Before revision:  We establish new connections between the encoding dimension and the number of unique terms in each document and query, using both theoretical and empirical analysis. We show an upper bound on the encoding size, which may be unsustainably large for long documents. For cross-attention models, we show an upper bound using much smaller encodings per token, but such models are difficult to scale to realistic retrieval problems due to computational cost .
After revision:  We establish new connections between the encoding dimension , the margin between gold and lower-ranked documents, and the document length, suggesting limitations in the capacity of fixed-length encodings to support precise retrieval of long documents .