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This paper introduces Differentiable Geometric Indexing (DGI), a novel approach to generative retrieval that addresses optimization blockage and geometric conflict issues in existing methods. DGI employs Soft Teacher Forcing with Gumbel-Softmax and Symmetric Weight Sharing for a fully differentiable pathway, aligning the indexing and decoding spaces. Furthermore, it uses scaled cosine similarity on the unit hypersphere to mitigate popularity bias and improve long-tail retrieval performance, demonstrating superior results on large-scale datasets.
By combining differentiable indexing with isotropic geometric optimization, DGI achieves state-of-the-art generative retrieval, especially for long-tail items that are often missed by other methods.
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 restore geometric fidelity, DGI introduces Isotropic Geometric Optimization. We replace inner-product logits with scaled cosine similarity on the unit hypersphere to effectively decouple popularity bias from semantic relevance. Extensive experiments on large-scale industry search datasets and online e-commerce platform demonstrate that DGI outperforms competitive sparse, dense, and generative baselines. Notably, DGI exhibits superior robustness in long-tail scenarios, validating the necessity of harmonizing structural differentiability with geometric isotropy.
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