# Towards Unsupervised Causal Representation Learning via Latent Additive Noise Model Causal Autoencoders

arXiv: https://arxiv.org/abs/2512.22150 · HTML: https://mlsanity.com/paper/2512.22150/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 22 references that are in the map.
- First posted on arXiv 15 Dec 2025.

## Builds on (most cited first, 16 of 16)

- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Disentangled Representation Learning](https://mlsanity.com/paper/2211.11695/) (2022)
- [Robustly Disentangled Causal Mechanisms: Validating Deep Representations for Interventional Robustness](https://mlsanity.com/paper/1811.00007/) (2018)
- [Weakly Supervised Disentangled Generative Causal Representation Learning](https://mlsanity.com/paper/2010.02637/) (2020)
- [SoftSort: A Continuous Relaxation for the argsort Operator](https://mlsanity.com/paper/2006.16038/) (2020)
- [CausalVAE: Structured Causal Disentanglement in Variational Autoencoder](https://mlsanity.com/paper/2004.08697/) (2020)
- [Differentiable DAG Sampling](https://mlsanity.com/paper/2203.08509/) (2022)
- [On Causally Disentangled Representations](https://mlsanity.com/paper/2112.05746/) (2021)
- [Identifiability Guarantees for Causal Disentanglement from Purely Observational Data](https://mlsanity.com/paper/2410.23620/) (2024)

## Abstract (arXiv)

Unsupervised representation learning seeks to recover latent generative factors, yet standard methods relying on statistical independence often fail to capture causal dependencies. A central challenge is identifiability: as established in disentangled representation learning and nonlinear ICA literature, disentangling causal variables from observational data is impossible without supervision, auxiliary signals, or strong inductive biases. In this work, we propose the Latent Additive Noise Model Causal Autoencoder (LANCA) to operationalize the Additive Noise Model (ANM) as a strong inductive bias for unsupervised discovery. Theoretically, we prove that while the ANM constraint does not guarantee unique identifiability in the general mixing case, it resolves component-wise indeterminacy by restricting the admissible transformations from arbitrary diffeomorphisms to the affine class. Methodologically, arguing that the stochastic encoding inherent to VAEs obscures the structural residuals required for latent causal discovery, LANCA employs a deterministic Wasserstein Auto-Encoder (WAE) coupled with a differentiable ANM Layer. This architecture transforms residual independence from a passive assumption into an explicit optimization objective. Empirically, LANCA outperforms state-of-the-art baselines on synthetic physics benchmarks (Pendulum, Flow), and on photorealistic environments (CANDLE), where it demonstrates superior robustness to spurious correlations arising from complex background scenes.