TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis
Authors: Shiyu Wang
Jiawei LI
Xiaoming Shi
Zhou Ye
Baichuan Mo
Wenze Lin
Ju Shengtong
Zhixuan Chu
Ming Jin
Venue: ICLR 2025 Oral (2025)
Keywords: time series
pattern machine
predictive analysis
Primary area: learning on time series and dynamical systems
TL;DR: TimeMixer++ is a time series pattern machine that employs multi-scale and multi-resolution pattern extraction to deliver SOTA performance across 8 diverse analytical tasks, including forecasting, classification, anomaly detection, and imputation.

Abstract: Time series analysis plays a critical role in numerous applications, supporting tasks such as forecasting, classification, anomaly detection, and imputation. In this work, we present the time series pattern machine (TSPM), a model designed to excel in a broad range of time series tasks through powerful representation and pattern extraction capabilities. Traditional time series models often struggle to capture universal patterns, limiting their effectiveness across diverse tasks. To address this, we define multiple scales in the time domain and various resolutions in the frequency domain, employing various mixing strategies to extract intricate, task-adaptive time series patterns. Specifically, we introduce TimeMixer++, a general-purpose TSPM that processes multi-scale time series using (1) multi-resolution time imaging (MRTI), (2) time image decomposition (TID), (3) multi-scale mixing (MCM), and (4) multi-resolution mixing (MRM) to extract comprehensive temporal patterns. MRTI transforms multi-scale time series into multi-resolution time images, capturing patterns across both temporal and frequency domains. TID leverages dual-axis attention to extract seasonal and trend patterns, while MCM hierarchically aggregates these patterns across scales. MRM adaptively integrates all representations across resolutions. TimeMixer++ achieves state-of-the-art performance across 8 time series analytical tasks, consistently surpassing both general-purpose and task-specific models. Our work marks a promising step toward the next generation of TSPMs, paving the way for further advancements in time series analysis.

Published as a conference paper at ICLR 2025
TIMEMIXER++: A GENERAL TIME SERIES PATTERN MACHINE FOR UNIVERSAL PREDICTIVE ANALYSIS
Shiyu Wang" Jiawei 1 Xiaoming Shi, Zhou Ye, Baichuan Mo Wenze Lin",
Shengtong Ju Zhixuan Chu Ming Jin
1 Griffith University 'The Hong Kong University of Science and Technology (Guangzhou) "Massachusetts Institute of Technology *Zhejiang University
'The State Key Laboratory of Blockchain and Data Security
Hangghou High-Tech Zone (Binjiang) Institute of Blockchain and Data Security kwuk i ng@gmail com, Jarvis-1a sirii-liious 1ellii@uulloo look. con, sxm728@hotma 11, com yezhoul 990326gma com, bai chiangmmmmi edu, zhi xuanchu@ edu. (1inwenze75, shengtongju, mi ninggi nedu) indu)
@gmai com
ABSTRACT
Time series analysis plays a critical role in numerous applications, supporting tasks such as forecasting, classification, anomaly detection, and imputation. In this work, we present the time series pattern machine (TSPM), a model designed to excel in a broad range of time series tasks through powerful representation and pattern extraction capabilities. Traditional time series models often struggle to capture uni- versal patterns, limiting their effectiveness across diverse tasks. To address this, we define multiple scales in the time domain and various resolutions in the frequency domain, employing various mixing strategies extract intricate, task-adaptive time series patterns. Specifically, we introduce TIMEMIXER+++ a general general-purpose purpose TSPM that processes multi-scale time series using (1) multi-resolution time imag- ing (MRTT), (2) time image decomposition (TID), (3) multi-scale mixing (MCM), and (4) multi- resolution mixing (MRM) to extract comprehensive temporal patterns. MRTI transforms multi-scale time series into multi-resolution time images, captur- ing patterns across both temporal and frequency domains. TID leverages dual-axis attention to extract seasonal and trend patterns, while MCM hierarchically aggre- gates these patterns across scales. MRM adaptively integrates all representations across resolutions. TIMEMIXER++ achieves ffate-of-the-ate performance across 8 time series analytical tasks, consistently surpassing both general-purpon and task-specific models. Our work marks a promising step toward the next generation of TSPMs, paving the way for further advancements in time series analysis.
INTRODUCTION
Time series analysis is crucial for identifying and predicting temporal patterns across various domains, including weather forecasting (Bi al. 2023), medical symptom classification (Kiyasseh al. 202T) anomaly detection in spacecraît monitoring (Xu et al. (022), and imputing missing data in wearable sensors (Wu et al., (2020). These diverse applications highlight the versatility and importance of time series analysis in addressing real-world challenges. A key advancement in this field is the development of time series pattern machines (TSPMss, which aim to create a unified model architecture capable of handling a broad range of time series tasks across domains (Zhou et al. 2023
Wu et al.) 2023).
At the core of TSPMs is their ability to recognize and generalize time series patterns inherent in time series data, enabling the model to uncover meaningful temporal structures and adapt to varying time series task scenarios. A line of research (Lai et al. 2018b] Zhao al. 2017)) has utilized recurrent neural networks (RNNs) to capture sequential patterns. However, these methods often struggle to capture long-term dependencies due to limitations like Markovian assumptions and inefficiencies. Temporal convolutional networks (TCNs) (Wu al. 2023 Wang et al.
2023a Liu et al. 2022a Wang
et al. 2024a) efficiently capture local patterns but face challenges with long-range dependencies (e.g..
Equal contribution
Project lead
Corresponding author

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Published as a conference paper at ICLR 2025
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Figure 1: Benchmarking model performance across eight tasks (left) and representation analysis in four tasks (right). For each model on the right, the centered kernel alignment (CKA) similarity (Ko) rbblihh et al. 2019) is computed between the representations from the first and last layers.
seasonality and trends) because of their fixed receptive fields. While some approaches reshape time series into 2D tensors based on frequency domain information (Wu et al. 2023) or downsample the time domain (Liu et al. (022a), they fall short in comprehensively capturing long-range patterns. In contrast, transformer-
architectures (Nie et al. 2023 Liu al., 2024 Zhou et al.) 2022b Wang et al. 2022 Shi et al. 2024) leverage wise self-attention to model long-range dependencies by allowing each token to attend to all others, overcoming the limitations of fixed receptive fields. However, unlike language tasks where tokens usually belong to distinct contexts, time series data often involve overlapping contexts at a single time point, such as daily, weekly, and seasonal patterns occurring simultaneously. This overlap makes it difficult to represent time series patterns effectively as tokens, posing challenges for transformer- based models in fully capturing the relevant temporal structures.
The recognition of the above challenges naturally raises a pivotal question:
What capabilities must model possess, and what challenges must it overcome, to function as a TSPM?
Before addressing the design of TSPMs, we first reconsider how time series are generated from continuous real-world processes sampled at various scales. For example, daily data capture hourly fluctuations, while yearly data reflect long-term trends and seasonal cycles. This multi-scale, multi- periodicity nature presents a significant challenge for model design, as each scale emphasizes different temporal dynamics that must be effectively captured. Figure T illustraess this challenge in constructing general TSPM. Specifically, lower CKA similarity (Kornblith et al. 2019) indicates more diverse representations across layers, which is advantageous for tasks like imputation and anomaly detection that require capturing irreullar patterns and handling missing data. In these cases, diverse representa- tions across layers help manage variations across scales and periodicities. Conversely, forecasting and classification tasks benefit from higher CKA similarity, where consistent representations across layers better capture stable trends and periodic patterns. This contrast emphasizes the challenge of designing a universal model flexible enough to adapt to multi-scale and multi-periodicity patterns across various analytical tasks, which may favor either diverse or consistent representations.
To address the aforementioned question and challenges, we propose TIMEMIXER++, general- purpose TSPM designed to capture general, task-adaptive time series patterns by tackling the com- plexities of multi-scale and multi-perion -ulti-periodicity dynamics. The key idea is to simultaneously capture intricate time series patterns across multiple scales in the time domain and various resolutions in the frequency domain. Specifically, TIMEMIXER++ processes multi-scale time series using (I) malti-resolution time imaging (MRTI), (2) time image decomposition (TID), (3) multi-scale mix- ing (MCM), and (4) multi-resolution mixing (MRM) to uncover comprehensive patterns. MRTI transforms scale time series into multi multi-resolution time images, enabling pattern extraction across both temporal and frequency domains. TID applies dual-axis attention to disentangle scasonal and trend patterns in the latent space, while MCM hierarchically aggregates these patterns across
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different scales. Finally, MRM adaptively integrates all representations across resolutions. As shown in Figure I TIMEMIXER++ achieves state-of sfate-of-the-re performance across analytical tasks, outper- forming both general-purpont and task-specifie models. Its adaptability is reflected in its varying CKA similarity scores across different tasks, indicating its ability to capture diverse task-specific patterns more effectively than other models. Our contributions summarized as follows:
We introduce TIMEMIXER++, a general-purpose time series analysis model that processes multi-scale, pulti-periodicity data by transforming time series into multi-resolution time images, enabling efficient pattern extraction across both temporal and frequency domains.
To capture intricate patterns, we disentangle seasonality and trend from time images using time image decomposition, followed by adaptive aggregation through multi-scale mixing and multi- resolution mixing, enabling patterns integration across scales and periodicities.
3. TIMEMIXER++ ++ sets a new state-of-the-art across 8 time series analytical tasks in different benchmarks, consistently outperforming both general-purpose and task-specific models. This marks a significant step forward in the development of next-generation TSPMs.
2 RELATED WORK
Time Series Analysis. A pivotal aspect of time series analysis is the ability extract diverse patterns from various time series while building powerful representations. This challenge has been explored across various model architectures. Traditional models like ARIMA (Anderson & Kendall 1976) and STL (Cleveland et al. 1990) are effective for periodic and trend patterns but struggle with non-linear dynamies. Deep learning models, such as those by (Lai et al., (0186) and (Zhao et al.) (017). capture sequential dependencies but face limitations with long-term dependencies. TCNs (Franceschi al. 2019) improve local pattern extraction but are limited in capturing long-range dependencies.
TimesNet (Wu et al., 2023) enhances long- Long-range pattern extraction by treating time series as 2D signals, while MLP-based methods (Zeng et al. 2023 [Ekambaram et al. 2023 Liu et al. 2023 Waan et al. 2023c) offer simplicity and effectiveness. Transformer- based models like PatchTST (Nie et al. 2023 and iTransformer (Liu et al. 2024) leverage self-attention to model long-range dependencies, demonstrating good forecasting performance. Given the strengths and limitations discussed above, there is a growing need for a TSPM capable of effectively extracting diverse patterns, adapting to various time series analytical tasks, and possessing strong generalization capabilities. As illustrated in Figure I TIMEMIXER++ meets this requirement by constructing robust representational capabilities, thereby demonstrating its potential for universal time series analysis.
Hierarchical Time Series Modeling. Numerous methodologies have been advanced utilizing specialized deep learning architectures for time series analysis, with an emphasis on the decomposition and integration of temporal patterns. For example, several studies (Wu et al.) 2021 Wang et al.
2024b; Zhou et al. 2022b Luo et al., [2023] Wang al. 2023b) utilize moving averages to discern scasonal and trend components, which are subsequently modeled using attention mechanisms (Wu al. 2021 Zhou et al. 20226 Shi et al. 2025), convolutional networks (Wang et al.) 2023a), or hierarchical MLP layers (Wang et al., 2024b; Wang (024). These components are individually processed prior to aggregation to yield the final output. Nonetheless, such approaches frequently depend on predefined and rigid operations for the disentanglement of seasonality and trends, thereby constraining their adaptability to complex and dynamic patterns. In contrast, as depicted in Figure 2 propose more flexible methodology that disentangles seasonality and trend directly within the latent space via dual-axis attention, thereby enhancing adaptability to a diverse range of time series patterns and task scenarios. Furthermore, by adopting a multi-scale, multi-resolution analytical framework (Mozer 1991 Harti 1993). we facilitate hierarchical interaction and integration across different scales and resolutions, substantially enhancing the effectiveness of time series modeling.
TIMEMIXER++
Building on the multi-scale and multi multii-errioiic characteristics of time series, we introduce TIMEMIXER++. general-pus purposs time series pattern machine that processes multi-scale time series using an encoder-only architecture, as shown in Figure 2 The architecture generally comprises three components: (1) inpul projection, (2) stack of Mixerblocks, and (3) output projection.
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Output
(e) Multi- Nulti-Resolution Mixing
Output Projection
(d) Multi-Scale Mixing
Embedding
Multi-
Weights
Top-down
Ballonspp
Scale
Multi Multi-Resolution Mixing
Multi-Scali S-Conv
Multi-Scale
Embadding (eckle 0)
T-Conv
Multi-Scalle Mixing
(b) Reatii-Resoltiinn Time Imaging
Seasons
1) Images
Seasons
(c) Time Image Decomposition
Multi- Scale
Dual-axis Attention
Seasons
Trends
Scale O
Punter
Mulli-Resolution Imaging
Col-attention
Row-attention
Mutti Rescluion
MixerBlock
peried
Input Projection
(a) Multi-Scale Time Series
Down -aamlinng
frequency
frequency
Down-
Sampling
Input
1 Scales
For
Time Image
Figure 2: The framework of TIMEMIXER++ The multi-scale time series first embedded through an input projection layer, followed by L stacked MixerBlocks. Each block converts the multi-scale input into multi-resolution time images, disentangles seasonality and trend via dual-axis attention, and mixes these patterns using multi-scale and multi-resolution mixing.
Multi-scale Time Series. We approach time series analysis using a multi-scale framework. Given an input time series TxC where T represents the sequence length and C' the number of variables, we generate multi-scale representation through downsampling. Specifically, the input time series Xo progressively downsampled across M scales using convolution operations with a stride of 2!, producing the multi-scale set Xin {x..... XM), where X.. R IRLLIIi |xC, The downsampling process follows the recursive relationship:
X Conv stride 2); (1,... M).
3.1 STRUCTURE OVERVIEW
strategy to avoid projecting multiple variables into indistinguishable channels (Liu et al.) (2024). In contrast, we adopt channel mixing to capture gross-variabl interactions, which are crucial for revealing comprehensive patterns in time series data. The input projection has two components: channel mixing and embedding.
Input Projection. Previous studies 2023 2023 employ a
We first apply self-attention to the variate dimensions at the coarsest scale E L X as it retains the most global context, facilitating the more effective integration of information across variables. This is formulated follows:
XM Channel-Attn( (Q.: KM, Var),
where Channel-Atta denotes the variate-wise self self-attention for channel mixing. The queries, keys, and values Qu, K,, VM CxL are derived from linear projections of XM- Then, we embed all multi-scale time series into deep pattern set . using an embedding layer, which can be expressed as X {xf..... .... x. 1 = Embed(Xmmi). where xff E IR 2 Xdd and dmodel represents the dimensionality of the deep patterns.
MixerBlocks, Next, apply stack of L Mixerblocks with the goal to capture intricate patterns across scales in the time domain and resolutions in the frequency domain. Within the MixerBlocks, convert multi-scale time series into multi-resolution time images, disentangle seasonal and
Setting stride maximizes the number of scales from recursive downsampling.
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trend patterns through time image decomposition, and aggregate these patterns across different scales and resolutions. The forward propagation is defined as X = MixerBlock(22) where
X = (xp. '. ; and xmm E [ We will elaborate on this block in the next section.
Output Projection. After Lx MixerBlocks, we obtain the multi-scale representation set X Since different scales capture distinct temporal patterns and tasks vary in demands, discussed in Section [ we propose using multiple prediction heads, each specialized for a specific scale, and ensembling their outputs. This design task-adaptive, allowing each head to focus on relevant features at its scale, while the ensemble aggregates complementary information to enhance prediction robustness.
output = Ensemble( (eneemble(HHedaane) [Headm (x )
(3)
where Ensemble(.) denotes the ensemble method (e.g., averaging or weighted sum), and Head the prediction head for the m-th scale, typically a linear layer.
3.2 MIXERBLOCK
We organize a stack of MixerBlocks in a residual way. For the (1 + 1)-th block, the input is the multi-scale representation set XC', and the forward propagation be formalized as:
x = LayerNorm (xc' + MixerBlock (2²)).
(4)
where LayerNorm normalizes patterns across scales and can stabilize the training. Time series
exhibits complex multi-scale and multi-periodic dynamics. Multi-resolution analysis (Harti) 1993)
models time series as composite of various periodic components in the frequency domain. We introduce multi-resolution time images, converting ID multi-scale time series into 2D images based on frequency analysis while preserving the original data. This captures intricate patterns across time and frequency domains, enabling efficient use of convolution methods for extracting temporal patterns and enhancing versatility across tasks. Specifically, we processes multi-scal time series using (1) multiiresolution time imaging (MRTI), (2) time image decomposition (TID), (3) multi-scale mixing (MCM), and (4) multi-resolution mixing (MRM) to uncover comprehensive time series patterns.
Multi-Resolution Time Imaging. At the start of each MixerBlock, we convert the input X' into (M + 1) x K multi-resolution time images via frequency analysis (Wu et al. 2023). To capture representative periodic patterns, we first identify periods from the coarsest scale X which enables global interaction. Specifically, we apply the fast fourier transform (FFT) on x'y and select the top-K K frequencies with the highest amplitudes:
A, (/..... .sk), (PI.... .PK] = FFT(x)))
(5)
where = (A,, ... Ask
represents the unnormalized amplitudes, (fi,"..,K"" are the top-K ...,. K} denotes the corresponding period lengths. Each time
frequencies, and pk Fz series representation x is then reshaped along the temporal dimension as follows:
E (l....,
MRTI(22 = (I,,, 1M m==
(1.k) m 0, O,..,,M; k = 1.....K] K.
=
2m
(6)
Reshape Reshapee,,,Paddiin.... (Paddingm (x4m) m = O,..,, 1, ID-2D
K
where Paddingm.. (.) zero-pads the time series to a length of pk
Lyvee and Reshape 1D-2D
converts it into a Ps x FT
image, denoted as zm (1,A) Here, Pk represents the number of rows
represent the corresponding L
(period length), and the number of columns, denoted by fmn frequency for scale
Pe
Time Image Decomposition. Time series patterns are inherently nested, with overlapping scales and periods. For example, weekly sales data reflects both daily shopping habits and broader seasonal trends. Conventional methods (Wu et al.) 2021; Wang et al.] 2024b) use moving averages across the entire series, often blurring distinct patterns. To address this, utilize multi-resolution time
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images, where each image (1,A) disentanglement of seasonality and trend. By applying 2D convolution to these images, we capture long-range patterns and enhance temporal dependency extraction. Columns in each image correspond to time series segments within a period, while rows represent consistent time points across periods, facilitating dual-axis attention: column-axis attention (Attention captures seasonality within periods, and row-axis attention (Attention,ow) extracts trend across periods. Each axis-specifie attention focuses on one axis, preserving efficieccy by transposing the con-target axis the batch dimension. For column-axis attention, queries, keys, and values Qanl, Keot, Voel R fn X are computed via 2D convolution, which are shared across all images, and similarly for row-axis attention Qrow Krows V The seasonal and trend components are then computed
IRPP encodes specific scale and period, enabling finer
mm.
(1.b)
Attention (Qol: K Veol),
(1.8) m
Attention,w (Qrw; Know, Viow);
where Sm : tm E XPPxXfmxXxx Xduok represent the seasonal and trend images, respectively. Here, the transposed axis is restored recover the original image size after the attention.
(1.k) (I.A)
Multi-scale Mixing, For each period Pk. we obtain M + seasonal time images and M + 1 trend (U.kk) time images, denoted as {Sm Jm=u and (tm ((.kk) J.M Jm=g. respectively. The 2D structure allows to model both seasonal and trend patterns using 2D convolutional layers, which are more efficient and effective at capturing long-term dependencies than traditional linear layers (Wang al.) 2024b). For multi-scaa scale seasonal time images, longer patterns can be interpreted as compositions of shorter ones (e-g., yearly rainfall pattern formed by monthly changes). Therefore, mix the seasonal patterns from fine-scale to coarse-scale. To facilitate this bottom-up information flow, we apply the 2D) convolutional layers at the m-th scale residual manner, formalized
for m: 1 + M do:
s (1,k) (1.k) + 2D-Conv(s (1.k)
(f.k)
(8)
where 2D-Conv is composed of two 2D convolutional layers with temporal stride of 2. Unlike seasonal patterns, for multi-scale trend time images, coarser scales naturally highlight the overall trend. Therefore, we adopt a top-down mixing strategy and apply the 2D transposed convolutional layer at the m-th scale in a residual manner, formalized as:
(1,R) + AiD-TransCon's (t.4)) for m: M 1 do: (1.k) t
(9)
where 2D- DD-TransConv is composed of two 2D transposed convolutional layers with temporal stride of 2. After mixing, the scasonal and trend patterns are aggregated via summation and reshaped back to ID structure, as follows:
(L.k) Reshapem.. (1.)) + (..))) m E (0, (0,..,My M,,
(10)
2D-1D
where Reshape (.) convert pk fm, image into time series of length pk fm, 2D-1D Multi-resolution Mixing, Finally, at each scale, we mix the K periods adaptively. The amplitudes
capture the importance of each period, and we aggregate the patterns (zmn (x((,1)) =k=1 as follows:
[A, Softmax((A 1K
X = - o (L.)), me (0. M),
(11)
where Softmax normalizes the weights, and o denotes element-wise multiplication.
EXPERIMENTS
To verify the effectiveness of the proposed TIMEMIXER++ as a general time series pattern machine, we perform extensive experiments across 8 well-established analytical tasks, including (1) long-term forecasting, (2) univariate and (3) multivariate short-term forecasting, (4) imputation, (5) classification, (6) anomaly detection, as well as (7) few-shot and (8) zero-shot forecasting. Overall, as summarized Figure TIME.MXXR++ consistently surpasses contemporary state-of-the-art models range of critical time series analysis tasks, which is demonstrated by its superior performance across 30 well-known benchmarks and against 27 advanced baselines. The detailed experimental
configurations and implementations in Appendix A

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4.1
MAIN RESULTS
4.1.1 LONG-TERM FORECASTING
Setups. Long-term forecasting is pivotal for strategic planning in areas such as weather prediction, traffic management, and energy utilization. To comprehensively assess our model's effectiveness over extended periods, we perform experiments on 8 widely-used real-world datasets, including the four subsets of the ETT datasets (ETThI, ETTh2, ETTml, ETTm2), as well as Weather, Solar- Energy, Electricity, and Traffic, consistent with prior benchmarks set by Zhou et al. [2021b); Liu et al. (2022a).
Table I: Long-term forecasting results. We average the results across 4 prediction lengths: {96, 192, 336, 720}. The best performance is highlighted red, and the second-bes underlined. Full results can be found in Appendix
Models
TimeMiseree
TimeMiser
slranstormer
PoneTTST
Crestomme
TDE
Timeseet
DLineer
SCINet
IiiDornee
Statenary
Autetorner
(Ours)
2004
2025
M025
Metric
MSE MAB MSB MAB
MSE
MAE
MSE
MAE
MSE
MAE
MSB
MAE
MSE
MAE
MSE
MAB
MSE
MAE
MSE
MAE
MSB
MAL
MSE
MAE
Electricity
(0.165 0.353
18182
0.323
1.178 0:270
1.205 0.200
(4.444 0.334 (1251 0.344 0.205 0:300 0.266 0:365
0.114 0.337/01198 0.198
0.296/0.227
ETT (Avr) (0.349
0,390
0.567 0.398
(0.53 0,377
[.338 0.397
(1665 0,578
[n482 0,470 0.391 0.404
0.442
0.444 (0.689 0.597 0.406 0.428) 0.428/04411 0,464 0,464/0.465 (o.465 0.45)
Exchange
10.357
0.391
[0.391
0.433
|0.376 0.360
[0.403 0.404
(0.940
0.707 (1.70 0.413 (.4116
0.443
0.354
0:414
0.414/0.750
(0.750 0.626
0.519 0.429
0,454/0611 0.539
Trafsic 00.416
0.364
[0.484
0.297
[0.42
0.252
[0.48 0.304 (0.550
(1.700 0.473 (.020
0.336
0,382 |0.304 0,509
0.630
0.376fau22
0.340jo.225
Weather
00.336
0.263
[2.240
0.271
(0.258
0.278
(0:259
0.281 (0.259
0,315
(0.271 0.520
0.287
0.287|0.205
0.312/0.292
(0229 0.363
0.309
0.300fo
0,314|o.335 0.382
Solar-Encgyy (0,205 0.338
(0.216 0.290/0.233 02262 (0227 0,307 (0.641 0.039 [0.327 0.417 00300 0.319/0.330 0.401 (0.282 0.378 0.291 0.s01
a.201/a.20 |0251 0.381 Josss 0.711
Results. Table shows TIMEMIXER+ outperforms other models in long-term forecasting across various datasets. On Electricity, it surpasses i'Tranffrmmer by 7.3% in MSE and 6.3% in MAE. For ETT (Avg), TIMEMIXER++ achieves 4.9% lower MSE than TimeMixer. On the challenging Solar-Energy dataset (Table 8), it exceeds the second-bes model by 6.0% in MSE and 9.2% in MAE, demonstrating its robustness in handling complex high-dimensional time series.
4.1.2 UNIVARIATE SHORT-TERM FORECASTING
Setups. Univariate short-term forecasting is crucial for demand planning and marketing. We evaluate our model using the M4 Competition dataset Makridakis et al. (2018), comprising 100, 000 marketing time series with six frequencies from hourly to yearly, enabling comprehensive assessment across varied temporal resolutions.
Table 2: Univariate short-term forecasting results, averaged across all M4 subsets. Full results are available in Appendix H
Modals
TimeMiseree
TimeMixer Transformer
TIDE
TimesNet H-TS N-BATT PuichTST
MICN
FILM
LightTSS
DLiinarr
FED.
Stationary 20222
(Ours)
20246
2024
20.4
21255
3023
(319
(2023)
220250
2012m
2022
202220
SMAPF]
11.448
11,723
12,684
13.950
11.5 829
11.927
11.851
13.152
19.638
14,863
13:525
13,639
12.840
12,780
12,909
MASE
1,887
1.59
1.764
1,940
1.585
1.613
1.559
1.945
5.947
2.207
2.111
2,095
1.701
1.756
1.771
OWA
0.861
0.855
0.998
1.125
1.051
1.051
0.918
Results. dabletedemossstattes that TimeMixer++ significantly outperforms state-of-the-ae art models across all metrics. Compared to iTransformer, reduces SMAPE by 9.7% and MASE by 15.7% %
with even larger improvements over TiDE, achieving up to 23.3% reduction in MASE. Additionally, TixeMixer++ records the lowest OWA, outperforming TimesNet by 3.5 % and iTransformer by 11.6%.
4.1.3 MULTIVARIATE SHORT-TERM FORECASTING
Setups. We further evaluate the short-term forecasting performance in multivariate settings on the PeMS benchmark (Chen al. 2001), which includes four publicly available high-dimensional traffic network datasets: PEMSO3, PEMS04, PEMS07, and PEMS08. These datasets feature large number of variables, ranging from 170 to 883, offering a challenging testbed for assessing the scalability and effectiveness of our model in predicting complex time series patterns across multiple variables.
Results. The results in Jabhliihgghlght the superior performance of TIMEMIXER++ across all key metrics in multivariate short-term forecasting. TIMEMIXER++ achieves a 19.9% reduction in MAE
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Table 3: Results of multivariate short-term forecasting, averaged across all PEMS datasets. Full
results can be found in Table 18 of Appendix H
Models
MimeMixer-+ TimeMiser minformnr
TiBe
SCINet Crossormer PatckTNT
MICN
DI MLnncar Holorrner Suttinnnntttinnn Autofarmer
(Ours)
20045
(2024)
2030
2202m
20963
2202
20>hm
[0223]
(20225
21225
2022
MAE
15.91
17.41
19.87
21.86
19.12
19.03
23.01
20.54
19.34
23.31
23.50
21.32
22.62
MAPE
10.08
10.59
12:55
13.80
12:24
12.22
14.95
12.69
12.38
14.68
15.01
14.09
14.89
RMSE.
28.01
31.29
30.17
36.05
33.25
30.40
37.32
36.78
36.20
and a 19.6% reduction in MAPE compared to iTransformer, and an 8.6% and 4.8% reduction in
MAE and MAPE, respectively, compared to TimeMixer. Notably, PatchTST, a strong baseline, is outperformed by TIMEMIXER++ with a 30.8% improvement in MAE, 92.5% in MAPE, and 24.9% % in RMSE, highlighting the effectiveness of TIMEMIXER++ in handling high-dimensional datasets.
4.1.4 IMPUTATION
Setups. Accurate imputation of missing values is crucial in time series amalysis, affecting predictive models in real-world applications. To evaluate our model's imputation capabilities, we use datasets from electricity and weather domains, selecting ETT (Zhou et al. (2021b)), Electricity (UCI). and Weather (Wetterstation) as benchmarks.
Table 4: Results of imputation task across six datasets. To evaluate our model performance, we randomly mask (12.5%, 25%, 5%, 50%} of the time points in time series of length 1024. The final results are averaged across these 4 different masking ratios.
Models
TimeMixere+ TimeMixer Transformer PatcTTST
Crossformer FEDiormer
TIDE
DLincar
TimesNet
MICN
Autoformer
(Ours)
20244
2123
2022h
20123
2022
20233
2023a
2021
Metric MSE MAE IMSE MSE MAE MAH]
MAH MAE MSE MAB MSE MAE MSE MAR
ETT(Agg) 0,055 0.154
|0.097 0,205
0.25/00055 0.258 jo. 124 o 230 14 0.366 15 0.229/0.079 0. 19 0.234 jo. 0.215
BCL 0.109
0.197
|0.1420.2610..1 140 0.223 jo. 12 a 19880..115 0.204 181 o. 0.314 182 0.202/0.080 0.200J0.133 0.255 jo. 38 2.246/0.14 0.234
Weather 0.049 0,078 [0.091 0.114fo.0s 0.102 jo.022 o 159 1.111 Jo.064 00.00o00..3330..
0.131/0007 0.107
a (0.075 0.126 12/000066 107
Results. Table presents TIMEMIXER++'s performance in imputing missing values across six datasets. It consistently outperforms all baselines, achieving the lowest MSE and MAE in the majority of cases. Compared to the second-best model, TimesNet, TIMEMIXER++ reduces MSE by an average of 25.7% and MAE by 17.4%. Notably, TIMEMIXER+ excels even when handling imputation tasks with input lengths of up to 1024, demonstrating its robust capability as a TSPM.
4.1.5 FEW-SHOT FORECASTING
Setups. Transformer-be based models excel in various forecasting scenarios, especially with limited data. To evaluate their transferability and pattern recognition, we test across 6 diverse datasets, training each model on only 10% of available timesteps. This approach assesses adaptability sparse data and the ability to discern general patterns, which is crucial for real-world predictive analysis where data is often limited.
Table Few-shot learning on 10% training data. All results are averaged from 4 prediction lengths: (96, 192, 336, 720}.
Modells
Iinchisene TingMaur Hlaadonee
RDE
Choadeenec
Dlane
Pack
TimesNis
FElloeeer Autofonser Statieary
Liche''s PI
Incoenee
Refoemer 200
(Das)
Mori: MS: MAR
MSR MAR MST MAR: MMS:
MARIMSS
MAR
MSs MAR MSn Mar MSn MAR MiSi MARI Mas MAFE MAF MAR pass MAR MAll MAS MAr MAR
BTTEAss: 9.205 0.21
0443 p455 u497 past2 tus4 0471 jusos (4444/0445 uoe sase 408 113 044 5.50 ans duee I 407 e a0t pa ars ssapp 1.11
Werter
RCT. |8300 0.21
(118)12773244 u33 pa 2113 0.a0e ja 1.000 a2ng 2
nea ti 4414440000 c.eo) 200 o ju cones
In few-shot learning, TIMEMIXER++ achieves superior performance across all datasets, reducing MSE by 13.2% compared to PatchTST. DLinear performs well on some datasets but degrades in zero-shot experiments, suggesting overfitting. TIMEMIXER++ outperforms TimeMixer with 9,4% lower MSE and 4.6% lower MAE, attributed to its attention mechanisms enhancing general time series pattern recognition.
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Published as a conference paper at ICLR 2025
4.1.6 ZHRO-SHOT FORECASTING
Setups. We explore zero-shot learning to evaluate models' ability to generalize across different contexts. As shown in Table 6. models trained on dataset Da are evaluated on unseen dataset Db without further training. This direct transfer (D, - D2) tests models' adaptability and predictive robustness across disparate datasets.
Table 6: Zero-shot learning results. The results averaged from 4 different prediction lengths: {96, 192, 336, 720}.
Meduads
TimeMiser++
TimeMixeer [000
LLMITme
DLinear
PuchTST
TimesNer
[Transfocnter
Crrssfommer
Pedfooeer
Ausatormer
TIDB 200
Segg
Memi
MSE
MAE
MSH
MAb
MSE
MAR!
MSB
MAG
MSI:
MAU
MSL
MAI:
MSU
MAII
MSI
MAD
MSU
MAI]
MSL
MAUi
MSU
ETTN:
0.367
0.427
0.444 0.992 0.706 [.493 0.488 (0.500
0.405 0.421 0.431
[0.43 0.474
(o.555
0.574 (0.712 0.693 1.634 0.611
0..933
ETTM + m2
0.301 0.37
[03361
0,39) [1307 0.000 [1415 0.55E
10.314
(1700)
(0.327
0.961
[1311
0.361
0.629)
0.681 0.588
(1647 0,009
|0,66 0,567
E77N2 ETT01
00511
0,69
(0,679
0,577
[196] 0.811
10,00
0,504
(0.500
0,513
(1,00
[1552
0.511
(0557
0,518
00012
0622
[0.508
ETTss BTT12
[.417
[0452
0:441
[0,992
0.706 [0464
0,475
(0.439
0.438]
(0.457
0,454
[0443
0.438
[0.624
0.541 (0.533
(.594
[.37 0.568
[0.54
ETTml FTTm2
0.291
0.331
(0,529
0,157
1,300 0.000
00335
0,399
(0.296
0,354
(0,322
0.354
(0,324
0.351
(0,055
0,572
00,022
0611
[1,00
0,092
|0.54 0,527
BTTww 53Tml (0427 [0,554
0:478
1,933
0.944
[..49
0,537
0.492]
0.567
(a,39
0.491
[068
00500
0,507
[0555 0.571
Results. As demonstrated in 6 TIMEMIXER++ consistently outperforms other models in our zero-shot learning evaluation across all datasets. Notably, TIMEMIXER++ achieves significant reduction in MSE by 13.1 % and in MAE by 5.9% % compared to iTransformer. Moreover, it exhibits a reduction in MSE of 9.6% % and in MAE of 3.8 % when compared with PatchT'ST. These improvements demonstrate the superior generalization capability and robustness of TIMEMIXER++ in handling unseen data patterns, highlighting its potential for real-world applications where adaptability to new scenarios is crucial.
4.1.7 CLASSIFICATION AND ANOMALY DETECTION
Setups. Classification and anomaly detection test models' ability to capture coarse and fine-grained patterns in time series. We use 10 multivariate datasets from UEA Time Series Classification
Archive (2018) for classification. For anomaly detection, we evaluate on SMD 2019). SWaT (2016).
PSM (202)). MSL and SMAP (2018).
RSNi
Courdetion
MLPbard
Transfenecrbeeel
Oars
Nasagg houanay (h)
Mureep 11 noves Ph)
Rocker
scfter
Lawer
FxD
Flam.
Cinse
hearey
SCAter sict
Vi
Esjors
stfer
RuLL Anemade
Crast Pore
Classification Results
Anomaly Detection Results
Figure 3: Results of classification and anomaly detection. The results are averaged from several datasets. Higher accuracy and Fl score indicate better performance. *, indicates the Transformer- based models. See Table 19 and 2n the Appendix H for full results.
Results. Results for both tasks are shown in Figure 4.1.7 For classification, TIMEMIXER++ achieves 75.9% accuracy, surpassing TimesNet by 2.3% and outperforming other models. Forecasting models like iTransformer and PatchTST perform poorly, highlighting TIMEMIXER+++ versatility. In anomaly detection, TIMEMIXER++ achieves F1-score of 87.47% exceeding TimesNet by 2.59 %. SCINet by %, and Anomaly Transformer by 6.62 %. These results emphasize TIMEMIXER++'s strong pattern learning capability, attributed to its multi-scale and multi-resolution architecture.

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Published as a conference paper at ICLR 2025
4.2 MODEL ANALYSIS
Ablation Study. To verify the effectiveness of each component of TIMEMIXER++, we con- ducted an ablation study by removing individual components (wlo). The results are in Table 7 TIMEMIXER++ with all components-chunee mixing, time image decompose, mulli-scale mixing, and multi-resolution serinn--achevee the best performance. On datasets like ECL, Traffic, and Solar. thannel-mixing improves performance by 5.36%. Time image decomposition yields an 8,81 % improvement, especially on seasonal datasets like ECL and Traffic. Multi-scale mixing provides a 6.25 % improvement, particularly for less predictable datasets like ETT. Multi-resolution mixing adds a 5.10% improvement, highlighting the importance of a multi-resolltion hybrid ensemble. We provide more ablation studies in Appednix C
Table 7: MSE for long-term forecasting across 8 benchmarks, evaluated with different model components. We provide more analysis on other tasks in Tables [T and
12
ETTh]
ETTh2
ETTml
ETTm2
ECL
Traffic
Weather
Solar
Average
Promotion
TIMEMIXER++
0.419
0.339
0.369
0.269
0.165
0.416
0.226
0.203
0.300
w/o channel mixing
0.424
0.346
0.374
0.271
0.197
0.442
0,233
0.245
0.317
5.36%
w/o time imuge decomposition
0.441
0.358
0.198
0.329
w/o multi-scale mixing
0.447
0.361
0.391
0.284
0.172
0.427
0,239
0.234
0,320
6.25%
w/o multi-ccsolution mixing
0.431
0.350
0.374
0.280
0.181
0.432
0.241
0.233
0.316
5.10%
Representation Analysis. Our anal- ysis, depicted in Figure present the original, seasonality, and trend images across two scales and three resolu- tions (periods: 12,8 8, 6; frequencies: 16, 24, 32). TIMEMIXER++ demon- strates efficacy in the separation of dis- tinct seasonality and trends, precisely capturing multi-periodicities and time- varying trends. Notably, the periodic characteristics vary across different scales and resolutions. This hierarchi- cal structure permits the simultaneous capture of these features, underscor- ing the robust representational capabilities of TIMEMIXER++ as a pattern machine.
Spectrum
Shansoall by)
(heent)
(Toud
Scale (length#192)
Scale (lentth-36)
Figure 4: Visualization of representation on Time Image under Traffic dataset. More showcases in Figure TO
13
the right side of Figure I from the perspective of representation learning, TIMEMIXER++ shows superior performance in prediction and anomaly detection with higher CKA similarity 2019 compared to imputation and classification tasks. Lower CKA similarity indicates more distinctive layer-wise representations, suggesting a hierarchical structure. Figure demonstrates that TIMEMIXER++ captures distinct low-level lew-eeell representations for forecasting and anomaly detection. and hierarchical ones for imputation and classification. This highlights TIMEMIXER++* potential as a general time series pattern machine, capable of identifying diverse patterns across tasks and domains, essential for universal predictive analysis in time series, See Appendix for more details.
Furthermore,
5 CONCLUSION
In this paper, we present TIMEMIXER++, novel framework designed universal time series pattern machine for predictive analysis. By leveraging multi-resolution imaging, we construct time images at various resolutions, enabling enhanced representation of temporal dynamics. The use of dual-axis attention allows for effective decomposition of these time images, disentangling seasonal and trend components within deep representations. With multi-scale and multi-resolution mixing techniques, TIMEMIXER++ seamlessly fuses and extracts information across different hierarchical levels, demonstrating strong representational capabilities. Through extensive experiments and comprehensive evaluations, TIMEMIXER++ consistently outperforms existing seneral-purpose and task-specific time series models. establishing itself as state-of-the-art solution with significant potential for broad applications in time series analysis. Limitations and directions for future research are discussed in Appendix K
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ACKNOWLEDGEMENT
M. Jin was supported in part by the NVIDIA Academic Grant Program and CSIRO National Science Foundation (US) Al Research Collaboration Program.
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A IMPLEMENTATION DETAILS
Datasets Details. We evaluate the performance of different models for long-term forecasting on well-establiseed datasets, including Weather, Traffic, Electricity, Exchange, Solar-Energy, and ETT datasets (ETThI, ETTh2, ETTml, ETTm2). Furthermore, we adopt PeMS and M4 datasets for short-term forecasting. We detail the descriptions of the dataset in Table To comprehensively evaluate the model's 's performance in time series analysis tasks, we further introduced datasets for classification and anomaly detection. The classification task is designed to test the model's ability to capture coarse-gras grarsned patterns in time series data, while anomaly detection focuses on the recognition of fine-ge graingg patterns. Specifically, we used 10 multivariate datasets from the UEA Time Series Classification Archive (2018) for the evaluation of classification tasks. For anomaly detection, selected datasets such as SMD (2019), SWaT (2016), PSM (2021), MSL, and SMAP (2018). We detail the descriptions of the datasets for classification and anomaly detection in Table 9 and Table TO
Table 8: Dataset detailed descriptions. The dataset size is organized in (Train, Validation, Test).
Tasks
Dataset
Dim
Series Length
Dataset Size
Frequency
Forecastabilitys
Information
ETTml
(96, 192, 336, 720)
(34465, 11521, 11521)
15min
Temperature
ETTm2
7
(96, 192, 336, 720)
(34465, 11521, 11521)
15min
0.55
Temperature
ETThl
7
(96, 192, 336, 720)
(8545, 2881, 2881)
15 min
0.38
Temperature
ETTh2
7
[96, 192, 336, 720)
(8545, 2881, 2881)
15 min
0).45
Temperature
Long-term
Electricity
321
196, 192, 336, 720]
(18317, 2633, 5261)
Hourly
0.77
Electricity
Forecasting
Traffic
862
(96, 192, 336, 720)
(12185, 1757, 3509)
Hourly
0.68
Transportatin
Exchange
8
196, 192, 336, 720)
(5120, 665, 1422)
Duily
0.41
Weather
Weather
21
192, 336,
(36792, 5271, 10540)
10 min
0.75
Weather
Bolar-Energy
137
196, 192, 336, 720)
(36601, 5161, 10417)
10min
0.33
Electricity
PEMS03
358
(15617,513555113)
5min
0.65
Transportation
PEMS04
307
12
(10172,3375,3375)
Smin
0.45
Transportaiion
PEMS07
883
12
(16911,5622,5622)
5min
0.58
Transportation
Short-term
PEMS08
170
(10690,3548,265)
5min
0.52
Transportation
Forecasting
M4-Ycadte Yearly
(23000, 0, 23000)
Yearly
0.43
Demagraphic
M4- M4-Quarterly
1
(24000, 0, 24000)
Quarterly
0.47
Finance
M4-Monthly
I
18
(48000, 0, 48000)
Monthly
0.44
Industry
M4-Weakly
I
(359, 359)
Weakly
0.43
M4-Daily
(4227, 4227)
Daily
0.44
Mixro
M4-Hourly
48
(414, 0, 414)
Hourly
0.46
Other
The forecastability is calculated by one minus the entropy of Fourier decomposition of time series (Guerg 2013 A larger value indicates better predictaiiitty.
Table 9: Datasets and mapping details of UEA dataset (Bagnall et al. 2018).
Dataset
Sample Numbers(train set, set)
Variable Number
Series Length
EthanolConcentration
(261, 263)
3
1751
FaceDetection
(5890, 3524)
144
62
Handwriting
(150, 850)
3
152
Heartbeat
(204, 205)
61
405
Japanese Vowels
(270, 370)
12
29
PEMSSF
(267. 173)
963
144
SelfRegulationSCPP
(268, 293)
6
896
SelfReggulatonSSCP2
(200, 180)
7
1152
SpokenArabic-Diiite
(6599, 2199)
13
93
U WaveGestturLLirra
(120, 320)
3
315
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Table 10: Datasets and mapping details of anomaly detection dataset.
Dataset
Dataset sizes(train vet, set, test set)
Variable Number
Sliding Window Length
SMD
(566724, 141681, 708420)
38
100
MSL
(44653, 11664, 73729)
55
100
SMAP
(108146, 27037, 427617)
25
100
SWaT
(396000, 99000, 449919)
51
100
PSM
(105984, 26497, 87841)
25
100
Baseline Details. To assess the effectiveness of our method across various tasks, we select 27 advanced baseline models spanning wide range of architectures. Specifically, we utilize CNN-based models: MICN (2023a). SCINet (2022a), and TimesNet (2023); MI.P-hased mod- els: Time.Mixer (2024b), LighTTS (022a)) and DLinear (2023); RML.&RLLinen (2023a) and Transformer-baid based models: iTranstormer (2024), PatchTST (2023). Crossformer (2023). FED- former (2022b), Stationary (2022c), Autoformer (2021), and Informer (2021b). These models have demonstrated superior capabilities in temporal modeling and provide a robust framework for comparative analysis. For specific tasks, TiDE (2023b), FiLM (2022a), N-HiTS (2023), and N-BEATS (2019) address long- or short-term forecasting; Anomaly Transformer (2022) and MTS- Mixers (2023b) target anomaly detection; while Rocket (2023a), LSTNet (2018c), LSSL (2022a), and Flowformer (2022) are utilized for classification. Few/zero-shot forecasting tasks employ ETS- former (022). Reformer (2020), and LLMTime (2023).
Metric Details. Regarding metrics, we utilize the mean square error (MSE) and mean absolute error (MAE) for long-term forecasting. In the case of short-term forecasting, we follow the metrics of SCINet (Liu et al., (022a) on the PeMS datasets, including mean absolute error (MAE), mean absolute percentage error (MAPE), root mean squared error (RMSE). As for the M4 datasets, we follow the methodology of N-BEATS (Oreshkin et al. 2019) and implement the symmetric mean absolute percentage error (SMAPE), mean absolute scaled error (MASE), and overall weighted average (OWA) metrics. It is worth noting that OWA is specific metric utilized in the M4 competition. The calculations of these metrics are:
F RMSE
Σ
X
3)
MAE Σ
X;
X,
i=1
SMAPE 200
F
X; X,
100 F
F
X, X,|
MAPE =
F
+ X
X
i=1
MASE= 1
Σ
F
X; X, x-
OWA 2
SMAPE
MASE
F
SMAPENaive
MASE
F-
where s the periodicity of the data. the future with F time pints and C dimensions. X, means the i-th future time point.
X E FxC are the ground truth and prediction results of
Experiment Details. All experiments were run three times, implemented in Pytorch (Paszke et al.) 2019), and conducted on multi NVIDIA A100 80GB GPUs. We set the initial learning rate as a range from 10-3 to 10-1 and used the ADAM optimizer (Kingma & Ba 2015) with L2 loss for model optimization. And the batch size was set to be 512. We set the number of resolutions K to range from to 5. Moreover, we set the number of MixerBlocks L to range from to 3. We choose the number of scales M according to the time series length to balance performance and efficiency. To handle longer series in long-term forecasting, we usually set M to 3. As for short-term forecasting with limited series length, we usually set A 1. We pretrained the model with learning rate decay after linear warm-up. For baselines under the same experimental settings as our main study, we directly report the results from TimesNet (Wu et al. 2023). In scenarios where experimental settings differed or tasks were not previously implemented, we reproduced the baseline results referring to the benchmark framework from the will be provided in GitHub
Library 2. The source code and pretrained model Min...iiiiiiiiieeeeee...........
https: /i thub. www.ccoo//hua. thuml / Series-
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B DETAILS OF MODEL DESIGN
In this section, we present a comprehensive exposition of our model design, encompassing five key components: channel mixing and embedding (input projection), multi-resolution time imaging, time image decomposition, multi-scale mixing, and multi-resolution mixing, To enhance comprehension, we provide visual illustrations that afford intuitive understanding of our structural design.
Channel Mixing and Embedding. We employ a channel mixing approach to effectively cap- ture inter-variable dependencies crucial for uncovering rich temporal patterns. Our method first applies variate-wise self-attention, as formulated in Equation 2 at the coarsest temporal scale XM E R - JxC ensuring the preservation of global context. This mechanism fuses information across variables, enabling the extraction of inter-variable patterns. Subsequently, the multivariate time
series is projected into an embedding space via the function Embed(.) R |xC + R - X
capturing temporal structure at different scales and facilitating comprehensive pattern learning across the input time series.
Crannel
Crannel 2
Embed
Time
Variate-wise
Embedding
Mixing
Figure 5: Illustration of the channel mixing approach and embedding function in the input projection process. This process highlights how variate-wise self-attention captures inter-variable dependencies the coarsest scale, followed by the projection into an embedding space.
Multi-resolution Time Imaging. Starting from the coarsest scale x the fast fourier transform (FFT) is applied to extract the top-K frequencies, corresponding to dominant periods in the series. These top-K periods, which capture global patterns, are applied across all scales. At each scale m, the input time series x/n is reshaped into K time images by padding the series according to the identified
(L.b) is pa x fm.k- As periods and reshaping it (Equation, 6). The size of each image, denoted as Zm shown in Figure 6 this process produces multi-resolution time images that capture both temporal and frequency domain patterns, enabling the extraction of comprehensive periodic structures.
Puree2 a
Fobelt
Top-K
Top
frequency
Period=12
Period=8
Period=6
Frequency Anabyis
Length
Scale 2
Scale
Scale O
Figure 6: Multi-resolution Time Imaging. We illustrate the generation of multi-resolution images using the top-3 frequencies and three scales.
Time Image Decomposition. As depicted in Figure each time image (1,b) R fax Xduiia corresponds to a specific scale and period. The columns represent time segments within each period, while the rows track consistent points across periods. This structure allows us apply column-axis
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Attention within period
815
810
Imaging
Image
View (time)
Dual-axin Attention
m
8.0
Palnd Potte
Row-axia Attention
2 (embedding)
Trand Image
(L.R)
Proquenccy
Attention periods
Figure 7: Time Image Decomposition. We demonstrate how the identified periods are used to convert the time series into the time image, and how dual-axis attention is applied to extract both seasonal and trend patterns from this image.
attention, capturing seasonality within period, and row-axis attention, capturing trend across periods. Column-axis attention processes temporal dependencies within periods using 2D convolution to compute the queries, keys, and values (Qeal Keol. Venl E I 1ms with the row axis transposed into the batch dimension. Similarly, row-axis attention employs 2D convolution to compute queries, keys, and values (Qiew; Koow V batch dimension. By leveraging this dual-axis attention, we disentangle seasonality and trends for
R (xpueee)))) where the column axis is transposed into the
each image. The seasonal image (L.k) and the trend image (L.K) effectively preserve key patterns, facilitating the extraction of long-range dependencies and enabling clearer temporal analysis.
Multi-scale Mixing, The Figure 8 illustrates the process of multi-scale mixing formalized Equations 8 and 9 this approach, we hierarchically mix multi-scale seasonal and trend patterns, For seasonal patterns, the mixing begins at the finest scale So (!.A) and proceeds in a bottom- up fashion through successive scales. Conversely, for trend patterns, the mixing starts from the
(L.k) and flows top-down to finer scales. This hierarchical flow enables effective integration of both long-term and short-term patterns, allowing finer patterns be aggregated into seasonal representations, while coarser trend information is propagated downward to refine trend representations finer scales. The effectiveness this multi-scale mixing further demonstrated by the representation analysis provided in Appendix D
coarsest scale *M
2D-Com
(UA)
(UA)
BUN)
2D- TransConv
2D-Conv
20-TransConv
O2-2
5g
ZD-TransConv
Bottom-up Multi-scale Mixing
Top-down
Multi-scale Mixing
Figure 8: Multi-Scale Mixing. We illustrate the hierarchical mixing of multi-scale seasonal and trend images. Each scale's output (red symbol) integrates all preceding information. 2D convolutions are used in the bottom-up path, while transposed convolutions are applied in the top-down path to accommodate changes size.
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Scale M
Embedding
FFT weights
Scale
Embedding (scale
FFT weights
Figure 9: Multi-resolution Mixing, At each scale, K period-based representations fused after season-trend mixing to produce M scale-specific embeddings, which can be further ensembled for the final output.
Multi-resolution Mixing. As shown Figure at each scale m, the K period representa- tions, denoted as Zm (t,k) are first weighted by their corresponding FFT amplitudes A f which capture the importance of each period, and then summed to produce the final representation for that scale. This process, repeated across all scales, yields comprchensive embedding for each scale, capturing multi-resolution information.
C ADDITIONAL ABLATION STUDIES
To verify the effectiveness of each component of TIMEMIXER++, we conducted detailed ablation study by performing experiments that remove individual components (w/o) across various tasks, in- cluding univariate short-ters term forecasting, multivariate short-term forecasting, and anomaly detection. Based on the Table II 12 provided, the conclusions are as follows: TIMEMIXER+ outperforms other configurations in short-term forecasting with the lowest average SMAPE and MAPE scores, indicating the importance of each component. As for PEMS datasets with large variable dimensions, the most sigmificant improvement is observed with channel mixing, showing a 14.95% improvement. anomaly detection, TIMEMIXER++ achieves the highest average score, with time image decom- position contributing the most to performance, showing a 9.8% improvement. Other components like channel mixing, multi-scale mixing, and multi-resolution mixing also enhance performance. Overall, each component plays crucial role in the effectiveness of TIMEMIXER++ for all tasks.
Table 11: SMAPE&MAPE for short-term forecasting across 5 benchmarks, evaluated with different model components.
M4
PEMS03
PEMS04
PEMSU7
PEMS08
Average
Promotion
TIMEMIXER++
11.45
13.43
11.34
7.32
8.21
10.35
w/o channel mixing
11.44
15.57
13.31
9.74
10.78
12.17
14.95%
woo time image decompostion
12.37
15.59
12.97
9.65
9.97
12.11
14.51%
w/o multi-seale mixing
11.98
14.97
13.02
9.17
9.69
11.79
12.06%
w/o multi-resolution mixing
11.87
15.02
13.14
8.72
9.53
11.68
11.23%
Table 12: Fl score for anomaly detection across 5 benchmarks, evaluated with different model components.
SMD
MSL.
SMAP
SWAT
PSM
Average
Promotion
TIMEMIXER++
86.50
85.82
73.10
94.64
97.60
87.47
w/o channel mixing
84.51
74.03
70.91
90.41
96.17
83.21
4.94%
w/o time image decompostion
81.21
72.43
66.02
82.41
92.53
78.92
9.84%
multi-scale mixing
82.37
75.12
92.79
86.48
94.53
86.26
1.46%
w/o multi-resolution mixing
83.37
79.24
77.49
88.46
96.02
86.26
2.99%
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D ADDITIONAL REPRESENTATION ANALYSIS
To evaluate the representational capabilities of TIMEMIXER++, selected three datasets: Traffic, Electricity, and ETTml, each exhibiting distinct periodic and trend characteristics. We conducted comprehensive analyses acToss various scales and resolutions, Initially, ID convolution was employed to downsample the original time series, yielding different scales. Subsequently, frequency spectrum analysis utilized to identify the primary frequency components within the time series, selecting the top three components by magnitude as the primary resolutions. This process transformed the then applied
original time series into multi-scale time image. Time image decomposition disentangle seasonality and trends from the original time image, resulting in distinct seasonality and trend images. Hierarchical mixing was performed facilitate interactions acToss different scales. The visualization of the resulting representations is depicted in Figures 10 and 13
Traffic Time Series
Frequency Spectrum
M Wallem i MM
Magnitude
Value
Top3 freq 32
hilmmbbblll Frequency Index
Index
langthy 182
P=6
Time Image
Col-Attention
Row-Attention (Trend)
Time Image
Col-Attention (Sessonalit)
Time Image
Col-Attention (Seasonalit)
Row-Attention
(Seasonaiity
(Trend)
(Trend)
Scale O (length=192)
Scale (length=96)
Scale 2 (length=48)
Figure 10: Visualization of representation on Time Image under Traffic dataset. We provide different
scales and different resolutions in Time Image, seasonality, and trend.
As shown in the Figure TO we visualized the representation of the time series in the Traffic dataset across three different scales (length: 192, 96, 48) and three resolutions (periods: 12, 8, 6; frequencies: 16, 24, 32). From the visualization, we can observe that we successfully disentangled the scasonality and trend within the traffic time series. The seasonal patterns vary across different scales and resolutions: at a fine scale (scale: 0), higher frequency seasonality (period:32; freq: 6) is more prominent, while at a coarse scale (scale: 2), lower frequency seasonality (period: 16; freq: 12) is more evident. Additionally, we successfully isolated the upward trend across all scales and resolutions. This demonstrates the strong representational capability of TIMEMIXER++ highlighting its potential as general time series pattern machine.
We can observe the visualization of the representation of the ETTml dataset, which exhibits multi- period characteristics and a downward trend, in Figure II We obtained findings consistent with previous observations: higher frequency components are more prominent at fine scale, while lower frequency components are more easily observed at coarse scale. This observation aligns perfectly with theoretical intuition (Harti 1993), as the fine scale retains more detailed information, such as higher frequency seasonality, from a microscopic perspective, whereas the coarse scale provides a macroscopic view where more low- www-freuency global information is more evident. Moreover, is important to note that the powerful representational capability of TIMEMIXER++ allows it to accurately capture the downward trend. These conclusions further underscore the necessity of our multi-scale and multi-nesolution design.
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ETTm1 Time Series
Frequency Spectrum
WwM
Magnitude
Value
T 12,
Time Index
Frequancy Index
P=24
P=16
P=4
Time
Col-Attention
Row-Attertion
Time Image
Col-Attantion
Row-Attention
Time
Col-Attantion
Row Attention
(Seasonaity)
(Trend)
(Seasonality)
(Trend)
(Soasonality)
(Trend)
Scale (length=192)
Scale (length=96)
Scale (length=48)
Visualization of representation Time Image under ETTml dataset. We provide different scales and different resolutions in Time Image, seasonality, and trend.
Figure 11:
In Figure we present the visualization of the representation of the Electricity dataset. prominent feature is that the trend is time-varying, initially declining and then rising over time. TIMEMIXER++ successfully captures this time-vane vareiia characteristic in its representation. From the figure, we can observe the gradient features in the trend image, which undoubtedly demonstrate the powerful repre- sentational capability the TIMEMIXER+* Especially when combined with our multi-scale and multi-resolutee design, the representation exhibits hierarchical performance across different scales and resolutions. This greatly enhances the richness the representation, making TIMEMIXER+* adept handling universal predictive analysis.
Through the preceding analyses, it is evident that the paradigm of multi-scale time series modeling (Mozer 1991) and multi-resolution analysis (Harti 1993) endows TIMEMIXER++ with robust representational capabilities. This enables proficient handling of high-frequency, low-frequency, seasonal, and trend components within time series data. Such capabilities are pivotal achieving state-of-the-ard performance across diverse and comprehensive time series analysis tasks, underscoring its essential role time series pattern machine.
As shown in Figure 12 TIMEMIXER++ consistently excels across all four tasks, achieving state-of- the-art performance each scenario. The model effectively adapts its representation transformations to meet the demands of different tasks. Whether preserving representations or enabling significant
511
1.30
Lis cie
si le
15a
slo sit 1ãr <ãn cia
Figure 12: Representation analysis in four tasks. For each model, the centered kernel alignment (CKA) similarity is computed between representations from the first and the last layers.
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Electricity Time Series
Frequency Spectrum
Magnitude
Value
Topl_feq-
Time Index
Frequancy Index
P=6
Time
Col-Attention
Row-Attertion
Time
Col-Attention
Row-Attention (Trend)
Time
Col-Attantion
Atteentenoon (Trend)
(Seasonaity)
(Trend)
(Seasonality)
(Soasonality)
Scale (length=192)
Scale (length=96)
Scale (length=48)
Figure 13: Visualization of representation Time Image under Electricity dataset. We provide different scales and different resolutions in Time Image, seasonality, and trend.
changes across layers, TimeMixer++ demonstrates versatility and robustness handling wide range of time-series analysis challenges.
E EFFICIENCY ANALYSIS
We comprehensively compare the forecasting and imputation in performance, training speed, and memory footprint of the following models: TIMEMIXER++, iTransformer(LLu et al. (024))
PatchTST(Nie et al., (023). TimeMixer Wang al. 2024b), TIDE(Das et al.] (003b). Fed-
Former(hhor et al. 2022b), TimesNet Wu et al. 2023), MICN(Wang et al. 2023a), and SCINet
al. 2022a).
Imputation Weather (imputation 1024)
Long-term forecasting ETTml (prediction length 720)
AM
MG3 SLiee
5dGa Kiles
XIND
TIDC
AD0
2.000 30mm
2008 Oiten.
FED Plane
6,05 4T7ee
Training Timo Lms (tet)
Training
(muN) (aer)
Figure 14: Model efficiency comparison under imputation and long-term forecasting.
As shown in Figure 14 TIMEMIXER+ achieves comparable balance among memory footprint, training time, and performance in both the Weather imputation and long-term forecasting tasks on ETTml, delivering the MSE scores.
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F HYPERPARAMTER SENSITIVITY
We conduct hyperparameter sensitivity analysis focusing on the four important hyperparameters within TIMEMIXER+++ namely, the number of scales M, the number of layers I,, the time series input length T, and the selection of the top K periods with the highest amplitudes in the spectrogram. The related findings are presented in Figure[T5] Based on our analysis, we have made the following observations: (1) As the number of scales increases, the MSE generally decreases. Increasing the number of scales benefits model performance across all prediction lengths, with noticeable improvements observed between 3 and scales. Considering overall performance and efficiency, the
Analysis on Number
Analysis on Number Layers
60
0.60
predice-720
prodict-720
prodict-336
predict
predict 192
prodict-192
53
predict 96
0.52
predics-96
MIE
MSE
0:34
0.30
0:30
Number of scales
Number Layers
Analysis Selection Top-K
Analysis Input Length
predict 720
predict 720
predict-336
prodict-336
predict-192
predice1922
0.2
prodict-96
prodict-96
MSR
MSE
0.39
Selection Top-K
Input Length
Figure 15: Analysis of hyperparameter sensitivity on ETTml dataset.
marginal benefits of increasing M significantly diminish, so we can set M from to 3. (2) Adding more layers typically reduces MSE, particularly between I and 2 layers where the change is most pronounced. For shorter prediction lengths (e.g., predict-96), increasing the number of layers results in more significant performance gains. (3) Increasing the selection of Top-K generally leads to reduction in MSE. For longer prediction lengths, the choice of Top-K has more substantial impact on the results. (4) As the input length increases, the MSE gradually decreases. Longer input lengths help improve prediction accuracy across all prediction lengths, which indicates that using longer inputs may achieve better predictive performance for the TIMEMIXER++.
G ERROR BARS
In this paper, we repeat all the experiments three times. Here we report the standard deviation of our model and the second best model, well as the statistical significance test in Table 13
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Table 13: Standard deviation and statistical tests for TIMEMIXER+ and second-best method (iTransformer) on ETT, Weather, Volar-Energy, Electricity and Traffic datasets.
Model
+ixeMixer++
Traansoommr 2024))
Confidence
Dataset
MSB
MAE
MSE
MAE
Level
Weather
0.226 + 0.008
0.262 + 0.007
0.258
0.009
0.278 + 0.006
99%
Solar-Energy
0.203 + 0.027
0.238 + 0.026
0.233 = 0.009
0.262 + 0.011
95%
Electricity
0,165 + 0.017
0.253 + 0.019
0.178 = 0.002
0.270 + 0.017
99%
Traffic
0.416 = 0.027
0.264 = 0.030
0.428 = 0.008
0.282 = 0.027
95%
ETTh1
0,419 = 0.023
0.432 - 0.021
0.454 0.004
0.447 + 0.007
99%
ETTh2
0.339 + 0.020
0.380 + 0.019
0.383 0.004
+
95%
ETTml
0.369 + 0.019
0.378 + 0.026
0.407 = 0.004
99%
ETTm2
0.269 + 0.021
0.320 + 0.019
0.288 = 0.010
0.332 + 0.003
95%
Table 14: Standard deviation and statistical tests for our TimeMixer++ method and second-best method (TimeMixer) on PEMS dataset.
Model
TimeMixer++
TimeMixer 2024bb
Confidence
Dataset
MAE
MAPE
RMSE
MAE
MAPE
RMSE
Level
PEMS03
13.99 1: 0.271
13.43 1 0.292 24.03 0.269
14.63 0.471
14.34 1 0.502 23.28 1 0.468
99%
PEMS04
0.951
11.34 1 0.970 28.83
0.916
19.21
0.511
12.33
0.523 30.92 1 0.519
95%
PEMS07
18.38 1 0.991
7.32 1 0.977
31.75 0.890
20.37
0.372
8.62
1 0.399 33.50 1 0.375
95%
PEMS08 13.81 + 0.827
8.21 + 0.836
23.62 + 0.877
15.22 = 0.311
9.67 + 0.332 24.26 = 0.317
99%
Table 15: Standard deviation and statistical tests for our TimeMixer++ method and second-best method (TimesMixer) on M4 dataset.
Model
TimeMixer++
TixesMixer (2024b)
Confidence
Dataset
SMAPE
MASE
OWA
SMAPE
MASE
OWA
Level
Yearly
13.179 0.021 2.934 0.012
0.769 : 0.001
13.206
0.121
2.916 0.022 0.776 + 0.002
95%
Quarterly
9.755 =
1.159
0.005 0.865 = 0.009
9.996
1 0.101
1.166 = 0.015 0.825 = 0.008
95%
Monthly
12.432 + 0.015 0.904
0.012
0,841 = 0.001
12.605 0.115
0.919 = 0.011 0.869 = 0.003
95%
Others
4.698 + 0.114 2.931 + 0.027
1.01 0.011
4.564 0.114
3.115 = 0.027 0.982 = 0.011
99%
Averaged
11.448 + 0.007
1.487 0.010
0.821 = 0.002
11.723
1.559
0.022 0.840 = 0.001
99%
H FULL RESULTS
Due the space limitation of the main text, we place the full results of all experiments in the following: long-term forecasting in Table 16 univariate short-term forecasting in Table 17 multivariate short-
term forecasting Table T8 classification in Table 19 and anomaly detection Table 20
I SHOWCASES
To assess the performance of various models, we perform a qualitative comparison by visualiz- ing the final dimension of the forecasting results derived from the test set of each dataset (Fig- Among the various models, TIMEMIXER++ exhibits
ures 16 17
19
20 22
25 2T
superior performance.
J BROADER IMPACT
Real-world applications TIMEMIXER++ has achieved state-of-the-at art (SOTA) performance as general time series pattern machine in various time series analysis tasks, including forecasting,
24

---

Published as a conference paper at ICLR 2025
Table 16: Full results for the long-term forecasting task. We compare extensive competitive models under different prediction lengths. Aug is averaged from all four prediction lengths, that {96, 192, 336, 720).
Medels (Our)
TimeMixars
Timehiser
TTrnsfomnce
PaicTTT
Conafermer
TIDE
TimesNet
Di incar
SCTNe
PRDiormer
Stationsey
Autoformer
202
1081
Metric
MSE
MAE
MSE
MAB
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSB
MAB
MSE
MAE
96 10.155
0.305
0.162
0.209
0,174
0.214
0.186
0.227
0.195
0.271 0.202 0.261 0.172 0,220
901995 0.25210.221 0.306(0.117
0.296
0.223
0,266 0.336
Weather
192 00.201
0:250
0.221
0.354
0.234
0:265
0.209 0.277 0.242 0.298
0.219
0:361 (123)) 0.295 (.226) 0.340 2.76 0.336
0.367
336
0.237
0.265
1.25L
0.287
0.278
0.296
0.284
0.301
0.273
0.332 0,287
0.335
0.250
0,305
0.282
0.331 (0,309
0.278 0.339
0.331
0.338
0.359 0.395
720
00.312
0.339
0.341
0.355
0.347
0.356
0.349
0.379
0.401
0.351
0.386
0.365
0.359
(1.445
0.582 0.427 0..40 0.428
0.428
Avg: [0.236
11.240
0.271
0:358
0.378
(1.665 0.285
0.264
0.271
300
0.250
0:287
1.366
0.31 0.315
0633
0.360
314/0.3.3.333 0,362
Solar- Enengy
96
[0.171
0.231
0,259
0,203
0.257
102665
0,325
0.322.0000 0.302 0.312 0 0,330
0.358
000290
0.341
0.341
[0.32] 0.380 0:156 0.446
192
0.218
0.203
1.222
0.283
0.233
0.261
0.288
0.332 0.371 0.410 0.339
0.416 0.397 0.370
0.220
0.395 0.220
0.59%
0.38 0.337
0.346 0.369 0.588 0.561
336
00.212
0.269
1.231
0.292
0.223
0.301
0.339 0,495 015 0.368
0:430 0.420
0.353
0,415
389
354
0.357 0 3.787 0.5935 0,588
720
00.212
0.270
0.223
0.285
0.209
0.275
0.205
0,336 0.526 0.54 0,370
0.425
02500000000 0.420
081
3.557
0,413 0.500
388 380 0.437
0.375 0.44 0.73 0.633
|Avg| [0.203
0.238
10.216 0.280
0.233
0.233
0.262
(0.287 0.333
0.442 0.547 0.417
00.40
0.374 (0.330
0:401
00:::000000000 (0.2k2 0.375/0.328 0.383 0.333003300000000000000 0.330 0.556 0.557
Ellecticity
96
10.135
00.153
0.247
0.148
0.340
10.10 0.296/..1.99900
0.237 0.529
0.168 0.272
(..300
0:302
0.345|0.193
0.308
0.100 0.273
0.317
192
01.14
0.235
0,166
0.256
0.102
0:251
0.199 0,304 0.231 0:322. 0.236 a 310
1.184
0:302
0,310
0.305 0.305 355
0.315
0,1182
7866 0.222 0.354
336
00.16
0.345
0.185
0.277
0.128
0.269
0.217 0.319 0.2.1990.6266 0.337 0.249 0.34a
0.198 0,300
(.2223
0.319 0.369
0.529
0.200 0.304 0.231 0.443
730
11,212
0.310
0.225
0.310
0.225
0.317
0.255
0.352
0,280 0.330003366000
0.284 0 373
0.200 0:300
0.258 0,350 39000099090900000000000
390
0.355
0.222
0.311
0.255 0,361
Avg [0.165
0.253
0.2182..222
0.178
0,270
6.2216
0.334 0.251 0.543| 0.192 0.204
jo225
0.319
0.365j0.214
0.327
0.296 0.227 0.338
96
10,392
0.253
0.462
0.285
0.395
0.268
1.552
0,34770.666
0.644
0:429 0,805
0.493
0,593
0.321
606
0.396/0,788
0.499/0.55
0.366
0.338 0.613 0.388
Trafitc
192
00,402
0.25%
0.473
0.296
0:226
0.522
0.332
0.665
00.56
0.474
0.617
0:386
1.598
0.3700
505 604
8.671
340 0.616 0.362
336
00,488
0.263
0.496
0.296
0.433
0,283
0.517
0.3340.677.
0.674
0.420.0..000
0.762 0.477
0.629
0,396
0,605
0,373 0.797 0.508 0.621 0.383
0.618 0.328 0.622 0,337
720
00.411
0.506 0.313 0.467
0.302
0.552
0.352
0.683
0.424
0.719
0,449
0.640
0.350
0.645
0.394 0.844 0.523 0.382 0.382 0.355 0.660 0,408
Avg [0.416
10.484
0.297
0.282
10,529
0.341
|6667
0.426
0.473
0.630
0.336
60.625 0.385/o 804 0:505) 0.576/..224
0.379
Exchhinge
192
96
10.085
0.175
0.313
0.214
0.187
0:235
0.343 0.177
00033350.000
0,206
0.299
10.088
0.176
0.299
0.205
0.256
0,470
0.509 0,184 0.507
0.367
00.04
0.216
0.107
0.236
0:234
0.344
0.176
0.088
0.218/0.267
0,315
0,315
0.35) 0:459 0.271 0.315 0.2199 0.300 0.369
0.396/0 148 0,278
0.237 0,323
336
(0.316
0.420
0.353
0.473
0.331
0.417
0.301
0.397
1,268
0.8833
0.349 0.431
0.367
0.445
0.427 1.324
0.853 0.460 0.427 0.421
0.426
0.309 0.524
720
(0.851
0.689
0.934 0.761
0.542
0.691
0,001
0.714
1.767
0.068
0.852
0.698
0.964
0,746
0.339
0.695
1,058 0.797 1. 195 0.695
[,092 0.769)
1.447 0.941
Ave
[0.357
00.391
0.453
0.360
0.403
103667
0.404
0.940
0.707 0.370
0.416
0:443
(0.354
0.4299 0.446 0:451/004444000
0.454/0.613 0,539
96
[0.361
0.003
00,325
0.400
0.386
0.405
10,460
0.44770.40.0000
0.423
0.448
0.479
0.354
0.402
(0,29)
0.412
0.999 0.424
192
00.416
0.441
1.420
0.421
0.441
0.512
0.477
0.429.0447
0..44....3000 0.525
0.492
0.436
0.420
0.446
0:441
(1719
0.469
0.474
0.504 0.500 0.482
336
0.430
0.484
0:458
0.487
0.458
0.546
0.496
0.5
0.546 0.565
0.515
0.491
0.409
0.489
0.487
0.778
0.530
0.535
0.521 0.496
720
(0.467
0.451
0.498
0.482
0.520.000000
0.503
0,491
0.517 0.544
0.653
0.621
0..94
0.558
0.521
0,500
0.513
0.510 0.699
0.598
0.544
(1.643
0.616
0,514 0,512
Avg
10.419
0.432
h.44700.440)
0.484
0.447
0.5116
0.51660.4440053300
0.529
0.522 0.541
0.507
0.458
0,450
60446
0,457
0.484
(0.570 07..7700..37
0.496 0.487
96
10,276
0.328
0.289
0.341
0.297
0.349
00.308
0.355
0.584
0.400
0.440]
0.340
0.374
10.340
0,394
10,707 0.621 (0.358 0.397
0.397/0.476
(0.476 0.458 0.346 0.358
192
00.342
0.379
0.372
0.392
0.400
0.393
0.405
0.877
0,509
0.402
0.414
0.482
0.479
639 0.439
0.532
0.456 0.452
336
00.366
0.39%
1.386
0:414
0.428
0.483
1.437 0.436
1.043
0.645
0.452
0.482
(.591
0:541
1 1.000 0. 0..4 4966 0.487
0.487
0.552 0.551 (.448 0.486
720
00.392
0.412
0:434
0.427
0.445
0.436
0.450
0.763
0.6/
0.962
0:468
0.839
0.661
0.838 o 463 0,474
0.562 0.662...6660
0.515 0.511
Avg
(0.339
0.350
0.364
0.395
0.383
0.407
10.291
0.411
(0.922
0.6.2200.844....8 0.611 0.550
0.414 0.427
(0.563
0.519|0.955
0.723/0.437 0.449
0.459
96
10.310
0.334
0.357
0.357/0....334
0.334
0.365
l0.352
0,374
(0.400
0...0..6.6.... 0,364 o 387] 0.338
0.333333338 0,375
(0336
0.419/0.386
0.505 0.475
192
0..48
0.362
0.361
0.381
0.390
0.393
0.374
0.387 0.490 0.451 0.998 o
0.374
0.387
0.783
0.391 0.430
0.50 0.441
0.450
0.44000444444
0.553 0.496
336
0.376
0.391
0.390
0.400
0,426
0.420
0.421
0.414
0.532
0.515 0.428 0.425
0.410
0:411
0.415
0.415 0,
0.155 0.415
0.459
0.695
0.164
0.621 0.537
720
00.440
0.423
0.454
0:441
0.491
0.489
0.462
0.449
0.666
0.589
0.687 0.461
0.478 0.450
0.473
0:451 (0. (0.595 o 530 543 0.400
0.585
0.516
0.671 0.561
Avg
(0.369
0.378
003381
0.395
0.410
(0.406
0.407]o..533
0.495 0.419 0.419/ p.400 0.405 00.404
0.408|o..485 0.481 [0.448 0...220..55..... 0:446 0.588 0.517
96
10.170
10,175
0.258l0.180
0.180
0.264
10.183
0.270/0.287
0.366 0.207 0.305|
0.187 0:207
10.193
0.293
0.377/0.203 0.287
0.2.422..227.... 0.339
192
00.229
0.291
1.237
0.299
0.250
0.309
1.255
0.314
11140.4444
0.414
0.49 0,200 o 364
0.249
0.309
0.384 0.361 (0.399
0.445 0.2669
0.328 0.339
0.281 0.340
336
0.303
0.343
0.340
0.311
0.348
0.309
0.347 0.597
0.512 0.577
0.422
0.321
0.351
0.382
0.129
0.591 00.325 0.366
0.334
0.361
720
00.733
0.399
0.391
0.39
0.412
0.407
0.412
0.404
[.730 1.042 0.558 0.524
0.400l 0.403
(u.588 0,525
(0.960
0.735
0.421 0.415 0.417 0.413
0.433 0.432
Avg
(0.269
0.320
10.275
p.323
0.382
11200
0.334
0.334
(.777
01610 3.8 0.20
0.383 (0.354 0.402/0 0.723/0 305 0. 0.349/0.3000 00.360 347
0.327 0.371
25

---

Published as a conference paper at ICLR 2025
Table 17: Short-term forecasting results in the M4 dataset with a single variate. All prediction lengths are in [6, 48). A lower SMAPE, MASE or OWA indicates better prediction. x. in the Transformers indicates the name of =former. Stationary means the Non-stationary Transformer.
Models
TimeMixer++
Timedixer (Trasfomer
FDEE
VimesNetN-BHEE
BEATS'
PachESS
MICN
FILM
LightESDLiner
FED.
Stutionary
Autio.
(Oers)
30246
[02-]
(20225g
21025
[2088]
20019]
(225]
2025a
|0220
50226
[025]
50223
20022
2021
Yeary
13.179
13.200
13,923
15.320
15.387
13.418
15,436
16.463
17.431
14.247
16,965
13,728
13.717
13.974
MASE
29954
2.916
3.214
3,540
2,996
3.045
3.043
3.967
7.162
4,043
3.109
4.283
3.018
3.07%
3.134
OWA
0.769
0.776
0.830
0,910
0.786
0.795
0.794
1.003
1,667
1,042
0.827
1,058
0.803
0.807
0.822
Quanetty
SMAPE!
9.755
9,996
10.757
11:830
10.100
10.207
10.124
10.644
15:214
12.925
11,164
12.145
10.792
10.958
11,338
MASE
1.189
1166
1.283
1.410
1.182
1.194
1.169
1.278
1.963
1.664
1.328
1.520
1.283
1.325
1.365
OWA
0.865
0,825
0.956
1.050
0.890
0.899
0.886
0.949
1,407
1,193
1.000
1.106
0.958
0.981
1.012
Moodbly
SMAPE!
12,432
12.605
13.796
12.791
12.677
15.407
14.014
13.514
13.917
13,958
MASE
0.904
0.919
1.083
1.190
0.933
0.969
0.937
1.031
1,442
1.298
1.053
1.037
1.102
1.097
1.103
OWA
0.841
0.809
0.987
1,050
0.878
0.899
0.880
0.949
1,265
1,144
0,981
0.956
1.012
0.998
1.002
Others
SMAPE
5.569
5.061
6.558
15,880
6.708
6.302
5/185
MASE
2.311
3,115
3,940
4.330
3.302
3.216
3.391
4,511
62.734
5.09
11,434
4,953
3.264
4,064
3,865
OWA
1.01
0,982
1.207
1,330
1,035
1,040
1,053
1,401
14,313
1,553
3.474
1.487
1.036
1.304
1.187
Welghted
Asmaa
SMAPE
11,448
11.723
12.684
13.950
11.829
11:927
11,851
13.152
19.638
14,863
13.525
13.639
12,840
12,780
12,909
MASE
1.487
1,559
1.764
1,940
1.585
1,613
1.559
1.945
5.947
2.207
2.111
2,095
1.701
1.756
1.771
OWA
0.821
0.840
0.929
1,000
0.851
0.861
0,855
0.958
2.279
1.125
1.051
1.051
0.918
0.930
0.939
adopts special ensemble method to promote the performance. For fair comparisons, we remove the ensemble and only compare the pure forecasting models.
* The original paper of N-BEATS (2019]
Table 18: Short-term forecasting results in the PEMS datasets with multiple variates. All input lengths are 96 and prediction lengths are 12. A lower MAE, MAPE or RMSE indicates a better prediction.
Models
TimeMixure+
(Ours)
TimeMixer iTansformer
202-6
2024
20125
TIDE
SCINer
Crossformer PutchTST
BT233
TemesiNtt MICN incar FEDifemmr Stationary Autoformer
20033
20083
200325
2021
MAP
13.99
14,63
16.72
18.39
15.97
15.64
18:95
16.41
15:71
19.70
19.00
17.64
18.08
PEMS03 MAPE
11.54
15.81
15.89
15:74
17.29
15.17
15.67
18:35
18.57
17.56
18:75
RMSE
24.03
23.28
27.81
30.59
25.20
25.56
30.15
26.72
24.55
32.35
30.05
28.37
27.82
MAF
17.46
19.21
21.81
23.99
20.35
20.38
24.86
21.63
62
24.62
26.51
22.34
25.00
PEMSI4 MAPE
11.34
12.53
13:42
14.76
12.84
12.84
16.65
13.15
13.53
16.12
16.76
14.85
16.70
RMSH
28.83
30.92
33.91
37.30
32.31
32.41
40.46
34.90
34.3
39.51
41.81
35.47
38.02
MAE
18.38
20.57
23:01
22.79
22.54
25.12
22.28
28.65
27.92
26.02
26.92
PEMS07 MAPE
7.32
8.62
10.02
11.02
9.41
9.38
12.69
10.60
9.57
12.15
12.29
11.75
11.83
RMSH
31.75
33,59
35,56
39.12
35.61
35.49
42.56
-0.71
35. 40
45.02
42.29
42.34
40.60
MAE
13.81
15.23
17.94
19:75
17.38
17.56
20.35
19.01
17.76
26
20.56
19.29
20.47
PEMSO8 MAPE
8,21
9.67
10.93
12.02
10.50
10.92
13.15
11.83
10.76
12.09
12:41
12.31
12.27
RMSE
23.62
24.26
27.88
30.67
27.34
27.21
31,04
30.65
27.26
32.38
32.97
38.62
31.52
Table 19: Full results for the anomaly detection task. The P, R and F1 represent the precision, recall and FI-score (%) respectively. Fl-score is the harmonic mean of precision and recall. A higher value of P. R and F1 indicates better performance.
Datasets
SMD
MSL.
SMAP
SWaT
PSM
Avg F1
Metries
P
R
F1
P
R
F1
P
R
F1
P
R
F1
P
R
F1
(%)
LSTM
1997
78.52
65.47
71.41
78.04
86.22
81.93
91.06
$7.49
70.48
78.06
91.72
84.34
24
99.53
81.67
77.97
Transformer
2017
83.58
76.13
79.56
71.57
87.37
78.68
89.37
57.12
69.70
68.84
96.53
80.37
62.75
96.56
76.07
76.88
LogTruns
2019
83.46
70.13 76.21
73.05
87.37 79.57
89.15 57.59 69.97
68.67
.2 80.52
63.06
98.00 76.74
76.60
TCN
2019
84.06
79.07 81.49
75.11
82.44 78.60
86.90
59.23 70.45
76.59
95.71 85.09
54.59
99.77 70.57
77.24
Reformer
2020
82.58
69.24 75.32
85.51
83.31 84.40
90.91
57. 70.40
72.50
96.53 82.80
59.93 95.38 73.61
77.31
Informer
1a
86.60
77.23 81.65
81.77
86.48 84.06
90.11 57.13 69.92
70.29
96.75 81.43
64.27 96.33 77.10
78.83
Anomaly"
2022
88.91
82.23 85.49
79.61
87.37 83.31
91.85 58.11 71.18
72.51
97.32 83.10 10 68.35
94.72 79.40
80,50
Pyraformer
2022h
85.61
80.61 83.04
83.81
85.93 84.86
92.54 57.71 71.09
87.92
96.00 91.78 71.67 96.02 82.08
82,57
Autoformer
2021
88.06
82.35 85.11
77.27
80.92 79.05
90.40 58.62 71.12
89.85
95.81 92.74 99.08 88.15 93.29
84,26
LSSL
20226
78.51
65.32 71.31
77.55
88.18 82.53
89.43 53.43 66.90
79.05
93.72 85.76 66.02
92.93 77.20
76.74
Stationary
2022cc
88.33
81.21 84.62
68.55
89.14 77.50
89.37 59.02 71.09
68.03
96.75 79.88
97.82 96.76 97.29
82.08
DLincar
2023
83.62
71.52 77.10
84.34
85.42 84.88
92.32 55.41 69.26
80.91
95,30 87.52 98.28 89.26 93.55
82.46
ETSformer
2022
87.44
79.23 83.13
85.13
84.93 85.03
92.25 55.75 69.50
90.02
80.36 84,91 99.31 85.28 91.76
82.87
LighTTS
2022a
87.10
78.42 82.53
82.40
75.78 78.95
92.58 55.27 69.21
91,98
94,72 93.33 98.37 95.97 97.15
84,23
FEDÍomeer
20226
87.95
82.39 85.00
77.14
80.07 78.57
90.47 58.10 70.76
90.17
92 93.19
97.31
97.16 97.23
84.97
TimesNet
2023
88.66
83.14 85.81
83.92
86.42 85.15
92.52
58.29 71.52
86.76
97 91.74
19.19
96.76 97.47
86.34
TIDE
2023a
76.00
63.00
68.91
84.00
60.00 70.18
88.00
50.00 64.00
98.00
63.00 76.73 93.00
92.00 92.50
74.46
Trranformer
2024
78.45
60.10 71.15
86.
62.65 72.54
90.67
52,96 66.87
99,96
65.55 79.18 95.65 94.69 95.17
76.98
TimesMixer++
(Ours)
88.59
84.50 86.50
89.73
82.23 85.82
93.47 60.02 70.10 92.96 94.33 94.64 98.33 96.90 97.60
87.47
The original paper of Anomaly Transformer (Xu et al.
2022 adopts the temporal association and recon-
struction error as a joint anomaly criterion. For fair comparisons, we only use reconstruction error here.
26

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Published as a conference paper at ICLR 2025
Table 20: Full results for the classification task. in the Transformers indicates the name of *forerr. We report the classification accuracy (%) as the result. The standard deviation is within 0.1%.
Classical methods
RNN
TCN
Transforneess
MLP
CNN
Dataacia/ Moalch
SciRee Resiet LATM
EASI
TEN
Re-
In
Pyra, Auto Station,
FED:
ETS.
PlooeTramman inniort apprEs.
Ner Miseres
[222
32.3
43.7
45.2
32.3
39.9
31.1
28,9
32.2
31.9
31.6
30.8
31.6
30.7
28.1
31.2
3588
28.1
32.6
29.7
27.1
35.7
39.9
RadDitstiio
63.3
64.7
57.7
52.8
67.3
68.6
68.4
68.0
66.0
66.3
676
66.3
68.0
67.5
65.3
66.6
71.8
Basdwringg
28.6
15.8
58.
15.2
253
26.6
53.3
32.0
22.4
52.8
29.4
36.7
31.6
28.0
32.5
358
24.2
22.0
26.1
23.2
32.1
26.5
71.7
73.2
756
72.
77.1
72.7
75.6
76.1
77.1
80.5
75.6
74.6
73.7
73.7
71.
776
75.6
75.1
75.1
74.6
78.0
79.1
94.9
56.5
962
79.7
98.1
984
98.9
96.7
97.8
98.9
98.4
96.2
99.2
98.6
95.9
98.9
96.5
9622
96.2
95.6
98.4
97.9
71.1
98.3
751
89.9
56.7
86.1
68.8
82.1
82.7
81.5
83.2
82.7
87.3
80.9
86.0
838
67.9
75.1
86.4
86.9
89.6
910
94.6
90.8
68.9
$4.0
14.5
50.4
84.0
89.4
N5.7
39.6
92.5
90.2
87.3
89.8
99.2
91.8
93.1
53.9
48.9
53.3
46.6
52.8
52.
55.6
53.9
96.7
53.3
53.3
50.6
57.2
54.4
55.0
56.1
54.4
50.5
51.1
53.4
$7.2
65.6
69.6
712
319
1000
100.0
95.6
97.0
100.0
100.0
100.0
100.0
100.0
98.8
96.0
81.4
100.0
95.0
99.0
99.8
90.3
75,9
98.4
412
57.8
85.9
89.4
85.6
85.5
85.6
53.4
85.9
87.5
85.3
$5.0
86.6
K5.9
82.1
80.3
$4.9
55.3
88.2
Avcrgg Aucuracy 67.0
56.0
72.5
48.6
71.8
70.9
70.3
71.9
71.5
72.1
70.8
71.1
72.7
70.7
71.0
73.0
70,5
67.5
70.4
69.5
73.6
75.3
classification, anomaly detection, as well as few-shot and zero-shot tasks, demonstrating remarkable capabilities. This gives it broad prospects in various real-world applications, such as energy and power forecasting with significant seasonal fluctuations, complex and variable weather forecasting, rapidly changing financial market predictions, and demand forecasting in supply chains, all of which it is highly applicable to. It can also excel in various anomaly detection scenarios commonly found in the industry. By leveraging the capabilities of TIXEMIXER++ we can effectively promote the development of various real-world applications related to time series analysis tasks.
Academic research As the pioncering study on general time series pattern machine, we posit that TIMEMIXER++ holds significant potential to advance research in the domain of time series analysis. Our innovative approach involves converting time series data into time images and implementing hierarchical mixing across different scales and resolutions, which can provide substantial inspira- tion for future research endeavors this field. Furthermore, it is noteworthy that our method of employing axial attention within the depth space to extract seasonality and trends from time images surpasses traditional shallow decomposition techniques, such as moving averages and FFT-based decomposition. This represents the first effective methodology for decomposing time series within the deep embedding, promising to catalyze further scholarly investigation.
Model Robustness The robustness of TIMEMIXER++ is evidenced by its performance across a diverse range of time series analysis tasks. In our extensive evaluation, TIMEMIXER++ was tested on different types of tasks and over 30 well-known benchmarks, competing against 27 advanced baseline models. The results highlight its ability to consistently deliver high performance, demonstrating resilience to the variability and complexity inherent in time series data. This robustness is indicative of TIMEMIXER++'S capability to maintain accuracy and reliability across various scenarios, making it a versatile tool in the field time series analysis. Its robust nature ensures that can effectively handle noise and fluctuations within data, providing stable and dependable outcomes even in challenging conditions.
K LIMITATIONS AND FUTURE WORK
TIMEMIXER++ consistently delivers state-of-the-art performance across a wide range of tasks, including long-term and short-term forecasting, classification, anomaly detection, as well as few- shot and zero-shot learning. This underscores its exceptional representational capacity and robust generalization as a time series pattern machine. However, it important to acknowledge the recent shift in focus toward large time series language and foundation models, which emphasize continuous scaling of data and parameters, becoming a dominant paradigm in the field. In contrast, due to limitations in the quality and scale of available time series data, the parameter sizes of current advanced deep time series models remain relatively modest. Addressing the challenge of applying scaling laws time series pattern machines is therefore essential. In this study, we introduced an effective backbone model as a first step toward building a universal time series pattern machine. Future research will focus on constructing large-scale time series datasets to further explore scaling laws for TIMEMIXER++ +. an exciting and promising direction for continued investigation.
27

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Published as a conference paper at ICLR 2025
Praditiess
Predition
-13
-15-
-1.-
-15-
-13
MixeMixer++
(b) |Transformer
(c) PStchTST
-12
Craanctunn
Groand
-1.2
-144
-12-
125 Stationary
(d) Crossformer
TIDE
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Or Treueehuus
Whrth MAM
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-23
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100
(g) Autoformer
(h) DLinear
(i) FEDformer
Figure 16: Prediction cases from ETTh1 by different models under the aaput-96-rredict-a settings. Blue lines are the ground truths and orange lines are the model predictions.
28

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Published as a conference paper at ICLR 2025
25
M
NW
00-
-10
TimeMixer+
18
iTransformer
225
200
PatchTST
350
135
WW
NV
NU
M
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GruedTur
25
168
135
150
249
125
155
Crossformer
(e) TiDE
Stationary
WWNN
MV
Pracecior
Parid
150
175
(g) Autoformer
(h) DLinear
FEDformer
Figure 17: Prediction cases from Electricity by different models under input-96--re settings.
29

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Published as a conference paper at ICLR 2025
Grundruh
25
TimeMixer
(b) iTrrnsformmr
201
PatchTST
360
225
335
Prodictio
106
359
204
(d) Crossformer
TIDE
Stationary
15c
(g) Autoformer
(h) DLinear
FE FEDDformr
Figure 18: Prediction cases from Traffic by different models under the input 96 predict-96 96 settings.
30

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Published as a conference paper at ICLR 2025
Grandihu
1.00
3.0
111
331
24
11
330
2
200
130
(a) TimeMixer +
(b) iTransformer
(c) PatchTST
2.2
115
1.50
435
2.2-
832
1.00
200
125
(d) Crossformer
(e) TIDE
Stationary
517
0.65
005-
3.5
3.34
0.6
3.54
042
(g) Autoformer
(h) DLinear
(i) FEDformer
Figure 19: Prediction cases from Weather by different models under the 16pur-96--r settings.
31

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Published as a conference paper at ICLR 2025
15-
20-
23-
15-
85-
65-
-35-
(a) TimeMixer++
(b) iTransformer
(c) PatchTST
15-
66
-35
Prrtt
Andd
25
150
125
330
100
125
135
200
(d) Crossformer
(e) TIDE
Stationary
2.0
20-
154
-00
-12
ads
(g) Autoformer
(h) DLinear
(i) FEDformer
Figure 20: Showcases from Solar-Energy by different models under the 9nput-9--preiict-96 settings.
32

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Published as a conference paper at ICLR 2025
Prddctor
1040
1030
31383
1330-
11390
31003-
13354
2000
(a) TimeMixer +++
(b) iTransformer
(c) PatchTST
13554
Diruul Sircch
30503
12500
13400
12A43
13200
32389
13209
13200
2:103-
1230e
1240
1283
1040
(d) Net
(e) TiDE
Stationary
1030
13300
22443
11330
11000
1188
0990
1000
Autoformer
(h) DLinear
FEDformer
Figure 21: Showcases from the M4 dataset by different models under the 18 settings.
33

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Published as a conference paper at ICLR 2025
Feesles
-03
-0.2
noul Mm
-06-
-03-
-0a-
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mm
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100
103
389
(a) TimeMixer++
(b) iTransformer
(c) PatchTST
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(e) TiDE
(f) Stationary
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0.--
Shourdhutt hradcciion
0.0
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-06-
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1.2
12
(g) Autoformer
(h) DLinear
FEDformer
Figure 22: Showcases from PEMS03 by different models under the input-96-predict-1 settings.
34

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Published as a conference paper at ICLR 2025
Tradicion
Mnp Ap hymhhhm
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Myp M AMM
1.2
1.0
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(d) Crossformer
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Stationary
2.2
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2.0
16-
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33
60-
-1.
100
Autoformer
(h) DLinear
FEDformer
Figure 23: Showcases from PEMS04 by different models under the input 96 -repire 12 settings.
35

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Published as a conference paper at ICLR 2025
139
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Figure 24: Showcases from PEMS07 by different models under the input 0a predict- 12 settings.
36

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Published as a conference paper at ICLR 2025
Greae 20u
1/0 SMMMMAA
2.0
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Figure 25: Showcases from PEMS08 by different models under the input-96-predict 12 settings.
37


Reviews:
[{"review_id": "PygUsAWjj8", "reviewer": "Reviewer_e5Jj", "summary": "The paper presents TIMEMIXER++, a general-purpose model for various time series tasks, including forecasting, classification, anomaly detection, and imputation. Utilizing a multi-scale, multi-resolution framework, the proposed method transforms time series data into multi-resolution images to capture complex temporal and frequency-domain patterns, enabling flexibility across analytical applications. The model’s approach includes dual-axis attention for decomposing seasonal and trend components and hierarchical multi-scale and multi-resolution mixing to integrate patterns across scales. The proposal achieves strong performance across eight benchmark tasks, outperforming both general-purpose and task-specific models. This work contributes to advancing time series analysis with new state-of-the-art benchmarks across settings.", "questions": "Q1. The proposed architecture adds significant computational cost to the internal representation of the model compared to vanilla transformers and some of the previously proposed models. It seems this does not have a significant effect on the training time compute and memory complexity of the model. Have the authors conducted any studies to compare the inference-time cost of TM++ compared to other methods? \n\nQ2. As mentioned by authors, some time series tasks (imputation, anomaly detection) benefit more from diverse representations while others like forecasting and classification benefit from consistent representation. Given this, is there any way to leverage a routing model dependent on the proposed task type, which could lower the inference-time cost of this model?\n\nQ3. MTS-Mixer (Li et. al., 2023) presents another approach to channel decomposition which similarly outperformed competing models, but they found the approach worked best with MLPs rather than attention-based models. Have the authors explored this technique for separating from attention mechanisms which could lead to further efficiency and model performance?", "limitations": "", "rating": 10, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "S1. The proposed model captures both short- and long-term dependencies by transforming time series data into multi-resolution images, enabling the analysis of complex temporal and frequency-domain patterns that challenge traditional models. The authors validate this with experimental results showing the new architecture outperforms SOTA models on most standard benchmarks. The ablation study helps validate the importance of the individual parts of the architecture – the channel mixing, image decomposition, and multi-scale and multi-resolution mixing. This approach continues to validate the benefits of integrating image analysis techniques with time series tasks.\n\nS2. The architecture is flexible for supporting different kinds of time-series tasks. The hierarchical multi-scale and multi-resolution mixing modules enable the model to flexibly adapt across various time series tasks, from forecasting to anomaly detection, promoting robust and accurate performance across applications.\n\nS3. Empirical Validation: the testing in this paper on eight benchmark time series tasks, including the hyperparameter ablation results, shows TIMEMIXER++ consistently surpasses both general-purpose and task-specific models, affirming its potential as a high-performance, general-purpose solution for time series analysis. The experiments were very thorough.", "weaknesses": "W1. There is little exploration of scaling of model size, which would be an interesting avenue for validating the model architecture in a zero shot setting. The current zero-shot experiments are primarily in-domain and not cross-task.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "a3W9a64BWy", "reviewer": "Reviewer_LKyA", "summary": "The paper presents TimeMixer++, an advanced framework designed to enhance general time series analysis. TimeMixer++ integrates multi-resolution time imaging, multi-scale mixing, and dual-axis attention mechanisms to effectively capture and adapt to diverse patterns within time series data. This innovative approach allows for robust and flexible analysis across various temporal scales and resolutions.", "questions": "See weaknesses (W2, W3, W4).", "limitations": "", "rating": 8, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "1. the authors introduce a robust framework TimeMixer++ that leverages multi-resolution time imaging, multi-scale mixing, and dual-axis attention to enhance general time series analysis. They present SOTA results on four different tasks.\n2. the integration of both multi-scale and multi-resolution mixing strategies for adaptive pattern extraction demonstrates innovation.\n3. the manuscript and appendix are well-prepared, but the authors have not yet released the promised code.", "weaknesses": "1. the fonts in the figures should be enlarged for better readability. For example, in Figure 1 (right), the label \"Benchmarking model performance across representation analysis in four tasks\" appears blurred. Additionally, consider using a single set of legends for all four tasks to enhance clarity.\n2. the source code repository has not released for reproducing, i will consider raising the score if the released repository and the consistency of the results.\n3. more detail on how it compares to recent models like TimesNet and iTransformer on specific time series tasks would strengthen the paper’s claims.\n4. including a discussion on computational efficiency (e.g., FLOPs, memory usage) for different tasks could enhance the paper’s utility.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "kSFvMmo42o", "reviewer": "Reviewer_9h69", "summary": "The paper introduces a time series pattern machine method called TimeMixer++ for processing multiscale time series. The method transforms time series into multi-resolution time images to enable pattern extraction with respect to temporal and frequency domains followed by three dominant modules - (1) input projection; (2) a stack of Mixerblocks; (3) output projection.  Extensive experiments show the proposed method obtains improvement over the well-established competing methods.", "questions": "[1] Questions follow from the points listed in the weakness section.\n[2] What is the naming of the method, i.e., TimeMixer++ in terms of? or just because both the methods target processing multi-scale time series? \n[3] What is the connection with the method TimeMixer?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "The methods used in the paper (e.g., time imaging and image decomposition) are very interesting. The evaluation is comprehensive: the authors discuss long and short-term forecasting, zero-short forecasting, classification, and anomaly detection.", "weaknesses": "In terms of the forecasting results shown in Tables 3 and 4, the performance gain is negligible, and such minor improved performance certainly can be attributed to the parameter tuning, e.g., a well-tuned parameter settings for TimeMixer++ while a weak parameter settings for other competing methods.  \n\nThe paper barely offers insights both theoretically and experimentally. The theoretical understanding of the improvement as well as its time imaging and multi-resolution mixing is lacking, mostly based on intuition and simply blending the models. \n\nThere are some papers that already discussed the use of frequency analysis and the frequency components extraction for model deployment (e.g., [1][2][3]) to capture the periodic patterns, and they all claim it can capture the global interaction and patterns among time series, so what is the benefits of introducing multi-resolution time imaging, and it is worthwhile to compare them in ablation study? In addition, it is encouraged to cite the papers [1][2][3] if not yet in the references. \n\n\n\nReferences:\n[1] Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors https://arxiv.org/pdf/2305.18803\n[2] TFDNet: Time-Frequency Enhanced Decomposed Network for Long-term Time Series Forecasting https://arxiv.org/abs/2308.13386\n[3] FEDNET: FREQUENCY ENHANCED DECOMPOSED NETWORK FOR OUT-OF-DISTRIBUTION TIME SERIES CLASSIFICATION https://openreview.net/forum?id=OVu9DsOjgH", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Oral)