aiqbench analysis
GeoFlowVLM introduces a novel post-hoc adapter for vision-language models that leverages Riemannian flow matching on hyperspherical embeddings to simultaneously quantify both aleatoric and epistemic uncertainty. By deriving conditional retrieval entropy and marginal-typicality scores from a single velocity field, the method achieves near-ideal calibration across multiple benchmarks without requiring architectural changes to standard dual-encoder frameworks. This approach offers a rigorous geometric solution for assessing model confidence in cross-modal tasks where existing methods often fail to capture joint distributional properties.
GeoFlowVLM: Geometry-Aware Joint Uncertainty for Frozen Vision-Language Embedding
arXiv:2605.13352v2 Announce Type: replace Abstract: Standard dual-encoder vision-language models that map images and text to deterministic points on a shared unit hypersphere through $\ell_2$ normalization typically expose neither \emph{aleatoric} uncertainty (cross-modal ambiguity) nor \emph{epistemic} uncertainty (lack of training-distribution support). Existing post-hoc methods either recover at most one of the two uncertainty components, or ignore the hyperspherical geometry of these models' embeddings. We propose \textbf{GeoFlowVLM} as a post-hoc adapter that learns the joint distribution of paired $\ell_2$-normalised dual-encoder VLM embeddings on the product hypersphere $\mathbb{S}^{d-1} \times \mathbb{S}^{d-1}$ via Riemannian flow matching with a single masked velocity field. A consistency result shows that, in the population limit, the trained network exposes the joint flow and both cross-modal conditional flows as valid Riemannian flow-matching velocity fields on their respective domains. We derive two quantities from this single model: a conditional retrieval entropy that quantifies aleatoric ambiguity with a decision-theoretic interpretation via a Fano-type bound, and a marginal-typicality epistemic score justified by an exact chain-rule decomposition of the joint NLL. This decomposition isolates a cross-modal pointwise-mutual-information term that is structurally discriminative rather than epistemic, and is empirically the only consistently uninformative standalone component. Empirically, the entropy tracks Recall@1 with near-ideal monotonic calibration across three retrieval benchmarks in both directions, and the marginal-typicality sum yields consistently calibrated selective accuracy across four zero-shot classification benchmarks.
Abstract:Standard dual-encoder vision-language models that map images and text to deterministic points on a shared unit hypersphere through $\ell_2$ normalization typically expose neither \emph{aleatoric} uncertainty (cross-modal ambiguity) nor \emph{epistemic} uncertainty (lack of training-distribution support). Existing post-hoc methods either recover at most one of the two uncertainty components, or ignore the hyperspherical geometry of these models' embeddings. We propose \textbf{GeoFlowVLM} as a post-hoc adapter that learns the joint distribution of paired $\ell_2$-normalised dual-encoder VLM embeddings on the product hypersphere $\mathbb{S}^{d-1} \times \mathbb{S}^{d-1}$ via Riemannian flow matching with a single masked velocity field. A consistency result shows that, in the population limit, the trained network exposes the joint flow and both cross-modal conditional flows as valid Riemannian flow-matching velocity fields on their respective domains. We derive two quantities from this single model: a conditional retrieval entropy that quantifies aleatoric ambiguity with a decision-theoretic interpretation via a Fano-type bound, and a marginal-typicality epistemic score justified by an exact chain-rule decomposition of the joint NLL. This decomposition isolates a cross-modal pointwise-mutual-information term that is structurally discriminative rather than epistemic, and is empirically the only consistently uninformative standalone component. Empirically, the entropy tracks Recall@1 with near-ideal monotonic calibration across three retrieval benchmarks in both directions, and the marginal-typicality sum yields consistently calibrated selective accuracy across four zero-shot classification benchmarks.
Machine Learning (cs.LG)
arXiv:2605.13352 [cs.LG]
(or arXiv:2605.13352v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.13352 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 306 words
Related coverage
WNM-3D: A World Navigation Model with 3D Scene Conditioning for Closed-Loop VLN
arXiv · Aug 21, 2026
FabriVLA: A Lightweight Vision-Language-Action Model with Conformal Action Chunk Uncertainty
arXiv · Aug 4, 2026
StrataVLA: Hierarchical and Efficient 3D Geometric Grounding for Vision-Language-Action Models
arXiv · Sep 24, 2026
Geometry-Aware Distillation for Prompt Tuning Biomedical Vision-Language Models
arXiv · Jun 5, 2026