Title: Exploring Neural Granger Causality with xLSTMs: Unveiling Temporal Dependencies in Complex Data
Venue: NeurIPS 2025
Accepted: yes
Keywords: Granger causality

xLSTM

time series
Abstract: Causality in time series can be challenging to determine, especially in the presence of non-linear dependencies. 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 GC-xLSTM.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper develops Granger causal xLSTMs that use xLSTMS to learn granger causal relations from complex time series data with long time dependencies. The paper introduces a new model (GC-LSTM), formulates an optimization process for strict sparsity and provides evaluation of the model compared to benchmark models using six datasets.\n\nSTRENGTHS AND WEAKNESSES:\nThis paper has good quality and clarity: it is organized logically, explains the background extremely well, and describes the framework in a straightforward manner. The formulations seem technically sound and the model architecture and training seem logical. In terms of originality, the paper does propose a new model type of granger causal xLSTMs and includes an additional optimization and loss function focused on sparsity. The results show that the model is able to robustly find temporal dependencies from diverse data sources.\n\nHowever, the point that is unclear for me is the significance: Why do we need this new model type? The introduction does a good job at defining granger causality, framing recent renewed interest in recurrent models and xLSTMs, and describing the combination of granger causality and xLSTMs, but what is missing here is a discussion about *why* these methods specifically should be combined, and why previous methods are not sufficient for learning long range dependencies in time series (and thereby justifying the need for this new model type).\n\nThis problem is further reiterated in the results section. I appreciate that the results section includes a wide range of results, including an ablation study, compares to many benchmarks, uses multiple datasets and provides some intuitive figures (e.g., Figure 4 in particular is very nice) showing the ability of the model to find underlying dependencies. However, these results do not convince me that this *specific* GC-xLSTM model is needed to solve the problem. For example, in Table 1 there is not a huge improvement compared to GVAR (and in some cases GVAR actually does better). Moreover, the figures (e.g., figures 3, 4, 5) do not compare with other models, making it unclear if this model learns dependencies any better than other methods.\n\nOverall, I am willing to reevaluate if the authors can provide more compelling evidence about (a) why other methods are not sufficient and (b) show a major performance improvement with this model that justifies its need. For instance, if the authors are trying to make the claim that this method is better at finding long range dependencies between time series, from the current results it is not clear that the other methods do poorly for such dependencies – addition of other figures that might show much better found dependencies for the GC-xLSTM model compared to others would be helpful (e.g., like figures 3, 4 or 5), or additional performance tables (like Table 1 or 2) on the other datasets that show a large performance improvement across a range of tasks.\n\nQUESTIONS:\n(Please see additional discussion related to these questions 1a and 1b in the Strengths & Weaknesses section).\n1a. Why are other methods not sufficient for this problem?\n1b. What is the significance of the GC-xLSTM model? Put another way, what is the particular advantage of this model? Does it better find long temporal dependencies? Can the authors provide evidence of this, and show that it has some major improvement over prior methods (as, with the current results it seems other methods actually work well.)\n\n2. Appendix C – how many samples are in each dataset? The number of variables and timesteps are listed, but not the total number of samples.\n\n3. I have additional concerns about scale, since this is a common issue with neural granger causality. Appendix F shows the scale with the variates V but how does the model scale over the number of timesteps T or the number of samples in the dataset?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper improves the detection of Granger causality using recent advances in deep learning for time series. In particular, it uses xLSTMs, which have demonstrated the ability to track longer-horizon relationships than traditional LSTMs. The paper introduces a loss function consisting of a sparsity-promoting feature selection and the xLSTM reconstruction. The new architecture is tested against a variety of GC methods on real and simulated data, where the method demonstrates good performance.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n\n**Clarity** The paper is very well-written and easy to understand.\n\n**Performance** The proposed method performs better than baselines, which are largely state-of-the-art. This is occasionally by somewhat large margins in the case of cLSTMs and cMLPs.\n\n## Weaknesses\n\n**Theoretical Analysis** I don't find the theoretical analysis particularly convincing. In particular, the point of the paper is that cLSTMs/cMLPs/etc. are not sufficient for Granger causality in complex settings, but unless I'm mistaken, the theoretical analysis applies equally well to those other architectures.\n\n**AUROC Metric** GC-xLSTM is never the best model in terms of the reported AUROC, but I'm not super sure this is a meaningful metric, anyways. If I understand correctly, it is computed by sweeping over $\\lambda$ -- but because of the group LASSO procedure done here, it's not obvious that $\\lambda = 5$ for xLSTM is similar to $\\lambda = 5$ in some other model.\n\n**Lack of Ablation** This paper contributes both xLSTM-based GC, and a novel group LASSO-based sparsity penalty -- but these are not properly ablated. Thus, we cannot properly understand to what extent performance gains are due to xLSTMs, due to the new sparsity penalty, or both.\n\n**Novelty** The use of xLSTMs rather than LSTMs is practically relevant and useful for the community, but is not significantly novel.\n\n## Minor Typos\n- Figure 6 Caption: \"extracs\" should be \"extracts\".\n- Line 313, Left Column: \"effectively inflating W it to rank\" shouldn't have \"it\".\n\nQUESTIONS:\n1. What is the effect of the xLSTM vs. the new sparsity penalty?\n\n2. Do you have any practical guidance on how to choose $\\lambda$? This would greatly improve the practicality of the method, as it seems quite sensitive.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces GC-xLSTM, a model to discover Granger causal relations from complex time series data, with a focus on long-range dependencies.\nThe method is based on a three step procedure. First, a sparse feature selector projects the input variables onto an embedding space using a sparse projection, that enables understanding what variables are relevant for predicting the future for each variable. Second, this time series of embeddings is fed to a xLSTM model trained to predict the next token. Finally, the coefficients of the sparse projection can be analyzed to reveal Granger causality. The whole method is trained end-to-end using a joint optimization technique that simulateously learns the parameters of the model and enforces sparsity. \nThe authors evaluate their method of diverse time series causality tasks such as Lorenz96 and fMRI datasets, showing it outperforms previous baselines.\n\nSTRENGTHS AND WEAKNESSES:\n- The paper tackles an important problem of inferring causality from time series. It is well written and proposes an elegant solution to the problem.\n- The authors propose an effective optimization scheme to jointly train their model while enforcing strict sparsity in the coefficients.\n- Despite the focus on long range  dependencies that may not be captured by other models, I could not find much experimental evidence for this advantage in the paper.\n- The theoretical section 3.3 is not really a theoretical section but rather a high-level motivation for their architecture. Although obvious from the architecture, the authors could consider formalizing the Granger causality inferred by their model from the sparse coefficients.\n- The long term dependency feature is directly inherited by using xLSTM and does not represent a major contribution.\n\nQUESTIONS:\n- I would like the experiments to demonstrate the added value of the optimization strategy proposed by the authors. Could the authors have an ablation of their model where they use common regularization on W and $\\alpha$ and binarize entries using a threshold $\\tau$ ? In my sense, this would validate the added value of the optimization strategy.\n- Could the authors demonstrate more directly the impact of modeling long term dependencies in practice ? \n- Similarly, the same method could be applied to any auto-regressive model. Could the authors show that using xLSTM rather than another autoregressive approach is beneficial ?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes Granger causal xLSTMs (GC-xLSTM), which leverage the recent xLSTM architecture to capture long-range relations between variables. GC-xLSTM enforces sparsity between the time series components. The authors test the method on six diverse simulated and real-world datasets.\n\nSTRENGTHS AND WEAKNESSES:\nQuality: The submission is technically sound, with appropriate explanations in the background and methods sections.\n\nClarity: The paper is clearly written and well-organized, with informative background and methods sections. I especially liked the paragraph on explaining the intuition behind the gradient update step.\n\nSignificance: Although the paper is well-structured, I do not think the paper goes beyond the current neural Granger causality methods to be impactful for the community. I think the contribution of the paper is lacking.\n\nOriginality: Although the paper explores how the recently developed xLSTM architecture performs in recovering the Granger causal relations,  I do not think that the work provides sufficiently new insights, deepens understanding, or highlights important properties of existing methods.\n\nQUESTIONS:\nI wonder how recent deep state space models perform. Some examples include [1-2], which has excelled in long-sequence modeling. I would like to get a justification for using xLSTM over other deep state space models.\n\n[1] Smith, Jimmy TH, Andrew Warrington, and Scott W. Linderman. \"Simplified state space layers for sequence modeling.\" arXiv preprint arXiv:2208.04933 (2022).\n\n[2] Gu, Albert, and Tri Dao. \"Mamba: Linear-time sequence modeling with selective state spaces.\" arXiv preprint arXiv:2312.00752 (2023).\n\nIn the architecture details paragraph, it says the linear layer predicts the next 10 steps from the preceding 10 timesteps. This number seems quite small compared to some of the long-range sequencing tasks that are used to evaluate modern long-range sequence models.\n\nIn the Main Results section, I am not fully convinced that GC-xLSTM outperforms other baseline models or provides an intuitive understanding.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-02"}

comments: SUMMARY:
This paper investigates the problem of learning Granger causality from time series with long-range dependencies. The authors propose an Extended Long Short-Term Memory (xLSTM) architecture, designed to enhance the model's ability to capture temporal dependencies relevant for Granger causal inference. Experimental results on both synthetic and real-world datasets, such as the Moléne dataset, demonstrate improved performance over existing methods.

STRENGTHS AND WEAKNESSES:
Strengths:

1. The paper is well-organized and clearly written.

2. Experiments on real-world data validate the practical utility and efficiency of the proposed approach.

Weaknesses:

1. A central concern is the identifiability of Granger causality using GC-xLSTM. Although the authors acknowledge this issue in the conclusion, it remains a critical point. In the causal discovery community, theoretical guarantees for identifiability are often essential to justify empirical findings.

2. The set of baseline methods appears outdated. I recommend organizing the baseline algorithms in a table with details such as publication year and key differences, to clarify the novelty and time-effectiveness of the proposed method.

3. The claim that existing methods fail to capture interactions between time series requires more justification. Many neural network-based methods, especially with sufficient depth and capacity, can model complex temporal dependencies. Furthermore, it remains unclear how modeling interactions enhances the identifiability of Granger causality. A more detailed explanation or illustrative example would help clarify this point.

QUESTIONS:
See Weaknesses.

LIMITATIONS:
See Weaknesses.
TITLE: Official Review
CLARITY: 3
IMPACT: 2
ORIGINALITY: 2
DATE: 2025-07-05