@inproceedings{oh-etal-2026-hyperspherical,
title = "Hyperspherical Semantic Expansion via von {M}ises{--}Fisher Mixtures for Zero-Shot Dense Retrieval",
author = "Oh, Sehong and
Kim, DongHui and
Kwon, Junseok",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.175/",
pages = "4013--4026",
ISBN = "979-8-89176-459-0",
abstract = "Dense retrieval relies on aligning document and query embeddings; however, its performance is often constrained by the scarcity of labeled queries. Although prior work has attempted to model the many-to-one relationship between documents and queries using Gaussian Mixture Models (GMMs), such Euclidean-based approaches induce norm shrinkage ($\|\mu\| < 1$) in normalized semantic spaces, resulting in distorted similarity scores. To address this fundamental geometric inconsistency, we propose vMF-HSE, a training-free hyperspherical semantic expansion framework that models the latent query space using a von Mises-Fisher (vMF) mixture distribution on the unit hypersphere $\mathbb{S}^{d-1}$. We leverage Sra{'}s Newton-based optimization within the Expectation-Maximization (EM) algorithm to ensure robust parameter estimation even in high-dimensional semantic spaces. Building upon this stable estimation, we propose a novel adaptive stopping mechanism ($\kappa$-Stop) that adaptively determines the optimal number of synthetic queries per document by monitoring the convergence of marginal information gain. Experimental results on the BEIR benchmark demonstrate that vMF-HSE consistently outperforms conventional Euclidean-based methods in zero-shot retrieval settings, establishing the necessity of geometrically consistent modeling for normalized semantic spaces."
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<abstract>Dense retrieval relies on aligning document and query embeddings; however, its performance is often constrained by the scarcity of labeled queries. Although prior work has attempted to model the many-to-one relationship between documents and queries using Gaussian Mixture Models (GMMs), such Euclidean-based approaches induce norm shrinkage (\|μ\| < 1) in normalized semantic spaces, resulting in distorted similarity scores. To address this fundamental geometric inconsistency, we propose vMF-HSE, a training-free hyperspherical semantic expansion framework that models the latent query space using a von Mises-Fisher (vMF) mixture distribution on the unit hypersphere \mathbbS^d-1. We leverage Sra’s Newton-based optimization within the Expectation-Maximization (EM) algorithm to ensure robust parameter estimation even in high-dimensional semantic spaces. Building upon this stable estimation, we propose a novel adaptive stopping mechanism (ąppa-Stop) that adaptively determines the optimal number of synthetic queries per document by monitoring the convergence of marginal information gain. Experimental results on the BEIR benchmark demonstrate that vMF-HSE consistently outperforms conventional Euclidean-based methods in zero-shot retrieval settings, establishing the necessity of geometrically consistent modeling for normalized semantic spaces.</abstract>
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%0 Conference Proceedings
%T Hyperspherical Semantic Expansion via von Mises–Fisher Mixtures for Zero-Shot Dense Retrieval
%A Oh, Sehong
%A Kim, DongHui
%A Kwon, Junseok
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F oh-etal-2026-hyperspherical
%X Dense retrieval relies on aligning document and query embeddings; however, its performance is often constrained by the scarcity of labeled queries. Although prior work has attempted to model the many-to-one relationship between documents and queries using Gaussian Mixture Models (GMMs), such Euclidean-based approaches induce norm shrinkage (\|μ\| < 1) in normalized semantic spaces, resulting in distorted similarity scores. To address this fundamental geometric inconsistency, we propose vMF-HSE, a training-free hyperspherical semantic expansion framework that models the latent query space using a von Mises-Fisher (vMF) mixture distribution on the unit hypersphere \mathbbS^d-1. We leverage Sra’s Newton-based optimization within the Expectation-Maximization (EM) algorithm to ensure robust parameter estimation even in high-dimensional semantic spaces. Building upon this stable estimation, we propose a novel adaptive stopping mechanism (ąppa-Stop) that adaptively determines the optimal number of synthetic queries per document by monitoring the convergence of marginal information gain. Experimental results on the BEIR benchmark demonstrate that vMF-HSE consistently outperforms conventional Euclidean-based methods in zero-shot retrieval settings, establishing the necessity of geometrically consistent modeling for normalized semantic spaces.
%U https://aclanthology.org/2026.emnlp-main.175/
%P 4013-4026
Markdown (Informal)
[Hyperspherical Semantic Expansion via von Mises–Fisher Mixtures for Zero-Shot Dense Retrieval](https://aclanthology.org/2026.emnlp-main.175/) (Oh et al., EMNLP 2026)
ACL