# Common-Witness Certificates and Sharp Feature Bounds for Counterfactual Image Auditing

arXiv: https://arxiv.org/abs/2609.03973 · HTML: https://mlsanity.com/paper/2609.03973/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 32 references that are in the map.
- First posted on arXiv 3 Sep 2026.

## Builds on (most cited first, 4 of 4)

- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [Morpho-MNIST: Quantitative Assessment and Diagnostics for Representation Learning](https://mlsanity.com/paper/1809.10780/) (2018)
- [Counterfactual Image Editing](https://mlsanity.com/paper/2403.09683/) (2024)

## Abstract (arXiv)

An image editor may satisfy every regional plausibility constraint separately even when no single latent explanation fits the complete output. We formalize this local-to-global failure using a common witness grade and witness nerve. The framework separates auditing from causal identification: shared exogeneity alone allows every coupling of the regime marginals, whereas an externally justified witness relation yields sharp partial-identification bounds for prespecified image features. Helly-type arguments provide short incompatibility certificates for quasiconvex losses, heterogeneous action strata, and finite witness atlases; a blocker-hypergraph formula gives exact repair counts. Simultaneous confidence regions for the regime marginals give finite-sample outer coverage of the complete identified interval. Controlled MNIST, Morpho-MNIST, and smallNORB studies demonstrate the predicted local-global separation, while synthetic experiments test sharp bounds, certificate recovery, and structured computation. The method audits a declared feature relation and does not identify unrestricted pixel-level counterfactuals.