Grokking Beyond the Euclidean Norm of Model Parameters

Grokking refers to a delayed generalization following overfitting when optimizing artificial neural networks with gradient-based methods. In this work, we demonstrate that grokking can be induced by regularization, either explicit or implicit. More precisely, we show that when there exists a model with a property $P$ (e.g., sparse or low-rank weights) that generalizes on the problem of interest, gradient descent with a small but non-zero regularization of $P$ (e.g., $\ell_1$ or nuclear norm regularization) results in grokking. This extends previous work showing that small non-zero weight decay induces grokking. Moreover, our analysis shows that over-parameterization by adding depth makes it possible to grok or ungrok without explicitly using regularization, which is impossible in shallow cases. We further show that the $\ell_2$ norm is not a reliable proxy for generalization when the model is regularized toward a different property $P$, as the $\ell_2$ norm grows in many cases where no weight decay is used, but the model generalizes anyway. We also show that grokking can be amplified solely through data selection, with any other hyperparameter fixed.

Lost in Translation: The Algorithmic Gap Between LMs and the Brain

Language Models (LMs) have achieved impressive performance on various linguistic tasks, but their relationship to human language processing in the brain remains unclear. This paper examines the gaps and overlaps between LMs and the brain at different levels of analysis, emphasizing the importance of looking beyond input-output behavior to examine and compare the internal processes of these systems. We discuss how insights from neuroscience, such as sparsity, modularity, internal states, and interactive learning, can inform the development of more biologically plausible language models. Furthermore, we explore the role of scaling laws in bridging the gap between LMs and human cognition, highlighting the need for efficiency constraints analogous to those in biological systems. By developing LMs that more closely mimic brain function, we aim to advance both artificial intelligence and our understanding of human cognition.