# Causal Abstraction Inference under Lossy Representations

arXiv: https://arxiv.org/abs/2509.21607 · HTML: https://mlsanity.com/paper/2509.21607/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2025.

## Built on by (most cited first, 2 of 2)

- [Cluster-Dags as Powerful Background Knowledge For Causal Discovery](https://mlsanity.com/paper/2512.10032/) (2025)
- [Efficient Fairness Auditing Across Guidance Scales in Text-to-Image Diffusion Models via Causal Abstraction](https://mlsanity.com/paper/2609.09486/) (2026)

## Abstract (arXiv)

The study of causal abstractions bridges two integral components of human intelligence: the ability to determine cause and effect, and the ability to interpret complex patterns into abstract concepts. Formally, causal abstraction frameworks define connections between complicated low-level causal models and simple high-level ones. One major limitation of most existing definitions is that they are not well-defined when considering lossy abstraction functions in which multiple low-level interventions can have different effects while mapping to the same high-level intervention (an assumption called the abstract invariance condition). In this paper, we introduce a new type of abstractions called projected abstractions that generalize existing definitions to accommodate lossy representations. We show how to construct a projected abstraction from the low-level model and how it translates equivalent observational, interventional, and counterfactual causal queries from low to high-level. Given that the true model is rarely available in practice we prove a new graphical criteria for identifying and estimating high-level causal queries from limited low-level data. Finally, we experimentally show the effectiveness of projected abstraction models in high-dimensional image settings.