Title: xLSTM-Mixer: Multivariate Time Series Forecasting by Mixing via Scalar Memories
Venue: NeurIPS 2025
Accepted: yes
Keywords: time series

xLSTM

forecasting

mixing

recurrent
Abstract: Time series data is prevalent across numerous fields, necessitating the development of robust and accurate forecasting models.
 Capturing patterns both within and between temporal and multivariate components is crucial for reliable predictions.
  We introduce xLSTM-Mixer, a model designed to effectively integrate temporal sequences, joint time-variate information, and multiple perspectives for robust forecasting.
    Our approach begins with a linear forecast shared across variates, which is then refined by xLSTM blocks.
    They serve as key elements for modeling the complex dynamics of challenging time series data.
   xLSTM-Mixer ultimately reconciles two distinct views to produce the final forecast.
    Our extensive evaluations demonstrate its superior long-term forecasting performance compared to recent state-of-the-art methods while requiring very little memory.
    A thorough model analysis provides further insights into its key components and confirms its robustness and effectiveness.
    This work contributes to the resurgence of recurrent models in forecasting by combining them, for the first time, with mixing architectures.

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

Abstract

Time series data is prevalent across numerous fields, necessitating the development of robust and accurate forecasting models. Capturing patterns both within and between temporal and multivariate components is crucial for reliable predictions. We introduce xLSTM-Mixer, a model designed to effectively integrate temporal sequences, joint time-variate information, and multiple perspectives for robust forecasting. Our approach begins with a linear forecast shared across variates, which is then refined by xLSTM blocks. They serve as key elements for modeling the complex dynamics of challenging time series data. xLSTM-Mixer ultimately reconciles two distinct views to produce the final forecast. Our extensive evaluations demonstrate its superior long-term forecasting performance compared to recent state-of-the-art methods while requiring very little memory. A thorough model analysis provides further insights into its key components and confirms its robustness and effectiveness. This work contributes to the resurgence of recurrent models in forecasting by combining them, for the first time, with mixing architectures.

1 Introduction

Time series are an essential data modality ubiquitous in many critical fields of application, such as medicine [Hosseini et al., 2021], manufacturing [Essien and Giannetti, 2020], logistics [Seyedan and Mafakheri, 2020], traffic management [Lippi et al., 2013], finance [Lin et al., 2012, Divo et al., 2025], and weather modeling [Lam et al., 2023]. While significant progress in time series forecasting has been made over the decades, the field is still far from being solved. Further increasing the forecast quality obtained from machine learning models promises a manifold of improvements, such as more accurate medical treatments, increased efficiency in manufacturing and transportation, and higher crop yields.

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Historically, recurrent neural networks (RNNs) and their powerful successors were natural choices for deep learning-based time series forecasting [Hochreiter and Schmidhuber, 1997, Cho et al., 2014]. Today, large Transformers [Vaswani et al., 2017] are applied extensively to time series tasks, including forecasting. Many improvements to the vanilla architecture have since been proposed, including patching [Nie et al., 2023], decompositions [Zeng et al., 2023], and tokenization inversions [Liu et al., 2023]. Newer approaches include pretrained models, which, however, usually cannot capture relationships between multiple variables [Ansari et al., 2024]. Yet, some fundamental limitations of Transformers are yet to be lifted. For instance, they are inefficient when applied to long sequences due to the cost of the attention mechanism being quadratic in the number of variates and time steps. As embedded devices and edge computing platforms are gaining importance, the demand for lightweight forecasting models that balance accuracy with minimal memory and computational overhead grows. Therefore, recurrent and state space models (SSMs) [Patro and Agneeswaran, 2025] are experiencing a resurgence of interest in overcoming such limitations. Specifically, Beck et al. [2024] revisited recurrent models by borrowing insights gained from Transformers in many domains, specifically natural language processing. They propose Extended Long Short-Term Memory (xLSTM) models as alternatives to current sequence models.

We propose xLSTM-Mixer 1 , a new state-of-the-art method for time series forecasting using recurrent deep learning methods, which strikes a balance by providing strong forecasting accuracy while remaining highly efficient, as Fig. 1 shows. Architecturally, we combine the highly expressive xLSTM architecture with carefully crafted time, variate, and multi-view mixing. These operations regularize the training and limit the number of model parameters by weight-sharing, effectively improving the learning of features necessary for accurate forecasting. xLSTM-Mixer initially computes a channel-independent linear forecast shared over the variates. It is then up-projected to a higher hidden dimension and subsequently refined by an xLSTM stack. It performs multi-view forecasting by producing a forecast from the original and reversed up-projected embedding. The powerful xLSTM cells thereby jointly mix time and variate information to capture complex patterns from the data. Both forecasts are eventually reconciled by a learned linear projection into the final prediction, called view mixing. An overview of our method is shown in Fig. 2.

Overall, we make the following contributions:

(i) We investigate time and variate mixing in the context of recurrent models and propose a joint multistage approach that is highly effective for multivariate time series forecasting. We argue that marching over the variates instead of the temporal axis yields better results if suitably combined with temporal mixing.

(ii) We propose xLSTM-Mixer, a state-of-the-art method for time series forecasting, for the first time combining recurrent deep learning with a mixing architecture.

(iii) We extensively compare xLSTM-Mixer with existing methods for multivariate long-term time series forecasting and perform in-depth model analyses. The experiments demonstrate that xLSTM-Mixer consistently excels in a wide range of benchmarks.

Outline. In the upcoming Sec. 2, we introduce preliminaries to allow us to motivate and explain xLSTM-Mixer in Sec. 3. We then comprehensively evaluate its effectiveness and inner workings in Sec. 4. We finally review related work in Sec. 5 and close with a conclusion and outlook in Sec. 6.

2 Background

After introducing the notation used throughout this work, we review xLSTM blocks and discuss whether leveraging channel mixing or their independence is beneficial in time series models.

Notation. In multivariate time series forecasting, the model is presented with a time series X = ( x 1 , . . . , x T ) ∈ R V × T consisting of T time steps with V variates each. Given this context, the forecaster shall predict the future values Y = ( x T +1 , . . . , x T + H ) ∈ R V × H up to a horizon H . A variate (sometimes called a channel) can be any scalar measurement, such as the occupancy of a road or the temperature in a power plant. The measurements are assumed to be carried out jointly, such that the T + H time steps reflect a regularly sampled signal. A time series dataset consists of N such pairs {( X ( i ) , Y ( i ) )} i ∈{ 1 ,...,N } divided into train, validation, and test portions.

2.1 Extended Long Short-Term Memory (xLSTM)

Beck et al. [2024] propose xLSTM consisting of two building blocks, namely the sLSTM and mLSTM modules. To harness the full expressivity of xLSTMs within each step and across the computation sequence, we employ a stack of sLSTM blocks without any mLSTM blocks. The latter are less suited for joint mixing due to their independent treatment of the sequence elements, making it impossible to learn any relationships between them directly. See App. B for a deeper discussion. We will continue by recalling how sLSTM cells function. The standard LSTM architecture of Hochreiter and Schmidhuber [1997] involves updating the cell state c t through a combination of input, forget, and output gates regulating the flow of information across tokens. sLSTM blocks enhance this by incorporating exponential gating and memory mixing [Greff et al., 2017] to handle complex temporal and cross-variate dependencies better. The sLSTM updates the cell c t and hidden state h t as follows:

In this setup, the matrices W z , W i , W f , and W o are input weights mapping the input token x t to the cell input z t , input gate, forget gate, and output gate, respectively. The states n t and m t serve as necessary normalization and training stabilization, respectively. As Beck et al. have shown, it is beneficial to restrict the memory mixing performed by the recurrent weight matrices R z , R i , R f , and R o to individual heads , inspired by the multi-head setup of Transformers [Zeng et al., 2023], yet more restricted and efficient. In particular, each token gets broken up into groups of features, where the input weights W z,i,f,o act across all of them, but the recurrence matrices R z,i,f,o are implemented as block-diagonal. This permits specialization of the individual heads to patterns specific to the respective section of the tokens and empirically does not sacrifice expressivity.

2.2 Channel Independence and Mixing for Time Series

Multiple works have investigated whether it is beneficial to learn representations of the time and variate dimensions jointly or separately. Intuitively, because joint mixing is strictly more expressive, one might think it should always be preferred. And, indeed, it is used in many works including Temporal Convolutional Networks [Lea et al., 2016], N-BEATS [Oreshkin et al., 2019], N-HiTS [Challu et al., 2023], and many Transformers [Lim et al., 2021, Wu et al., 2021, Zhou et al., 2022]. However,

treating slices of the input data independently assumes an invariance to temporal or variate positions and serves as a strong regularization against overfitting, reminiscent of kernels in CNNs. Prominent models implementing some aspects of channel independence in multivariate time series forecasting are PatchTST [Nie et al., 2023] and iTransformer [Liu et al., 2023]. TiDE [Das et al., 2023], on the other hand, contains a time-step shared feature projection and temporal decoder but treats variates jointly. As Tolstikhin et al. [2021] have shown with MLP-Mixer, interleaving mixing of all channels per token and all tokens per channel does not empirically sacrifice any expressivity and instead improves performance and efficiency. This idea has since been applied to time series too, namely in architectures such as TimeMixer(++) [Wang et al., 2024a, 2025a], TSMixer [Chen et al., 2023c], WPMixer [Murad et al., 2025], and PMformer [Lee et al., 2024], and is, therefore, one key component of our method xLSTM-Mixer.

3 xLSTM-Mixer

We now explain xLSTM-Mixer shown in Fig. 2 in more detail. It carefully integrates several key components: an initial linear forecast with time mixing, joint mixing using powerful sLSTM blocks, and an eventual combination of two views by a final fully connected layer. The transposing steps between the components enable capturing complex temporal and intra-variate patterns while facilitating easy trainability and limiting parameter counts. The sLSTM blocks, in particular, can learn intricate non-linear relationships hidden within the data along both the time and variate dimensions. The architecture is furthermore equipped with normalization layers and skip connections to improve training stability and overall effectiveness.

3.1 Normalization and Initial Linear Forecast

Normalization has become an essential ingredient of modern deep learning architectures [Huang et al., 2023]. For time series in particular, reversible instance norm (RevIN) [Kim et al., 2022] is a general recipe for improving forecasting performance, where each time series instance is normalized by its mean and variance and furthermore scaled and offset by a learnable scale γ and offset β :

We apply it as part of xLSTM-Mixer, and at the end of the entire pipeline, we invert the RevIN operation to obtain the final prediction. In the case of xLSTM-Mixer, the typical skip connections found in mixer acrchitectures [Tolstikhin et al., 2021, Chen et al., 2023c] are taken up by RevIN, the normalization in the NLinear forecast [Zeng et al., 2023], and the integral skip connections within each sLSTM block.

It has been shown previously that simple linear models equipped with appropriate normalization schemes are, already by themselves, decent long-term forecasters [Zeng et al., 2023, Li et al., 2023]. Our observations confirm this finding. Therefore, we first process each variate separately by an NLinear model by computing:

where FC( · ) : R T → R H denotes a fully-connected linear layer with bias term. Sharing this model across variates limits parameter counts, and the weight-tying serves as a useful regularization. The quality of this initial forecast will be investigated in Sec. 4.1 and 4.5.

3.2 sLSTM Refinement

While the NLinear forecast x initial ∈ R V × H captures the basic patterns between the historic and future time steps, its quality alone is insufficient for today's challenging datasets. We, therefore, refine it using powerful sLSTM blocks. As a first step, it is crucial to increase the embedding dimension of the data to provide sufficient latent dimensions D for the sLSTM cells as x up = FC up ( x initial ) . This prior up-projection is similar to what is commonly performed in SSMs [Beck et al., 2024]. We weight-share FC up : R H → R D across variates to perform time-mixing similar to the initial forecast. Note that this step does not maintain the temporal ordering within the embedding token dimensions, as was the case up until this step, and instead embeds it into a higher latent dimension.

The stack of M sLSTM blocks S ( · ) transforms x up ∈ R V × D as defined in Eq. 1 to 8. The recurrent model strides over the data in variate order, i.e., where each token represents all time steps from a single variate as in the work of Liu et al. [2023]. The sLSTM blocks learn intricate non-linear relationships hidden within the data along both the time and variate dimensions. The mixing of the hidden state is still limited to blocks of consecutive dimensions, aiding efficient learning and inference while allowing for effective cross-variate interaction during the recurrent processing. Striding over variates has the benefit of linear time scaling in the number of variates at a constant number of parameters. It, however, comes at the cost of possibly fixing a suboptimal order of variates. While this is empirically not a significant limitation (see Sec. 4.4), we leave investigations into how to find a suitable ordering for future work. In addition to a large embedding dim, we observed a high number of heads being crucial for effective forecasting.

The sLSTM cells' first hidden state h 0 must be initialized before each sequence of tokens can be processed. Extending the initial description of these blocks, we propose learning a single initial embedding token η ∈ R D that gets prepended to each encoded time series x up . These initial embeddings draw from recent advances in Large Language Models, where learnable "soft prompt" tokens are used to condition models and improve their ability to generate coherent outputs [Lester et al., 2021, Li and Liang, 2021, Chen et al., 2023a,b]. Recent research has extended the application of soft prompts to LLM-based time series forecasting [Cao et al., 2023, Sun et al., 2024, Jin et al., 2024], emphasizing their adaptability and effectiveness in improving model performance across modalities. These tokens enable greater flexibility by conditioning its initial memory representation to specific dataset characteristics for dynamically interacting with the time and variate data. Soft prompts can be readily optimized through back-propagation with very little overhead.

3.3 Multi-View Mixing

To further regularize the training of the sLSTM as with the linear projections, we compute forecasts from the original embedding x up as well as the reversed embedding ̂ x up , where the order of the latent dimensions including the representation of η is inverted. Learning forecasts y ′ , y ′′ ∈ R V × D for both views while sharing weights helps learn better representations. Such multi-task learning settings are known to benefit training [Zhang and Yang, 2022]. It can also be viewed as ensembling over different variate orderings with weight sharing. The final forecast is obtained by a linear projection FC view : R D × R D → R H of the two forecasts, again per-variate. Specifically, we compute y norm = FC view ( y ′ , y ′′ ) , where y ′ = S ( x up ) and y ′′ = S ( ̂ x up ) . The final forecast is obtained after de-normalizing the reconciled forecasts as y = RevIN -1 ( y norm ) .

4 Experiments

Weconduct a series of experiments to evaluate the forecasting capabilities of xLSTM-Mixer, aiming to provide comprehensive insights into its performance. Our primary focus is on long-term forecasting, following the works of Das et al. [2023], Chen et al. [2023c], Lin et al. [2024], and Liu et al. [2025]. Further tasks are explored in Sec. 4.3. Additionally, we perform an extensive model analysis, including visualizations of the initial embedding tokens, hyperparameter sensitivity, and performance measurement. Finally, an ablation study identifies the contributions of the individual components.

Datasets. We generally follow the established benchmark procedure of Wu et al. [2021] and Zhou et al. [2021] for best backward and future comparability. The datasets we thus used are provided as an overview in App. D. Training. We follow standard practice in the forecasting literature by evaluating long-term forecasts using mean squared error (MSE) and mean absolute error (MAE). Based on our experiments, we used MAE as the training loss function since it yielded the best results. The datasets were standardized for consistency across features. In addition, we conducted all experiments three times and reported the averaged values. Further details on hyperparameter selection, metrics, and implementation can be found in App. C. Baseline Models. We compare xLSTMMixer to the recurrent models xLSTMTime [Alharthi and Mahmood, 2024] and LSTM [Hochreiter and Schmidhuber, 1997]; mixer models TimeMixer++ [Wang et al., 2025a], TimeMixer [Wang et al., 2024a], and TSMixer [Chen et al., 2023c]; MLP-based models CycleNet/MLP [Lin et al., 2024], DLinear [Zeng et al., 2023], and TiDE [Das et al., 2023]; the SSMs S-Mamba [Wang et al., 2025b] and Chimera [Behrouz et al., 2024]; the Transformers PatchTST [Nie et al., 2023] and iTransformer [Liu et al., 2023]; the convolutional architectures ModernTCN [Donghao and Xue,

Zero-shot forecasting. † Taken from Wu et al. [2022a]. ‡ Traffic/PEMS are often used during pre-training [Liu et al., 2025]. Thus, no zero-shot results are available.

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2023] and TimesNet [Wu et al., 2022a]; and the pretrained zero-shot forecasters Timer-XL [Liu et al., 2025] and MoiraiBase [Woo et al., 2024]. On choosing lookback lengths L . Some prior works on long-term forecasting fix the lookback window L for the sake of a fair comparison. However, Abdelmalak et al. [2025] and Brigato et al. [2025] argue that fixing especially to 96, which is common in today's benchmarks, can substantially distort the comparisons. When allowed to tune each model's input length, most baselines improve and simple linear or MLP backbones close much of the gap to Transformers, whereas at fixed L = 96 they appear artificially weak. We agree with these findings and therefore provide results for optimal hyperparameters for all baselines and xLSTM-Mixer in our experiments. See also Fig. 4b in Sec. 4.4 for a sensitivity analysis on L .

4.1 Long-Term Time Series Forecasting

We present the performance of xLSTM-Mixer compared to prior models in Tab. 1. The full results and standard deviations are provided in App. E. As shown, xLSTM-Mixer consistently delivers highly accurate forecasts across a wide range of datasets. It achieves the best results in 11 out of 28 cases for MSE and 16 out of 28 cases for MAE, demonstrating its superior performance in long-term forecasting. xLSTM-Mixer defines a new state-of-the-art on six out of seven datasets. This shows that xLSTM-Mixer consistently delivers excellent performance in long-term forecasting. A qualitative comparison with several baselines, including the initial forecast extracted before the sLSTM refinement, is shown in Fig. 3. Here, both the lookback window and the forecasting horizon are fixed at 96.

Significance Testing. In addition to the common practice of evaluating by counting wins across models and datasets, we perform statistical testing following the well-known practice of Demšar [2006]. First, a Friedman test ensures the model's performances follow different distributions ( p < 10 -10 ). We can then perform a Conover post-hoc test while adjusting for the family-wise error rate using Holm's method. We must restrict this comparison to one metric (MSE) and horizon (96 steps), to avoid the strongly correlated results for different horizons to artificially inflate significance levels. At a significance threshold of p = 0 . 05 , we find that xLSTM-Mixer is statistically significantly better than all other methods, except for xLSTMTime. Yet, the difference in average rank is still impressive, with 1.5 for xLSTM-Mixer and 4.0 for xLSTMTime. Furthermore, xLSTMTime is statistically inseparable from many other models, namely TimeMixer, TSMixer, ModernTCN, Chimera, PatchTST, and TiDE.

4.2 Forecasting on the GIFT-Eval Benchmark

To showcase xLSTM-Mixer's versatility beyond multivariate long-term point forecasting, we evaluate it on GIFT-Eval [Aksu et al., 2024]. It is a comprehensive benchmark for general time-series forecasting spanning diverse domains, frequencies, horizons, and both univariate and multivariate regimes. The benchmark emphasizes probabilistic assessment and supports standardized (including zero-shot) evaluation protocols. Following the official setup, we report aggregated Mean Absolute Scaled Error (MASE) and Continuous Ranked Probability Score (CRPS), where lower is better. To extend xLSTM-Mixer to probabilistic forecasting capabilities, we equip it with a head predicting quantiles, yielding full predictive distributions rather than point estimates.

Results are summarized in Tab. 2 and detailed in App. F. By CRPS, xLSTM-Mixer is the top purely supervised model (i.e., without using the GIFT-Eval pretraining corpus) and ranks 2nd overall. This demonstrates that although xLSTM-Mixer is designed for multivariate forecasting, it remains highly competitive among methods across univariate and multivariate settings and for both short and long horizons in the probabilistic regime.

Significance Testing. As in the previous Sec. 4.1, we rigorously test for the significance of the improvement of xLSTM-Mixer over the existing methods. After the initial Firedman test on the MSE, we see that xLSTM-Mixer is significantly better than all other 38 methods, except for sundial_base_128m, TiRex, and TTM-R2-Finetuned. See Fig. 5 in App. F for a complete critical difference diagram.

4.3 Outlook on Classification

To illustrate performance beyond forecasting, we evaluate xLSTM-Mixer on time-series classification by using it as an embedding model. For this, we replace the final projection layer with a single classification head. xLSTM-Mixer achieves very strong performance on standard time-series classification benchmarks (cf. App. J). These findings suggest that approaches reconciling recurrent and mixing architectures, such as xLSTM-Mixer, are highly flexible yet powerful.

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(b) Increasing the lookback window T increases forecasting performance, with xLSTM-Mixer virtually always providing the best results. Shows the MSE ( ↓ ) on the ETTm1 dataset.

4.4 Model Analysis

Initial Token Embeddings. We qualitatively inspect decodings of the initial embedding tokens η on multiple datasets to further understand and interpret the initializations learned by xLSTM-Mixer. η are decoded to a forecast y by transforming them through the sLSTM stack S and applying multi-view mixing. The resulting output of FC view can then be interpreted as the conditioning time series used to initialize the sLSTM blocks. Fig. 6 in Appendix App. G shows the dataset-specific patterns the initial embedding tokens have learned for various horizons H . Increasing prediction horizons eventually reveal underlying seasonal patterns and respective dataset dynamics.

Model Efficiency. To assess the computational resources required for using xLSTM-Mixer, we measured the average wall-clock time and peak graphics card memory required to perform a training step. Fig. 1 shows how this changes over multiple lookback lengths T and two datasets at a forecast horizon of H = 336 . Compared to baselines, xLSTM-Mixer scales extremely favorably in T , only exhibiting a negligible increase in time and memory requirements. While computations take slightly longer for larger lookback sizes, the increase is much smaller than for Transformer-based models. One advantage of TimeMixer was its efficiency over Transformers, upon which xLSTM-Mixer now significantly improves by requiring one to two orders of magnitude less memory.

Sensitivity to the xLSTM Hidden Dimension. In Fig. 4a, we visualize the performance of xLSTMMixer on the Electricity dataset with increasing sLSTM embedding hidden dimension D realized by FC up . The results indicate that a larger D enables xLSTM-Mixer to better capture the complexity of the series over extended horizons, leading to improved forecasting accuracy.

Robustness to the Lookback Length. Fig. 4b illustrates the performance of xLSTM-Mixer across varying lookback lengths T and prediction horizons H . Note that we had to rerun some experiments for TimeMixer at T = 720 with varying seeds since many training runs diverged. We observe that xLSTM-Mixer can effectively utilize longer lookback windows than the baselines, especially when compared to transformer-based models. This advantage stems from xLSTM-Mixer's avoidance of selfattention, allowing it to handle extended lookback lengths efficiently. On short prediction lengths with T ∈ { 96 , 192 } , information of more than 768 time steps in the past becomes redundant to inform the comparatively short forecast, causing models to deteriorate slightly. On longer horizons, increasingly farther lookbacks become useful for forecasting. Additionally, xLSTM-Mixer demonstrates stable and consistent performance with low variance across scales.

xLSTM-Mixer Captures Cross-Variate Patterns. To determine if our chosen ordering of variates is viable, we conduct additional experiments investigating the impact of different variate permutations in Tab. 12 in App. H. While we observe that the performance does depend to a certain extent on the ordering of variates, this does not pose a significant limitation in practice since the standard ordering provided with each dataset already yields strong forecasts. Moreover, our attribution analysis (cf. Fig. 7) confirms that xLSTM-Mixer effectively captures cross-variate interactions.

Ensembling over More than Two Views. Following the perspective that multi-view mixing is an ensemble over variate orderings, we extend our method to accommodate additional randomly permuted views beyond the original and reverse order. To this end, FC view is extended accordingly. The full results in App. I show that this does not improve the modeling accuracy of xLSTM-Mixer.

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MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE

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0.143 0.184

0.148 0.192 0.148 0.190 0.147 0.193 0.148 0.194 0.145 0.187 0.145 0.186 0.144 0.185 0.144 0.186 0.173 0.223 0.149 0.193 0.151 0.195 0.149 0.192 0.152 0.195

192

0.186 0.226

0.193 0.235 0.191 0.232 0.188 0.233 0.196 0.239 0.188 0.229 0.188 0.228

0.186 0.226

0.188 0.228 0.219 0.257 0.192 0.233 0.192 0.234 0.191 0.234 0.193 0.236

336

0.237 0.266

0.241 0.272 0.241 0.271 0.238 0.272 0.252 0.281

0.237

0.267 0.239 0.267 0.241 0.270 0.242 0.270 0.261 0.288 0.240 0.271 0.242 0.273 0.242 0.273 0.244 0.274

720

0.310 0.324 0.313 0.325 0.327 0.344 0.345 0.361 0.315 0.328 0.312 0.325 0.310 0.324

0.309 0.323 0.309 0.323

0.320 0.334 0.320 0.329 0.319 0.329 0.322 0.330 0.319 0.328

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96

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0.285 0.339 0.317 0.367 0.312 0.361 0.298 0.348

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0.329 0.277 0.329 0.278 0.331 0.279 0.333 0.295 0.338 0.282 0.339 0.285 0.341 0.281 0.337 0.284 0.339

192

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0.321 0.356 0.322 0.358 0.329 0.357 0.329 0.364 0.330 0.365 0.337 0.367 0.335 0.366

336

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0.363 0.384 0.383 0.403 0.375 0.395 0.368 0.388

0.351

0.376 0.354 0.375 0.355 0.377 0.357 0.379 0.359 0.376 0.367 0.385 0.367 0.385 0.366 0.384 0.366 0.385

720

0.409 0.407

0.417 0.414 0.440 0.432 0.447 0.441 0.420 0.416

0.409

0.408 0.411 0.408 0.413 0.411 0.414 0.411 0.412

0.407

0.422 0.412 0.422 0.413 0.417 0.410 0.418 0.411

4.5 Ablation Studies

To assess the contributions of each component in xLSTM-Mixer to its strong forecast performance, we conducted ablation studies of thirteen different model configurations with the results listed in Tab. 3. Each configuration represents a different combination of the four key components: mixing time with NLinear/DLinear, using sLSTM/mLSTM/LSTM/GRU for joint mixing, striding over the variate or time dimension, learning initial embedding tokens η , and multi-view mixing.

The full version of xLSTM-Mixer (#1), which integrates all components, achieves the best performance overall. Ablating components of xLSTM-Mixer each causes both error metrics to increase, entailing that they contribute positively to the overall architecture. Specifically, omitting xLSTM (only having LSTM, #3) raises the MAE by 6.2%/the MSE by 7.0%, variate recurrence (#5) by 4.3%/4.7%, learning initial token embedding (#7) by 0.4%/0.7%, view mixing (#8) by 0.6%/0.7%, and time mixing (#11) by 2.7%/3.1%. For example, removing the time mixing (#11) increases the MAE by 3.4% on ETTm1 at length 96 or 3.1% at length 192, highlighting its critical role in capturing cross-time dependencies. When we now omit everything except for time mixing on Weather at 192, we suffer a 13.7% performance decrease. Additionally, substituting sLSTM blocks with mLSTM, LSTM, or GRU (#2-#4) consistently degrades performance, particularly for LSTM and GRU at longer horizons. We attribute this to the sLSTM's inherent structure, which provides stronger mixing capabilities and mitigates the degradation commonly observed over extended prediction windows. However, we also observe that some configurations of xLSTM-Mixer, which exclude specific components, remain competitive. For instance, #7, which excludes the initial embedding token, still performs very well. This suggests that while it contributes positively to the overall performance, the model can sometimes still achieve competitive results without it. Similarly, depending on the dataset and target metric, initial forecasting with DLinear instead of NLinear is a viable option, too (#6).

The ablation study confirms that all components of xLSTM-Mixer contribute to its effectiveness, with the full configuration yielding the best results. Furthermore, we identified the sLSTM blocks and time-mixing components as critical for ensuring high accuracy across datasets and prediction lengths.

5 Related Work

Time Series Forecasting. Along line of machine learning research led from early statistical methods like ARIMA [Sims, 1980, Box et al., 2015] to contemporary models based on deep learning, where six architectural families take center stage: based on recurrence, state spaces, convolutions, Multilayer Perceptrons (MLPs), mixing, and Transformers. While all of them are used by practitioners today, the research focus for long-term time series forecasting is gradually shifting over time. Initially, the naturally sequential recurrent models such as Long Short-Term Memory (LSTM) [Hochreiter and Schmidhuber, 1997] and Gated Recurrent Units (GRUs) [Cho et al., 2014] were used for time series analysis. Their main benefits are the high inference efficiency and arbitrary input and output lengths due to their autoregressive nature. While their effectiveness has historically been constrained by a limited ability to capture long-range dependencies, active research remains to alleviate these limitations [Salinas et al., 2020], including the xLSTM architecture presented in Sec. 2 [Beck et al.,

2024, Alharthi and Mahmood, 2024] and SutraNets [Bergsma et al., 2023]. Closely related are state space models (SSMs) such as Mamba [Gu and Dao, 2024, Wang et al., 2025b] or Chimera [Behrouz et al., 2024], which permit parallel inference for improved efficiency. Similarly efficient, yet more restricted in their output length, are the location-invariant CNNs [Li et al., 2022, Lara-Benítez et al., 2021], such as TCN [Lea et al., 2016], TimesNet [Wu et al., 2022a], and MICN [Wang et al., 2022]. Recently, some MLP-based architectures have also shown good success, including the simplistic DLinear and NLinear models [Zeng et al., 2023], the encoder-decoder architecture of TiDE [Das et al., 2023], and the older hierarchical N-BEATS [Oreshkin et al., 2019] and N-HiTS [Challu et al., 2023] models. They are closely related to other mixing architectures such as TimeMixer(++) [Wang et al., 2024a, 2025a] and TSMixer [Chen et al., 2023c]. A lot of accurate models with significant compute costs have been proposed based on Transformers [Vaswani et al., 2017], such as Autoformer [Wu et al., 2021], TFT [Lim et al., 2021], FEDFormer [Zhou et al., 2022], PatchTST [Nie et al., 2023], and iTransformer [Liu et al., 2023]. Finally, the most recent development are pretrained models fitted on multiple time series datasets [Kraus et al., 2024]. Examples include Chronos [Ansari et al., 2024], Moirai [Woo et al., 2024], and Timer-XL [Liu et al., 2025]. xLSTM-Mixer combines two model families, namely the highly expressive mixing models with efficient recurrence, to benefit from the strengths of both.

xLSTM Models for Time Series. Some initial experiments of applying xLSTMs [Beck et al., 2024] to time series were already performed by Alharthi and Mahmood [2024] with their proposed xLSTMTime model. While it showed promising forecasting performance, these initial soundings did not surpass stronger models at that time, such as TimeMixer [Wang et al., 2024a], on multivariate benchmarks. Furthermore, despite our best efforts, the experimental findings unfortunately could not be replicated with either the official implementation or the scarce details in the paper. We ensure that our method xLSTM-Mixer is well-suited as a foundation for further research by providing extensive model analysis, an ablation study with 13 variations, and ensuring that results are readily reproducible. Our methodology draws from xLSTMTime yet improves on it by several key components. Most importantly, our novel multi-view mixing consistently enhances forecasting performance. Furthermore, we find the trend-seasonality decomposition redundant and a simple NLinear normalization scheme [Zeng et al., 2023] to suffice. Concurrently, Kong et al. [2024] also investigate using xLSTMs for time series forecasting, arriving at similar conclusions. Poonia et al. [2025] successfully employ xLSTMs to detect Granger Causality in time series.

6 Conclusion

In this work, we introduced xLSTM-Mixer, a method that combines a linear forecast with refinement through xLSTM blocks. Our architecture integrates time, joint, and view mixing to capture complex dependencies. In long-term forecasting, xLSTM-Mixer consistently achieves state-of-the-art performance, outperforming a large set of previous methods in 27 out of 56 cases. We also evaluate xLSTM-Mixer in heterogeneous probabilistic settings on GIFT-Eval, where it delivers strong, competitive performance. Beyond forecasting, xLSTM-Mixer performs strongly on time-series classification when used as an embedding model. Moreover, xLSTM-Mixer attains these results at a low memory footprint. Our model analysis provided insights into the contribution of each component and demonstrated robustness to hyperparameter variations.

Limitations. While xLSTM-Mixer achieves strong accuracy with limited compute, certain assumptions need to be met for it to be applicable. Specifically, it assumes that all variables are sampled on a uniform time grid, meaning that irregular or missing timestamps must still be handled in pre-processing. Furthermore, treating variates as the sequential axis ties runtime and memory directly to the number of channels, which can become a bottleneck for extremely high-dimensional multivariate time-series. Moreover, the simultaneous mixing of multiple views blends temporal and cross-channel information in ways that make detailed attributions difficult.

Future Work. Addressing these aspects through adaptive variate grouping, continuous-time embeddings, and lightweight explanation modules are potential paths forward beyond the current work. Finally, extending xLSTM-Mixer to tasks such as imputation or anomaly detection offers promising future directions.

References

Ibram Abdelmalak, Kiran Madhusudhanan, Jungmin Choi, Maximilian Stubbemann, and Lars Schmidt-Thieme. Channel Dependence, Limited Lookback Windows, and the Simplicity of Datasets: How Biased is Time Series Forecasting? ArXiv:2502.09683 , 2025.

Takuya Akiba, Shotaro Sano, Toshihiko Yanase, Takeru Ohta, and Masanori Koyama. Optuna: A Next-generation Hyperparameter Optimization Framework. In Proceedings of the ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) , 2019.

Taha Aksu, Gerald Woo, Juncheng Liu, Xu Liu, Chenghao Liu, Silvio Savarese, Caiming Xiong, and Doyen Sahoo. GIFT-eval: a benchmark for general time series forecasting model evaluation. ArXiv:2410.10393 , 2024.

Alexander Alexandrov, Konstantinos Benidis, Michael Bohlke-Schneider, Valentin Flunkert, Jan Gasthaus, Tim Januschowski, Danielle C. Maddix, Syama Sundar Rangapuram, David Salinas, Jasper Schulz, Lorenzo Stella, Ali Caner Türkmen, and Yuyang Wang. GluonTS: Probabilistic and neural time series modeling in python. Journal of Machine Learning Research , 21:116:1-116:6, 2020.

Musleh Alharthi and Ausif Mahmood. xLSTMTime: Long-Term Time Series Forecasting with xLSTM. MDPI AI , 5(3):1482-1495, 2024.

Abdul Fatir Ansari, Lorenzo Stella, Ali Caner Turkmen, Xiyuan Zhang, Pedro Mercado, Huibin Shen, Oleksandr Shchur, Syama Sundar Rangapuram, Sebastian Pineda Arango, Shubham Kapoor, Jasper Zschiegner, Danielle C. Maddix, Hao Wang, Michael W. Mahoney, Kari Torkkola, Andrew Gordon Wilson, Michael Bohlke-Schneider, and Bernie Wang. Chronos: Learning the Language of Time Series. Transactions on Machine Learning Research , 2024.

Andreas Auer, Patrick Podest, Daniel Klotz, Sebastian Böck, Günter Klambauer, and Sepp Hochreiter. TiRex: Zero-shot forecasting across long and short horizons with enhanced in-context learning. ArXiv:2505.23719 , 2025.

Maximilian Beck, Korbinian Pöppel, Markus Spanring, Andreas Auer, Oleksandra Prudnikova, Michael K. Kopp, Günter Klambauer, Johannes Brandstetter, and Sepp Hochreiter. xLSTM: Extended Long Short-Term Memory. In Proceedings of the Conference on Neural Information Processing Systems (NeurIPS) , 2024.

Ali Behrouz, Michele Santacatterina, and Ramin Zabih. Chimera: Effectively Modeling Multivariate Time Series with 2-Dimensional State Space Models. In Proceedings of the Conference on Neural Information Processing Systems (NeurIPS) , 2024.

Shane Bergsma, Tim Zeyl, and Lei Guo. SutraNets: Sub-series Autoregressive Networks for LongSequence, Probabilistic Forecasting. In Proceedings of the Conference on Neural Information Processing Systems (NeurIPS) , 2023.

Donald J Berndt and James Clifford. Using Dynamic Time Warping to Find Patterns in Time Series. In KDD Workshop: Knowledge Discovery in Databases , 1994.

George EP Box, Gwilym M Jenkins, Gregory C Reinsel, and Greta M Ljung. Time series analysis: forecasting and control . John Wiley & Sons, 2015.

Lorenzo Brigato, Rafael Morand, Knut Strømmen, Maria Panagiotou, Markus Schmidt, and Stavroula Mougiakakou. Position: There are no Champions in Long-Term Time Series Forecasting. ArXiv:2502.14045 , 2025.

David Campos, Miao Zhang, Bin Yang, Tung Kieu, Chenjuan Guo, and Christian S. Jensen. LightTS: Lightweight Time Series Classification with Adaptive Ensemble Distillation. Proc. ACM Manag. Data , 1(2):171:1-171:27, 2023.

Defu Cao, Furong Jia, Sercan O. Arik, Tomas Pfister, Yixiang Zheng, Wen Ye, and Yan Liu. TEMPO: Prompt-based Generative Pre-trained Transformer for Time Series Forecasting. In Proceedings of the International Conference on Learning Representations (ICLR) , 2023.

Cristian Challu, Kin G. Olivares, Boris Oreshkin, Federico Ramirez, Max Canseco, and Artur Dubrawski. NHITS: Neural Hierarchical Interpolation for Time Series Forecasting. In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI) , 2023.

Jiuhai Chen, Lichang Chen, Chen Zhu, and Tianyi Zhou. How many demonstrations do you need for in-context learning? Findings of the Association for Computational Linguistics , pages 1114911159, 2023a.

Lichang Chen, Heng Huang, and Minhao Cheng. Ptp: Boosting stability and performance of prompt tuning with perturbation-based regularizer. In Proceedings of the Conference on Empirical Methods in Natural Language Processing (EMNLP) , 2023b.

Si-An Chen, Chun-Liang Li, Nathanael C Yoder, Sercan Ö Arık, and Tomas Pfister. TSMixer: An All-MLP Architecture for Time Series Forecasting. Transactions on Machine Learning Research , 2023c.

Tianqi Chen and Carlos Guestrin. XGBoost: A Scalable Tree Boosting System. In Proceedings of the ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) , 2016.

Kyunghyun Cho, Bart van Merriënboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Holger Schwenk, and Yoshua Bengio. Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation. In Proceedings of the Conference on Empirical Methods in Natural Language Processing (EMNLP) , 2014.

Abhimanyu Das, Weihao Kong, Andrew Leach, Shaan K. Mathur, Rajat Sen, and Rose Yu. Long-term Forecasting with TiDE: Time-series Dense Encoder. Transactions on Machine Learning Research , 2023.

Angus Dempster, François Petitjean, and Geoffrey I. Webb. ROCKET: exceptionally fast and accurate time series classification using random convolutional kernels. Data Mining and Knowledge Discovery , 34(5):1454-1495, 2020.

Janez Demšar. Statistical Comparisons of Classifiers over Multiple Data Sets. Journal of Machine Learning Research , 7:1-30, 2006.

Felix Divo, Eric Endress, Kevin Endler, Kristian Kersting, and Devendra Singh Dhami. Forecasting Company Fundamentals. Transactions on Machine Learning Research , 2025.

Luo Donghao and Wang Xue. ModernTCN: A Modern Pure Convolution Structure for General Time Series Analysis. In Proceedings of the International Conference on Learning Representations (ICLR) , 2023.

Aniekan Essien and Cinzia Giannetti. A Deep Learning Model for Smart Manufacturing Using Convolutional LSTM Neural Network Autoencoders. IEEE Transactions on Industrial Informatics , 16(9):6069-6078, 2020.

Klaus Greff, Rupesh Kumar Srivastava, Jan Koutník, Bas R. Steunebrink, and Jürgen Schmidhuber. LSTM: A Search Space Odyssey. IEEE Transactions on Neural Networks and Learning Systems , 28(10):2222-2232, 2017.

Albert Gu and Tri Dao. Mamba: Linear-Time Sequence Modeling with Selective State Spaces. In Proceedings of the Conference on Language Modeling (COLM) , 2024.

Albert Gu, Karan Goel, and Christopher Re. Efficiently Modeling Long Sequences with Structured State Spaces. In Proceedings of the International Conference on Learning Representations (ICLR) , 2022.

Sepp Hochreiter and Jürgen Schmidhuber. Long Short-Term Memory. Neural Computation , 9(8): 1735-1780, 1997.

Mohammad-Parsa Hosseini, Amin Hosseini, and Kiarash Ahi. A Review on Machine Learning for EEG Signal Processing in Bioengineering. IEEE Reviews in Biomedical Engineering , 14:204-218, 2021.

Lei Huang, Jie Qin, Yi Zhou, Fan Zhu, Li Liu, and Ling Shao. Normalization Techniques in Training DNNs: Methodology, Analysis and Application. IEEE Transactions on Pattern Analysis and Machine Intelligence , 45(8):10173 - 10196, 2023.

E. Hurst. Long-Term Storage Capacity of Reservoirs. Transactions of the American Society of Civil Engineers , 116(1):770-799, 1951.

Ming Jin, Shiyu Wang, Lintao Ma, Zhixuan Chu, James Y. Zhang, Xiaoming Shi, Pin-Yu Chen, Yuxuan Liang, Yuan-Fang Li, Shirui Pan, and Qingsong Wen. Time-LLM: Time Series Forecasting by Reprogramming Large Language Models. In Proceedings of the International Conference on Learning Representations (ICLR) , 2024.

Taesung Kim, Jinhee Kim, Yunwon Tae, Cheonbok Park, Jang-Ho Choi, and Jaegul Choo. Reversible Instance Normalization for Accurate Time-Series Forecasting against Distribution Shift. In Proceedings of the International Conference on Learning Representations (ICLR) , 2022.

Diederik P. Kingma and Jimmy Ba. Adam: A Method for Stochastic Optimization. In Proceedings of the International Conference on Learning Representations (ICLR) , 2015.

Nikita Kitaev, Łukasz Kaiser, and Anselm Levskaya. Reformer: The Efficient Transformer. In Proceedings of the International Conference on Learning Representations (ICLR) , 2020.

Narine Kokhlikyan, Vivek Miglani, Miguel Martin, Edward Wang, Bilal Alsallakh, Jonathan Reynolds, Alexander Melnikov, Natalia Kliushkina, Carlos Araya, Siqi Yan, and Orion ReblitzRichardson. Captum: A unified and generic model interpretability library for PyTorch. ArXiv.2009.07896 , 2020.

Yaxuan Kong, Zepu Wang, Yuqi Nie, Tian Zhou, Stefan Zohren, Yuxuan Liang, Peng Sun, and Qingsong Wen. Unlocking the Power of LSTM for Long Term Time Series Forecasting. In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI) , 2024.

Maurice Kraus, Felix Divo, David Steinmann, Devendra Singh Dhami, and Kristian Kersting. United We Pretrain, Divided We Fail! Representation Learning for Time Series by Pretraining on 75 Datasets at Once. ArXiv 2402.15404 , 2024.

Maurice Kraus, David Steinmann, Antonia Wüst, Andre Kokozinski, and Kristian Kersting. Right on Time: Revising Time Series Models by Constraining their Explanations. In Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases (ECML PKDD) , 2025.

Guokun Lai, Wei-Cheng Chang, Yiming Yang, and Hanxiao Liu. Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks. In Proceedings of the International ACM SIGIR Conference on Research & Development in Information Retrieval (SIGIR) , 2018.

Remi Lam, Alvaro Sanchez-Gonzalez, Matthew Willson, Peter Wirnsberger, Meire Fortunato, Ferran Alet, Suman Ravuri, Timo Ewalds, Zach Eaton-Rosen, Weihua Hu, Alexander Merose, Stephan Hoyer, George Holland, Oriol Vinyals, Jacklynn Stott, Alexander Pritzel, Shakir Mohamed, and Peter Battaglia. Learning skillful medium-range global weather forecasting. Science , 382(6677): 1416-1421, 2023.

Pedro Lara-Benítez, Manuel Carranza-García, and José C. Riquelme. An Experimental Review on Deep Learning Architectures for Time Series Forecasting. International Journal of Neural Systems , 31(03):2130001, 2021.

Colin Lea, René Vidal, Austin Reiter, and Gregory D. Hager. Temporal Convolutional Networks: A Unified Approach to Action Segmentation. ECCV Workshops , 2016:47-54, 2016.

Jaehoon Lee, Hankook Lee, Sungik Choi, Sungjun Cho, and Moontae Lee. Partial-multivariate model for forecasting. ArXiv:2408.09703 , 2024.

Brian Lester, Rami Al-Rfou, and Noah Constant. The Power of Scale for Parameter-Efficient Prompt Tuning. In Marie-Francine Moens, Xuanjing Huang, Lucia Specia, and Scott Wen-tau Yih, editors, Proceedings of the Conference on Empirical Methods in Natural Language Processing (EMNLP) , 2021.

Xiang Lisa Li and Percy Liang. Prefix-tuning: Optimizing continuous prompts for generation. In Proceedings of the International Joint Conference on Natural Language Processing (AACL) , 2021.

Zewen Li, Fan Liu, Wenjie Yang, Shouheng Peng, and Jun Zhou. A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospects. IEEE Transactions on Neural Networks and Learning Systems , 33(12):6999-7019, 2022.

Zhe Li, Shiyi Qi, Yiduo Li, and Zenglin Xu. Revisiting Long-term Time Series Forecasting: An Investigation on Linear Mapping. ArXiv:2305.10721 , 2023.

Bryan Lim, Sercan Ö. Arık, Nicolas Loeff, and Tomas Pfister. Temporal Fusion Transformers for interpretable multi-horizon time series forecasting. International Journal of Forecasting , 37(4): 1748-1764, 2021.

Shengsheng Lin, Weiwei Lin, Xinyi Hu, Wentai Wu, Ruichao Mo, and Haocheng Zhong. CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns. In Proceedings of the Conference on Neural Information Processing Systems (NeurIPS) , 2024.

Wei-Yang Lin, Ya-Han Hu, and Chih-Fong Tsai. Machine Learning in Financial Crisis Prediction: A Survey. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews) , 42(4):421-436, 2012.

Marco Lippi, Matteo Bertini, and Paolo Frasconi. Short-Term Traffic Flow Forecasting: An Experimental Comparison of Time-Series Analysis and Supervised Learning. IEEE Transactions on Intelligent Transportation Systems , 14(2):871-882, 2013.

Shizhan Liu, Hang Yu, Cong Liao, Jianguo Li, Weiyao Lin, Alex X. Liu, and Schahram Dustdar. Pyraformer: Low-Complexity Pyramidal Attention for Long-Range Time Series Modeling and Forecasting. In Proceedings of the International Conference on Learning Representations (ICLR) , 2021.

Yong Liu, Haixu Wu, Jianmin Wang, and Mingsheng Long. Non-stationary transformers: exploring the stationarity in time series forecasting. In Proceedings of the Conference on Neural Information Processing Systems (NeurIPS) , 2022.

Yong Liu, Tengge Hu, Haoran Zhang, Haixu Wu, Shiyu Wang, Lintao Ma, and Mingsheng Long. iTransformer: Inverted Transformers Are Effective for Time Series Forecasting. In Proceedings of the International Conference on Learning Representations (ICLR) , 2023.

Yong Liu, Guo Qin, Xiangdong Huang, Jianmin Wang, and Mingsheng Long. Timer-XL: LongContext Transformers for Unified Time Series Forecasting. In Proceedings of the International Conference on Learning Representations (ICLR) , 2025.

William Merrill, Zhaofeng Wu, Norihito Naka, Yoon Kim, and Tal Linzen. Can you learn semantics through next-word prediction? The case of entailment. In Lun-Wei Ku, Andre Martins, and Vivek Srikumar, editors, Findings of the association for computational linguistics (ACL) , 2024.

Md Mahmuddun Nabi Murad, Mehmet Aktukmak, and Yasin Yilmaz. WPMixer: Efficient multiresolution mixing for long-term time series forecasting. In Toby Walsh, Julie Shah, and Zico Kolter, editors, Proceedings of the AAAI Conference on Artificial Intelligence (AAAI) , 2025.

Yuqi Nie, Nam H. Nguyen, Phanwadee Sinthong, and Jayant Kalagnanam. A Time Series is Worth 64 Words: Long-term Forecasting with Transformers. In Proceedings of the International Conference on Learning Representations (ICLR) , 2023.

Boris N. Oreshkin, Dmitri Carpov, Nicolas Chapados, and Yoshua Bengio. N-BEATS: Neural basis expansion analysis for interpretable time series forecasting. In Proceedings of the International Conference on Learning Representations (ICLR) , 2019.

Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala. PyTorch: An Imperative Style, High-Performance Deep Learning Library. In Proceedings of the Conference on Neural Information Processing Systems (NeurIPS) , 2019.

Badri Narayana Patro and Vijay Srinivas Agneeswaran. Mamba-360: Survey of State Space Models as Transformer Alternative for Long Sequence Modelling: Methods, Applications, and Challenges. Engineering Applications of Artificial Intelligence , 159:111279, 2025.

Harsh Poonia, Felix Divo, Kristian Kersting, and Devendra Singh Dhami. Exploring neural granger causality with xLSTMs: Unveiling temporal dependencies in complex data. In Proceedings of the Conference on Neural Information Processing Systems (NeurIPS) , 2025.

David Salinas, Valentin Flunkert, Jan Gasthaus, and Tim Januschowski. DeepAR: Probabilistic forecasting with autoregressive recurrent networks. International Journal of Forecasting , 36(3): 1181-1191, 2020.

Mahya Seyedan and Fereshteh Mafakheri. Predictive big data analytics for supply chain demand forecasting: methods, applications, and research opportunities. Journal of Big Data , 7(1):53, 2020.

Christopher A. Sims. Macroeconomics and Reality. Econometrica , 48(1):1-48, 1980.

Chenxi Sun, Hongyan Li, Yaliang Li, and Shenda Hong. TEST: Text prototype aligned embedding to activate LLM's ability for time series. In Proceedings of the International Conference on Learning Representations (ICLR) , 2024.

Maksim A. Terpilowski. scikit-posthocs: Pairwise multiple comparison tests in Python. Journal of Open Source Software , 4(36):1169, 2019.

Ilya O Tolstikhin, Neil Houlsby, Alexander Kolesnikov, Lucas Beyer, Xiaohua Zhai, Thomas Unterthiner, Jessica Yung, Andreas Steiner, Daniel Keysers, Jakob Uszkoreit, Mario Lucic, and Alexey Dosovitskiy. MLP-Mixer: An all-MLP Architecture for Vision. In Proceedings of the Conference on Neural Information Processing Systems (NeurIPS) , 2021.

Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is All you Need. In Proceedings of the Conference on Neural Information Processing Systems (NeurIPS) , 2017.

Huiqiang Wang, Jian Peng, Feihu Huang, Jince Wang, Junhui Chen, and Yifei Xiao. MICN: Multiscale Local and Global Context Modeling for Long-term Series Forecasting. In Proceedings of the International Conference on Learning Representations (ICLR) , 2022.

Shiyu Wang, Haixu Wu, Xiaoming Shi, Tengge Hu, Huakun Luo, Lintao Ma, James Y. Zhang, and Jun Zhou. TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting. In Proceedings of the International Conference on Learning Representations (ICLR) , 2024a.

Shiyu Wang, Jiawei Li, Xiaoming Shi, Zhou Ye, Baichuan Mo, Wenze Lin, Ju Shengtong, Zhixuan Chu, and Ming Jin. TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis. In Proceedings of the International Conference on Learning Representations (ICLR) , 2025a.

Yuxuan Wang, Haixu Wu, Jiaxiang Dong, Yong Liu, Mingsheng Long, and Jianmin Wang. Deep Time Series Models: A Comprehensive Survey and Benchmark. ArXiv.2407.13278 , 2024b.

Zihan Wang, Fanheng Kong, Shi Feng, Ming Wang, Xiaocui Yang, Han Zhao, Daling Wang, and Yifei Zhang. Is Mamba effective for time series forecasting? Neurocomputing , 619:129178, 2025b.

Gerald Woo, Chenghao Liu, Doyen Sahoo, Akshat Kumar, and Steven Hoi. ETSformer: Exponential Smoothing Transformers for Time-series Forecasting. ArXiv.2202.01381 , 2022.

Gerald Woo, Chenghao Liu, Akshat Kumar, Caiming Xiong, Silvio Savarese, and Doyen Sahoo. Unified Training of Universal Time Series Forecasting Transformers. In Proceedings of the International Conference on Machine Learning (ICML) , 2024.

Haixu Wu, Jiehui Xu, Jianmin Wang, and Mingsheng Long. Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting. In Proceedings of the Conference on Neural Information Processing Systems (NeurIPS) , 2021.

Haixu Wu, Tengge Hu, Yong Liu, Hang Zhou, Jianmin Wang, and Mingsheng Long. TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis. In Proceedings of the International Conference on Learning Representations (ICLR) , 2022a.

Haixu Wu, Jialong Wu, Jiehui Xu, Jianmin Wang, and Mingsheng Long. Flowformer: Linearizing Transformers with Conservation Flows. In Proceedings of the International Conference on Machine Learning (ICML) , 2022b.

Ailing Zeng, Muxi Chen, Lei Zhang, and Qiang Xu. Are Transformers Effective for Time Series Forecasting? In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI) , 2023.

Yu Zhang and Qiang Yang. A Survey on Multi-Task Learning. IEEE Transactions on Knowledge and Data Engineering , 34(12):5586-5609, 2022.

Haoyi Zhou, Shanghang Zhang, Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, and Wancai Zhang. Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting. In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI) , 2021.

Tian Zhou, Ziqing Ma, Qingsong Wen, Xue Wang, Liang Sun, and Rong Jin. FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting. In Proceedings of the International Conference on Machine Learning (ICML) , 2022.

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A Societal Impact

This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here.

Our research advances machine learning by enhancing the capabilities of long-term forecasting in time series models, significantly improving both accuracy and efficiency. By developing xLSTM-Mixer, we introduce a robust framework that can be applied across various industries, including finance, healthcare, energy, and logistics. The improved forecasting accuracy enables better decision-making in critical areas, such as optimizing resource allocation, predicting market trends, and managing risk.

However, we also recognize the potential risks associated with the misuse of these advanced models. Time series forecasting models could be leveraged for malicious purposes, especially when applied at scale. For example, in the financial sector, adversarial agents might manipulate forecasts to create market instability. In political or social contexts, these models could be exploited to predict and influence public opinion or destabilize economies. Additionally, the application of these models in sensitive domains like healthcare and security may lead to unintended consequences if not carefully regulated and ethically deployed.

Therefore, it is essential that the use of xLSTM-Mixer, like all machine learning technologies, is guided by responsible practices and ethical considerations. We encourage stakeholders to adopt rigorous evaluation processes to ensure fairness, transparency, and accountability in its deployment, and to remain vigilant to the broader societal implications of time series forecasting technologies.

B Rationale for Employing sLSTM over mLSTM

Beck et al. [2024] present a comprehensive case for xLSTM blocks over earlier recurrent models. Here, we explain why, within those, we choose scalar-memory sLSTM blocks as our mixing primitive rather than mLSTM. The primary motivation is the state tracking via memory mixing. sLSTM preserves hidden-to-hidden recurrences in its gates and cell update, enabling conditional, historyaware updates. mLSTM removes these paths to allow full parallelization, which limits this state tracking capability.

Mechanisms of sLSTM and mLSTM. The sLSTM block maintains the LSTM-style memory mixing, augmented with exponential gates and a stabilization term:

Here, f t , i t , o t each depend on h t -1 through recurrent matrices (Beck et al. [2024], Greff et al. [2017]), allowing the block to blend past and present conditionally. By contrast, mLSTM writes key-value pairs into a matrix memory:

with gates that depend only on the current input (no hidden-to-hidden paths) [Beck et al., 2024, Sec. 2.3]. This design eliminates memory mixing. Note that we use the scalar formulation for simplicity, whereas Sec. 2.1 directly presented the full vector-valued xLSTMs.

Importance of Latent Phases. In long-horizon forecasting, tracking latent phases (e.g., heating ↔ cooling; up ↔ down) is critical. With sLSTM, gates can be trained such that, upon detection of a switch cue, the cell overwrites ( i t ≈ 1 , f t ≈ 0 ); otherwise, it retains ( i t ≈ 0 , f t ≈ 1 ). Because the gates read h t -1 , the decision is conditional on the current internal state. In mLSTM, gates cannot use h t -1 , meaning updates become fixed linear functionals of the input history. Empirically, architectures lacking memory mixing (mLSTM, Mamba, Transformers) fail simple state-tracking tasks such as parity, as shown by Merrill et al. [2024] and Beck et al. [2024].

Design Consequences. For long-horizon forecasting, state-tracking capacity outweighs raw matrixmemory capacity, precluding the direct learning of inter-token relations during joint mixing. We, thus, exclusively employ sLSTM in xLSTM-Mixer. In our ablations, replacing sLSTM with mLSTM, GRU, or LSTM consistently harms long-horizon accuracy, particularly at 336/720 steps (cf. Tab. 3). Prior and concurrent work supports this finding: xLSTMTime uses sLSTM on smaller forecasting datasets where precise phase tracking dominates and opts for mLSTM only when raw storage capacity is paramount [Alharthi and Mahmood, 2024]. TiRex likewise attributes gains to retaining state tracking [Auer et al., 2025].

C Implementation Details

Experimental Details. Our codebase is implemented in Python 3.11, leveraging PyTorch version 2. [Paszke et al., 2019] in combination with Lightning version 2.4 2 for model training and optimization. We used the custom CUDA implementation 3 for sLSTM, which relies on NVIDIA Compute Capability ≥ 8.0. Thus, our experiments were conducted on a single NVIDIA A100 80GB GPU. The majority of our baseline implementations, along with data loading and preprocessing steps, are adapted from the Time-Series-Library 4 of Wang et al. [2024b]. For GIFT-Eval [Aksu et al., 2024], we integrated xLSTM-Mixer into the official evaluation harness via a GluonTS -style [Alexandrov et al., 2020] estimator. For xLSTMTime, we used code based on the official repository 5 . We employ Captum 6 [Kokhlikyan et al., 2020] to compute the SHAP values used in model analysis. We used scikit-posthocs [Terpilowski, 2019] for significance analyses.

Training and Hyperparameters. We optimized xLSTM-Mixer in 32 bits for up to 60 epochs with a cosine-annealing scheduler with the Adam optimizer [Kingma and Ba, 2015], using β 1 = 0 . 9 and β 2 = 0 . 999 and no weight decay. Hyperparameter (HP) tuning was conducted using Optuna [Akiba et al., 2019] with the choices provided in Tab. 4. We optimized for the L1 forecast error, also known as the Mean Absolute Error (MAE). To further stabilize the training process, gradient clipping with a maximum norm of 1 . 0 was applied. All experiments were run with the three different random seeds { 2021 , 2022 , 2023 } . For most models, the initial publications already provide HPs appropriate for the well-known datasets, where we thus directly adopt these results. For xLSTMTime, this was not the case, and we were not able to fully reproduce the results in the paper despite our best efforts (cf. Sec. 5). We still present the better results from Alharthi and Mahmood [2024] so as not to erroneously underestimate the method. For the datasets ETTh2, ETTm1, and ETTm2 without such results, we ran individual HP searches analogously to our method to ensure a fair comparison.

Forecasting Metrics. We follow common practice in the literature [Wu et al., 2021, Wang et al., 2024a] for maximum comparability and, therefore, evaluate deterministic long-term forecasting of all models on the mean absolute error (MAE), mean squared error (MSE). For probabilistic evaluation (as in GIFT-Eval [Aksu et al., 2024]), we use the Mean Absolute Scaled Error (MASE) and the Continuous Ranked Probability Score (CRPS). All metrics are computed per variate and averaged over all variates. Formally,

The CRPS for predictive CDF ˆ F and outcome y is

where y are the targets, ˆ y the predictions; H is the horizon length, T the in-sample length, m a seasonal period, d the MASE scaling constant (computed per variate), ˆ F the predictive CDF, and X,X ′ ∼ ˆ F i.i.d. When forecasts are provided as quantiles { ˆ q t,τ k } K k =1 , we use the standard discrete approximation to CRPS via the pinball loss:

D Benchmark Datasets

Tab. 5 provides an overview of the datasets we used to compare xLSTM-Mixer with other time series forecasting models. The last column shows the range of Hurst exponents [Hurst, 1951] over the variates measuring long-term patterns. The larger the values are over 0.5, the more long-term patterns are in the time series.

E Full Results for Long-Term Forecasting

Tab. 6 shows the full results for long-term forecasting. This work involves conducting all experiments three times using seeds 2021, 2022, and 2023, following the setup of prior research [Wu et al., 2021, Nie et al., 2023, Wang et al., 2024a]. We therefore present the standard deviation of our model and the second-best models in terms of MSE and MAE in Tab. 7. This table, along with our experiments described in Fig. 4a and Fig. 4b, further underscores the robustness of xLSTM-Mixer.

Models

Recurrent

Mixer

MLP

State Space

Transformer

Convolutional

Pretrained

*

xLSTM-

xLSTMTime

LSTM

TimeMix.++ TimeMix.

TSMixer

CycleNet

DLinear

TiDE

S-Mamba

Chimera

PatchTST

iTransf.

Mod.TCN

TimesNet

Timer-XL

MoiraiBase

Mixer

2024

1997

†

2025a

2024a

2023c

2024

2023

2023

2025b

2024

2023

2023

2023

2022a

2025

2024

Metric

MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE MSE MAE

Weather

96

0.143 0.184

0.144 0.187 0.369 0.406

0.155 0.205 0.147 0.197 0.145 0.198 0.148 0.200 0.176 0.237 0.166 0.222 0.165 0.210 0.146 0.206 0.149 0.198 0.174 0.214 0.149 0.200 0.172 0.220 0.171 0.225 0.220 0.217

192

0.186 0.226

0.192 0.236 0.416 0.435

0.201 0.245 0.189 0.239 0.191 0.242 0.190 0.240 0.220 0.282 0.209 0.263 0.214 0.252 0.189 0.239 0.194 0.241 0.221 0.254 0.196 0.245 0.219 0.261 0.221 0.271 0.271 0.259

336

0.236

0.266 0.237 0.272 0.455 0.454

0.237

0.265

0.241 0.280 0.242 0.280 0.242 0.283 0.265 0.319 0.254 0.301 0.274 0.297 0.244 0.281 0.306 0.282 0.278 0.296 0.238 0.277 0.280 0.306 0.274 0.311 0.286 0.297

720

0.310 0.323 0.313 0.326 0.535 0.520

0.312 0.334 0.310 0.330 0.320 0.336 0.312 0.333 0.323 0.362 0.313 0.340 0.350 0.345

0.297 0.309

0.314 0.334 0.358 0.347 0.314 0.334 0.365 0.359 0.356 0.370 0.373 0.354

Avg

0.219 0.250

0.222 0.255 0.444 0.454

0.226 0.262 0.222 0.262 0.225 0.264 0.223 0.264 0.246 0.300 0.236 0.282 0.251 0.276

0.219

0.258 0.241 0.264 0.258 0.278 0.224 0.264 0.259 0.287 0.256 0.294 0.287 0.281

Electricity

96

0.126 0.218

0.128 0.221 0.375 0.437

0.135 0.222 0.129 0.224 0.131 0.229

0.126

0.221 0.140 0.237 0.132 0.229 0.139 0.235 0.132 0.234 0.129 0.222 0.148 0.240 0.129 0.226 0.168 0.272 0.141 0.237 0.160 0.250

192

0.144 0.235 0.150 0.243 0.442 0.473

0.147 0.235

0.140 0.220

0.151 0.246 0.144 0.237 0.153 0.249 0.147 0.243 0.159 0.255 0.144 0.223 0.147 0.240 0.162 0.253 0.143 0.239 0.184 0.289 0.159 0.254 0.175 0.263

336

0.157 0.250 0.166 0.259 0.439 0.473

0.164

0.245

0.161 0.255 0.161 0.261 0.159 0.255 0.169 0.267 0.161 0.261 0.176 0.272

0.156

0.259 0.163 0.259 0.178 0.269 0.161 0.259 0.198 0.300 0.177 0.272 0.187 0.277

720

0.183 0.276

0.185

0.276

0.980 0.814

0.212 0.310 0.194 0.287 0.197 0.293 0.196 0.290 0.203 0.301 0.196 0.294 0.204 0.298 0.184 0.280 0.197 0.290 0.225 0.317 0.191 0.286 0.220 0.320 0.219 0.308 0.228 0.309

Avg

0.153 0.245

0.157 0.250 0.559 0.549

0.165 0.253 0.156 0.246 0.160 0.256 0.156 0.251 0.166 0.264 0.159 0.257 0.170 0.265 0.154 0.249 0.159 0.253 0.178 0.270 0.156 0.253 0.192 0.295 0.174 0.278 0.187 0.274

Traffic

96

0.357

0.236

0.358 0.242 0.843 0.453

0.392 0.253 0.360 0.249 0.376 0.264 0.374 0.268 0.410 0.282

0.336

0.253 0.382 0.261 0.366 0.248 0.360 0.249 0.395 0.268 0.368 0.253 0.593 0.321

-

‡

-

-

‡

-

192

0.377

0.241

0.378 0.253 0.847 0.453

0.402 0.258 0.375 0.250 0.397 0.277 0.390 0.275 0.423 0.287

0.346

0.257 0.396 0.267 0.394 0.292 0.379 0.256 0.417 0.276 0.379 0.261 0.617 0.336

-

-

-

-

336

0.394

0.250

0.392 0.261 0.853 0.455

0.428 0.263 0.385 0.270 0.413 0.290 0.405 0.282 0.436 0.296

0.355

0.260 0.417 0.276 0.409 0.311 0.392 0.264 0.433 0.283 0.397 0.270 0.629 0.336

-

-

-

-

720

0.439 0.283 0.434 0.287 1.500 0.805

0.441 0.282 0.430 0.281 0.444 0.306 0.441 0.302 0.466 0.315

0.386 0.273

0.460 0.300 0.443 0.294 0.432 0.286 0.467 0.302 0.440 0.296 0.640 0.350

-

-

-

-

Avg

0.392

0.253

0.391 0.261 1.011 0.541

0.416 0.264 0.387 0.262 0.408 0.284 0.403 0.282 0.434 0.295

0.356

0.261 0.414 0.276 0.403 0.286 0.391 0.264 0.428 0.282 0.396 0.270 0.620 0.336

-

-

-

-

ETTh1

96

0.359 0.386

0.368 0.395 1.044 0.773

0.361 0.403 0.361 0.390 0.361 0.392 0.382 0.403 0.375 0.399 0.375 0.398 0.386 0.405 0.362 0.391 0.370 0.400 0.386 0.405 0.368 0.394 0.384 0.402 0.369 0.391 0.376 0.392

192

0.402 0.417 0.401 0.416 1.217 0.832

0.416 0.441 0.409 0.414 0.404 0.418 0.421 0.426 0.405 0.416 0.412 0.422 0.443 0.437

0.398

0.415 0.413 0.429 0.441 0.436 0.405

0.413

0.436 0.429 0.405 0.413 0.412 0.413

336

0.408 0.429 0.422 0.437 1.259 0.841

0.430 0.434 0.430 0.429 0.420 0.431 0.449 0.444 0.439 0.443 0.435 0.433 0.489 0.468 0.402 0.416 0.422 0.440 0.487 0.458

0.391 0.412

0.491 0.469 0.418 0.423 0.433 0.428

720

0.419

0.448 0.441 0.465 1.271 0.838

0.467 0.451 0.445 0.460 0.463 0.472 0.486 0.487 0.472 0.490 0.454 0.465 0.502 0.489 0.458 0.477 0.447 0.468 0.503 0.491 0.450 0.461 0.521 0.500 0.423

0.441

0.447 0.444

Avg

0.397

0.420 0.408 0.428 1.198 0.821

0.419 0.432 0.411 0.423 0.412 0.428 0.435 0.440 0.423 0.437 0.419 0.430 0.455 0.450 0.405 0.424 0.413 0.434 0.454 0.448 0.404 0.420 0.458 0.450 0.404

0.417

0.417 0.419

ETTh2

96

0.267 0.329 0.273 0.333 2.522 1.278

0.276 0.328 0.271 0.330 0.274 0.341 0.293 0.352 0.289 0.353 0.270 0.336 0.296 0.348

0.257 0.325

0.274 0.337 0.297 0.349 0.263 0.332 0.340 0.374 0.283 0.342 0.294 0.330

192

0.338 0.375 0.340 0.378 3.312 1.384

0.342 0.379 0.317 0.402 0.339 0.385 0.359 0.395 0.383 0.418 0.332 0.380 0.376 0.396

0.314 0.369 0.314

0.382 0.380 0.400 0.320 0.374 0.402 0.414 0.340 0.379 0.365 0.375

336

0.367 0.401 0.373 0.403 3.291 1.388

0.346 0.398 0.332 0.396 0.361 0.406 0.392 0.423 0.448 0.465 0.360 0.407 0.424 0.431 0.316 0.381 0.329 0.384 0.428 0.432

0.313 0.376

0.452 0.452 0.366 0.400 0.376 0.390

720

0.388 0.424 0.398 0.430 3.257 1.357

0.392 0.415

0.342 0.408

0.445 0.470 0.425 0.451 0.605 0.551 0.419 0.451 0.426 0.444 0.388 0.427 0.379 0.422 0.427 0.445 0.392 0.433 0.462 0.468 0.397 0.431 0.416 0.433

Avg

0.340 0.382 0.346 0.386 3.095 1.352

0.339 0.380

0.316

0.384 0.355 0.401 0.367 0.405 0.431 0.447 0.345 0.394 0.381 0.405 0.318

0.375

0.324 0.381 0.383 0.407 0.322 0.379 0.414 0.427 0.347 0.388 0.362 0.382

ETTm1

96

0.275 0.328

0.286 0.335 0.863 0.664

0.310 0.334 0.291 0.340 0.285 0.339 0.297 0.351 0.299 0.343 0.306 0.349 0.333 0.368 0.293 0.351 0.293 0.346 0.334 0.368 0.292 0.346 0.338 0.375 0.317 0.356 0.363 0.356

192

0.319 0.354

0.329 0.361 1.113 0.776

0.348 0.362 0.327 0.365 0.327 0.365 0.338 0.377 0.335 0.365 0.335 0.366 0.376 0.390 0.329 0.362 0.333 0.370 0.377 0.391 0.332 0.368 0.374 0.387 0.358 0.381 0.388 0.375

336

0.353

0.374

0.358 0.379 1.267 0.832

0.376 0.391 0.360 0.381 0.356 0.382 0.374 0.400 0.369 0.386 0.364 0.384 0.408 0.413

0.352

0.383 0.369 0.392 0.426 0.420 0.365 0.391 0.410 0.411 0.386 0.401 0.416 0.392

720

0.409

0.407

0.416 0.411 1.324 0.858

0.440 0.423 0.415 0.417 0.419 0.414 0.431 0.425 0.425 0.421 0.413 0.413 0.475 0.448

0.408

0.412 0.416 0.420 0.491 0.459 0.416 0.417 0.478 0.450 0.430 0.431 0.460 0.418

Avg

0.339 0.366

0.347 0.372 1.142 0.782

0.369 0.378 0.348 0.375 0.347 0.375 0.360 0.388 0.357 0.379 0.355 0.378 0.398 0.405 0.345 0.377 0.353 0.382 0.407 0.410 0.351 0.381 0.400 0.406 0.373 0.392 0.406 0.385

ETTm2

96

0.157 0.244

0.164 0.250 2.041 1.073

0.170 0.245 0.164 0.254 0.163 0.252 0.176 0.265 0.167 0.260 0.161 0.251 0.179 0.263 0.168 0.261 0.166 0.256 0.180 0.264 0.166 0.256 0.187 0.267 0.189 0.277 0.205 0.273

192

0.213 0.285

0.218 0.288 2.249 1.112

0.229 0.291 0.223 0.295 0.216 0.290 0.231 0.305 0.224 0.303 0.215 0.289 0.250 0.309 0.215 0.289 0.223 0.296 0.250 0.309 0.222 0.293 0.249 0.309 0.241 0.315 0.275 0.316

336

0.269

0.322

0.271

0.322

2.568 1.238

0.303 0.343 0.279 0.330 0.268 0.324 0.282 0.338 0.281 0.342

0.267

0.326 0.312 0.349 0.278 0.337 0.274 0.329 0.311 0.348 0.272 0.324 0.321 0.351 0.286 0.348 0.329 0.350

720

0.351

0.377

0.361 0.380 2.720 1.287

0.373 0.399 0.359 0.383 0.420 0.422 0.361 0.388 0.397 0.421 0.352 0.383 0.411 0.406

0.341

0.378 0.362 0.385 0.412 0.407 0.351 0.381 0.408 0.403 0.375 0.402 0.437 0.411

Avg

0.248 0.307

0.254 0.310 2.395

1.177 0.269 0.320 0.256 0.315 0.267 0.322 0.263 0.324 0.267 0.332 0.249 0.312 0.288 0.332 0.250 0.316 0.256 0.317 0.288 0.332 0.253 0.314 0.291 0.333 0.273 0.336 0.311 0.337

Wins

11

16

0

2

0

0

0

2

2

2

0

0

1

0

0

0

5

1

0

0

8

3

1

0

0

0

2

3

0

0

0

1

0

0

*

Zero-shot forecasting.

†

Taken from Wu et al. [2022a].

‡

Traffic/PEMS are often used during pre-training [Liu et al., 2025]. Thus, no zero-shot results are available.

F Full Results on GIFT-Eval

This section completes Tab. 2 by reporting the full GIFT-Eval results: the overall leaderboard in Tab. 8, the multivariate and univariate subsets in Tab. 9 and Tab. 10, and the domain-wise Top-10 in Tab. 11. We follow the official GIFT-Eval protocol and scoring. The tables report the aggregate CRPS and MASE, and ranks are computed by the CRPS aggregate (lower is better). Values reflect the online leaderboard at the time of submission.

Across all datasets, xLSTM-Mixer ranks 2 out of 39 models with CRPS 0.512 and MASE 0.780 (Tab. 8) and is the strongest supervised method without pretraining. On the univariate and multivariate subsets, xLSTM-Mixer also ranks 2 with CRPS 0.543 and 0.474, respectively (Tab. 9, Tab. 10). These results are consistent with the other evaluations and show that the method transfers well to probabilistic forecasting with a simple quantile head. In particular, because the multivariate CRPS is lower than the univariate CRPS (0.474 vs. 0.543), this further confirms our previous observations and design decision that mixing of variates is beneficial, suggesting that xLSTM-Mixer effectively shares information across related series (e.g., common seasonality or shocks) without domain-specific tuning in the quantile head.

The domain breakdown indicates robust behavior across heterogeneous sources. The Top-10 perdomain tables show a first place in Healthcare and typically top-five performance across the remaining domains (Tab. 11). This suggests that the model adapts well to different frequencies, scales, and noise levels without domain-specific architectural changes.

10

15

20

25

30

sundiabase_128m

xlstmmixer

lama

TiRex

seasonalnaive

TTM-R2-Finetuned

AutoETS

TEMPo_ensemble

YingLong300m

8

Auto-Theta

Auto-Arima

timesfm-20500m

chronos_boltbase

YingLong=110m

Timer

BE

Toto_OpenBase

chronogbong-0n

Moiraismall

Crossformer

TBPN-TS

N-BEATS

Chronos_small

YingLong6m

Chronos-large

hronos

pase

itransformer

DLinear

Moirailarge

TFT

TimesFM

TTM-Rl-Zeroshot

TTM-R2-Zeroshot

Moiraibase

G Visualizing Initial Token Embeddings

Fig. 6 shows how the learned initial tokens η reflect common patterns found in the datasets. A row-by-row inspection of the figure reveals that similar patterns are learned per dataset, albeit at different scales. Specifically, these patterns repeat in proportion to the forecast horizon. The fact that essentially the same patterns are learned for each dataset across different initializations and horizons supports the conclusion that they are data-driven and meaningful to the domain.

2

1

0

1

Weather

Prediction Length 96

Prediction Length 192

Prediction Length 336

Prediction Length 720

1

0

1

ETTm1

0

24

48

72

96

Time

2

1

0

1

ETTh2

0

48

96

144

192

Time

0

85

170

255

336

Time

0

180

360

540

720

Time

H Learning Cross-Variate Patterns

As the sLSTM refinement blocks S process the variates recurrently, it is insightful to assess the extent to which inter-variate relationships are effectively captured. To this end, we adopt a perturbationbased approach to compute attributions, approximating Shapley Values through sampling. Hereby, we use a zero baseline and follow the horizon aggregation method proposed by Kraus et al. [2025], where the forecasts over the entire horizon are aggregated into a single scalar, which serves as the target for the attribution computation. We visualize these Shapley-based feature attribution scores, illustrating the degree to which each output variate of the xLSTM-Mixer depends on each input variate. Fig. 7 demonstrates the ability of xLSTM-Mixer to model cross-variate relationships effectively. Due to the design of the sLSTM refinement module, which strides over the variates, each variate can only be influenced by the ones preceding it. This restriction is reflected in the attribution scores, which appear exclusively in the lower-left triangle.

xLSTM-Mixer fixes one variate ordering to learn multivariate relationships efficiently. We investigate its impact by randomly permuting variate orders and comparing results with the baseline. Tab. 12 shows the results for four such permutations over four horizons on the Weather and ETTm1 datasets. We observe that the specific ordering does play some role in forecasting performance. However, the standard ordering provided by the dataset sources already permits highly effective forecasting.

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Input Variate

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Output Variate

-0.46

0.07 -0.30

0.08 -0.07 -0.57

0.05 -0.03 -0.04 -0.12

0.01

0.02 -0.01 0.08

0.36

0.09 -0.11

0.01 -0.13

0.10 -0.44

0.04 -0.04 -0.03 0.02 -0.05 0.02

0.10

0.04 -0.04 0.02

0.11

0.02

0.11 -0.18 -0.22

0.01 -0.10 -0.01 0.06

0.01

0.07 -0.09 -0.18 -0.19

-0.04 -0.08 -0.07 0.17

0.04 -0.03 0.00

0.04 -0.14 -0.25

0.01 -0.07 -0.01 0.03

0.07

0.14

0.08

0.08 -0.34 0.21

0.66

0.03 -0.06 -0.09 0.02

0.13 -0.05

0.24 -0.05

0.01 -0.23

-0.01 -0.00 -0.02 -0.07

0.06 -0.03 -0.01 0.05

0.01

0.05 -0.20 -0.18 -0.62

-0.02 -0.00

0.00 -0.01

0.04 -0.00 -0.07 -0.01 -0.02 -0.03 0.01

0.06 -0.05 0.25

0.00 -0.01 0.00 -0.01 0.02

0.02 -0.00

0.02 -0.02 0.01 -0.00 0.03

0.05

0.07

0.12

-0.00 -0.01 -0.00 -0.00 -0.01 0.02 -0.02 0.03

0.01 -0.01 -0.01 0.01

0.06 -0.05 0.09

0.06

-0.00 -0.01 0.01

0.05

0.00

0.02 -0.02

0.11 -0.03 -0.06 -0.01 -0.04 -0.03

0.19 -0.21

0.29 -0.58

-0.02 -0.00 -0.02

0.05 -0.02 -0.01 -0.02 0.11

0.06 -0.06 -0.04 -0.06

0.04 -0.05 -0.35

0.18 -0.01 -0.68

-0.02 -0.02 -0.04

0.05 -0.06 -0.01 -0.13

0.03 -0.04

0.02 -0.03

0.00 -0.04

0.10 -0.12 -0.20 -0.15 -0.13 -0.54

0.00 -0.03 -0.03 -0.02 -0.01 -0.01 0.03

0.01 -0.07 -0.01 -0.03 -0.05 -0.11

0.15 -0.05

0.15 -0.12 -0.15 -0.24 -0.33

-0.01 -0.02 -0.02 -0.01

0.01 -0.01 -0.01

0.07 -0.06

0.04 -0.00 -0.04 -0.01 0.15

0.06

0.13 -0.14 -0.04 -0.22 -0.67 1.00

1.00

0.75

0.50

0.25

0.00

0.25

0.50

0.75

1.00

Variate Attribution Score

(a) Weather dataset.

#1

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Input Variate

#1

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Output Variate

0.41

-0.07

0.30

-0.12

-0.31

0.68

-0.09

-0.12

-0.08

-0.21

-0.12

-0.10

-0.10

-0.51

0.76

-0.10

-0.09

-0.07

-0.14

-0.11

-0.64

-0.09

-0.07

-0.06

-0.14

-0.12

-0.36

1.00

1.00

0.75

0.50

0.25

0.00

0.25

0.50

0.75

1.00

Variate Attribution Score

(b) ETTh2 dataset.

#1

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Input Variate

#1

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#5

#6

#7

Output Variate

0.30

-0.17

0.63

0.35

-0.09

0.78

-0.03

0.12

0.01

0.79

0.03

-0.07

0.08

0.03

0.66

-0.04

0.02

-0.07

0.04

0.16

0.72

-0.08

-0.07

0.06

-0.14

0.18

-0.28

1.00

(c) ETTm1 dataset.

1.00

0.75

0.50

0.25

0.00

0.25

0.50

0.75

1.00

Variate Attribution Score

I Ensembling over More than Two Views

Tab. 13 shows the results for ensembling varying numbers of views. Note that even if E > 2 , the first two views are always fixed to be forward and backward.

As we can see, the base version of using two views is the overall best choice. We observed this on multiple datasets and show ETTh2 as a representative sample.

J Outlook: Classification

Tab. 14 compares xLSTM-Mixer to common time series classification models and standard benchmark datasets. Summarizing the individual results, xLSTM-Mixer is on par with the best model, ModernTCN [Donghao and Xue, 2023].

To adapt xLSTM-Mixer for classification, we replace the final regression projection layer with a single fully connected classification head followed by a softmax activation. We train this variant end-to-end on labeled sequences using cross-entropy loss, applying the same data preprocessing and augmentation pipeline as in our forecasting experiments.

These results highlight xLSTM-Mixer's flexibility: with minimal architectural changes and no specialized classification tricks, it achieves state-of-the-art performance while preserving the same core building blocks used for forecasting. This unified design suggests that xLSTM-Mixer can serve as a general backbone for a wide range of sequence modeling tasks.

Peer reviews:
comments: SUMMARY:
As fall we know, the several patterns both within and between temporal and multivariate components is crucial for reliable predictions. In this work, the authors introduce xLSTM-Mixer method, a model designed to effectively integrate temporal sequences, joint time-variate information, and multiple perspectives for robust forecasting. The proposed approach begins with a linear forecast shared across variates, which is then refined by xLSTM blocks. They serve as key elements for modeling the complex dynamics of challenging time series data. xLSTM-Mixer ultimately reconciles two distinct views to produce the final forecast. This is a model design scheme from an interesting perspective.

STRENGTHS AND WEAKNESSES:
Strengths:
1. It seems to be the first attempt to integrate recurrent models (xLSTM) with mixing architectures (time/variate/view mixing). The three-stage design (linear forecast → sLSTM refinement → view reconciliation) is novel and well-justified.
2. Evaluated on 7 time series forecasting benchmark datasets (Weather, Electricity, ETT, etc.) across 4 horizons (96–720 steps). Outperforms 20+ SOTA baselines (Table 1), achieving best results in 11/28 MSE and 16/28 MAE cases.
3. Uses exponential gating and memory mixing (i.e., Eqs. 1–8) to capture cross-variate dependencies in the xLSTM network. Multi-head recurrence matrices enhance efficiency without sacrificing expressiveness.

Weaknesses:
1. Ablation (in Table 2) shows omitting the initial token embedding still yields competitive results. Its necessity and interpretability (Fig. 5) require deeper analysis.

QUESTIONS:
Please see Weaknesses!

LIMITATIONS:
Please see Weaknesses!
TITLE: Official Review
CLARITY: 2
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-06-19

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors introduces the xLSTM-Mixer, a new model that leverages scalar LSTM units in a multi-stage setup to blend temporal and variate information for more accurate and efficient multivariate time series forecasting. The architecture moves from a channel-independent linear forecast, through a joint mixing phase with sLSTM blocks, to a final stage that reconciles forecasts from both original and reversed data views, which really boosts generalization and stability. Benchmarks show xLSTM-Mixer consistently outperforms top models in accuracy and efficiency, especially for long-term forecasting, and it’s robust across short-term, classification, and probabilistic tasks—making it a strong, practical advance for time series modeling.\n\nSTRENGTHS AND WEAKNESSES:\nThis  paper stands out for its thorough empirical validation and thoughtful design, showcasing impressive forecasting accuracy and efficiency across diverse datasets and tasks, thanks to best practices like RevIN normalization and a clever three-stage architecture that mixes both original and reversed data views. While the model’s efficiency and systematic approach are big strengths—especially compared to Transformer-based methods—the complexity and dense terminology may make it less accessible to those outside deep learning, and key details being in the appendices doesn’t help. The novelty lies more in the integration of existing ideas than in brand-new algorithms, and the focus on standard benchmarks leaves some questions about real-world performance. Still, it’s a strong, timely contribution, and with more emphasis on clarity and practical deployment, its impact could be even bigger\n\nQUESTIONS:\n1. The use of forward and reversed embeddings with shared weights for forecast reconciliation is interesting. Can the authors more clearly explain how this approach differs fundamentally from data augmentation or bidirectional recurrence? What is the theoretical or empirical basis for expecting this mixing to yield better generalization?\n\nSuggestion: A more detailed ablation isolating this component—including results without reversal or with separate weights—would help clarify whether the gains come from view diversity, weight sharing, or both.\n\n2.  The experiments are conducted on standard benchmark datasets. Can the authors provide results or at least discussion on how xLSTM-Mixer might generalize to noisier or domain-specific settings (e.g., irregular sampling, missing data, non-stationary series)?\n\nSuggestion: Including at least one example or case study from a real-world applied domain (e.g., energy load forecasting, medical monitoring) would help demonstrate the model’s robustness and practical utility.\n\n\n3. Given the layered and multistage nature of the architecture, how feasible is it to interpret model outputs in operational settings? Are there mechanisms in xLSTM-Mixer that support interpretability?\n\nSuggestion: It would be good to have a section discussing the trade-offs between predictive accuracy and interpretability, and any practical tools available for model explainability.\n\n4. The authors suggest all components contribute positively, but their quantitative contribution is not deeply discussed. Could the authors provide more granular comparisons—e.g., percentage drop in MAE/MSE for each omitted feature?\n\nSuggestion: It would be good to include a clearer, perhaps tabular, breakdown of performance degradation when omitting each core block (e.g., RevIN, view mixing, soft prompt, variate striding).\n\n5. The author chooses to exclude mLSTM blocks in favor of sLSTM due to their “independent treatment of sequence elements.” Could the authors expand on why sLSTM is uniquely suited for joint time-variate mixing?\n\nSuggestion: a short side-by-side comparison (theoretical or empirical) would  be great.\n\nLIMITATIONS:\nThe authors do not explicitly address limitations of xLSTM-Mixer in the current version of the paper. While the model is clearly presented as efficient and performant, some critical factors are missing: \n\n1. Limitations in Real-World Applicability: Please provide how xLSTM-Mixer performs in real-world scenarios involving irregular sampling, missing data, or non-stationary trends, which are common in many industrial time series applications.\n\n2. Resource and Deployment Context: The author highlights memory and computational efficiency, but should also reflect on how this might enable broader deployment, including in settings where technical oversight or monitoring is limited (e.g., automated decision-making in low-resource regions), and what risks that might entail.\n\n3. Societal Impact Consideration: Given that time series forecasting models can be deployed in sensitive domains (e.g., energy systems, financial markets, healthcare), the authors should consider discussing how model biases, mispredictions, or over-reliance on automation might affect stakeholders.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces xLSTM-Mixer, a model for multivariate time series forecasting. It combines a linear forecast with further refinement using xLSTM blocks, effectively integrating temporal sequences and view mixing to capture complex dependencies. The model demonstrates superior long-term forecasting performance compared to previous methods in most cases, while maintaining a very low memory usage. The authors also provide a thorough model analysis, offering insights into the contributions of each component and confirming the model's robustness and effectiveness.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. The paper presents a new model xLSTM-Mixer that combines linear forecasting with xLSTM blocks and a multi-view mixing approach to effectively capture complex patterns in multivariate time series data.\n\n2. xLSTM-Mixer achieves state-of-the-art long-term forecasting results across multiple datasets, outperforming previous methods in the majority of cases.\n\n3. The model maintains a low memory usage and is computationally efficient, making it suitable for deployment on devices with limited resources.\n\n\nWeakness:\n\n1. The paper focuses primarily on empirical results without providing any theoretical analysis to justify the design choices or explain the model's performance. Theoretical insights into why and how xLSTM-Mixer works could strengthen the contributions.\n\n2. While the paper discusses some limitations of xLSTM-Mixer, a more comprehensive discussion of potential weaknesses would be beneficial. This includes limitations related to the model's assumptions, data requirements, and failure modes.\n\n3. The paper briefly mentions the model's ability for probabilistic forecasting, but the evaluation is limited.\n\n4. The authors acknowledge that the performance of xLSTM-Mixer depends on the ordering of variates, but they only provide limited experiments on this aspect. A more thorough investigation into how different variate orderings affect the model's performance and the development of strategies to optimally determine variate orderings could enhance the model's applicability and effectiveness.\n\n5. The comparisons are limited to existing time series forecasting models. Incorporating more recent state-of-the-art approaches could provide a more comprehensive evaluation.\n\na) TimeCMA: Towards LLM-Empowered Multivariate Time Series Forecasting via Cross-Modality Alignment. AAAI 2025\n\nb) HDT: Hierarchical Discrete Transformer for Multivariate Time Series Forecasting. AAAI 2025\n\nc) Unlocking the Power of LSTM for Long Term Time Series Forecasting. AAAI 2025\n\nQUESTIONS:\n1. Why sLSTM is more suitable for the mixer framework than the other RNN unit? Is there any theoretical explanation for this phenomenon?\n\nLIMITATIONS:\nThe authors only provide limited discussion about the limitation in the Conclusion section.  The discussions about the model's assumptions, data requirements, and failure modes would be beneficial.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a new approach for time-serles multivariate forecasting, eg providing point forecast on a group of time-series. The authors propose a novel architecture based on xLSTM which refines a simple linear forecast with sLSTM cells before projecting the output back to the desired dimension. Experiments are conducted on 7 real-world datasets with different forecast horizons to study the effect of long-term forecasting which shows empirical gain against the set of methods compared.\n\nSTRENGTHS AND WEAKNESSES:\n**Quality.** The architecture proposed is well motivated. The authors shows also empirical gains against the set of baselines considered, they also consider many practical scenarios: classification, probabilistic forecasting, different forecast length. However, I have concern about 1) the validity of the claims made due to the lack of statistical analysis 2) the choice of baselines which seems a bit outdated, see questions 3) the hyperparameter optimization protocol which seems to be applied only to their method (despite searching for context lengths).\n\n**Clarity.** The method description is not well written at the moment. While the high-level description is clear, the notations have many issues and inconsistencies which makes it hard to understand all the details.\n\nFor instance, the author use bold notations very inconsistently (eg in Eq l98-l99, c_t and h_t are bold and not bold very inconsistently). In 3.1, $\\mathbf{x_t}$ is used to denote a single time-series whereas it refers to list of $V$ values the page before. This makes it impossible to me to understand what the authors exactly means for instance in Eq l139 where $x_T^\\text{norm}$ has no proper definition. Those imprecise notations are almost everywhere in the model section, for instance l162 $h_0$, l180 $FC^\\text{view}$ takes two arguments while having an input space of $\\mathbb{R}^D$...\n\n**Significance.** Time-series forecasting is an important applications and as such, the potential impact is significant. One caveat is that the paper use baselines that may be slightly outdated, they also use 7 datasets while more recent benchmarks such as gift-eval typically use a much larger number to ensure significance. One important aspect of the contribution is the gain in inference runtime and memory which is clearly demonstrated.\n\n**Originality.** This paper is one of the first to apply xLSTM to time-series forecasting.\n\nQUESTIONS:\nHere are my questions, sorted roughly by order of importance.\n\n* Regarding baselines selection, the baselines you use are quite outdated, for instance you use Moirai_base and PatchTST which are #14 and #15 in gifteval leaderboard, why not using more recent approaches for instance the latest extension of Chronos or methods performing better on this leaderboard? (which you cite)\n\n* Regarding benchmarking, could you report results on Gifteval leaderboard? This would allow to know better the performance of your method, currently you report results on only 7 datasets (where 4 are ETT variants which are quite related), this may be limited to draw conclusions.\n\n> l605: Hyperparameter tuning was conducted using Optuna [Akiba et al., 2019] with the choices provided in Tab. 4.We optimized for the L1 forecast error, also known as the Mean Absolute Error (MAE).\n\n* Are you tuning the hyperparameters (other than context lengths) only for your method?\n\n* Could you provide a statistical analysis of your results? Are the method statistically tied for instance if you draw a critical diagram? (it seems 7 datasets may not be enough). For instance, it feels that almost all results would be statistically tied between #1 and #6 in your ablation\n\n\nThose are mostly for curiosity:\n- have you considering ensembling different ordering? (right now you just consider two orders, one being reversed)\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 1, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}