# Tangent Space Causal Inference: Leveraging Vector Fields for Causal Discovery in Dynamical Systems

arXiv: https://arxiv.org/abs/2410.23499 · HTML: https://mlsanity.com/paper/2410.23499/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 48 references that are in the map.
- First posted on arXiv 30 Oct 2024.

## Builds on (most cited first, 3 of 3)

- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Beyond Normal: On the Evaluation of Mutual Information Estimators](https://mlsanity.com/paper/2306.11078/) (2023)

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

- [CausalDynamics: A large-scale benchmark for structural discovery of dynamical causal models](https://mlsanity.com/paper/2505.16620/) (2025)
- [Deep Koopman operator framework for causal discovery in nonlinear dynamical systems](https://mlsanity.com/paper/2505.14828/) (2025)
- [Rethinking Chronological Causal Discovery with Signal Processing](https://mlsanity.com/paper/2602.19903/) (2026)
- [Identifiability Guarantees for Drivers and Dynamics of Delayed Physical Systems](https://mlsanity.com/paper/2609.37944/) (2026)

## Abstract (arXiv)

Causal discovery with time series data remains a challenging yet increasingly important task across many scientific domains. Convergent cross mapping (CCM) and related methods have been proposed to study time series that are generated by dynamical systems, where traditional approaches like Granger causality are unreliable. However, CCM often yields inaccurate results depending upon the quality of the data. We propose the Tangent Space Causal Inference (TSCI) method for detecting causalities in dynamical systems. TSCI works by considering vector fields as explicit representations of the systems' dynamics and checks for the degree of synchronization between the learned vector fields. The TSCI approach is model-agnostic and can be used as a drop-in replacement for CCM and its generalizations. We first present a basic version of the TSCI algorithm, which is shown to be more effective than the basic CCM algorithm with very little additional computation. We additionally present augmented versions of TSCI that leverage the expressive power of latent variable models and deep learning. We validate our theory on standard systems, and we demonstrate improved causal inference performance across a number of benchmark tasks.