Hubness, the tendency for a few points to be among the nearest neighbours of a disproportionate number of other points, commonly arises when applying standard distance measures to high-dimensional data, often negatively impacting distance-based analysis. As autoregressive large language models (LLMs) operate on high-dimensional representations, we ask whether they are also affected by hubness. We first prove that the only large-scale representation comparison operation performed by LLMs, namely that between context and unembedding vectors to determine continuation probabilities, is not characterized by the concentration of distances phenomenon that typically causes the appearance of nuisance hubness. We then empirically show that this comparison still leads to a high degree of hubness, but the hubs in this case do not constitute a disturbance. They are rather the result of context-modulated frequent tokens often appearing in the pool of likely candidates for next token prediction. However, when other distances are used to compare LLM representations, we do not have the same theoretical guarantees, and, indeed, we see nuisance hubs appear. There are two main takeaways. First, hubness, while omnipresent in high-dimensional spaces, is not a negative property that needs to be mitigated when LLMs are being used for next token prediction. Second, when comparing representations from LLMs using Euclidean or cosine distance, there is a high risk of nuisance hubs and practitioners should use mitigation techniques if relevant.

We study last-layer outlier dimensions, i.e. dimensions that display extreme activations for the majority of inputs. We show that outlier dimensions arise in many different modern language models, and trace their function back to the heuristic of constantly predicting frequent words. We further show how a model can block this heuristic when it is not contextually appropriate, by assigning a counterbalancing weight mass to the remaining dimensions, and we investigate which model parameters boost outlier dimensions and when they arise during training. We conclude that outlier dimensions are a specialized mechanism discovered by many distinct models to implement a useful token prediction heuristic.