arXiv: Norm growth in two-tower retrieval gives popular items extra exposure
_reachsumit · x · 2026-11-10
arXiv 2611.09294 studies norm growth of item vectors in unified search & recommendation, where the same vectors are updated from two interaction streams.
- With a cosine-only loss, the output gradient is tangent to the item vector's constant-norm sphere—but since encoder parameters change, realized item movement need not stay tangent. The paper derives sufficient conditions under which it does; every nonzero update then increases squared norm by its squared length.
- When both tasks share an item encoder, sequential updates accumulate in the same norm, and unnormalized dot-product serving can expose this growth as a popularity mechanism for either task.
- Controlled ablations on MovieLens 32M and Amazon Books confirm: accumulated tangent movement accompanies a frequency-norm association, and raw-dot ranking gives head items more exposure than normalized-item ranking.
- In a nonlinear tower with per-item ID vectors plus a shared content encoding, the authors decompose norm change into ID-update vs. other contributions, and apply a matched training intervention removing ID-row-induced norm growth—reducing norm-related exposure at some cost to recommendation quality (abstract truncated).
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