# PLOT: Progressive Localization via Optimal Transport in Neural Causal Abstraction

arXiv: https://arxiv.org/abs/2605.06979 · HTML: https://mlsanity.com/paper/2605.06979/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 22 of its 34 references that are in the map.
- First posted on arXiv 7 May 2026.

## Placed in

- Mechanistic interpretability / [Circuits and mechanistic analysis](https://mlsanity.com/mechinterp/circuits-and-mechanistic-analysis/)

## Builds on (most cited first, 22 of 22)

- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [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)
- [Linear Representations of Sentiment in Large Language Models](https://mlsanity.com/paper/2310.15154/) (2023)
- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Inducing Causal Structure for Interpretable Neural Networks](https://mlsanity.com/paper/2112.00826/) (2021)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Interpretability at Scale: Identifying Causal Mechanisms in Alpaca](https://mlsanity.com/paper/2305.08809/) (2023)
- [MIB: A Mechanistic Interpretability Benchmark](https://mlsanity.com/paper/2504.13151/) (2025)
- [Scaling Algorithms for Unbalanced Transport Problems](https://mlsanity.com/paper/1607.05816/) (2016)
- [Evaluating Open-Source Sparse Autoencoders on Disentangling Factual Knowledge in GPT-2 Small](https://mlsanity.com/paper/2409.04478/) (2024)
- [Causal Optimal Transport of Abstractions](https://mlsanity.com/paper/2312.08107/) (2023)
- [Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization](https://mlsanity.com/paper/1611.02610/) (2016)
- [Optimal transport and Wasserstein distances for causal models](https://mlsanity.com/paper/2303.14085/) (2023)
- [HyperDAS: Towards Automating Mechanistic Interpretability with Hypernetworks](https://mlsanity.com/paper/2503.10894/) (2025)
- [Neural Estimation for Scaling Entropic Multimarginal Optimal Transport](https://mlsanity.com/paper/2506.00573/) (2025)

## Abstract (arXiv)

Causal abstraction offers a principled framework for mechanistic interpretability, aligning a high-level causal model with low-level neural computation through interchange intervention analysis. Finding such an alignment, however, often requires fitting and evaluating separate learned mappings across many candidate neural locations. We introduce PLOT, a gradient-free approach for joint correspondence discovery via a global matching of intervention effects. PLOT represents abstract and neural interventions by geometric signatures of their effects on the shared task output and fits an optimal transport coupling between the two collections. The coupling can be calibrated directly into an executable intervention handle or used progressively to select coarse parent sites for finer localization, reducing the cost of searching broad collections of neural sites. Experiments on hierarchical equality, binary addition, and multiple-choice question answering (MCQA) demonstrate fast and accurate direct handles without learning intervention rotations and show that progressive localization can improve accuracy under intervention-size constraints while reducing computational cost. PLOT can also guide gradient-based subspace learning, with PLOT-guided distributed alignment search (DAS) attaining accuracy comparable to full DAS at approximately 3.6× and 20× lower serial runtime on binary addition and MCQA, respectively. PLOT thus separates the search for candidate correspondences from optional subspace learning and provides a common framework for constructing and testing neural intervention handles for a given causal model.