Retrieval finds a small number of relevant candidates from a large corpus for information retrieval and recommendation applications. A key component of retrieval is to model (user, item) similarity, which is commonly represented as the dot product of two learned embeddings. This formulation permits efficient inference, commonly known as Maximum Inner Product Search (MIPS). Despite its popularity, dot products cannot capture complex user-item interactions, which are multifaceted and likely high rank. We hence examine non-dot-product retrieval settings on accelerators, and propose \textit{mixture of logits} (MoL), which models (user, item) similarity as an adaptive composition of elementary similarity functions. This new formulation is expressive, capable of modeling high rank (user, item) interactions, and further generalizes to the long tail. When combined with a hierarchical retrieval strategy, \textit{h-indexer}, we are able to scale up MoL to 100M corpus on a single GPU with latency comparable to MIPS baselines. On public datasets, our approach leads to uplifts of up to 77.3\% in hit rate (HR). Experiments on a large recommendation surface at Meta showed strong metric gains and reduced popularity bias, validating the proposed approach's performance and improved generalization.
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