# How Many Counterfactuals Does It Take? Probing VLM Hallucinations Through Circuits and Causal Effects

arXiv: https://arxiv.org/abs/2606.08777 · HTML: https://mlsanity.com/paper/2606.08777/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Hallucination mitigation in LVLMs, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 8 of its 11 references that are in the map.
- First posted on arXiv 7 Jun 2026.

## Placed in

- Multimodal LLMs / vision-language models / [Hallucination mitigation in LVLMs](https://mlsanity.com/mllm/hallucination-mitigation-in-lvlms/)

## Builds on (most cited first, 8 of 8)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Evaluating Object Hallucination in Large Vision-Language Models](https://mlsanity.com/paper/2305.10355/) (2023)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [HallusionBench: An Advanced Diagnostic Suite for Entangled Language Hallucination and Visual Illusion in Large Vision-Language Models](https://mlsanity.com/paper/2310.14566/) (2023)
- [A Survey on Hallucination in Large Vision-Language Models](https://mlsanity.com/paper/2402.00253/) (2024)
- [Have Faith in Faithfulness: Going Beyond Circuit Overlap When Finding Model Mechanisms](https://mlsanity.com/paper/2403.17806/) (2024)
- [Treble Counterfactual VLMs: A Causal Approach to Hallucination](https://mlsanity.com/paper/2503.06169/) (2025)

## Abstract (arXiv)

Visual Language Models (VLMs) are known to produce hallucinated predictions that are not grounded in visual evidence, yet existing approaches lack a principled understanding of how robust such predictions are under counterfactual perturbations. In this work, we study the sample complexity of counterfactual robustness for hallucinated outputs in VLMs. We define a causal influence metric based on log-probability differences between factual, counterfactual, and activation-patched runs, and use it to characterize the stability of hallucinated predictions. By leveraging circuit discovery techniques (CD-T), we identify model components responsible for these predictions and track their activation differences across counterfactual samples. We then derive empirical bounds on the minimum number of counterfactual samples m required to reliably detect instability in hallucinated outputs, using concentration inequalities and variance estimates of the causal influence distribution.