xLSTM-Mixer: Multivariate Time Series Forecasting by Mixing via Scalar Memories
Authors: Maurice Kraus
Felix Divo
Devendra Singh Dhami
Kristian Kersting
Venue: NeurIPS 2025 poster ()
Keywords: time series
xLSTM
forecasting
mixing
recurrent
Primary area: deep_learning
TL;DR: xLSTM-Mixer integrates temporal, joint, and multi-view mixing with xLSTM blocks, achieving consistent SOTA performance in a wide range of long-term forecasting tasks.

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
Maurice Kraus!
Felix Divo
Devendra Singh Dhami?
Kristian Kersting 134.5
'AI & ML Group, TU Darmstadt TU Eindhoven
*Hessian Center for AI (hessian.Al) *German Research Center for AI (DFKI) 'Centre for Cognitive Science, TU Darmstadt
(maurice, kraus, arlus, felix. divo, kersting) tu-darmstadt.de d.s. dhami@tue nl
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 linear forecast shared across variates, which is then refined by xL.TTM blocks. They serve key elements for modeling the complex dynamics of challenging time series data. xLSTM- ultimately reconciles two distinct views to produce the final forecast. Our extensive evalu- ations demonstrate its superior long-term forecasting performance compared recent tate-o 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 re- current models forecasting by combining them, for the first time, with mixing architectures.
1 Introduction
Time series are essential data modality ubiquitous in many critical fields of appli- cation, such as medicine [Hosseini et al. 2021], manufacturing [Essien and Giannetti
Weather
Electricity dataset
Performance relative
to XLSTM
1.10%
Nineer PaleTTT
2020 logistics [Seyedan and Mafakheri
Tereftoa our
(oues)
2020). traffic management [Lippi et al. 2013
40%
finance (Lin et al.) 2012 Divo al. and weather modeling Lam et al. While significant progress in time series fore-
2025
MAE
MSE
MAE
HSE
2023
10*
GPU Memory
Lockbacc 7
[ogi MB
104
casting 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 manifold of improvements, such as more accurate med- ical treatments, increased efficiency in manu- facturing and transportation, and higher crop yields.
10
10
9.10 1022
0.4
per
per Iteration
Figure MixTM-Mixer provides excellent fore- casts with a very low memory footprint while be- ing sufficiently fast. Details are found in Sec. 4.4
Authorr contributed equally.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Time
Forecust
Initial Embedding
Variate
V
Forecast
Reverse View
sLSTM Stack
Transpose
Weights
Time Series
Time Mixing
Joint Mixing
View Mixing
Figure 2: The X-STM-Mixer architecture consists of three stages: (1) An initial NLinear forecast assuming channel independence and performing time mixing: (2) subsequent joint mixing, which mixes variate and time information through crucial applications of sLSTM blocks; and (3) view mixing, where the latent forecast views are reconciled into coherent final forecast.
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. 20144).
Today, large Transformers [Vaswani al. 2017 are applied extensively time series tasks, including forecasting. Many improvements to the vanilla architecture have since been proposed, including patching (Nie et al., [023], 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 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 the number variates and time steps. As embedded devices and edge computing platforms 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 experiencing a resurgence of interest 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 MixeM- new state-of-the-art method for time series forecasting using recurrent deep learning methods, which strikes balance by providing strong forecasting accuracy while remaining highly efficient, as FFg.. shows. Architecturally, we combine the highly expressive XLSTM architecture with carefully crafted time. variate, and mulli-view mixing. These operations regularize the training and limit the number model parameters by weight-sharing, effectively improving the learning of features necessary for accurate forecasting. XLSTM-Mixer initially computes a inneeeedenne linear forecast shared over the variates. It is then up-projected to higher hidden dimension and subsequently refined by xLSTM stack. It performs multi-view forecasting by producing& a forecast from the original and reversed up pr-jeeeected 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 method is shown in Fig. 2
Overall, we make the following contributions:
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 XL.STM- M-xxeer, state-of-the-ar method for time series forecasting, for the first. time combining recurrent deep learning with mixing architecture.
(iii We extensively compare STMMM-Mee with existing methods for multivariate long-term time series forecasting and perform in-depth model analyses. The experiments demonstrate that XL.STM-Mxxer consistently excels in wide range of benchmarks.
'Code available https:://// http://tttt....o.eaaaaacaaaaaaaa

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In the upcoming Sec. 2] we introduce preliminaries to allow us to motivate and explain XLstM-Mixer Sec. 3 We then comprehensively evaluate its effectiveness and inner workings in We finally review related work in Sec. 5 3n close with conclusion and outlook in Sec.. 6
Outline.
Sec. 4
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 (......, ØT) E V consisting of 7" time steps with V variates each. Given this context, the forecaster shall predict the future values = (TT+1 #T+H) E RV*H variate (sometimes called a channel) can be any scalar measurement, such as the occupancy of road or the temperature a power plant. The measurements are assumed to be carried out jointly, such that the T + H time steps reflect regularly sampled signal. A time series dataset consists of N such pairs {xx() Y()) (EE...... divided into train, validation, and test portions.
X up to a horizon H. A
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, 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 learn any relationships between them directly. See Appp. 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 C₁ 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 al. 2017] to handle complex temporal and cross-variate dependencies better. The sLSTM updates the cell and hidden state h, as follows:
C. ft 3 C + & 2 2t
cell state
(1)
n4: f. 11-11 +
normalizer state
h4 o, ① C 3 n,
hidden state
Z: tanh W att + R. Rhhi-1 bz)
cell input
i exp -m:)
i W,x. Rihi-1 + bi
input gate
ft exp f++ + m mi)
f. Wyst + R1h1-1 by
forget gate
O: a (W,x: + Rohre1 bb)
output gate
m. = max 1, 7s)
stabilizer state
In this setup. the matrices W., W,, W,, and W. are input weights mapping the input token æ; to the cell input 2,, input gate, forget gate, and output gate, respectively. The states n, and m. serve as necessary normalization and training stabilization, respectively. As Beck al. have shown, is beneficial to restrict the memory mixing performed by the recurrent weight matrices R. R, Ry, and R, 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....f.o act across all them, but the recurrence matrices R....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 al., 2016), N-BEATS [Oreshkin al. 2019); N-HiTS [Challu et al.)
2023), and many Transformers [im al. 2021
Wu et al. 202 Zhou et al. 2022
However,
3

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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 al. 2023 and iTTrasffrmme [Liu al.) 2023] TiDE (Das al. 2023 on the other hand, contains time-step shared feature projection and temporal decoder but treats variates jointly. As Toosttikhin et al. [222]] have shown with MLP- M-xier, 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 TimeMixer(+++) [Wang et al.
2024a 2025a), TSMixer [Chen et al., 2023c), WPMixer [Murad et al. 2025]. and PMformer [ee et al. 2024 and 18, therefore, one key component of our method xLSTM
3 XLSTM-Mixer
We now explain XLSTM-Mixer shown in Fig. 2 in more detail. It carefully integrates several key components: 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 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 7 and offset B:
xt - Var x +
E
norm ReeeIN(x,)) - y
+ B.
We apply it as part of X-STMr 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. [202cc] are taken up by RevIN, the
normalization in the NLincar forecast [Zegg 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 [Zeg al.) [023]] [i et al., (023). Our observations confirm this finding. Therefore, we first process each variate separately by an NLinear model by computing:
a
initial (2 FC (a
TT
norm
norm 27
where FC(.): RT + R denotes 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. and 4.5
and
3.2 sLSTM Refinement
While the NLinear forecast initiall VVH captures the basic patterns between the historic and future time steps, its quality alone is insufficient for today's '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 " FC (x: initial This prior up-projection is similar to what is commonly performed in SSMs [Beck et al. 2024). We weight-share FC R - RD 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 the case up until this step, and instead embeds it into a higher latent dimension.

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The stack of M sLSTM blocks S(-) transforms x"P E RVx as defined in Eq. 1 to The recurrent model strides over the data in variate order, i.e. where each token represents all time steps from 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 constant number of parameters. It, however, comes at the cost of possibly fixing a suboptimal order of variates. While this is empirically not significant limitation (see See. 4.4.. we leave investigations into how to find 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 hg 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 v) TRD that gets prepended to each encoded time series x.P, 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 bj. 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 pack-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 xp as well as the reversed embedding SuP, where the order of the latent dimensions including the representation of 17 is inverted. Learning forecasts y', y" E RR VxD 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 linear projection FC R RD + R of the two forecasts, again per-variate. Specifically, we compute g FC (y' y"", where y' = S(="P) and y S(ØU)). The final forecast is obtained after de-normalizing the reconciled forecasts y RevIN (eelN--(gaomm)) mgm))
Experiments
We conduct 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). [Cen et al. [2023c]. Lin et al. 2202], and Liu al. [2025). Further tasks are explored in Sec. 4.3 Additionally, we periorm 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. [222]] and Zhou et al. [222]] for best backward and future comparability. The datasets we thus used are provided overview in Appp. D Training. We follow standard practice in the forecasting literature by evaluating long-term forecasts using mean squared error (MSE) and mean absolute error (MAF). 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 xLSTM- Mixer to the recurrent models xLSTM'mmme [Alharthi and Mahmood, 2024] and LSTM (Hochreiter and Schmidhuber, et al. 2024aa], and TSMixer CCen et al. 2023c]: MI.P-based models CycleNet/MIPP [Lin al. 2024], DLinear (Zeng et al. 2023), and TIDE [Das et al. 2023]; the SSMs S-Mamba (Wang et al.
1997]: mixer models TimeMixer++ [Wang et al. 2025a]. TimeMixer [Wang
20255) and Chimera [Behrouz et al. 2024]; the Transformers PatchTST [Nie et al.] [023] and
iTransformer Liu et al. 2023]; the convolutional architectures MCdemnTNN [Doghhao and Xue
5

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Table 1: xLSTM-Mixer is effective in long-term forecasting. The results averaged from 4 different prediction lengths (96, 192, 336, 720). A lower MSE or MAE indicates a better prediction. The best result for each dataset is highlighted bold red and second- blue and underlined. Wins for each model out of all 28 settings are shown at the bottom. Full results are provided in App. E
Recurvent
Miser
MLP
State Space
Trans:
Cony.
Pretrained
Models
-LSTM-
ALSTMTace
LSTM 1597
TaneMiic
Tinidii, MoEnn
TSMina Nol
CydeaNit
TIDE KOaJ
S.Maniio MOk
Chinaaa bOoC
PaddrSS
Mod
Times
Minrii ho0
Minor
NOEE
Hoad
Datnset
JusE: MAL:
Mist
MAD
MIEE
MAL:
MSE MAR
MAL
MAE
Mist
MAL Jesi
MAU
MAR:
bist
MAL
Mai MAL
MAL MAR: Mint MAR Mes
MALI
hist MAR
MIE MAR
Wenther
6.219
Hlectrcity
8.13
KL157
0359
0.55
0155
0.255
0L155
2.000
Trafii
0.392 0,301 0:26
1001
0.54
(446 0.200
0.408
0.25400400
0.205
0.286
0:20
0414
0.206
0,391
0.9 220
ETThl
8.30 2.9700420000
0.7004404406 0428
1199 0.621
0419-044000
941 0.425
0:43
0.435 0
2/423
0.437
0.419
0.40
0445 0.400
0.444
0.424
0.433
0-314
420
6.47 04477047780 0417
ET
330
5,08 1,550
0:40
0.631
529
ETTal
ETTm2
1.340 11354
0L300
2.345 1,23
(1 0:200
03377
Wins
16
Zem-shot forecasting available.
Taken from Wa al..
2022a
TTafliPPMSS are othen used during pre-triniig ot
2005
Thus, no zero-shor results are
Lookback
Target
Prodiction
XLSTM-MSAW
XLSTMTinM
TimeMizer
PetchTST
Weather
1240
1220
96
192 96 192
192 96
192
966
192
Figure 3: XLSTM-Mixer provides convincing forecasts. This figure shows example forecasts on the Weather and ETTml datasets for multiple models with lookback windows and forecasting horizons fixed at 96. The first panel illustrates the forecast from XLSTM-Mixer, while the second shows the initial forecast extracted before the up up-projection step, highlighting the effectiveness of our added components. Comparisons with further baselines are provided for context.
and TimesNet [Wu et al. 2022a]: : and the pretrained zero-shot f'reeaaterss Timer-XL Liu et al. 2025 and Moiraigase [Wo 20024. On choosing lookback lengths L. Some prior works on Longteerm forecasting fix the lookback window L for the sake of a fair comparison. However, Abdelmalak al. (2025) and Brigato et al. (2025] argue that fixing especially 96, which 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 I, = 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.
2023
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, XixeM- 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. ILLTT--MixE defines a new ofttee----h--tttt-- on six out of seven datasets. This shows that X-eeer consistently delivers excellent performance long-term forecasting. A qualitative comparison with several baselines, including the initial forecast extracted before the SLS refinement, shown Fig. Here, both the lookback window and the forecasting horizon are fixed at 96.

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Table 2: XLSTM-Mixer excels on GIFT-Eval. The table reports the top 10 across all categories.
Model
MASE
CRPS
Rank (CRPS)
TiRex
0.724
0.498
XLSTM-Mixer (ours)
0.780
0.510
TEMPO_enncmble
0.862
0.514
3
Toto
0.750
0.517
4
TabPFN-TS
0.771
0.544
5
Yingl_ong_3000 30000m
0.798
0.548
timesfm 2_0 2_0_500m
0.758
0.550
YingL.ong_ 110m
0.809
0.557
8
sundial base 128m
0.750
0,559
9
YingLong 50m
0.822
0.567
10
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 (006). First, Friedman test ensures the model's performances follow different distributions (p < 10-10). We can then perform Conover post-hoc test while adjusting for the family-wise error rate using Holm's method. We must restrict this comparison 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-Mixe is statistically significantly better than all other methods, except for xLSTMTime. Yet, the difference in average rank is still impressive, with 1.5 for X-STM-Mixer and 4.0 for XLSTMTime. Furthermore, xLSTMTime is statistically inseparable from many other models, namely TimeMixer, TSMixer, ModernTCN, Chimera, PatchTST, and TiDE.
metric (MSE) and horizon (96
4.2 Forecasting on the GIFT-Eval Benchmark
To showcase Mixer''sxer's versatility beyond multivariate long-term point forecasting, evaluate on GIFT-Eval [Aksu et al.) [2024). It 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, 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, equip it with head predicting quantiles, yielding full predictive distributions rather than point estimates.
Results are summarized in Tab. 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 is designed for multivariate forecasting, it remains highly
demonstrates that although competitive among methods across univariate and multivariate settings and 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 significantly better than all other 38 methods, except for App. for complete critical
sundial base base_128m, TiRex, and STMM-R-FFinttunl See Fig. 5 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 classi- fication head. STMM--iierr achieves very strong performance on standard time-series classification benchmarks (cf. App. Jp. These findings suggest that approaches reconciling recurrent and mixing architectures, such XLSTM-Mixer, are highly flexible yet powerful.
7

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Prediction Langtt: 26
Fredicton Langtn:
Pradice 14
3.14
2.12
0.34
Prodiction Langth 335
Predition Langth:
2.35
0.20
316--
0.38
27
2/
2/
(a) Increasing the hidden dimension D becomes in- creasingly beneficial at longer prediction lengths H.
(b) Increasing the lookback window T increases fore- casting performance, with xLSTM- M-xieer virtually Shown is the MSE for varying D on the Electricity always providing the best results. Shows the MSE (L) dataset.
on the ETTml dataset.
Figure 4: Impact of model parameters on forecasting performance.
4.4 Model Analysis
Initial Token Embeddings. We qualitatively inspect decodings of the initial embedding tokens r on multiple datasets to further understand and interpret the initializations learned by XLSTM-Mixer. n are decoded to forecast y by transforming them through the sLSTM stack S and applying multi-view mixing. The resulting output of FC can then be interpreted as the conditioning time
series used to initialize the sLSTM blocks. Fig. 6 in Appendix App. G shows the dataset-specifer 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. ] shows how this changes over multiple lookback lengths T' and two datasets at a forecast horizon of H = 336. Compared to baselines, XLSTM- 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-bases models. One advantage of TimeMixer was its efficiency over Transformers, upon which xLSTM- now significantly improves by requiring one to two orders of magnitude less memory.
Sensitivity to the xLSTM Hidden Dimension. In Fig. 4a Mixer on the Electricity dataset with increasing sLSTM embedding hidden dimension D realized by FC"P, The results indicate that a larger 1) enables XLSTM-Mixer better capture the complexity of the series over extended horizons, leading to improved forecasting accuracy.
visualize the performance of X--
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 -T.eerr can effectively utilize longer lookback windows than the baselines, especially when compared to transformer-based models. This advantage stems from XLSTMM avoidance of self- attention, allowing it to handle extended lookback lengths efficiently. On short prediction lengths with T E (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.
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 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 -L--M-eixer effectively captures cross-variate interactions.
XLSTM-Mixer Captures Cross- Variate Patterns.
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, FCriow extended accordingly. The full results in App. show that this does not improve the modeling accuracy of XLSTM-
8

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Table 3: Each component of XLSTM-Mixer is essential for its overall strong performance. The
notation follows Tab.
Results are averages over three seeds.
#1 (full)
#2
.83
#4
25
a6
#7
AK
#9)
A10
A111
A12
A1.3
414
Time Mixing
xI.TTM type
2STM
ml. STL
LSTM
GRU Variates
S.STM
6.5TM Varines
<LSTM
<LSTM
+LSTM
Nece
<LSTM
+LSTM
4LSTM
ALSTM
Recurt order Varites
Viritees
Time
Varizes
Variies
Varizes
None
Vasiaes
Varioes
Values
Vuiitts
Inir. Taken
View Mixing
Metric
MSE MAE MSE MAE MSE SIA MSE MAE MSE MAE IISE MAE ISSE MAE MSE MAE MSE MAE MSE
MAE
MSE MAE
MSE
MAE
MSE
MAE
MSE
MAE
Weatee
0L156 0,150 EAS 190 EOT 0.55 FOR 0.194 O.ERT (19611
144 1195
141
1966
19560 1.51
195
199
0.193 0.225 0.22 CLESE
0.2E0 CLEEE 0.2ER
0.257 0119
0.33
01193 0.336
336
0.237 0,266 2.24 0.272 11241 0,211 1.205 0L272 21222 0.251 1L233 CLONT 11279 0L26
0.240 0L210
2.222
0.200
0LE71
0.275
0.044 0.243
0.194
1.1 10 ST7 346
ETTml
(122A 0,328
0.244
192
11.59 0,354 1.229 3.555 11554 0. 0.352 0.000 1150 0 0.354
2222
0.350
0.157
0.529 a
0.530
0.335 0.
11202 01.74
0.405
375 9959
0.35
0,497 0.412
0,414
0.400 0.422 0.447 0.441 0430
selll
0.08
0411
24414
0411
2412
0.422 0412
0.13
0417 04138
0.11
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 different combination of the four key components: mixing time with NLinear/DLinean using ..STTM/LLSTM/LSTMMIE variate or time dimension, learning initial embedding tokens 17, and multi-view mixing.
for joint mixing, striding over the
The full version of XLSTM-Mixer (#1), which integrates all components, achieves the best perfor- mance overall. Ablating components of --STTM-Mxxr each causes both error metrics to increase, entailing that they contribute positively to the overall architecture. Specifically, omitting xL.TTM (only having LSTM, #3) raises the MAE by 6/2%/ MSE by 7.0%, variate recurrence (#5) by 4.3% learning initial token embedding (#7) by 0.4 %,0.7%, view mixing (#8) by 0.6%/0.779 and time mix- ing (#11) by 2.7%/ %. For example, removing the time mixing (#11) increases the MAE by 3.4% on ETTml at length 96 or 3.1 1% at length 192, highlighting its critical role in capturing cross-time dependencies. When we now omit everything except for time mixing 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 Sl'M'sss 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 ALSTM-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 critical for ensuring high accuracy across datasets and prediction lengths.
5 Related Work
Time Series Forecasting. A long line of machine learning research led from early statistical methods like ARIMA [Sims] 1980 Box et al. 2015) 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 Thort-Term Memory (LSTM) (Hochreiter and Schmidhuber 1997] and Gated Recurrent Units (GRUs) (Cho et al. [014]] 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 rangerange dependencies, active research remains to alleviate these
limitations (Salinas et al. 2020), including the xLSTM architecture presented in See. BBeck 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 | 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 al., 2022 Lara-Benítez et al. 2021], such as TCN [Lea et al. [2016], TimesNet (Wu et al. 2022a and MICN Waang et al. |022]. 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. [019] 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. (017), such as Autoformer [Wu et al. 2021]. TFT [Lim et al., 2021] FRDFormer (Zhou et al. 2022] PatchTST (Nie et al. 2023].
and i'l ransforrer [Liu 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 al., (024), and Timer-XL. [Lu 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 AAlharthi 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 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 the scarce details in the paper. We ensure that our method XL.STM-Mixe 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. Further- more, we find the trend send-seasonality decomposition redundant and 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.
Conclusion
In this work, we introduced XLSTM-Mixer, method that combines a linear forecast with refinement through xLSTM blocks. Our architecture integrates time, joint, and view mixing to capture com- plex dependencies. In long-term forecasting, XLSTM-Mixer consistently achieves sfate-of-the-a performance, outperforming a large set of previous methods in 27 out of 56 cases. We also evalu- ate XLSTM-Mixer in heterogeneous probabilistic settings GIFT-Eval, where it delivers strong, competitive performance. Beyond forecasting, XLSTM--Mxer performs strongly on time-series classification when used as an embedding model. Moreover, LLSTTMMMixe attains these results at low memory footprint. Our model analysis provided insights into the contribution of each component and demonstrated robustness hyperparameter variations.
Limitations. While XLSTM-Mixer achieves strong accuracy with limited compute, certain as- sumptions 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 rrepprocessing. 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 Xi-eer-Mieer to tasks such as imputation or anomaly detection offers promising future directions.
10

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Acknowledgements
This work received funding from the EU project EXPLAIN, under the German Federal Ministry of Research, Technology and Space (BMFTR) (grant 16IS22030D). Furthermore, it was funded by the ACATIS Investment KVG mbH project "Temporal Machine Learning for Long-Term Value Investing" and the BMFTR KompAKI project within the "The Future of Value Creation Research on Production, Services and Work" program (funding number 02L19C150), managed by the Project Management Agency Karlsruhe (PTKA). The author of Eindhoven University of Technology received support from their Department of Mathematics and Computer Science and the Eindhoven Artificial Intelligence Systems Institute. Furthermore, this work benefited from the HMWK project "The Third Wave of Artificial Intelligence - 3AI", the BMFTR project "XEI" (FKZ. 16IS24079B), and from early stages of the Clusters of Excellence "Reasonable AI" (EXC-3057) and "The Adaptive Mind" (EXC-3066) funded by the German Research Foundation (DFG) under Germany's 's Excellence Strategy; funding will begin 2026. The authors are responsible for the content of this publication.
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A
Societal Impact
This paper presents work whose goal is to advance the field of Machine Learning. There 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 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 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 si SLMS blocks as our mixing primitive rather than ML.TMM The primary motivation is the state tracking via memory mixing. sLSTM preserves uidden-to-hiddee recurrences in its gates and cell update, enabling conditional, history- aware 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:
C = fict- + i,zt,
h4 = o.g(c).
Here, [t, de, or each depend on /t-1 through recurrent matrices (Beck et al. 2024 Greff et al. (017 ), allowing the block to blend past and present conditionally. By contrast, mLSTM writes key-value pairs into a matrix memory:
f.C- +uuck,
(10)
with gates that depend only on the current input (no hidden-to-hidder 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- long-horizon forecasting, tracking latent phases (e.g., heating <> cooling; up <+ down) critical. With sLSTM, gates can be trained such that, upon detection of a switch cue, the cell overwrites (i, 2 1, fa x 0); otherwise, it retains (ú. RV 0, ft R 1). Because the gates read 1t-1, the decision is conditional on the current internal state. In mLSTM, gates cannot use 14-1, meaning updates become fixed linear functionals of the input history. Empirically, architectures lacking memory mixing (mLSTM. Mamba, Transformers) fail simple state-trackig 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 matrix- memory capacity. precluding the direct learning of inter-token relations during joint mixing. We, thus, exclusively employ sLSTM in xLSTM-Mixee In our ablations, replacing sLSTM with mLSTM. GRU, or LSTM consistently harms long- long-horizon accuracy, particularly at 336/720 steps (cf. Tab. 3). Prior and concurrent work supports this finding: XLSTTTTme uses sLSTM on smaller forecasting datasets where precise phase tracking dominates and opts for ML only when raw storage TiRex likewise attributes gains to retaining
capacity is paramount [Alharthi and Mahmood 2024
state tracking [uer et al. 2025
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C Implementation Details
Experimental Details. Our codebase is implemented in Python 3.11, 1, leveraging PyTorch version 2. [Paszke et al. 2019] in combination with Lightning version 2.4 for model training and optimiza- tion. We used the custom CUDA implementation for SLSTM, which relies on NVIDIA Compute Capability 2 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- Siarries-LbbarPPeee of Wang et al. [2024b). For GIFT-Eval [Aksu et al. 2024]. Wann we integrated xLSTM-Mixer into the official evaluation harness via GluonTS -tsole Alexandrov et al. 2020 estimator. For ALSTMTime, we used code based on the official repository i We employ
Captun Kokhlikyan et 2020 to compute the SHAP values used in model analysis.
We used
scikit-posthore [Terpilowski 2019
for significance analyses.
Training and Hyperparameters. We optimized XLSTM-Mixer in 32 bits for up to 60 epochs with a cosine- -anilllinnn scheduler with the Adam optimizer Kingma and Ba 2015), using 61 = 0.9 and 3g 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 LI 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 KLSTTTimm,, this was not the case, and we were not able to fully reproduce the results the paper despite our best efforts (cf. Se. We still present the better results from Alharthi and Mahmood [2024] so not to erroneously underestimate the method. For the datasets Th2 ETTml, and mTTm2 without such results, we ran individual HP searches analogously our method to ensure fair comparison.
Table 4: Hy Hyperparameters and their choices.
Hyperparameter
Choices
Batch size
(16, 32, 64, 128, 256, 512)
Initial learning rate
(1-10-2, 10-",3 10-1-00 1.- 10-1, 110
Scheduler warmup steps
(5, 10, 15)
Lookback length
[96, 256, 1024, 2048|
Embedding dimension D
(32, 64, 128, 256, 512, 768, 1024)
sLSTM conv. kemee width
(disabled, 2, 4)
sLSTM dropout rate # sLSTM blocks M
(0.1, 0.25)
21, 4)
# sLSTM heads
[4, 8, 16, 32)
Forecasting Metrics. We follow common practice in the literature Wu et al. 202 Wang et al. 2024a] for maximum comparability and, therefore, evaluate deterministic long-term 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)), D, 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,
MAE(y. 0)
Σ 1=1
3/ Usl.
MSE(V.
Σ
(U:
9:)
1=1
MASE y.
1t Del
1
Σ
1ys
mm
yt-
d
m
https://ggttiiigg./ptttrraaalll
httpa///itthbbbcc////saaaaa///11 https://captum.ai
25

---

The CRPS for predictive CDF F and outcome is
CRPS(F, / - 1 ==)===))=+0 = dz = E yl - _ -1,,
where are the targets, ÿ the predictions; H is the horizon length, T the in-sample length, m seasonal period, the MASE scaling constant (computed per variate), F the predictive CDF, and X, ~ i...d. When forecasts are provided quantiles (Ór.7, ) k== we use the standard discrete approximation CRPS via the pinball loss:
CRPS:
Pr 91.2)): K
Σ
pr(u) = -K( < <0})
k=1
CRPS
CRPS,-
H
D Benchmark Datasets
Tab. 5 provides overview of the datasets used to compare xLSTM- 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 over 0.5, the more long-term patterns are the time series.
Table 5: The long-term forecasting benchmark datasets and their key properties.
Dataset
Source
Domain
Horizons
Sampling
#Variates
Hurst exp.
Weather
Zhou et al.
2021
Weather
96-720
10 min
21
0.333-1.000
Electricity
Zhou et al.
2021
Power Usage
96-720
I hour
321
0.555-1.000
Traffic
Wu al.
212T
Traffic Load
96-720
hour
862
0.162-1.000
ETT
Zhou et al.
202
Power Production
96-720
15&60 min
7
0.906-1.000
E
Full Results for Long-Term Forecasting
Tab. 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 [u et al.) 2021 Nie et al.] [2033] Wang et al.) 2024a] We therefore present the standard deviation of our model and the second-best models in terms MSE and MAE Tab. 7, This table, along with our experiments described in Fig. 4a and Fig. 4b further underscores the robustness of XLSTM-Mixer.
Table XLSTM-Mixer provides state-of-the-ard performance at low variance across datasets. This table shows the average performance and average standard deviation over all four prediction lengths in Tab. 6
They are contextualized by the competitive baselines TimeMixer and TiDE.
Model
xLSTM-Mixe (ours)
TimeMixer
TiDE
Metric
MSE
MAE
MSE
MAE
MSE
MAE
Weather
0.219
=0.000
0.250
+:0000
0.240
20.010
0.271
+0.009
0.236
+0.001
0.282
+0.001
Electricity
0.153
-0.00
0.245
1.0.001
0.182
10.017
0.272
1..006
0.159
10.002
0.257
10.001
Traffic
0,392
-0.000
0,253
1:0.000
0.484
1..015
0.297
1.0.013
0.356
10.001
0.261
1.0001
ETTh1
0.397 =0.001
0.420
1:0.001
0.047
:.0.002
0.440
1-0.005
0.419
1.00000
0.430
100000
ETTh2
0.340 =0.001
0.382
1:0000
0.364
=0.008
0.375
+:0011
0.345
#0.002
0.394 10.001
ETTml
0.339
=0.000
0.366
1:00000
0.381
::00003
0.395
1:00066
0.355
=0.000
0.378
+0.000
ETTm2
0,248
=0.001
0,307
1:0000
0.275
10.001
0.323
10.003
0,249
20.000
0.312
10.000
26

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Table 6: Full long-term forecasting results for Tab. 1, Avg is averaged from all four prediction lengths [96, 192, 336. 720 A lower MSE or MAE indicates better prediction. The best result for each dataset highlighted bold red and second-best blue and underlined. Wins for each model out of all 28 settings are shown at the bottom.
Rasarent
Mises
MLP
Space
Trataformes
Connolatinall
Pretuined
MAd
0.354
2.39
0.400
135
c.20 JuLsT 0.097 1.145 oure
ses 200
ALTT wozonoouee buss 0.20 ause
burs
L 0.214 0.445 ouzrel 172 (223 0.225 0:22 6217
192
9.220
5.52
0489
201
0.44 AL1S bu1s 0222
290 240
LEE 20
2214 a 252
1.200 0.154 0.24
12211
0.254 cuere suee
219 c22 juzz 1.271
B22 0225
0.236
1.200
0444
1024 9:242
3420
0222 122 222 c:55 juze4 4.911 buze 1220
1.1000 125
2,31
0-34
0S54 MUSS4 Mh 6:39 (330//se-on Bosd 1204
(.219
0444
229
02224 sL204j 299 0287 juze 0,24 RG20 0220
1.136
335
0457
120
0.34 szzels 385 2222 0.257 duted 0,20
1144 1.250
1,15
040
154 c22 Hu 2224 0.173
220 2222110 ses 0ots
u220/p 192 225 (1 0224
345 040
uzzel 25s 0-21
1220
condl 354 642 2.90012911 Dave 1202
soope u.s Dee
hua eart 0477 Belk
sond the 0.05
sain son 33s
san 3e use sa cas po te
1277 120 weed
330 115 for o inded ooss
134 187 t7a. tei
357
201
331
0- 1417 (78 1780453p.coo to Doct
J.w.a.s 200 1.1 pmm
1000
1 100050 0 ma 191 091 1710 pet pris
66
ina me cal 1075
160
36:
10 c10 120 1 oies on0
100
4215
1700
330
0:5
n00 3 100
5oa 1.7%
0.77
p. 321 0351 a 30 2333 6.50
700
8377
133 1.37 335 0.00 2000 030 p430 0-33
301 311
307
2412 977 050 0.31 408 c403 44 0.922 0437 6-13
Kug
325 1177/0 300 0333 200 p200 030
3510 33
28
www..acea........... 355 23..0300000000 200.0000000000 025 031
0311 6357
Winl
11
16|
0
ZZrosdot feecensting
Taken frum Wucttal 2022
TTalic/EMS are ofln used during prostaining Linetal
Thas nn semoohot roulls are souilable
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. and Tab. 10 and the domain 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, MiXTM ranks 2 out of 39 models with CRPS 0.512 and MASE 0.780 (Ta.. 8) and is the strongest supervised method without pretraining. On the univariate and multivariate subsets, XLSTM-MMxer 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 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 STM--Mre 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 per- domain tables show first place in Healthcare and typically top-five performance across the remaining domains Tab. IT. This suggests that the model adapts well to different frequencies, scales, and noise levels without domain specific architectural changes.
27

---

Table 8: GIFT-Eval Overall Leaderboard (full). Lower is better.
Model
MASE
CRPS L
Rank (CRPS) J
TiRex
0.724
0.498
XLSTM-Mixer (ours)
0.780
0.510
2
TEMPO _eppemleeeblee
0.862
0.514
3
Toto Open Base_ 1.0
0.750
0.517
4
TabPFN-TS
0.771
0.544
YingLong_ 33000m
0.798
0.548
6
1enesfm___0_$t0
0.758
0,550
7
Yinglongg_ 110m
110m
0.809
0.557
8
sundial_base_ 128m
0.750
0.559
YingLong_550
0.822
0.567
10
chronos bolt base
0.808
0.574
11
chronos bolt small
0.822
0.577
12
TTM-R2-Finetuned
0.756
0.583
13
PatchTST
0.849
0.587
Moirai_large
0.875
0.599
15
TFT
0.915
0.605
16
YingLong 6m
0.880
0.609
17
0.901
0.610
18
iTransformer
0.893
0.620
19
Chronos_lare
0.870
0.647
20
Moirai_small
0.946
0,650
21
Chronos bass
0.876
0.652
22
Chronos small
0,892
0.663
23
TimesFM
1.077
0.680
24
VisionTS
0.863
0.755
25
TIDE
1.091
0.772
26
N-BEATS
0.938
0.816
27
DLinear
1.061
0.846
28
DeepAR
1.343
0.853
29
VTM-R2-Zerosee
1.020
0.873
30
Lag- Lgg-Llama
1.228
0.880
31
TTM-RI-22 TT---ot-eroshoo
1.079
0.891
32
Auto_A Auim_Arrma
1.074
0.912
33
Timer
1.136
0..970
34
scasonal_naive
1.000
1.000
35
Auto Theta
1.090
1.244
36
Naive
1,270
1.591
37
Crossformer
2.574
1.637
38
Auto_ETS
1.212
7.489
39
Sundial xetm mixer
(35) LeY
Nalve
TTM RTM-R--Finetlee Finetuned
1h1 AdOo
TEMPO eisemble timggam Wogtöng 110m chrones 6aL
Theta
TeE Open Yng chronoxe 60 maa
Fal Chronos small
Chronos
Itrasfomer
TTM Zerbsiit
Visiont
Base
Figure 5: XLSTM-Mixer is statistically significantly better than most baselines. Shown is the critical difference diagram for the MSE. Horizontal connected bars indicate that those methods are not significantly different at = 0.05.
28

---

Table 9: GIFT-Eval Multivariate Leaderboard (full). Lower is better.
Model
MASE
CRPS 4
Rank (CRPS) 4
TEMPO ensemble
0.752
0.427
X.STM-Mixer (ours)
0.839
0.473
2
Toto OeeOOOpeee______
0.767
0.484
3
TiRex
0.771
0.490
YingLong 300m
0.840
0.519
YingLong 110m
0.830
0.520
6
YingLong 50m
0.853
0.530
7
Lundial_base_1250
0.778
0.530
8
TabPFN-TS
0.818
0.544
timesfm_2_0 200_ffm_200500m
0.803
0.553
10
PatchTST
0.906
0.556
11
YingLong_of 6m
0.905
0.566
12
iTransformer
0.940
0.589
13
TTM-R2 FOM-RR-Finetune
0.808
0.591
chronos_ bolt_ small
0.939
0.600
15
chronos_bolt,
0.925
0.604
16
TFT
1.071
0.610
17
Moirai_larg
1.023
0.635
18
Moirai_bas
1.054
0.636
19
Moirai small
1.021
0.640
20
Chronos large
1.005
0.680
21
Chronos small
1.026
0.684
22
Chronos base
1.013
0.685
23
TimesFM
1.497
0.717
24
VisionTS
0.887
0.721
25
N-BEATS
0.998
0.790
26
Lag-Llama
1.221
0.798
27
TIDE
1,284
0.812
28
DLinear
1.228
0.817
29
Crossformer
1.479
0.825
30
TTM-R2 RerZohot
1.072
0.833
31
TTM-R1 -e-Zooot
1.186
0.856
Timer
1.141
0.883
33
DecpAR
1.908
0.989
34
scasonal_naiv
1.000
1.000
35
Auto Arima
1.318
1.032
36
Auto Theta
1.022
1.141
37
Naive
1.167
1.455
38
Auto_ETS
1.346
4.996
39
29

---

Table 10: GIFT-Eval Univariate Leaderboard (full). Lower is better.
Model
MASE
CRPS 4
Rank (CRPS) 4
TiRex
0.688
0.505
X.STM-Mixer (ours)
0.737
01551
2
TabPFN-TS
0.735
0.544
3
Toto Toto_Open Base_ 1.0
Open_Base________
0.737
0.545
timesfim 2 0 500m
0.724
0.549
chronos bolt base
0.725
0.552
6
chronos bolt small Moirai_large
0.739
0.559
7
0.773
0.572
8
YingLong_300m
0.766
0.573
TTM-RR-Finctuued
0.717
0.576
10
sundial base 128m
0.729
0.583
11
Moirai_ basee__bsse
0.795
0.589
12
YingLong 110m
0.793
0.589
13
0.960
0.596
YingLong_50m
0.799
0.598
15
TFT
0.808
0.601
16
PatchTST
0.805
0.613
17
Chronos_lam _aarg
0.775
0.622
18
Chronos_base
0.780
0.627
19
YingLong 6m
0.861
0.646
20
Chronos small
0.797
0.647
21
iTransformer
0.857
0.647
22
TimesFM
0.829
0.652
23
Moirai_small
0.890
0.659
24
TIDE
0.959
0.741
25
DeepAR
1.016
0.758
26
VisionTS
0.845
0.783
27
Auto_Arima Arima
Auto
0.912
0.826
28
N-BEATS
0.892
0.837
29
DLinear
0.944
0.869
30
TTM-R2-Zeroon
0.980
0.907
31
TTM-RI-Zeroon
1.001
0.920
32
Lag-Llama
1.233
0.952
33
scasonal_nate __ivee
1.000
1.000
34
Timer
1.131
1.047
35
Auto Theta
1.147
1.332
36
Naive
1.358
1.709
37
Crossformer
4.000
2.824
38
Auto_ETS
1.115
10.337
39
30

---

Table 11: GIFT-Eval Domain Leaderboards (Top-10 per domain). Lower is better.
Donali
Model
MASE
CRPS
Kank
timeddm_2 2amesfm___0_00000 0_3000
0.640
0.580
TiRex
0.746
0.709
chreacs small TimesFM chrones, bollbase base
Rooe/Fin
0.799
0.762
Domain
Model
MASE
CRPS
Rank
Morra large
TabPi- TS
0.845
0.785
0.778
TabPFN-TS
TiRex
0.682
0.415
Chrenos_Jarg Jarge
MLseM-Miner (ours)
0.782
0.975
D.SU5
0.806
10
chronce boli buse
Times
0.684
0.701
0.700
0.421
0.422
Solez
Maini
YingLong_ 300m
TEMMP_enkenblle
Sen__Opestta Has__
ensemble
0.870
1.D63
0.627
D-613
Toto Open Base, 1.0
chrunce, bult small
PSschTTT
0.691
0:705
0.698
0.426
0.424
0.424
Energy
SLSTM-Mixer (omrs)
TabPYN- IS sundial hase. YingLong chrones bolt small
chroaes, holt, hase
0.546
0.879
0.640
0.841
Mairai
TiRex
0.624
0.601
0.468
0.451
Open. Moiira, base
0.864
0.656
10
sLSTM--Miver (ours)
0.635
0.637
0.487
0.478
MLSTM-Mieer
Trotsport
Fingtuned
0.627
Healtheure
TaNPPN-TS
Chronos large
Toto, Can__Opes_BBBe Hase__s
TTM-R2-Fischuned
0.625
0.559
0.467
0.460
TPT
sundial 128m
2000
0.068
0.679
0.634
0.504
0.514
0.504
Choono Jase Chronos
limesfm O.O. 5.500m
0.644
0.628
0.507
0.513
0.481
TEMPO_ _asemble
ALSTM-Miivr (ours)
0.585
0.779
0.387
0.457
Bar
chrones
0.671
0.54
10
WeNCClmilOpr
sunchal bee 128m
0.695
0.552
TEMPO cusemble
bolt
0.601
D.317
TebPEN
PichEST
0.727
0.780
U.D53
0.573
YongLong
Toto, Tpem_Opem. Buse 1.0
limesfm 2.0 500m
0.624
0.736
0.348
0.350
D.328
YingLong_ 300m
Hinnsdormer
0.823
0.845
0.584
0.575
10
bolt.
YingLong 300m
0.746
0.354
Vingl seg 110m
0.745
0.356
sundial hase. 128m
0.703
0.361
YingLong 50m
31

---

G Visualizing Initial Token Embeddings
Fig. shows how the learned initial tokens 1 reflect common patterns found 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 learned for each dataset across different initializations and horizons supports the conclusion that they are data-driven and meaningful to the domain.
Prediction Length 96
Prediction Length 192
Prediction Length 336
Prediction Length 720
Weather
0
-1-
1 Mrn
ETTm1
1
ETTh2
0
24
72
96
96 Time
192
85
170 Time
255
336
180
360
540
720
Time
Time
Figure 6: Initial tokens capture dataset characteristics. The plot illustrates the learned tokens across multiple datasets and prediction lengths. The lookback length is set to 96 for all evaluations. For clarity and the high noise levels of the data, only single seed is shown for ETTml and ETTh2.
H Learning Variate Patterns
As the sLSTM refinement blocks S process the variates recurrently, is insightful assess the extent to which inter-variate relationships are effectively captured. To this end, we adopt a perturbation- based approach to compute attributions, approximating Shapley Values through sampling. Hereby, we a zero baseline and follow the horizon aggregation method proposed by Kraus et al. [2025], where forecasts over the entire horizon are aggregated into 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 KLSTM-Mixer depends on each input variate. Fig. 7 demonstrates the ability of XLSTM-Mixx to model cross- 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 lofer-left triangle.
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 the Weather and ETTml datasets. We observe that the specific ordering does play some role forecasting performance. However, the standard ordering provided by the dataset sources already permits highly effective forecasting.
32

---

1.00
#1
0:46
0.07
4.30
0.08
-0.07
40.57
-0.75
0.05
40.03
.0.04
-0.12
0.01
-0.01 0.08
0.36
0.09
.0.11
0.01 .0.13
0.10
-0.44
0.04
00.04
00.03
0.02
Variate Attribution Score
0.04
-0.04
0.02
0.11
0.02 0.11
-0.18 -0.22
-0.25
Output Varite
0.01
0.07
0.18
0.19
#20
0.04
0.24
0.01
0.24
0:34
0.06
*12
40.05
0.01
0.25
#24
-0.02
-0.02
0.00
0.02
#16
0.06
0.03
-0.04
0..20
0.75
-0.01
0.07
0.13
1.00
-1.00
Input Variate
Weather dataset.
0.11
6.32
0.57
0:30
+5.17
2.63
0:60
-1.09
0:71
3.34
0.34
4.07
4.66
3.31
412
-3.07
0.06
4.11
Irput
Fout Vatteta
(b) ETTh2 dataset.
(c) ETTml dataset.
Figure 7: XLSTM-Mixer effectively learns cross-variate patterns, as this feature attribution of each output input variate on the Weather dataset demonstrates.
33

---

Table 12: X-sTMr provides strong performance regardless of the variate permutations. All measurements are averaged over three initializations each.
From Dataset
Perm.
#1
Perm.
#2
Perm, #3
Perm.
#4
Metric
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
Weather
0.143
0.184
0.149
0.189
0.146
0.187
0.147
0.188
0.148
0.188
192
0.186
0.226
0.192
0.229
0.191
0.229
0.192
0.229
0.192
0.230
336
0.236
0.266
0.242
0.269
0.241
0.269
0.242
0.269
0.240
0.269
720
0.310
0.323
0.310
0.323
0.310
0.323
0.310
0.323
0.310
0.323
96
0.275
0.328
0.278
0.331
0.276
0.330
0.277
0.330
0.275
0.329
ETTml
192
0.319
0.354
0.321
0.356
0.321
0.356
0.320
0.355
0.319
0.355
336
0.353
0.374
0.355
0.376
0.355
0.376
0.354
0.376
0.354
0.376
720
0.409
0.407
0.412
0.409
0.413
0.410
0.413
0,410
0.413
0.410
Electricity
96
0.126
0.218
0.127
0.220
0.126
0.218
0.127
0.219
0.125
0.218
192
0.144
0.235
0.237
0.144
0.235
0.145
0.236
0.144
0.235
336
0.157
0.250
0.160
0.252
0.159
0.251
0.157
0.248
0.159
0,250
720
0.183
0.276
0.230
0.315
0.225
0.312
0.206
0.295
0.218
0.306
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 a representative sample.
Table 13: Ensembling over more than two views does not yield further benefits. Results are for different numbers of views E for varying forecast horizons H/ on ETTh2. The values in parentheses represent the relative change over (only forward view), where lower numbers are better. = is the base variant of LLST---Miie showing the strongest improvement each.
H 96
H
192
H 336
H
720
E
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
10.274
0.330
0.345
0.375
0.377
0.402
0.397
0.426
2
0.267
22.55%
0.329
0.30%
0.338
2.03%
0.375 +0.00%
0.367
22.68%
0.401
.0.25%
0.388
2.27%
0.424
-0.7%
0.273
.0.36%
0.333
+0.91%
0.340
0.380
0.374
-0.00%
0.408
+1.49%
0.393
.1.1%%
0.430
0..755
+0.36%
0.336
+1.82%
0.344
.0.9%%
0.382
+1.87%
0.373
11.6%
0.407
+1.24%
0.408
+2.77%
0.439
+3.05%
10
0.274
+0.00%
0.336
+1.82%
0.345
+0.00%
0,383
+2.13%
0.372
11.33%
0.405
+0.75%
0.411
+3.53%
0.441
+3.52%
34

---

Outlook: Classification
Tab. 14 compares XLSTM-Mixer common time series classification models and standard bench- mark datasets. Summarizing the individual results, XLSTM-Mixer is on par with the best model, MCNemnTN [Donghao and Xue 2023].
To adapt XLSTM-Mixer for classification, we replace the final regression projection layer with single fully connected classification head followed by softmax activation. We train this variant end-to-end on labeled sequences using cross-entropy loss, applying the same data preprocessing and augmentation pipeline in our forecasting experiments.
These results highlight xLsc''Mixer's flexibility: with minimal architectural changes and no specialized classification tricks, it achieves state-of-the-arr performance while preserving the same core building blocks used for forecasting. This unified design suggests that XLSTM-Mixer can serve general backbone for wide range of sequence modeling tasks.
Table 14: Mixeer is effective time series classification. We report the averaged accuracy in percent. Adapted from Wu et al. 2022a
Chasical
Trassfene
Canndational
UTW
XiGifooo: Bocket xLSTM-
LSTM LSTNe
In
Satton
FED:
EIS.
Flrx
illadd
DLa
Lightts
TIDE
VinsaNer
TCN
32.5
43.7
45.2
31.7
32.3
39.9
31.1
32.7
31.9
31.6
30.8
31.6
32.7
28.1
31.2
33.8
28.1
32.6
29.7
27.1
35.7
56.3
FeceDssction
67.3
66.0
Handwritng
25.6
15.8
58.8
31.8
15.2
25.8
24.5
32.0
27.4
32.8
29.4
36.7
31.6
25.0
32.5
33.8
24.2
2710
26.1
23.2
32.1
30.6
Hasnheat
94.9
56.5
06.2
92.5
70.3
98.1
96.4
98.7
97.8
98.9
98.4
96.2
09.
98.4
95.9
96.9
96.6
06.2
96.2
95.6
95.4
98.8
PEMS-SF
$9.1
SclReggheinSCPP
92.3
89.4
83.7
91.8
91.4
Sel SelReyuhriuSCPP
53.9
48.9
53.3
59.8
46.6
52.5
53.2
53.9
56.7
53.3
53.3
50.6
57.2
54.4
55.0
56.1
54.4
50.5
51.1
53.4
57.2
60.3
Spolen//eaiciigtt
99.3
98,4
100,0
130,0
98.7
90.5
75.9
94.4
39.0
41.2
87.8
15.9
85.6
85.6
35.6
834
85.9
87.5
85.3
85.0
99.6
R5.9
82.1
90.3
84.9
85.3
M6.7
Averae Accuray
67.0
860
72.5
78.1
71.8
10.9
71.9
71.5
72.1
10.8
71.1
72.7
20.7
71.0
70.5
67.5
70.4
69.5
73.6
74.2
35


Reviews:
[{"review_id": "G714WjWufm", "reviewer": "Reviewer_67JL", "summary": "This 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.", "questions": "Here 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)", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 1, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**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.", "was_revised": true, "final_justification": "My main initial concerns were on experiments and clarity:\n* Regarding experiments, the author provided a very comprehensive answer that significantly improves the empirical results and analysis. \n* Regarding clarity, they mention they will fix the issues I raised but the method description was very poor, while I think it will be improved I have some uncertainty whereas the final description will be clear and with a low number of typos.\n\nFor those reasons, I raised my score from 2 to 4. I did not raise to 5 given the uncertainty on the final clarity of the paper which cant be evaluated.", "rebuttal": "Dear Reviewer 67JL,\n\nWe thank the reviewer for recognizing the novel xLSTM-Mixer architecture and its empirical gains over the many baselines in multiple practical scenarios.\n\nWe gladly clarify the raised comments and questions:\n\n**Re. Clarity:** Thank you for thoroughly checking the notation and verifying its correctness. We already clarified the ambiguous pieces and incorporated the changes you suggested.\nSpecifically, we now consistently use the notation introduced in ll. 81ff. This includes the two missing bold notations in Eqs. (1) and (2) and comments regarding Sec. 3.1: There, $\\mathbf{x}_t \\in \\mathbb{R}^V$ intentionally denotes only a single time step of the multivariate time series $\\mathbf{X}$, hence the lower-case bold notation introduced before. The definition of $\\mathbf{x}^\\text{norm}_t$ follows that of the referenced Kim et al. (2022), where $\\gamma$ and $\\beta$ should also be bold as they are learned separately for each of the $V$ variates.\nIn l. 162, we changed the notation to $\\mathbf{h}_0$.\nRegarding l. 180, we now correctly define $\\operatorname{FC}^\\text{view}: \\mathbb{R}^D \\times \\mathbb{R}^D \\to \\mathbb{R}^H$ in the preceeding line.\nThank you again for verifying the notation. We are certain this improved the work.\n\n**Q1**: We aim for best comparability with the existing line of research on long-term time series forecasting—such as the long-term benchmarks evaluated by, for example, Chimera from Behrouz et al. (NeurIPS, 2024), PatchTST from Nie et al. (ICLR, 2023), TiDE from Das et al. (TMLR, 2023), and many preceding works.\nTherefore, we primarily focused on the benchmark of the classical seven datasets, each evaluated over four forecast horizons, along with an additional 17 datasets presented in the outlooks in Appendices F, G, and H. For the main comparison, we ensured evaluation against the state-of-the-art within each model category (e.g., recurrent, convolutional), which are not necessarily the most recent models. For instance, PatchTST remains the top-performing model in the \"deep learning\" category of the GIFT-eval leaderboard. Nevertheless, we also include three models from 2025 to reflect the latest advancements in the field.\n\n**Q2:** Thank you for directing us to GIFT-Eval. The benchmark targets probabilistic zero-shot evaluation, and more than half of its datasets are univariate. Its accompanying pre-training corpus is designed for foundation models rather than classical deep-learning methods, and it focuses on very short horizons, which was initially outside the planned scope of the manuscript. Nevertheless, we ran the benchmark and are pleased to report that xLSTM-Mixer surpasses classical deep-learning and statistical baselines by a large margin on univariate and multivariate datasets, while matching the strongest pre-trained models.\n\nWe are grateful for this insightful suggestion, which has broadened the scope of our work and strengthened the manuscript. We will include the full results in the camera-ready version and publish them on the public leaderboard.\n\n### Overall Leaderboard\n|model|MASE|CRPS|overall_rank|\n|:-------------------|-------:|-------:|---------------:|\n|TiRex|0.724|0.498|1|\n|TEMPO_ensemble|0.862|0.514|2|\n|👉 **xLSTM-Mixer**|0.783|0.515|3|\n|Toto_Open_Base_1.0|0.75|0.517|4|\n|TabPFN-TS|0.771|0.544|5|\n|YingLong_300m|0.798|0.548|6|\n|timesfm_2_0_500m|0.758|0.55|7|\n|YingLong_110m|0.809|0.557|8|\n|sundial_base_128m|0.75|0.559|9|\n|YingLong_50m|0.822|0.567|10|\n|chronos_bolt_base|0.808|0.574|11|\n|chronos_bolt_small|0.822|0.577|12|\n|TTM-R2-Finetuned|0.756|0.583|13|\n|PatchTST|0.849|0.587|14|\n|Moirai_large|0.875|0.599|15|\n|TFT|0.915|0.605|16|\n|YingLong_6m|0.88|0.609|17|\n|Moirai_base|0.901|0.61|18|\n|iTransformer|0.893|0.62|19|\n|Chronos_large|0.87|0.647|20|\n|Moirai_small|0.946|0.65|21|\n|Chronos_base|0.876|0.652|22|\n|Chronos_small|0.892|0.663|23|\n|TimesFM|1.077|0.68|24|\n|VisionTS|0.863|0.755|25|\n|TIDE|1.091|0.772|26|\n|N-BEATS|0.938|0.816|27|\n|DLinear|1.061|0.846|28|\n|DeepAR|1.343|0.853|29|\n|TTM-R2-Zeroshot|1.02|0.873|30|\n|Lag-Llama|1.228|0.88|31|\n|TTM-R1-Zeroshot|1.079|0.891|32|\n|Auto_Arima|1.074|0.912|33|\n|Timer|1.136|0.97|34|\n|seasonal_naive|1|1|35|\n|Auto_Theta|1.09|1.244|36|\n|Naive|1.27|1.591|37|\n|Crossformer|2.574|1.637|38|\n|Auto_ETS|1.212|7.489|39|\n\n### Multivariate Leaderboard Top 10\n|model|MASE|CRPS|overall_rank|\n|:-------------------|-------:|-------:|---------------:|\n|TEMPO_ensemble|0.752|0.427|1|\n|👉 **xLSTM-Mixer**|0.84|0.477|2|\n|Toto_Open_Base_1.0|0.767|0.484|3|\n|TiRex|0.771|0.49|4|\n|YingLong_300m|0.84|0.519|5|\n|YingLong_110m|0.83|0.52|6|\n|YingLong_50m|0.853|0.53|7|\n|sundial_base_128m|0.778|0.53|8|\n|TabPFN-TS|0.818|0.544|9|\n|timesfm_2_0_500m|0.803|0.553|10|\n\n### Univariate Leaderboard Top 10\n|model|MASE|CRPS|overall_rank|\n|:-------------------|-------:|-------:|---------------:|\n|TiRex|0.688|0.505|1|\n|TabPFN-TS|0.735|0.544|2|\n|Toto_Open_Base_1.0|0.737|0.545|3|\n|👉 **xLSTM-Mixer**|0.742|0.546|4|\n|timesfm_2_0_500m|0.724|0.549|5|\n|chronos_bolt_base|0.725|0.552|6|\n|chronos_bolt_small|0.739|0.559|7|\n|Moirai_large|0.773|0.572|8|\n|YingLong_300m|0.766|0.573|9|\n|TTM-R2-Finetuned|0.717|0.576|10|\n\n**Q3:** We put in substantial effort to ensure a fair comparison. We proceeded as follows: For most models, the initial publication already comprehensively evaluated the model on these well-known datasets and found appropriate hyperparameters. 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. ll. 330f). We still present the better results from Alharthi and Mahmood (2024) so as not to erroneously underestimate the method. For the datasets for which no such results were available (ETTh2, ETTm1, and ETTm2), we ran individual hyperparameter searches like we did for our method to ensure a fair comparison between all models.\n\n**Q4:** We followed the common practice of evaluating the forecast accuracy by counting wins across models and datasets. However, we agree that statistical testing is the more rigorous and desirable procedure to perform this.\nFollowing the well-known practice of Demšar (2006), we first perform a Friedman test to ensure the model's performances follow different distributions ($p < 10^{-10}$).\nUsing Holm's method, we can then perform a Conover post-hoc test while adjusting for the family-wise error rate.\nWe must restrict this comparison to one metric and horizon (here, MSE at 96 steps), since the performance results are strongly correlated for one model and dataset pair and would artificially inflate significance if not accounted for.\n\nAt a significance threshold of $\\alpha = 0.05$, we find that xLSTM-Mixer is statistically significantly better than all other methods, except for xLSTMTime.\nYet, the difference in average rank is still impressive, with 1.5 for xLSTM-Mixer and 4.0 for xLSTMTime.\nFurthermore, xLSTMTime is statistically inseparable from many other models, namely TimeMixer, TSMixer, ModernTCN, Chimera, PatchTST, and TiDE, in that order.\n\nWe will add this setup and the result as an easily digestible Critical Difference (CD) diagram to Sec. 4.1 of the paper.\n\n**Q5 (curiosity):** Thank you so much for the perspective that variate reordering can be seen as ensembling (with weight–sharing). It also sparked our curiosity! We thus performed additional variate experiments with permutations of the variates beyond one (standard order) and two (standard and reversed).\nAgain, using two views works best for all prediction lengths, while further increasing the ensemble size can also be beneficial over the single view. However, this may over-regularize the model for some prediction lengths and higher ensemble counts. We observed this on multiple datasets and show ETTh2 as a representative sample. Thank you again for suggesting this insightful perspective. We will include this in our revised manuscript.\n\n### Scaling Summary: ETTh2 (pred_len=96)\n\n| Ensemble Size | MSE (mean±imp. over #1) | MAE (mean±imp. over #1) |\n|---|---|---|\n| 1 | 0.274+0.00% | 0.330+0.00% |\n| 2 | 0.267-2.55% | 0.329-0.30% |\n| 5 | 0.273-0.36% | 0.333+0.91% |\n| 8 | 0.275+0.36% | 0.336+1.82% |\n| 10 | 0.274+0.00% | 0.336+1.82% |\n\n### Scaling Summary: ETTh2 (pred_len=192)\n\n| Ensemble Size | MSE (mean±imp. over #1) | MAE (mean±imp. over #1) |\n|---|---|---|\n| 1 | 0.345+0.00% | 0.375+0.00% |\n| 2 | 0.338-2.03% | 0.375+0.00% |\n| 5 | 0.340-1.45% | 0.380+1.33% |\n| 8 | 0.344-0.29% | 0.382+1.87% |\n| 10 | 0.345+0.00% | 0.383+2.13% |\n\n### Scaling Summary: ETTh2 (pred_len=336)\n\n| Ensemble Size | MSE (mean±imp. over #1) | MAE (mean±imp. over #1) |\n|---|---|---|\n| 1 | 0.377+0.00% | 0.402+0.00% |\n| 2 | 0.367-2.65% | 0.401-0.25% |\n| 5 | 0.374-0.80% | 0.408+1.49% |\n| 8 | 0.373-1.06% | 0.407+1.24% |\n| 10 | 0.372-1.33% | 0.405+0.75% |\n\n### Scaling Summary: ETTh2 (pred_len=720)\n\n| Ensemble Size | MSE (mean±imp. over #1) | MAE (mean±imp. over #1) |\n|---|---|---|\n| 1 | 0.397+0.00% | 0.426+0.00% |\n| 2 | 0.388-2.27% | 0.424-0.47% |\n| 5 | 0.393-1.01% | 0.430+0.94% |\n| 8 | 0.408+2.77% | 0.439+3.05% |\n| 10 | 0.411+3.53% | 0.441+3.52% |\n\nAgain, thank you very much for this constructive feedback. We hope to have sufficiently answered all questions.\nIn particular, the main concerns, namely the clarity, the statistical significance of the results, and new impressive results on GIFT-Eval, have substantially improved our manuscript.\nIn light of this, we would greatly appreciate it if you reconsidered your score to reflect this.\n\nBest\n\nThe Authors\n\n**References:**\n- Behrouz et al. Chimera: Effectively Modeling Multivariate Time Series with 2D State Space Models. NeurIPS, 2024. \n- Nie et al. A Time Series is Worth 64 Words: Long-term Forecasting with Transformers. ICLR, 2023. \n- Das et al. Long-term Forecasting with TiDE: Time-series Dense Encoder. TMLR, 2023. \n- Alharthi et al. xLSTMTime: Long-Term Time Series Forecasting with xLSTM. MDPI AI, 5(3), 2024. \n- Demšar. Statistical Comparisons of Classifiers over Multiple Data Sets. JMLR, 7, 2006."}, {"review_id": "NrkE4mnEVb", "reviewer": "Reviewer_V19p", "summary": "This 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.", "questions": "1. Why sLSTM is more suitable for the mixer framework than the other RNN unit? Is there any theoretical explanation for this phenomenon?", "limitations": "The 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.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\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", "was_revised": true, "final_justification": "The authors' responses have addressed some of my concerns. More experiment results are provided. I will update my score to 5.", "rebuttal": "Dear Reviewer V19p,\n\nWe are grateful for the recognition of the clear writing, the novel xLSTM-Mixer architecture, and excellent modeling capabilities while remaining efficient.\n\nWe gladly clarify the raised comments and questions:\n\n**W1:** We ground xLSTM‑Mixer in time‑ and variate‑mixing theory. A single shared NLinear forecaster that marches over the variates (Section 3.1, motivated by Section 2.2) imposes a strong channel‑independent inductive bias. After transposing the embedding—as shown by the inverted‑token iTransformer (Liu et al., 2023)—the sLSTM stack (Section 3.2) jointly mixes time and variates while keeping parameters and memory low. We then produce two complementary latent views (original and reversed), process both with the same sLSTM, and fuse them with one linear layer (Section 3.3); this weight‑tied multi‑view design follows the regularisation principles of multi‑task learning described by Zhang & Yang (2022). Analytically, block‑diagonal recurrence keeps each head focused on long‑range dynamics, while a learnable soft‑prompt token speeds adaptation—a mechanism also used in TEMPO (Cao et al., 2023). Together, these choices explain xLSTM‑Mixer’s state‑of‑the‑art long‑horizon accuracy and efficiency; additional theoretical insights appear in our response to Q1.\n\n**W2:** We welcome the suggestion to improve the manuscript even further by outlining xLSTM-Mixer's limitations. We amended the paper with a new section. Please refer to Reviewer fZrP Response for **Comments on Limitations** for the explicit paragraph.\n\n**W3:** We initially only provided an outlook to probabilistic forecasting.\nWe welcome your suggestion, and have since then massively extended this to the novel and large probabilistic GIFT-Eval benchmark (Aksu et al., 2024), as also suggested by Reviewer 67JL.\nIn summary, we are pleased to report that xLSTM-Mixer surpasses classical deep-learning and statistical baselines by a large margin on univariate and multivariate datasets, while matching the strongest pre-trained models.\nPlease refer to Reviewer 67JL's response for the benchmark tables.\n\nWe are grateful for this insightful suggestion, which has broadened the scope of our work and strengthened the manuscript. We will include the full results in the camera-ready version and publish them on the public leaderboard.\n\n**W4:** We agree that this is an intriguing idea for further in-depth analysis.\nThese different views can be seen as ensembling with weight-sharing.\nTherefore, extending the size of the ensemble is a natural next step.\nWe thus performed additional variate experiments with permutations of the variates beyond one (standard order) and two (standard and reversed). Please refer to Reviewer 67JL's response for the scaling summary tables.\nAgain, using two views works best for all prediction lengths, while further increasing the ensemble size can also be beneficial over the single view. However, this may over-regularize the model for some prediction lengths and higher ensemble counts. We observed this on multiple datasets and show ETTh2 as a representative sample. Thank you again for suggesting this insightful perspective. We will include this in our revised manuscript.\n\n**W5:** For the main comparison, we ensured that the comparison was against the *state-of-the-art* in each model group (recurrent, convolutional, etc.). Those are not necessarily the newest models. For instance, PatchTST is still the best model in the \"deep-learning\" category of the GIFT-eval leaderboard. However, we still include three models from 2025 to reflect the latest developments.\nRegarding the three concurrent works you suggested:\nTimeCMA shows worse performance than xLSTM-Mixer in all 48 comparable settings (Liu et al., 2025, Tab. 1).\nHDT is a model solely for probabilistic forecasting (Shibo et al., 2025), and thus not a natural baseline to compare against.\nSimilarly to TimeCMA, xLSTM-Mixer outperforms P-sLSTM in all 24 comparable settings (Kong et al., 2025, Tab. 2).\nHowever, we gladly incorporate these three recent works into our related work, especially Kong et al. (2025), which is closely related.\nAs already discussed in **W3**, we substantially expanded the empirical findings to the GIFT-eval benchmark, thereby adding new baselines via its leaderboard.\n\n**Q1:** Thank you for raising this point. \nBeck et al. (2024) provide an in-depth discussion of why xLSTMs are beneficial over previous recurrent models. Nevertheless, below, we clarify and give an intuition as to why we use sLSTM over mLSTMs. The core reason for that is the explicit state‑tracking via memory mixing in sLSTM, which is lacking from mLSTMs:\n\n- sLSTM keeps the hidden‑to‑hidden (memory mixing) connections of the classic LSTM and augments them with exponential gating and stabilisation (Beck et al. 2024; Greff et al. 2017).\n  $$\n  c_t = f_t c_{t-1} + i_t z_t,\\qquad\n  h_t = o_t \\, g(c_t)\n  $$\n  Because $f_t$, $i_t$, and $o_t$ all depend on the previous hidden state $h_{t-1}$, the block can learn to blend past and present information on demand.\n- mLSTM stores key–value pairs in a matrix\n  $$\n  C_t = f_t C_{t-1} + i_t v_t k_t^T .\n  $$\n  But to enable full parallelisation, it's gates depend only on the current input, i.e., all hidden‑to‑hidden paths are removed (Beck et al. 2024, Sec 2.3). Thus, memory mixing is absent.\n\nWhy this matters for forecasting: Time‑series forecasting often requires the model to keep track of latent phases such as \"heating ↔ cooling\" or \"upward ↔ downward\" movement. The model must retain that phase until evidence of a switch appears and flip its internal indicator when the switch occurs.\n\n* In sLSTM, gate values can be trained so that\n  *when a switch indicator is detected* $i_t = 0$, $f_t = 1$ (overwrite),\n  *otherwise* $i_t = 1$, $f_t = 0$ (retain).\n  Because the gates read $h_{t-1}$, the decision depends on the current internal phase as well as the new input, enabling reliable phase tracking.\n* In mLSTM, gate values cannot depend on $h_{t-1}$. Instead, the update is a linear function of the input history, i.e., it can integrate evidence but cannot implement a conditional flip.  Empirically, models without memory mixing (mLSTM, Mamba, Transformers) fail even simple state‑tracking tasks such as parity (Merrill et al. 2024; Beck et al. 2024).\n\nAn illustrative Example: Consider a binary series where $x_t = 1$ signals a phase switch; the desired hidden phase $s_t$ obeys $s_t = s_{t-1} \\oplus x_t$, where $\\oplus$ denotes the XOR operation.\n\nsLSTM case: Choose weights so that $f_t = \\sigma(\\alpha(1-x_t))$ and $i_t = \\sigma(\\alpha x_t)$ with large $\\alpha$.\nLet the output gate turn $c_t$ into two well‑separated values (e.g., −1 vs 1).\nThen $c_t$ flips sign exactly when $x_t=1$, reproducing $s_t$. Because $f_t$ and $i_t$ both read $h_{t-1}$, more complex phase logic (e.g., multi‑step confirmation) can also be learned.\n\nmLSTM case: Unfolding the recurrence shows that $C_T$ is a weighted sum of outer products of current inputs. In other words, the weights are fixed functions of those inputs alone. Hence, $h_T$ is a linear function of $x_t$. Parity (and any phase‑flip automaton) are not linearly representable—therefore mLSTM cannot track the phase.\n\nEmpirical evidence in our work:\n* We employ only sLSTM blocks because mLSTM \"treat\\[s] sequence elements independently, making it impossible to learn relationships between them directly\" (Beck et al. 2024, Sec 2.1).\n* Replacing sLSTM with mLSTM, GRU, or vanilla LSTM consistently degrades long‑horizon accuracy, especially on 336‑ and 720‑step forecasts (cf. Sec 4.4).\n* xLSTMTime uses sLSTM for smaller forecasting datasets where accurate phase tracking dominates, while mLSTM is chosen only when raw storage capacity outweighs this need (Alharthi & Mahmood 2024). TiRex attributes its performance gains to retaining state tracking as well (Auer et al. 2025).\n\nThus, sLSTM’s memory‑mixing recurrence preserves and updates time‑varying hidden phases, a property indispensable for high‑fidelity forecasts over long horizons. mLSTM's parallel‑friendly design diminishes this ability. Our empirical results and prior literature confirm that, in forecasting contexts, state‑tracking capacity outweighs raw matrix‑memory capacity—hence our exclusive use of sLSTM blocks in xLSTM‑Mixer. We again thank the reviewer for this question and will integrate this much more extensive theoretical view with illustrative examples in the camera-ready version.\n\nThank you again for your thoughtful review. We hope this review answered all outstanding questions. Specifically, having elaborated on the theory and limitations. Furthermore, we provided impressive leaderboard placements on the more practical and probabilistic GIFT-Eval set, and discussed and validated additional variate ordering findings. \nHence, we have addressed all key concerns regarding the work. In light of this, we would greatly appreciate it if you could raise your score to reflect this.\n\nBest\n\nThe Authors\n\n**References:**\n- Liu et al. TimeCMA: Towards LLM-Empowered Multivariate Time Series Forecasting via Cross-Modality Alignment. AAAI, 39(18):18780–18788, 2025. \n- Shibo et al. HDT: Hierarchical Discrete Transformer for Multivariate Time Series Forecasting. AAAI, 39(1):746–754, 2025. \n- Kong et al. Unlocking the Power of LSTM for Long Term Time Series Forecasting. AAAI, 39(11):11968–11976, 2025. \n- Aksu et al. GIFT-Eval: A Benchmark for General Time Series Forecasting Model Evaluation. NeurIPS Workshop on Time Series in the Age of Large Models, 2024. \n- Zhang et al. A Survey on Multi-Task Learning. IEEE TKDE, 34(12):5586–5609, 2022. \n- Liu et al. iTransformer: Inverted Transformers are Effective for Time Series Forecasting. ICLR, 2024. \n- Cao et al. TEMPO: Prompt-based Generative Pre-trained Transformer for Time Series Forecasting. ICLR, 2023."}, {"review_id": "xnzKQb3vdy", "reviewer": "Reviewer_fZrP", "summary": "The 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.", "questions": "1. 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.", "limitations": "The 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.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "This  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", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer fZrP,\n\nWe thank the reviewer for recognizing the thoughtful design and thorough empirical validation of xLSTM-Mixer. \n\n**W1:** Thank you for mentioning this interesting perspective.\nThis multi-view prediction is primarily related to multi-task learning (Zhang et al., 2022), which is similar to data augmentation in its goal to regularize training. Mixing operations can be interpreted as a latent data augmentation or alternatively as ensembling with weight-sharing as suggested by Reviewer 67JL. We can imagine these perspectives as a guide for future improvements to xLSTM-Mixer, and we will add them to Sec. 3.3.\n\n**W2:** Yes, we indeed conducted the very extensive real-world benchmark GIFT-Eval (Aksu et al., 2024) encompassing 97 scenarios. It also includes missing values as you suggested, empirically strengthening our contribution. Furthermore, multiple benchmark datasets are also non-stationary. We also note that the existing benchmark datasets already exhibit a diverse range of substantial levels of noise. This is also shown by the Hurst exponent in Appendix A, Tab. 3.\nWe added this discussion to the limitations section of the manuscript as laid out at the end of this response.\n\n**W3:** Explainable AI is indeed an important aspect, and often at conflict with model fidelity.\nOn one hand, the multistage approach makes certain interpretations harder, like for any deep learning model. See also the limitations section at the end of this response.\nOn the other hand, it permits, for instance, interpreting the initial token embeddings as shown in ll. 234ff and in Appendix D.\nOverall, attribution methods, such as Integrated Gradients and SHAP, still function as normal, permitting inspection of the learned patterns, such as shown in ll. 266ff and in Appendix E.\n\n**W4:** Highlighting the differences of the variants in the ablation by including performance drops relative to the full xLSTM-Mixer baseline (#1) is a very useful suggestion. We will improve Sec. 4.4 by adding the following information.\n> Ablating components of xLSTM-Mixer each causes both error metrics to increase, entailing that they contribute positively to the overall architecture.\n> Specifically, ommiting 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%.\n\n**W5:** Thank you for mentioning this. Reviewer V19p raised a similar point. Please refer to the response of Reviewr V19p **Q1**, where we clarify and give an intuition why state‑tracking via memory mixing in sLSTM is indispensable, whereas mLSTM's design cannot provide this functionality.\n\n**Comments on Limitations:**\nWe welcome your comments on the limitations of xLSTM-Mixer. We added the following to the paper: (1) A dedicated limitations paragraph in Section 6 and (2) a dedicated section on broader societal impact as encouraged by NeurIPS. We attached them both to this response:\n\n> **Limitations.**\n> 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.\n> Moreover, the simultaneous mixing of multiple views blends temporal and cross‑channel information in ways that make detailed attributions difficult and may leave the network sensitive to regime shifts or extremely noisy signals. Addressing these aspects through adaptive variate grouping, continuous‑time embeddings, and lightweight explanation modules are potential paths forward beyond the current work.\n\n> **Societal Impact.**\n> This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here.\n> \n> 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.\n> \n> 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.\n> \n> 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.\n\nThank you again for your thoughtful review. We hope this review answered all outstanding questions. Specifically, having improved the clarity of the work (theory and writing) and provided impressive new benchmark results on the more practical GIFT-Eval. Furthermore, we added a new limitation section and a more extensive discussion of ablation results.\nTherefore, we have addressed all key concerns regarding our work. In light of this, we would greatly appreciate it if you could raise your score to reflect this.\n\nBest\n\nThe Authors\n\n**References:**\n- Zhang et al. A Survey on Multi-Task Learning. IEEE TKDE, 34(12):5586–5609, 2022. \n- Aksu et al. GIFT-Eval: A Benchmark for General Time Series Forecasting Model Evaluation. NeurIPS Workshop on Time Series in the Age of Large Models, 2024. \n- Beck et al. xLSTM: Extended Long Short-Term Memory. NeurIPS, 2024. \n- Greff et al. LSTM: A Search Space Odyssey. IEEE T-NNLS, 2017. \n- Merrill et al. Unlocking State-Tracking in Linear RNNs Through Negative Eigenvalues. NeurIPS Workshop on MML, 2024. \n- Alharthi et al. xLSTMTime: Long-Term Time Series Forecasting with xLSTM. MDPI Sensors, 2024. \n- Auer et al. TiRex: Zero-Shot Forecasting Across Long and Short Horizons with Enhanced In-Context Learning. arXiv:2505.23719, 2025."}, {"review_id": "YmYnD85v93", "reviewer": "Reviewer_cGWV", "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.", "questions": "Please see Weaknesses!", "limitations": "Please see Weaknesses!", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. 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.\n2. 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.\n3. 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.\n\nWeaknesses:\n1. Ablation (in Table 2) shows omitting the initial token embedding still yields competitive results. Its necessity and interpretability (Fig. 5) require deeper analysis.", "was_revised": true, "final_justification": "The author has addressed all my concerns, mainly by elaborating on the issue of interpretability.", "rebuttal": "Dear Reviewer cGWV,\n\nThank you for your strongly affirmative review and for recognizing the novelty, clarity, and empirical efficacy of xLSTM-Mixer.\n\nWe are happy to provide further insights into the initial token embedding:\n\n**W1 (necessity):** The benefit of learning $\\mathbf\\eta$ can be observed by comparing ablation #7 to the base xLSTM-Mixer model #1 in Table 2. Model #1 consistently performs at least as well as #7 and, in 13 out of 16 cases, learning the initial token embedding yields strictly better results. While the effect is not dramatic, it offers a consistent benefit: on average, learning the initial token embedding reduces MAE by 0.4% and MSE by 0.7% across all eight settings.\n\n**W1 (interpretability):** We are pleased to expand on the interpretation of Fig. 5, as outlined in lines 237–240. 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 the same datasets across different initializations and horizons supports the conclusion that they are data-driven and meaningful to the domain.\n\nWe also invite you to review our response to Reviewer 67JL, where we significantly expanded our empirical analysis on the GIFT-eval benchmark, reaching impressive leaderboard placements (Q2), conducted statistical significance tests (Q4), and extended the experiments on variate orderings (Q5).\n\nThank you again for your overwhelmingly positive review. In light of this, we would greatly appreciate it if you could consider raising your score to reflect your assessment.\n\nBest\n\nThe Authors"}]

Author rebuttal:

Meta-review: This paper proposes a new algorithm for time series multivariate forecasting based on xLSTM which refines a linear forecast across variates with xLSTM blocks before projecting the output back to the desired dimension. The authors have conducted an extensive set of evaluations on different datasets and baseline algorithms, and added the GIFT-Eval during the rebuttal phase. Their results show that xLSTM has promising performance. There were some concerns about quality of writing and clarity of the paper, as well as a discussion of trade-offs and limitations of the approach. The authors have promised to address these issues in the camera-ready. Overall, the reviewers were uniformly positive about the paper.
Decision: Accept (poster)