# Symmetry-Aware Likelihood-Orbit Aggregation for Selective Left-Right Claim Verification

arXiv: https://arxiv.org/abs/2609.17004 · HTML: https://mlsanity.com/paper/2609.17004/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in VLM benchmarks and visual reasoning, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 20 of its 23 references that are in the map.
- First posted on arXiv 15 Sep 2026.

## Placed in

- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 20 of 20)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [InternVL3: Exploring Advanced Training and Test-Time Recipes for Open-Source Multimodal Models](https://mlsanity.com/paper/2504.10479/) (2025)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Mitigating Object Hallucinations in Large Vision-Language Models through Visual Contrastive Decoding](https://mlsanity.com/paper/2311.16922/) (2023)
- [Winoground: Probing Vision and Language Models for Visio-Linguistic Compositionality](https://mlsanity.com/paper/2204.03162/) (2022)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Visual Spatial Reasoning](https://mlsanity.com/paper/2205.00363/) (2022)
- [What's "up" with vision-language models? Investigating their struggle with spatial reasoning](https://mlsanity.com/paper/2310.19785/) (2023)
- [SpatialSense: An Adversarially Crowdsourced Benchmark for Spatial Relation Recognition](https://mlsanity.com/paper/1908.02660/) (2019)
- [Selective "Selective Prediction": Reducing Unnecessary Abstention in Vision-Language Reasoning](https://mlsanity.com/paper/2402.15610/) (2024)
- [Consistency and Uncertainty: Identifying Unreliable Responses From Black-Box Vision-Language Models for Selective Visual Question Answering](https://mlsanity.com/paper/2404.10193/) (2024)
- [Predicting When to Trust Vision-Language Models for Spatial Reasoning](https://mlsanity.com/paper/2601.11644/) (2026)
- [Self-Evolving Spatial Reasoning in Vision Language Models via Geometric Logic Consistency](https://mlsanity.com/paper/2605.18162/) (2026)
- [Look Again Before You Abstain:Budgeted Conformal Evidence Acquisition for Reliable Vision-Language Model](https://mlsanity.com/paper/2606.16667/) (2026)
- [SEER: A Self-Grounded Evidence Interface for Controlled Spatial Relation Classification](https://mlsanity.com/paper/2608.03631/) (2026)
- [Grounding Isn't Knowing: Do VLMs Need Object Localization for Spatial Reasoning?](https://mlsanity.com/paper/2608.23074/) (2026)

## Abstract (arXiv)

Frozen vision-language models (VLMs) remain unreliable on fine-grained left-right claims, and raw claim likelihoods need not reliably rank verification errors. After a horizontal-reflection intervention is fixed, how should its induced likelihood measurements be combined into a selective verification signal? We introduce Relation-Orbit, a closed-form contrast with no learned fusion parameters that assigns eight normalized likelihoods to query-supporting and counterfactual roles determined by reflection, inverse relation, and entity exchange. A claim is asserted only when the signed contrast exceeds a threshold selected on held-out data using pointwise Clopper-Pearson upper confidence bounds. On VSR and GQA across four frozen VLMs, Relation-Orbit yields higher mean test coverage at a 10% selective-risk calibration target than an all-eight Orbit-Max baseline in all eight dataset-backbone settings; gains over a nearly abstain-all one-sided intervention score are reported separately. A separate LLaVA-1.5/COCO evaluation, reduced-orbit controls, and a two-sided partition diagnostic further characterize the structural advantage.