Research map / Probabilistic and scientific modeling / Causal discovery
Tangent Space Causal Inference: Leveraging Vector Fields for Causal Discovery in Dynamical Systems
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes Tangent Space Causal Inference (TSCI), a drop-in replacement for the CCM cross-map test that scores causality by how well the pushed-forward vector field of a learned cross map aligns with the target system's vector field.
Problem
Observational causal discovery in coupled dynamical systems, where Granger causality fails and convergent cross mapping (CCM) gives unreliable, hard-to-interpret test statistics.
Approach
Instead of checking the predictability of x from a cross map (CCM's skill), TSCI learns a cross map F between shadow manifolds and checks whether F's Jacobian maps the velocity field of one manifold onto the velocity field of the other, using the cosine/correlation of tangent vectors as the test statistic.
Key results
- On the double pendulum task, Latent TSCI (MLP) gives Z→X correlation 0.915±0.006 versus 0.737±0.019 for Latent CCM, and Z→Y 0.612±0.053 versus 0.475±0.043.
- On the Rössler-Lorenz system, Granger causality infers bidirectional causality for all C>0, while TSCI's cosine statistics separate the true direction from the reverse.
- TSCI is reported to show larger separation than CCM across coupling strengths and to be more robust at lower SNR, while adding little computation over the kNN CCM version.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace latent CCM with latent TSCI using an MLP cross map | Latent CCM framework · Double Pendulum, Z → X | correlation coefficient: 0.747 ± 0.015 -> 0.915 ± 0.006 | Helped |
| replace latent CCM with latent TSCI using an MLP cross map | Latent CCM framework · Double Pendulum, Z → Y | correlation coefficient: 0.578 ± 0.030 -> 0.612 ± 0.053 | Helped |
| replace latent CCM with latent TSCI using an MLP cross map | Latent CCM framework · Double Pendulum, true-negative directions | correlation coefficient | No clear effect |
| vary the embedding dimension (ablation) | TSCI and CCM on the Rössler-Lorenz system · Rössler-Lorenz, C=1 | causal inference performance | Mixed |
| add Gaussian noise to observations (ablation) | TSCI on the Rössler-Lorenz system · Rössler-Lorenz, C=1.0, varying SNR | causal inference performance | Hurt |
| add a periodic sine-wave trend to observations (ablation) | TSCI on the Rössler-Lorenz system · Rössler-Lorenz, C=1 | causal inference performance | Hurt |
| use mutual information instead of cosine similarity (ablation) | TSCI on the Rössler-Lorenz system · Rössler-Lorenz, varying coupling C | separation between causal and non-causal directions | Hurt |
Surprising findings
- Mutual information estimates gave less separation than cosine similarity, and RECI picked X→Y even when coupling C=0, suggesting it detects an artifact rather than causality.
Limitations
- Strong unidirectional coupling leads to general synchrony, where a bidirectional causal relation is spuriously detected; TSCI resists this better but not fully.
- Requires a well-constructed shadow manifold and accurate vector-field (derivative) estimates; kNN version is unsuitable for noisy or sparse data.
- Assumes the data come from continuous-time dynamical systems (ODEs).
Experimental setup
Datasets: Unidirectionally-coupled Rössler-Lorenz system (simulated) Coupled double pendulum (latent CCM data generation)
Benchmarks: Rössler-Lorenz coupled system Double pendulum system (latent CCM setup)
Metrics: correlation / cosine similarity test statistic p-values (Granger) separation between causal directions
Baselines: CCM latent CCM Granger causality RECI IGCI ANM
Builds on: convergent cross mapping Takens' theorem latent CCM Granger causality
Closest papers by meaning
- CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discovery (ICLR 2024 · similarity 0.90)
- CausalDynamics: A large‐scale benchmark for structural discovery of dynamical causal models (NeurIPS 2025 · similarity 0.89)
- Causal Discovery from Conditionally Stationary Time Series (ICML 2025 · similarity 0.88)
- UnCLe: Towards Scalable Dynamic Causal Discovery in Non-linear Temporal Systems (NeurIPS 2025 · similarity 0.87)
- Discovering Mixtures of Structural Causal Models from Time Series Data (ICML 2024 · similarity 0.87)
- Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noises (NeurIPS 2025 · similarity 0.87)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.