# Jacobian Regularizer-based Neural Granger Causality

arXiv: https://arxiv.org/abs/2405.08779 · HTML: https://mlsanity.com/paper/2405.08779/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 14 May 2024.

## Builds on (most cited first, 13 of 13)

- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Robust Learning with Jacobian Regularization](https://mlsanity.com/paper/1908.02729/) (2019)
- [Improving DNN Robustness to Adversarial Attacks using Jacobian Regularization](https://mlsanity.com/paper/1803.08680/) (2018)
- [Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causality](https://mlsanity.com/paper/1911.09879/) (2019)
- [Causal Recurrent Variational Autoencoder for Medical Time Series Generation](https://mlsanity.com/paper/2301.06574/) (2023)
- [Neural graphical modelling in continuous-time: consistency guarantees and algorithms](https://mlsanity.com/paper/2105.02522/) (2021)
- [CUTS+: High-dimensional Causal Discovery from Irregular Time-series](https://mlsanity.com/paper/2305.05890/) (2023)
- [CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discovery](https://mlsanity.com/paper/2310.01753/) (2023)
- [NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledge](https://mlsanity.com/paper/2109.04286/) (2021)
- [CUTS: Neural Causal Discovery from Irregular Time-Series Data](https://mlsanity.com/paper/2302.07458/) (2023)
- [Rhino: Deep Causal Temporal Relationship Learning With History-dependent Noise](https://mlsanity.com/paper/2210.14706/) (2022)
- [Neural Additive Vector Autoregression Models for Causal Discovery in Time Series](https://mlsanity.com/paper/2010.09429/) (2020)
- [Local Disentanglement in Variational Auto-Encoders Using Jacobian L1 Regularization](https://mlsanity.com/paper/2106.02923/) (2021)

## Built on by (most cited first, 9 of 9)

- [LOCAL: Learning with Orientation Matrix to Infer Causal Structure from Time Series Data](https://mlsanity.com/paper/2410.19464/) (2024)
- [UnCLe: Towards Scalable Dynamic Causal Discovery in Non-linear Temporal Systems](https://mlsanity.com/paper/2511.03168/) (2025)
- [Coarse-to-Fine Learning of Dynamic Causal Structures](https://mlsanity.com/paper/2602.22532/) (2026)
- [Transformer Is Inherently a Causal Learner](https://mlsanity.com/paper/2601.05647/) (2026)
- [LinBridge: A Learnable Framework for Interpreting Nonlinear Neural Encoding Models](https://mlsanity.com/paper/2410.20053/) (2024)
- [A Gradient-based Causal Discovery Framework with Applications to Complex Industrial Processes](https://mlsanity.com/paper/2507.11178/) (2025)
- [Mask2Cause: Temporal Causal Discovery Beyond Causality in Mean](https://mlsanity.com/paper/2605.07280/) (2026)
- [Function-Valued Causal Influence in Nonlinear Time Series](https://mlsanity.com/paper/2605.26408/) (2026)
- [CausalMoE: A Billion-Scale Multimodal Foundation Model for Granger Causal Discovery with Pattern-Routed Heterogeneous Experts](https://mlsanity.com/paper/2606.13024/) (2026)

## Abstract (arXiv)

With the advancement of neural networks, diverse methods for neural Granger causality have emerged, which demonstrate proficiency in handling complex data, and nonlinear relationships. However, the existing framework of neural Granger causality has several limitations. It requires the construction of separate predictive models for each target variable, and the relationship depends on the sparsity on the weights of the first layer, resulting in challenges in effectively modeling complex relationships between variables as well as unsatisfied estimation accuracy of Granger causality. Moreover, most of them cannot grasp full-time Granger causality. To address these drawbacks, we propose a Jacobian Regularizer-based Neural Granger Causality (JRNGC) approach, a straightforward yet highly effective method for learning multivariate summary Granger causality and full-time Granger causality by constructing a single model for all target variables. Specifically, our method eliminates the sparsity constraints of weights by leveraging an input-output Jacobian matrix regularizer, which can be subsequently represented as the weighted causal matrix in the post-hoc analysis. Extensive experiments show that our proposed approach achieves competitive performance with the state-of-the-art methods for learning summary Granger causality and full-time Granger causality while maintaining lower model complexity and high scalability.