (ii) trained on unlabeled text corpora curated from the Internet with minimal human intervention, and (iii) trained in an online fashion. These stark contrasts prevent researchers from transferring lessons learned on model generalization and adaptation in deep learning contexts to LLMs.To this end, our short paper introduces empirical observations that aim to shed light on further training of already pretrained language models. Specifically, we demonstrate that training a model on a text domain could degrade its perplexity on the test portion of the same domain. We observe with our subsequent analysis that the performance degradation is positively correlated with the similarity between the additional and the original pretraining dataset of the LLM. Our further token-level perplexity analysis reveals that the perplexity degradation is due to a handful of tokens that are not informative about the domain. We hope these findings will guide us in determining when to adapt a model vs when to rely on its foundational capabilities.