xLSTM-Mixer: Multivariate Time Series Forecasting by Mixing via Scalar Memories

Thank you for your detailed review of our paper and the time you took to evaluate our work, as well as for highlighting opportunities for improvement. We are pleased that you found the motivations well-summarized and the writing easy to follow. Below, we address each of the points you raised in detail:

• W1 (key properties of xLSTM-Mixer): We are happy to elaborate further. The key contribution of xLSTM-Mixer lies in the careful integration of the three mixing steps and a thorough evaluation of their effectiveness. As shown in Table 3, the use of xLSTM modules alone, without additional projections, normalizations, or appropriate weight-sharing, results in poor performance. Identifying the effective combination for forecasting and motivating the choices in Sections 2.2 and 3 are significant advancements. We have now extended the ablation study to include an aggregate of 288 experiments. Specifically, as suggested, we investigated the refinement using mLSTM instead of sLSTM blocks (column #2) and different normalization strategies (column #4).

• W2 (bidirectional xLSTM): Thank you for pointing this out. We employed unidirectional xLSTM models in our work, which indeed fixes the order of variates. Despite this limitation, combined with the advancements discussed in W1, our approach still achieved state-of-the-art performance. Extending to bidirectional xLSTMs is a promising direction for future work, as we outlined (cf. lines 543ff). Please also refer to G3 for more insights regarding the order of variates.

• W3 (lookback length): The lookback length was a hyperparameter selected through a search process, as outlined in Appendix A.1/Table 4. In line with best practices in forecasting evaluation, we conducted out-of-sample testing by splitting off the test portion from the end of the timeline (using the same data splits as previous works [1,2,3,4]), effectively addressing overfitting concerns. We agree that exploring different lookback lengths is crucial for sensitivity analysis, and we have already investigated this in Figure 6 (see lines 479-488). We have now extended the lookback analysis to include lengths up to 2048 and discuss this in the revised manuscript.

• W4 (more recent work): We respectfully disagree regarding the significance of the improvement, as xLSTM-Mixer outperforms xLSTMTime with 45 wins compared to 6 (see updated Table 2), often by a very large margin. However, we agree that recent recurrent models should be discussed more in the related work section, and we have updated that section to reference the mentioned methods. We chose not to include them in Table 2 since models like P-sLSTM would not achieve even a second-place ranking in our benchmark across datasets.

• W5 (capturing multivariate relationships): Thank you for this interesting suggestion. We have conducted additional experiments to highlight how xLSTM-Mixer captures multivariate relationships. Please refer to G2.

• W6 (outlook): The focus of this work is long-term forecasting, following recent influential publications such as PatchTST (Nie et al. [2]), MICN (Wang et al. [5]), TiDE (Das et al. [7]), and N-HiTS (Challu et al., [6]). We provided initial short-term forecasting experiments in Appendix A.2. We defer further exploration of tasks such as classification, imputation, or anomaly detection to future work. The strong performance in long-term forecasting suggests promising future research opportunities.

• Q1 (temporal ordering): This is an interesting idea; we thought about it too. The main change would likely be a deterioration of the normalization in the initial forecast, which relies on the magnitude of the last time step being representative of the subsequent forecast horizon. However, the succeeding components, namely starting with $\operatorname{FC}^\text{up}(\cdot)$, would not be affected by the dataset being shuffled that way. This is because the fully-connected layer can model connections of any hidden state to any time step. Thereby, the hidden representations are not bound to fixed time steps and can model arbitrary relationships between any number of timesteps in a flexible manner.

• Q2 (lookback length and linear baselines): Adding LTSF baselines from Zeng et al. [4] is a great suggestion to further strengthen our claims. Consequently, we have updated Figure 5 to also include NLinear.

Thank you once again for your valuable feedback and constructive suggestions. We are confident that these changes have strengthened the manuscript and are happy to provide any further clarifications you may need.

Thank you once again.

• W1 We believe this showcases the need for an initial forecast, but it is task-dependent whether we use NLinear or DLinear. This further emphasizes the importance of the xLSTM refinement along with our other contributions. Without these contributions, we would be limited to the results of either NLinear or DLinear. Moreover, our contribution was not only to evaluate whether normalization is necessary; we also conducted extensive studies, such as using initial token embeddings, exploring xLSTM block variants, analyzing explainability, and comparing the influence of time and variates similar to iTransformer. These are shown in our ablation study in Table 3, many variants of simply using xLSTM or NLinear/DLinear do not yield SOTA results. Therefore, we conducted an extensive evaluation of possible architectures and provided a detailed analysis in Section 4.2 to thoroughly assess the properties of the resulting model. Lastly, our model has demonstrated SOTA performance while requiring very limited hardware resources. Therefore, we argue against the notion that our contribution is merely incremental.

• W2 Thank you for that comment. We conducted another experiment using a dataset with significantly more variates (see the updated table 7) and found that, for longer forecasting horizons, there is indeed a significant difference in the ordering. The initial ordering appears to provide results according to the chosen hyperparameters. This supports the rationale for using a unidirectional xLSTM. However, as seen in datasets with fewer variates and lower forecasting horizons, we believe that employing a bidirectional (x)LSTM can further improve the already SOTA performance. This is why we are excited to see this explored in future work.

• W3 We assume you probably mean a fixed lookback length of 96, since all baselines are evaluated across four forecast horizons, just as we have done. We agree that comparability is key in this study, and therefore, we double-checked to ensure the results are directly comparable. For example, previous SOTA methods such as TimeMixer (Wang et al., 2024, see specifically Table 14 on p. 18), TiDE (Das et al., 2024, see specifically Section 5.1, "Baselines and Setup", "the look-back window was tuned in {24, 48, 96, 192, 336, 720}"), and NLinear/DLinear (Zeng et al., 2023, Table 2) all compare under "optimal" lookbacks when reporting their results. In practical applications, one would nearly always optimize the lookback length. We acknowledge that some works compare under a fixed lookback length, which is unfortunately not always set to 96 (e.g., Autoformer uses a different value, such as 512, as in xLSTMTime). Thus, we are confident that our finding that xLSTM-Mixer provides superior forecasting accuracy is reliable.

We hope we have convinced you that our contribution is non-trivial as well as the new experiments have sufficiently answered your outstanding concerns. We will be happy to answer any further questions and hope that the reviewer reconsiders the score.

Dear Reviewer cZwn,

Thank you for the constructive discussion. We hope to have clarified all remaining questions.

As the reviewing period will soon close, we would kindly ask you to reconsider your currently unchanged score after our extensive clarifications and significant additions. We specifically addressed your constructive comments in the revised manuscript and comments.

Regards,

The Authors

Thank you very much for your positive and insightful review of our paper. We are delighted that you found our work well-presented and appreciated our contributions, including the thorough ablation study. We value your suggestions for improvement, and below we provide detailed responses to each of your comments.

• W1 (seeds): We fully agree that performing experiments with multiple seeds is crucial for obtaining reliable results. Therefore, all experiments, including those in the appendix, were conducted with three different seeds, and the averages were reported. This information is available in the technical details in Appendix A.1, under the "Training and Hyperparameters" section.

• W2 (relation to iTransformer): You are correct in noting the similarity to the iTransformer by Liu et al. [1]. We have now referenced this work in lines 206-208 and in Section 2.3. We believe these references are helpful in understanding the context, but we are open to extending the discussion further if you think it is necessary.

• W3 (motivation for the reverse-up projection): We motivate the multi-view mixing and $\mathbf{\widehat x}^\text{up}$ in Sec. 3.3. Indeed, the ablation is super interesting. Therefore, we did that in Tab. 3., where "Mix View" indicates if that exact multi-view mixing with the reversed up-projection has been included or if only a single xLSTM pass was performed.

• W4 (reasoning for the choice of baselines): Thank you for pointing out the omission of certain baselines. Due to space constraints, we opted to focus on a subset of recent baselines that provide challenging benchmarks. Specifically, we replaced older baselines (e.g., TFT, N-BEATS, and N-HiTS) with more recent models that are significantly better across multiple categories—Transformers, MLPs, and others. Including these newer, stronger baselines ensures a more competitive evaluation.

• Q1 (adding dimensions to Fig. 1): We appreciate this suggestion. While we found that adding dimensions to Figure 1 might have made it too cluttered, we instead added more descriptive information about intermediate dimensions in Sections 3.1 to 3.3 to assist readers in understanding the architecture more clearly.

• Q2 (data requirements for transformers): Thank you for double-checking these claims. We were inspired by language modeling, where multiple studies suggest that model performance scales with increasing dataset size/token counts [2,3]. However, we fully agree with your assessment regarding time-series models. We removed this claim from ll. 41f in the revised PDF.

• Q3.1 (computational efficiency): We appreciate this suggestion for a more in-depth analysis. We have now conducted a thorough benchmarking of xLSTM-Mixer against key baselines, including Transformer-based and MLP-based models, for both training and inference. Please refer to G3.

• Q3.2 (hyperparameters): For the hyperparameters of the baseline models, we primarily relied on the Time-Series-Library [4]. For models not covered there, such as LSTM and xLSTMTime, we used information from [5] and [6], respectively.

• Q4 (further datasets): This is indeed a useful extension. We chose to include Illness (ILI) as the more challenging of the two datasets in the extended Table 2. We extended the dataset overview in Table 1 to include the Hurst exponent to better judge the complexity of the dataset. Lower numbers entail more erratic long-term behavior than higher ones. Below, you can find the full table, including Exchange:

Thank you once again for your valuable comments. We are happy to answer any further questions or provide additional clarifications if needed.

We appreciate the reviewer’s thoughtful review and recognition of the key strengths of our work, particularly the acknowledgment of our innovative model architecture and empirical performance of xLSTM-Mixer. In the following we aim to address the concerns raised.

• W1 (novelty and significance): You are right in that view mixing provides only a small benefit on Weather. However, comparing #1 and #6 in (the updated) Tab. 3 on ETTm1 shows a rather consistent improvement due to Time Mixing. We agree that more ablations with other recurrent models would be helpful, and therefore replaced the sLSTM blocks with mLSTM blocks (see the new column #2). GRUs were not originally built for multivariate data, for which reason we opted for mLSTM. We furthermore show that even the selection of initial decomposition is non-trivial (new column #4). In summary, it shows that xLSTM-Mixer is a carefully crafted model with significant efforts beyond incremental changes required for its effectiveness.

• W2 (study on computational efficiency): We totally agree that this would help better estimate the practical benefits of xLSTM-Mixer in relation to previous work. Therefore, we added an additional study on run time and peak memory usage, making sure to compare to models previously presented in Sec. 4.1. Please see G3 for details.

• W3 (focus on long-term forecasting): We focus on effective long-term forecasting, as has also been done by the famous works PatchTST (Nie et al. [2]), MICN (top 5% ICLR; Wang et al. [3]) and many other, including the renowned TiDE (Das et al., [5]) and N-HiTS (Challu et al. [4]). To still embark on further challenges as guidance for future work, we provide the short-term as an outlook. It is placed in the Appendix as it is not the core focus of the paper. We see this as sufficient and encourage readers to investigate further. Furthermore, while xLSTM-Mixer overall places second on short-term evaluation after TimeMixer, the study on computational efficiency showed that this comes with the benefit of greatly reduced memory requirements.

• W4 (more horizons): We aim to be maximally comparable to the previous literature. This is facilitated by meticulously replicated setups and best practices, including the predictions horizons also used by xLSTMTime (Alharthi et al. [6]), TimeMixer (Wang et al. [1]), TSMixer (Chen et al. [8]), NLinear/DLinear (Zeng et al. [7]), iTransformer (Liu et al. [9]), FEDFormer (Zhou et al. [10]), Autoformer (Wu et al. [11]), MICN (Wang et al. [3]), TimesNet (Wu et al. [12]), and many more, including ones that exclusively perform forecasting, such as TiDE (Das et al. [5]), N-BEATS (Oreshkin et al. [13]), N-HiTS (Challu et al. [4]), PatchTST (Nie et al. [2]). We agree with these previous works, which, based on an investigation of the respective origins of datasets, arrived at the commonly used selection of forecast horizons.

• Q1 (analyzing the learned cross-variate relationships): We agree that investigating this would shed further light on the efficacy of xLSTM-Mixer. We thus performed an attribution study that we provide in our revised mansucript. Please refer to G2 for details.

• Q2 (variate heterogeneity and temporal patterns): The temporal patterns are key to (long-term) forecasting, as demonstrated by the effectiveness of channel-independent architectures such as NLinear/DLinear by Zeng et al. [7]. However, as shown by our variate attribution study in the revised manuscript (lines 409-419 and Fig. 5), capturing relationships between variates further enhances forecast accuracy. Empirically, the heterogeneity of the variates in the considered datasets does not pose a challenge to xLSTM-Mixer, presumably due to the highly expressive sLSTM blocks.

• Q3 (variate ordering): We completely agree that such a study would greatly strengthen the evaluation and, therefore, conducted the necessary experiments. Please see G2 for the respective findings.

Thank you once again for your valuable comments. We are happy to answer any further questions or provide additional clarifications if needed.

Thank you for the response. The authors provided additional statement and analyses adds credibility to the novelty claim, the Comprehensive Evaluation of Computational Efficiency confirms that xLSTM-Mixer is computationally efficient relative to comparable models regards to the aspect of time versus model size. However, despite the improvements and ablation studies, the overall design of xLSTM-Mixer still leans towards incremental innovation, the added experiments with mLSTM blocks improve this aspect but do not fully establish paradigm-shifting advancements. The additional analysis and further experiment on learning multivariate information variate ordering does not really show a significant impact on the performance, the experiments remain relatively preliminary and may not be sufficient to fully address the broader impact of variable ordering across different datasets and tasks. Although the new experiments and materials provided by the authors are limited in depth, they go beyond the initially stated “future work” scope, demonstrating the model’s potential in this area. Therefore, this effort is reasonable and commendable. I will therefore raise my score.

Thank you for your detailed review of our paper. We appreciate the time and effort you put into evaluating our work and your constructive feedback. Your comments are invaluable in improving the manuscript even further, and we are pleased that you recognized the superior long-term forecasting performance, robustness of our model, and our contributions to recurrent model research. Below, we address the opportunities for improvement and questions you raised.

• W1/Q1 (contribution): We argue that xLSTM is not just a "base model," but a new framework and family of models [1], similar to Convolutional Neural Networks and Transformers, which have now been adapted for various tasks, including vision, robotics, and other domains [2,3,4,5]. Our work enhances their effectiveness specifically for long-term time series forecasting. A straightforward application of xLSTMs to time series data is insufficient, as demonstrated by the variations examined in our ablation study (Table 3). We contribute several essential components, including normalization, a careful combination of time and variate mixing, key up- and down-projections, and the introduction of initial token embeddings. Furthermore, view mixing is one of our original contributions. We also provide extensive analysis, including comparisons to 12 baselines across seven datasets (now eight datasets, see G2), forecast visualizations, a comprehensive ablation study, sensitivity analysis of hidden dimensions and lookbacks, and visualizations of the learned initial tokens. Following the rebuttal, we are the first to explore feature importance for xLSTMs in forecasting and, to the best of our knowledge, also for general xLSTMs.

• Q2 (explore different input/output ratios): Figure 5 already includes all possible combinations of the lookback steps ($T$) and forecast horizons ($H$) for each model. Are you suggesting we present these results differently? We would be happy to revise the presentation if it would improve clarity. See also the next response for further details.

• W2/Q3 (lookback window in Fig. 5): Thank you for pointing this out. We extended the lookback length of our model and most baselines across all four scenarios to also include $T=2048$, updating Figure 5 accordingly. This addition helps illustrate the underlying dynamics more clearly:

  • For short prediction lengths, using more than 768 time steps in the past becomes redundant, slightly impairing the model's performance.
  • For longer horizons, extending the lookback becomes increasingly beneficial for forecasting.
  • xLSTM-Mixer demonstrates consistently strong and robust performances across all scales.

• W3/Q4 (trend-seasonality): Thank you for suggesting more empirical support for our choice to forgo trend-seasonality decomposition. We have now included a thorough ablation study to evaluate this decision further. Please refer to G1 for additional insights.

• W4 (computational complexity): Thank you for pointing this out. We agree that evaluating xLSTM-Mixer's practical deployment capabilities requires a comparison of computational complexity and cost against other methods. In addition to the extended experiments involving very long lookbacks (as reflected in the updated Figure 5), which demonstrate xLSTM-Mixer's practical applicability, we also quantified its runtime and memory requirements relative to the baselines. See G3 for details. Our findings show that xLSTM-Mixer is well-suited for devices with limited resources compared to other methods (requiring in some occasions ~160 times less GPU memory than PatchTST while maintaining similar speed) and still achieves SOTA performance. We appreciate the suggestion to conduct this important experiment, which has significantly improved the manuscript. In summary, xLSTM-Mixer is lightweight compared to other recent architectures, including PatchTST, in both memory requirements and compute time, while still providing SOTA results.

Thank you once again for your valuable comments. We are happy to answer any further questions or provide additional clarifications if needed.

Dear Reviewer,

Thank you for your response.

We would like to clarify once more that there is no base model in xLSTMs.

The xLSTMs [1] are a set of building blocks that can be used to construct various architectures, rather than a standalone model. To support this point, we refer to a statement from one of the follow-up works of the original xLSTM authors:

"The Extended Long Short-Term Memory (xLSTM) family [5] was recently introduced as a new architecture for language modeling." [2]

The authors explicitly describe xLSTM as a family and a set of architectures for language modeling.

Which is why finding viable combinations of building blocks (for example that the sLSTM block is a superior choice) is already a major contribution for the time modality. If we would decline such contributions we would today still use sigmoid or tanh activations in most of our deep networks.

Additionally, in our manuscript, we conduct an ablation study on block selection (see Table 3) and further evaluate #10, where we focus solely on the pure xLSTM blocks. Moreover, xLSTMTime is the closest candidate that might be considered as an xLSTM (timeseries) base model, which we evaluate against in Tables 2, 5, and 6. However, as we stated in response Q4.1 to reviewer xNaw, we were unable to reproduce the originally claimed scores. Please refer to that response for more details.

Furthermore, we contribute several additional essential components, such as time and variate mixing, key up- and down-projections, and the introduction of initial token embeddings, which, to the best of our knowledge, we are the first to explore. Additionally, we enhance the xLSTM and XAI community by demonstrating that attribution techniques can be transferred to forecasting and xLSTMs in general (again, to the best of our knowledge, we are the first to demonstrate this). Lastly, on average, we outperform all other methods by a large margin.

We are confused if this is still not sufficient for an ICLR publication according to the reviewer.

"The responses to the concerns raised about the experimental setup for varying input/output ratios, the model's behavior at different lookback lengths, and the omission of trend-seasonality decomposition, while present, do not fully address the concerns."

We also stated in our Global Response G1 that DLinear is a viable option and for nearly all tested scenarios it does not really matter which "backbone" to use. We are unsure what else we should test here. Furthermore, regarding "varying input/output ratios," could you please revisit our Q2 response and provide more concrete action points that we could address to satisfy your expectations? Your review was not entirely clear to us in this regard.

[1] Maximilian Beck and Korbinian Pöppel and Markus Spanring and Andreas Auer and Oleksandra Prudnikova and Michael K Kopp and Günter Klambauer and Johannes Brandstetter and Sepp Hochreiter (2024). xLSTM: Extended Long Short-Term Memory. NeurIPS

[2] Benedikt Alkin and Maximilian Beck and Korbinian Pöppel and Sepp Hochreiter and Johannes Brandstetter (2024). Vision-LSTM: xLSTM as Generic Vision Backbone. ArXiv

Thank you for your constructive feedback on our paper. We appreciate the time and effort you have invested in reviewing our work. Your comments provide valuable insights that will help us enhance the quality and clarity of our paper.

We're also glad that the clarity of our presentation and visual model representations contributed to your understanding of our approach. Your acknowledgment of our contribution to advancing the xLSTM architecture in time series is motivating, and we aim to continue building on this foundation.

Regarding your suggestions for improvement and specific questions, we address them below in detail:

• W1 (deeper analysis of forecasting results): We happily expand on our findings from Sec. 4.1. Firstly, xLSTM-Mixer provides SOTA results for most settings. In some cases, particularly on Traffic, it greatly improves the MAE while not surpassing TiDE and TimeMixer on the MSE. We conjecture that this follows from the strong regularization of our mixing operations, which does constrain what the model can learn and might be slightly adverse when capturing high-frequency values and outliers (note that the minimal Hurst exponent of Traffic is very low, as shown in the update Tab. 1). Similarly, as sLSTM-Mixer strides over the variates, some particularly long-running connections have to be learned, which is rather challenging. Our response to W3 provides additional insights.

• W2 (extending the ablation study): We have already performed the ablation study on two datasets, over four horizons each, and by initializing with three seeds (i.e., by training 24 models per variation, resulting in a total of 288 models). We do agree that the ablation could be meaningfully extended by adding more model variations; however, we do not believe that adding more datasets will provide any significant new insights. We, therefore, provide additional insights into normalization based on trend-seasonality decomposition and replacing sLSTM with mLSTM blocks. These additions have been included in our ablation in Table 3 in the revised manuscript and are also addressed in G1.

• W3/Q2/Q3 (variations of variate orders): The model is indeed dependent on the ordering of variates. We empirically found this to not be a significant limitation, as the standard ordering in the dataset source was already highly effective for forecasting. We, therefore, leave models like bi-directional xLSTMs to future work (cf. ll. 543ff). However, we conducted an attribution study to verify that the model indeed effectively captures cross-variate information. We achieved this without synthetic data, ensuring the findings are truthful to the models used in the wider evaluation. We also added a new experiment that investigates the impact of variate ordering. Please also see the revised manuscript in Appendix 5.

• Q1 (clarification on "Mix View"): Thank you for pointing this out. The term refers to multi-view mixing described in Section 3.3. We updated Table 3 to clarify this.

• Q2 (evaluation on yet more datasets): We followed recent related work [1,2,3,4], which do not evaluate on Exchange (and except of [2] neither ILI), as the remaining datasets already showcase the model capabilities. However, we agree that the long/trend forecasting of ILI is an interesting evaluation opportunity due to its limited data points and challenging trend forecasting. This is further discussed in our response to FwwC, Q4. We have added the evaluation of xLSTM-Mixer and all other methods on ILI. The results can be found in the revised manuscript in Tables 2 and 6.

• Q4.1 (reproducibility challenges): We tried to address the reproducibility issues as politely as possible in lines 515-520 of our submission. Unfortunately, the work by Alharthi & Mahmood [5] does not provide any details about the chosen hyperparameters or the range used in their hyperparameter search. Their code also lacks proper configuration settings, making it difficult to replicate their experiments without modifying the code directly. We contacted the authors, but they only shared a very minimal learning rate search strategy without providing detailed results. Critical factors, such as whether an mLSTM or sLSTM block should be used, were not specified, despite their claim that the block selection is crucial for each dataset. Consequently, we attempted to find suitable configurations ourselves but were unable to achieve the reported performance. Therefore, for fairness, the reported statistics in Tables 2 and 6 are sourced directly from the original paper.

• Q4.2 (trend-seasonality decomposition): Thank you for this suggestion to extend the rigor beyond describing findings from initial model analysis. As laid out in W2 and G1, we are happy to provide this as an additional thorough ablation.

Thank you again for your valuable comments, and we are happy to answer any remaining questions you may have.

We employed normalization akin to NLinear (Zeng et al., 2023) for the initial forecast (cf. Sec. 3.1). As pointed out by several reviewers (XNaw and GoVE), we investigated whether trend-seasonality decomposition is viable as well. We extended the ablation study and updated the PDF with an extended Table 3. Comparing the baseline with NLinear in column #1 to the DLinear variant in column #4, we can see that NLinear is indeed mostly superior. However, DLinear is a viable option to improve the MSE (preventing high individual errors) in ETTm1. The slight improvement by employing normalization based on a moving average is plausible, given that ETTm1 exhibits significantly more high-frequency dynamics (see Figure 2).

As noted by 9duf (W2), GoVE (W4), and FwwC (Q3), investigating the efficiency of xLSTM-Mixer in terms of computation time and memory requirements would help evaluate its suitability for applications. We updated the PDF to contain now a "Model Efficiency" section in ll. 421-477. In summary, xLSTM-Mixer scales extremely favourable in the lookback length compared to the other models while consuming significantly less memory.

Multiple reviews suggested further investigating the role of the specific order of the variates. We analyze this from two distinct perspectives:

(1) To show which cross-variate relationships are learned by xLSTM-Mixer, we added experiments in ll 408-419, "Learning Cross-Variate Patterns". Results on more datasets can be found in Appendix A.3. In summary, xLSTM-Mixer effectively learns relationships between variates in the provided order.

(2) To assess to which degree variate ordering influences forecasting effectiveness, we conducted experiments on four different randomized orders and compared them with the standard ordering provided by the dataset source. As the results in Appendix A.5 show, the specific ordering does play some role in forecasting performance. Yet, the standard ordering already permits highly effective forecasting.

Extending xLSTM-Mixer with bi-directionality might further unlock hidden potential. Yet, we leave this open for future work to explore, as xLSTM-Mixer is already highly effective at forecasting and provides a valuable new state-of-the-art for the forecasting community.