# Symmetries and Causality: Causal Effect Identification Beyond IID Data

arXiv: https://arxiv.org/abs/2609.03697 · HTML: https://mlsanity.com/paper/2609.03697/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 62 references that are in the map.
- First posted on arXiv 3 Sep 2026.

## Builds on (most cited first, 9 of 9)

- [Causal Discovery from Conditionally Stationary Time Series](https://mlsanity.com/paper/2110.06257/) (2021)
- [When does the ID algorithm fail?](https://mlsanity.com/paper/2307.03750/) (2023)
- [SpaceTime: Causal Discovery from Non-Stationary Time Series](https://mlsanity.com/paper/2501.10235/) (2025)
- [Reinterpreting causal discovery as the task of predicting unobserved joint statistics](https://mlsanity.com/paper/2305.06894/) (2023)
- [Causal discovery with endogenous context variables](https://mlsanity.com/paper/2412.04981/) (2024)
- [Causal reasoning in difference graphs](https://mlsanity.com/paper/2411.01292/) (2024)
- [Causal Modeling in Multi-Context Systems: Distinguishing Multiple Context-Specific Causal Graphs which Account for Observational Support](https://mlsanity.com/paper/2410.20405/) (2024)
- [Causal inference amid missingness-specific independencies and mechanism shifts](https://mlsanity.com/paper/2506.15441/) (2025)
- [Learning plug-in surrogate endpoints for randomized experiments](https://mlsanity.com/paper/2605.12051/) (2026)

## Abstract (arXiv)

In the natural sciences, symmetries and cause-effect relationships are ubiquitous. Yet for complex machine-learning tasks, like world-modeling in reinforcement learning, they appear difficult to harness. We propose a formal description of statistical systems based on symmetries in data leaving causal mechanisms invariant. The result is an abstract, simple and general mathematical language for causal reasoning. This paper provides formal descriptions of models and queries, setting up this language, and the formal infrastructure and strategies for their mathematically rigorous identification from data within this formalism. This approach reproduces and matches standard theoretical results on IID data and transport of experimental and non-experimental data. But its main purpose is to unify and substantially extend the scope of causal reasoning, in going beyond IID data and in approaching complex causal queries not captured by do- or soft-interventions. This new perspective on causally relevant aspects of data-modeling additionally sheds new light on well-known structures like c-components or hedges but also includes aspects of missing data and is inherently well-suited for the description of transfer and robustness properties.