# When Do Learned Blocks Preserve Causal Meaning? Block Identifiability and Constructive Causal Abstractions

arXiv: https://arxiv.org/abs/2610.18155 · HTML: https://mlsanity.com/paper/2610.18155/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 25 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 14 of 14)

- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations](https://mlsanity.com/paper/2303.02536/) (2023)
- [Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability](https://mlsanity.com/paper/2301.04709/) (2023)
- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Sparse Autoencoders Do Not Find Canonical Units of Analysis](https://mlsanity.com/paper/2502.04878/) (2025)
- [Approximate Causal Abstraction](https://mlsanity.com/paper/1906.11583/) (2019)
- [Additive Decoders for Latent Variables Identification and Cartesian-Product Extrapolation](https://mlsanity.com/paper/2307.02598/) (2023)
- [Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributions](https://mlsanity.com/paper/2301.05893/) (2023)
- [From Isolation to Entanglement: When Do Interpretability Methods Identify and Disentangle Known Concepts?](https://mlsanity.com/paper/2512.15134/) (2025)
- [Structuring Sparsity: Block-Sparse Featurizers Capture Visual Concept Manifolds](https://mlsanity.com/paper/2606.25234/) (2026)
- [Unsupervised Causal Abstractions Discovery](https://mlsanity.com/paper/2606.19594/) (2026)

## Abstract (arXiv)

Standard identifiability theory assumes one-dimensional latent factors, but learned representations can encode latent information across multidimensional blocks whose internal coordinates are not uniquely determined. When such blocks are used to represent and intervene on higher-level concepts, it is unclear whether their causal meaning survives the transformations left unresolved by block-identifiability. We connect block-identifiability to constructive causal abstraction. We show that block-diagonal invertible transformations followed by compatible coordinate permutations form the maximal class that preserves every constructive causal abstraction built on those blocks. This guarantee assumes that the correspondence between blocks and concepts is updated with the representation. A small synthetic experiment with additive autoencoders shows that high-level interventions can be transferred between independently learned representations while approximately preserving their intended effects.