Mean-Pooled Cosine Similarity is Not Length-Invariant: Theory and Cross-Domain Evidence for a Length-Invariant Alternative

ArXi:2605.07345v1 Announce Type: cross Mean-pooled cosine similarity is the default metric for comparing neural representations across languages, modalities, and tasks. We establish that this metric is not length-invariant: under the anisotropy that characterizes modern transformer representations, mean-pooled cosine grows monotonically in sequence length, independent of representational content.