# Measure-Theoretic Anti-Causal Representation Learning

arXiv: https://arxiv.org/abs/2510.18052 · HTML: https://mlsanity.com/paper/2510.18052/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 78 references that are in the map.
- First posted on arXiv 16 Oct 2025.

## Builds on (most cited first, 30 of 59)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [SWAD: Domain Generalization by Seeking Flat Minima](https://mlsanity.com/paper/2102.08604/) (2021)
- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [Learning to Generate Novel Domains for Domain Generalization](https://mlsanity.com/paper/2007.03304/) (2020)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [A Fourier-based Framework for Domain Generalization](https://mlsanity.com/paper/2105.11120/) (2021)
- [Learning Not to Learn: Training Deep Neural Networks with Biased Data](https://mlsanity.com/paper/1812.10352/) (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)
- [Quantifying the effects of data augmentation and stain color normalization in convolutional neural networks for computational pathology](https://mlsanity.com/paper/1902.06543/) (2019)
- [Deep Stable Learning for Out-Of-Distribution Generalization](https://mlsanity.com/paper/2104.07876/) (2021)
- [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)
- [Domain Adaptation with Conditional Distribution Matching and Generalized Label Shift](https://mlsanity.com/paper/2003.04475/) (2020)
- [Disentangled Representation Learning](https://mlsanity.com/paper/2211.11695/) (2022)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [Model Ratatouille: Recycling Diverse Models for Out-of-Distribution Generalization](https://mlsanity.com/paper/2212.10445/) (2022)
- [Towards a Theoretical Framework of Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.04496/) (2021)
- [Learning Linear Causal Representations from Interventions under General Nonlinear Mixing](https://mlsanity.com/paper/2306.02235/) (2023)

## Built on by (most cited first, 4 of 4)

- [AutoSOTA: An End-to-End Automated Research System for State-of-the-Art AI Model Discovery](https://mlsanity.com/paper/2604.05550/) (2026)
- [Structure-agnostic Causal Representation Learning](https://mlsanity.com/paper/2610.00968/) (2026)
- [Causal Memory Policy: Making Memory Utility Identifiable by Intervening on Retrieval](https://mlsanity.com/paper/2610.02070/) (2026)
- [Reasoning Models Are Accurate but Unsound on Identification](https://mlsanity.com/paper/2610.03519/) (2026)

## Abstract (arXiv)

Causal representation learning in the anti-causal setting (labels cause features rather than the reverse) presents unique challenges requiring specialized approaches. We propose Anti-Causal Invariant Abstractions (ACIA), a novel measure-theoretic framework for anti-causal representation learning. ACIA employs a two-level design, low-level representations capture how labels generate observations, while high-level representations learn stable causal patterns across environment-specific variations. ACIA addresses key limitations of existing approaches by accommodating prefect and imperfect interventions through interventional kernels, eliminating dependency on explicit causal structures, handling high-dimensional data effectively, and providing theoretical guarantees for out-of-distribution generalization. Experiments on synthetic and real-world medical datasets demonstrate that ACIA consistently outperforms state-of-the-art methods in both accuracy and invariance metrics. Furthermore, our theoretical results establish tight bounds on performance gaps between training and unseen environments, confirming the efficacy of our approach for robust anti-causal learning.