Differentiable Geometric Indexing For End-to-end Generative Retrieval

Abstract

Generative Retrieval (GR) has emerged as a promising paradigm to unify indexing and search within a single probabilistic framework. However, existing approaches suffer from two intrinsic conflicts: (1) an Optimization Blockage, where the non-differentiable nature of discrete indexing creates a gradient blockage, decoupling index construction from the downstream retrieval objective; and (2) a Geometric Conflict, where standard unnormalized inner-product objectives induce norm-inflation instability, causing popular "hub" items to geometrically overshadow relevant long-tail items. To systematically resolve these misalignments, we propose Differentiable Geometric Indexing (DGI). First, to bridge the optimization gap, DGI enforces Operational Unification. It employs Soft Teacher Forcing via Gumbel-Softmax to establish a fully differentiable pathway, combined with Symmetric Weight Sharing to effectively align the quantizer's indexing space with the retriever's decoding space. Second, to re

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