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Exploring Neural Granger Causality with xLSTMs: Unveiling Temporal Dependencies in Complex Data
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Proposes GC-xLSTM, a neural Granger causality method using per-variate sLSTM forecasters with a sparse input projection trained via a proximal, log-reduction group-lasso-style penalty to recover Granger causal graphs in time series.
Problem
Recovering Granger causal graphs from multivariate time series with non-linear, long-range dependencies, where existing neural Granger causality methods (cMLP, cLSTM, etc.) struggle with capacity and rely on thresholded L2 penalties.
Approach
Use sLSTM-based component-wise forecasters with a sparse input projection optimized for strict sparsity via a learned softmax reduction coefficient, a log-weighted reduction loss, and a proximal gradient compression step, avoiding post-hoc thresholds.
Key results
- On Lorenz-96 with F=40, GC-xLSTM reaches 96.3% accuracy and 96.6% balanced accuracy, outperforming all listed baselines on those metrics (GVAR 94.5/88.5).
- On fMRI, GC-xLSTM achieves 73.3% balanced accuracy versus 72.8% for TCDF and 51.3% for VAR.
- Ablation: replacing sLSTM with LSTM drops Lorentz BA from 96.6 to 93.0; replacing the joint optimization with standard group lasso drops it to 73.0.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GC-xLSTM instead of the strongest reported baseline | Lorenz-96 F=10 · Lorenz-96 F=10 | accuracy: 98.2±0.3 -> 99.1±0.2 | Helped |
| Use GC-xLSTM instead of the strongest reported baseline | Lorenz-96 F=10 · Lorenz-96 F=10 | balanced accuracy: 98.2±0.6 -> 98.5±1.0 | Helped |
| Use GC-xLSTM instead of the strongest reported baseline | Lorenz-96 F=10 · Lorenz-96 F=10 | AUROC: 99.7±0.1 -> 99.3±0.3 | Hurt |
| Use GC-xLSTM instead of the strongest reported baseline | Lorenz-96 F=40 · Lorenz-96 F=40 | accuracy: 94.5±1.0 -> 96.3±0.3 | Helped |
| Use GC-xLSTM instead of the strongest reported baseline | Lorenz-96 F=40 · Lorenz-96 F=40 | balanced accuracy: 88.6±1.4 -> 96.6±0.3 | Helped |
| Use GC-xLSTM instead of the strongest reported baseline | Lorenz-96 F=40 · Lorenz-96 F=40 | AUROC: 97.9±1.6 -> 88.0±0.2 | Hurt |
| Use GC-xLSTM instead of TCDF | fMRI · fMRI | balanced accuracy: 72.8±6.3 -> 73.3±3.0 | Helped |
| Use an xLSTM forecaster instead of a standard LSTM (ablation) | GC-xLSTM · Lorenz-96 F=40 | balanced accuracy: 93.0±0.3 -> 96.6±0.3 | Helped |
| Use an xLSTM forecaster instead of a standard LSTM (ablation) | GC-xLSTM · fMRI | balanced accuracy: 62.8±2.0 -> 73.3±3.0 | Helped |
| Use joint optimization instead of standard Group Lasso (ablation) | GC-xLSTM · Lorenz-96 F=40 | balanced accuracy: 73.0±4.6 -> 96.6±0.3 | Helped |
| Use joint optimization instead of standard Group Lasso (ablation) | GC-xLSTM · fMRI | balanced accuracy: 65.4±2.0 -> 73.3±3.0 | Helped |
Surprising findings
- On Lorenz-96 with F=40, cMLP attains the best AUROC (97.9) and GC-xLSTM's AUROC (88.0) is lower than several baselines.
Limitations
- No formal theoretical guarantees; theoretical analysis is qualitative and xLSTM blocks lack formal analysis.
- Scaling evaluated only up to dozens of variates.
- Real-world evaluation limited; sparsity hyperparameter lambda tuned per setting.
Experimental setup
Datasets: Lorenz-96 fMRI BOLD simulations simulated linear VAR Moléne weather human motion capture company fundamentals
Benchmarks: Lorenz-96 fMRI simulated VAR Moléne human motion capture company fundamentals
Metrics: accuracy balanced accuracy AUROC
Baselines: VAR cLSTM cMLP GC-KAN TCDF eSRU GVAR LSTM-based GC-xLSTM ablation
Builds on: cMLP cLSTM xLSTM group lasso adaptive lasso
Closest papers by meaning
- Jacobian Regularizer-based Neural Granger Causality (ICML 2024 · similarity 0.90)
- GCAD: Anomaly Detection in Multivariate Time Series from the Perspective of Granger Causality (AAAI 2025 · similarity 0.88)
- TNPAR: Topological Neural Poisson Auto-Regressive Model for Learning Granger Causal Structure from Event Sequences (AAAI 2024 · similarity 0.88)
- Towards the Disappearing Truth: Fine-Grained Joint Causal Influences Learning with Hidden Variable-Driven Causal Hypergraphs in Time Series (AAAI 2024 · similarity 0.86)
- Federated Granger Causality Learning For Interdependent Clients With State Space Representation (ICLR 2025 · similarity 0.86)
- CUTS+: High-Dimensional Causal Discovery from Irregular Time-Series (AAAI 2024 · similarity 0.85)
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