A Rank-One Popularity Component in Dot-Product Recommender Scores:Population Theory and Prior-Separation Evidence (opens in new tab)

Representation anisotropy in recommender systems is often attributed to Transformer architectures. We identify a more general source in the conditional training distribution. For any encoder using a dot-product softmax decoder, the population-optimal score decomposes into pointwise mutual information, an item-marginal term log p(i), and a context-dependent offset. After centering, the item marginal produces a context-shared rank-one score compon...