# Towards Causal Representation Learning with Observable Sources as Auxiliaries

arXiv: https://arxiv.org/abs/2509.19058 · HTML: https://mlsanity.com/paper/2509.19058/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 43 references that are in the map.
- First posted on arXiv 23 Sep 2025.

## Builds on (most cited first, 19 of 19)

- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)](https://mlsanity.com/paper/2001.04872/) (2020)
- [Multi-View Causal Representation Learning with Partial Observability](https://mlsanity.com/paper/2311.04056/) (2023)
- [Causal Machine Learning for Healthcare and Precision Medicine](https://mlsanity.com/paper/2205.11402/) (2022)
- [Causal Representation Learning from Multiple Distributions: A General Setting](https://mlsanity.com/paper/2402.05052/) (2024)
- [Causal Component Analysis](https://mlsanity.com/paper/2305.17225/) (2023)
- [Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systems](https://mlsanity.com/paper/2206.06169/) (2022)
- [From Ordinary Differential Equations to Structural Causal Models: the deterministic case](https://mlsanity.com/paper/1408.2063/) (2014)
- [Generalizing Nonlinear ICA Beyond Structural Sparsity](https://mlsanity.com/paper/2311.00866/) (2023)
- [Marrying Causal Representation Learning with Dynamical Systems for Science](https://mlsanity.com/paper/2405.13888/) (2024)
- [Counterfactual Image Editing](https://mlsanity.com/paper/2403.09683/) (2024)
- [Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite Information in Belief Networks and Influence Diagrams)](https://mlsanity.com/paper/1301.7412/) (2013)
- [Fine-Grained Causal Dynamics Learning with Quantization for Improving Robustness in Reinforcement Learning](https://mlsanity.com/paper/2406.03234/) (2024)
- [Identifying Causal Structure in Dynamical Systems](https://mlsanity.com/paper/2006.03906/) (2020)

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

- [Causal-JEPA: Learning World Models through Object-Level Latent Masking](https://mlsanity.com/paper/2602.11389/) (2026)

## Abstract (arXiv)

Causal representation learning seeks to recover latent factors that generate observational data through a mixing function. Needing assumptions on latent structures or relationships to achieve identifiability in general, prior works often build upon conditional independence given known auxiliary variables. However, prior frameworks limit the scope of auxiliary variables to be external to the mixing function. Yet, in some cases, system-driving latent factors can be easily observed or extracted from data, possibly facilitating identification. In this paper, we introduce a framework of observable sources being auxiliaries, serving as effective conditioning variables. Our main results show that one can identify entire latent variables up to subspace-wise transformations and permutations using volume-preserving encoders. Moreover, when multiple known auxiliary variables are available, we offer a variable-selection scheme to choose those that maximize recoverability of the latent factors given knowledge of the latent causal graph. Finally, we demonstrate the effectiveness of our framework through experiments on synthetic graph and image data, thereby extending the boundaries of current approaches.