# Structure-agnostic Causal Representation Learning

arXiv: https://arxiv.org/abs/2610.00968 · HTML: https://mlsanity.com/paper/2610.00968/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 64 of its 90 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 30 of 64)

- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [Confounding variables can degrade generalization performance of radiological deep learning models](https://mlsanity.com/paper/1807.00431/) (2018)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Learning to Generate Novel Domains for Domain Generalization](https://mlsanity.com/paper/2007.03304/) (2020)
- [A Fourier-based Framework for Domain Generalization](https://mlsanity.com/paper/2105.11120/) (2021)
- [Failing Loudly: An Empirical Study of Methods for Detecting Dataset Shift](https://mlsanity.com/paper/1810.11953/) (2018)
- [Deep Domain-Adversarial Image Generation for Domain Generalisation](https://mlsanity.com/paper/2003.06054/) (2020)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)
- [Causality matters in medical imaging](https://mlsanity.com/paper/1912.08142/) (2019)
- [Deep Stable Learning for Out-Of-Distribution Generalization](https://mlsanity.com/paper/2104.07876/) (2021)
- [Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2202.05441/) (2022)
- [The PRISM Alignment Dataset: What Participatory, Representative and Individualised Human Feedback Reveals About the Subjective and Multicultural Alignment of Large Language Models](https://mlsanity.com/paper/2404.16019/) (2024)
- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Weakly supervised causal representation learning](https://mlsanity.com/paper/2203.16437/) (2022)
- [Causality Inspired Representation Learning for Domain Generalization](https://mlsanity.com/paper/2203.14237/) (2022)

## Built on by (most cited first, 1 of 1)

- [Reasoning Models Are Accurate but Unsound on Identification](https://mlsanity.com/paper/2610.03519/) (2026)

## Abstract (arXiv)

Causal representation learning aims to discover robust features by exploiting the causal structure underlying data generation. Existing methods require specifying the causal structure a priori, yet different structures demand fundamentally incompatible invariance constraints, and misspecification leads to representations that discard predictive information. We introduce SaCRL, a framework that jointly identifies the causal structure and learns the corresponding invariant representation without prior structural knowledge. Our approach formulates structure selection as a soft optimization over candidate invariances using HSIC-based violation metrics, with adaptive weights that automatically concentrate on the achievable structure. We provide theoretical guarantees for structure identification, including under random-feature approximation, invariance satisfaction, and out-of-distribution generalization. Empirically, SaCRL recovers the true structure on synthetic and semi-synthetic Bayesian-network benchmarks, outperforms fixed-invariance baselines on Colored MNIST, achieves state-of-the-art accuracy on three DomainBed benchmarks (PACS, VLCS, OfficeHome), and degrades gracefully under structural misspecification and limited environment diversity. Code is available at: https://github.com/ArmanBehnam/sacrl.