Bottleneck-Minimal Indexing for Generative Document Retrieval

We apply an information-theoretic perspective to reconsider generative document retrieval (GDR), in which a document $x \in \mathcal{X}$ is indexed by $t \in \mathcal{T}$, and a neural autoregressive model is trained to map queries $\mathcal{Q}$ to $\mathcal{T}$. GDR can be considered to involve information transmission from documents $\mathcal{X}$ to queries $\mathcal{Q}$, with the requirement to transmit more bits via the indexes $\mathcal{T}$. By applying Shannon's rate-distortion theory, the optimality of indexing can be analyzed in terms of the mutual information, and the design of the indexes $\mathcal{T}$ can then be regarded as a *bottleneck* in GDR. After reformulating GDR from this perspective, we empirically quantify the bottleneck underlying GDR. Finally, using the NQ320K and MARCO datasets, we evaluate our proposed bottleneck-minimal indexing method in comparison with various previous indexing methods, and we show that it outperforms those methods.