Exploring Neural Granger Causality with xLSTMs: Unveiling Temporal Dependencies in Complex Data (2502.09981v4)

Abstract: Causality in time series can be difficult to determine, especially in the presence of non-linear dependencies. The concept of Granger causality helps analyze potential relationships between variables, thereby offering a method to determine whether one time series can predict - Granger cause - future values of another. Although successful, Granger causal methods still struggle with capturing long-range relations between variables. To this end, we leverage the recently successful Extended Long Short-Term Memory (xLSTM) architecture and propose Granger causal xLSTMs (GC-xLSTM). It first enforces sparsity between the time series components by using a novel dynamic loss penalty on the initial projection. Specifically, we adaptively improve the model and identify sparsity candidates. Our joint optimization procedure then ensures that the Granger causal relations are recovered robustly. Our experimental evaluation on six diverse datasets demonstrates the overall efficacy of our proposed GC-xLSTM model.

• The paper introduces GC-xLSTM, a novel model using extended LSTM architecture and adaptive sparsity to uncover Granger causal relationships in complex multivariate time series data.
• Empirical results on datasets like Lorenz-96 demonstrate GC-xLSTM's effectiveness in identifying Granger causal links and providing insights into complex temporal dynamics.
• GC-xLSTM is a significant methodological evolution in time series analysis, paving the way for future research and deployment in diverse domains.

Exploring Neural Granger Causality with xLSTMs: Unveiling Temporal Dependencies in Complex Data

The paper introduces a novel approach to uncovering Granger causal relationships in multivariate time series data through the use of an extended LSTM architecture, termed GC-xLSTM. This model addresses the challenge of identifying causality in time series analyses, particularly in instances characterized by non-linear dependencies and long-range interactions. This essay examines the methodological advancements presented, empirical validations performed, and the implications for future developments in time series forecasting and causality detection.

The concept of Granger causality serves as a foundational principle to determine whether one time series can provide statistically significant predictive relevance for another, without asserting a direct causal relationship. Traditional methods leveraging vector autoregressive models (VARs) often assume linear relationships between series. However, this assumption quickly degrades in practical scenarios with complex, non-linear interactions. Deploying neural architectures, such as LSTMs, offers a potential avenue to encapsulate these non-linearities due to their inherent capability to model temporal sequences with adaptive memory gates that regulate information flow.

GC-xLSTM innovatively incorporates extended LSTM blocks that blend gated mechanisms reminiscent of those found in transformers with efficient recurrent computations. This amalgamation leverages xLSTM architecture to bolster memory handling across extended time periods, effectively capturing the prolonged dependencies typical in many real-world time series scenarios. Crucially, the model advocates a strict sparsity constraint via adaptive sparsity-inducing penalties on the projection layers of the xLSTM. By enforcing this structured sparsity, GC-xLSTM enhances model interpretability and robustness in identifying genuine Granger causal interrelationships among time series variables.

Empirical assessments carried out demonstrate the prowess of GC-xLSTM, particularly on datasets characterized by strong temporal patterns and non-linear dynamics. When evaluated on the Lorenz-96 system—a paradigmatic example illustrating chaotic non-linear dynamics—GC-xLSTM manifests competitive or superior performance in extracting Granger causal links, evidenced by notable AUROC metrics. The model's ability to unravel both local and broader scale dependencies in the Molène temperature dataset further supports its practical authority in interpreting real-world temporal patterns without a reliance on external priors.

Moreover, the analysis of human motion capture data illustrates the method's utility in translating complex bodily motion into interpretable causal graphs. This application highlights how GC-xLSTM can serve beyond prediction, acting as a tool for deeper insights into the nature of observed phenomena across domains as diverse as biomechanics and climate science.

In conclusion, GC-xLSTM represents a significant methodological evolution in time series analysis. Its integration of xLSTM architectures with adaptive, sparse feature selection provides a pathway to enhance the discovery of meaningful Granger causal relationships within complex and high-dimensional datasets. Future research could extend these capabilities through improved modeling schemes, such as incorporating attention mechanisms or multi-scale temporal representations, further solidifying the role of advanced neural architectures in causality analysis. Additionally, deploying GC-xLSTM across a broader spectrum of domains may provide further validation and improvements, enhancing its usability in financial time series, environmental monitoring, and more. The advancement of GC-xLSTM underscores the broader potential of neural networks to offer novel interpretations and decisions across fields contingent upon intricate temporal dynamics.