BACH: A Bayesian Admixture of Contrastive Heads for Multi-Interest Two-Tower Retrieval

Two-tower retrievers compress each user into a single embedding, limiting their ability to serve diverse interests. Multi-interest models give each user several heads scored by a maximum inner product, but their hard-routing training under-utilizes heads (routing collapse) and gives no per-user estimate of how much each interest matters for serving. We present BACH (Bayesian Admixture of Contrastive Heads), which casts multi-interest two-tower retrieval as a per-user mixture over the heads, fit by variational inference. The soft mixture trains every head (mitigating collapse), produces a per-user weighting of the interests that is reused at serving, and admits a shared global-codebook variant with precomputable retrieval. On three large-scale benchmarks, MovieLens-20M, Taobao, and Netflix, BACH improves top-of-ranking retrieval over hard-routing multi-interest and single-vector baselines at every head count; we further find that scoring every candidate by its best head, consistent with serving, outperforms the usual target-routed training, and that BACH improves further still.