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

Traditional two-tower retrieval models often compress a user's diverse interests into a single embedding, leading to suboptimal recommendations. While multi-interest models use multiple heads to represent different facets of a user, they typically rely on hard-routing (selecting only one head per item), which causes 'routing collapse' where many heads remain unused. This paper asks: can we treat multi-interest retrieval as a probabilistic mixture model to improve head utilization and provide a principled way to weight user interests?

The authors introduce BACH (Bayesian Admixture of Contrastive Heads), which models the user-item interaction as a mixture of softmaxes. Instead of hard-routing, BACH uses variational inference to assign 'soft' responsibilities to each head. This allows every head to receive gradient updates during training, preventing the winner-take-all dynamics of traditional models. The model learns a per-user gating mechanism (a gating tower) that estimates the importance of each head, which is then reused at serving time to weight the retrieval results. The authors also explore a global-codebook variant, where heads are shared across users, allowing for precomputable retrieval lists.

BACH consistently outperforms both single-vector baselines and traditional hard-routing multi-interest models across three large-scale benchmarks (MovieLens-20M, Taobao, and Netflix). By replacing the hard argmax routing with soft responsibilities, the model effectively utilizes all available heads. Furthermore, the authors demonstrate that scoring candidates by their best head during training—consistent with the serving-time retrieval rule—significantly improves performance, and that BACH provides additional gains by incorporating the learned per-user interest weights.

This work provides a robust framework for multi-interest retrieval that is both more expressive and easier to train than existing hard-routing methods. By unifying the training and serving objectives through a variational approach, BACH offers a scalable solution for large-scale recommender systems that need to capture diverse user preferences without sacrificing the efficiency of two-tower architectures.