# Certifying Interventional Agreement Among Observationally Equivalent Causal Models

arXiv: https://arxiv.org/abs/2609.32247 · HTML: https://mlsanity.com/paper/2609.32247/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 62 of its 118 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 30 of 62)

- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Beyond Accuracy: Behavioral Testing of NLP models with CheckList](https://mlsanity.com/paper/2005.04118/) (2020)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Learning the Difference that Makes a Difference with Counterfactually-Augmented Data](https://mlsanity.com/paper/1909.12434/) (2019)
- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [Causal Reasoning and Large Language Models: Opening a New Frontier for Causality](https://mlsanity.com/paper/2305.00050/) (2023)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [DeepXplore: Automated Whitebox Testing of Deep Learning Systems](https://mlsanity.com/paper/1705.06640/) (2017)
- [Causal Confusion in Imitation Learning](https://mlsanity.com/paper/1905.11979/) (2019)
- [Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations](https://mlsanity.com/paper/2303.02536/) (2023)
- [Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability](https://mlsanity.com/paper/2301.04709/) (2023)
- [Predictive Multiplicity in Classification](https://mlsanity.com/paper/1909.06677/) (2019)
- [Causal Parrots: Large Language Models May Talk Causality But Are Not Causal](https://mlsanity.com/paper/2308.13067/) (2023)
- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)

## Abstract (arXiv)

Observationally equivalent causal models can still disagree about what happens under intervention, because interventions create inputs that never occur in observational data. We introduce Interventional Separation Selection (ISS), which repeatedly queries the true system with an admissible intervention on which the surviving candidate models disagree, discards the candidates the outcome contradicts, and stops once no intervention within a cost bound separates the survivors. If the true system is among the candidates, this stopping condition certifies that every survivor agrees with it on every admissible intervention within the bound, a guarantee that no observational learner can give, however much data it sees. The stopping condition depends only on the survivors, so it can be checked without knowing the truth. For continuous variables the candidates form an infinite version space, and mixed-integer linear programs decide the stopping condition exactly over all of it, with agreement holding up to a tolerance. On a three-digit colored MNIST causal abstraction task in which ink hue tracks digit size, plain convolutional networks trained on examples reach zero held-out error, yet disagree with shape-based labels on 26% of single-digit edits, as often as hue-based labels do. Auditing the causal abstractions of networks observed only on such images, ISS certifies what each network perceives with 13.6 interventions per image on average, and each certificate, checked against every admissible intervention, holds whenever the network's true abstraction is among the candidates. When a network bypasses a unit that every candidate abstraction relies on, certificates covering interventions on that unit can be silently void, and twenty random validation interventions refute 69% of them.