Multi-Modal View Enhanced Large Vision Models for Long-Term Time Series Forecasting
Authors: ChengAo Shen
Wenchao Yu
Ziming Zhao
Dongjin Song
Wei Cheng
Haifeng Chen
Jingchao Ni
Venue: NeurIPS 2025 poster ()
Keywords: Time Series Forecasting
Multi-Modal View
Deep Learning
Primary area: deep_learning

Abstract: Time series, typically represented as numerical sequences, can also be transformed into images and texts, offering multi-modal views (MMVs) of the same underlying signal. These MMVs can reveal complementary patterns and enable the use of powerful pre-trained large models, such as large vision models (LVMs), for long-term time series forecasting (LTSF). However, as we identified in this work, the state-of-the-art (SOTA) LVM-based forecaster poses an inductive bias towards "forecasting periods". To harness this bias, we propose DMMV, a novel decomposition-based multi-modal view framework that leverages trend-seasonal decomposition and a novel backcast-residual based adaptive decomposition to integrate MMVs for LTSF. Comparative evaluations against 14 SOTA models across diverse datasets show that DMMV outperforms single-view and existing multi-modal baselines, achieving the best mean squared error (MSE) on 6 out of 8 benchmark datasets. The code for this paper is available at: https://github.com/D2I-Group/dmmv.

Multi-Modal View Enhanced Large Vision Models for Long-Term Time Series Forecasting
ChengAo Shen', Wenchao Yu², Ziming Zhao', Dongjin Song', Wei Cheng", Haifeng Chen', Jingchao Ni'
'University of Houston, 2NEC Laboratories America, 'University of Connecticut (ccshen9,zzha035 jni7)@uh. edu, '(wyu, wei cheng, hwwfenninnnnnaaa @nee- com, ddongj in. songsuconn.ccc
Abstract
Time series, typically represented as numerical sequences, can also be transformed into images and texts, offering multi-modal views (MMVs) of the same underlying signal. These MMVs can reveal complementary patterns and enable the use of pow- erful pre-trained large models, such as large vision models (LVMss, for long-term time series forecasting (LTSF). However, as we identified in this work, the state-of- the-art (SOTA) LVM-based forecaster poses an inductive bias towards "forecasting periods". To harness this bias, we propose DMMV, novel decomposition multi-modal view framework that leverages wend-seasonal decomposition and a novel backcast-residee based adaptive decomposition to integrate MMVs for LTSF. Comparative evaluations against SOTA models across diverse datasets show that DMMV outperforms single-view and existing multi-modal baselines, achieving the best mean squared error (MSE) on 6 of benchmark datasets. The code for this paper is available at: https: //g/ /gtb com/D2I-Group/ Group/ dmmv.
Introduction
Long-term time series forecasting (LTSF) is vital across domains such as geoscience [1], neuroscience [3], energy [18], healthcare [28], and smart city [27]. Inspired by the success of Transformers and Large Language Models (L..Ms) in the language domain, recent research has explored similar architectures for time series [40, 14, 51]. Meanwhile, Large Vision Models (LVMs) like ViT [7], BEiT [2] and MAE [12], have achieved comparable breakthroughs in the vision domain, prompting interest their application LTSF [4]. These approaches transform time series into image-like representations, enabling LVMs to extract embeddings for forecasting [29]. The rationale is that LVMs, pre-trained on large-scale image datasets, can transfer useful knowledge LTSF due structural similarity: each image channel contains sequences of continuous pixel values analogous to univariate time series (UTS). This alignment suggests LVMs may be better suited time series than LLMs. which process discrete tokens.
This hypothesis is partially validated by the SOTA VisionTS model [4], which applies MAE [12] to imaged time series and achieves impressive forecasting performance. This progress has spurred interests in combining imaged time series with other representations. In the past, time series have been studied through various forms: (1) raw numerical sequences [49, (2) imaged representations [43, 4], and (3) verbalized (textual) descriptions [46, 10]. While they differ in modality, they represent alternative views of the same underlying data unlike typical multi-modal data, where modalities originate from distinct sources [23]. However, these malii-modal views (MMVs) enable the application of large pre-trained models, such as LLMs, LVMs, and vision- language models (VLMs) [16, 33], to time series analysis, specializing them from those in conventional multi-view learning [39], where multi-view is broader notion including both MMVs and views of the same modality (e.g., augmented image views [39]). To distinguish, we use MMVs for time series throughout this paper.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Leveraging MMVs offers two key advantages: (1) augmenting time series with alternative views can reveal patterns not evident in the original numerical data, and (2) pre-trained large models can extract complex patterns specific to certain views, such as visual representations. Motivated by these benefits and the recent success of LVMs, this work investigates the synergy of MMVs for LTSF, with focus on incorporating LV To our knowledge, integrating the visual view of time series via LVMs alongside other modalities remains underexplored. The most related effort, Time-VLM [52], uses a VLM (ViLT [16]) to encode visual view and contextual texts of time series, augmented with a Transformer for the numerical view. All embeddings are combined through a fusion layer. However, this simple combination strategy overlooks the unique inductive biases of individual views, leading to suboptimal performance (see $4.1). Moreover, its use of textual inputs provides only marginal improvements while introducing significant computational overhead due to the large language encoder.
We propose DMMV, Decomposition-basee grates numerical and visual views in a compact architecture. We exclude the textual view due to its marginal gains in Time- Time-VLM [52] and recent doubts about the effectiveness and cost-efficiency of LLMs for LTSF [36]. DMMV comprises two specialized forecasters: a numerical forecaster and a visual forecaster. The visual forecaster, inspired by VisionTS [4], uses MAE [12] self-supervised
Multi-Modal View Framework for LTSF, which inte-
LVM capable of reconstructing masked images - leveraging its strong performance on continuous values (i.e., pixels). Time series are transformed into images using a period- period-based patching technique [43], which, although effective, imposes an inductive bias on LVMs towards periodic signals. To address this, we design two DMMV variants illustrated in Fig. 1: (a) DMMV-S (simple decomposi- tion), which splits the time series into trend and seasonal components, assigning them to the numerical and visual forecasters, respectively; (b) DMMV-A (adaptive decomposition), which adaptively learns the decomposition via a backcast-residual mechanism aligned with the two forecasters. DMMV employs late fusion [17] via a gating mechanism, as intermediate fusion (e.g., embedding-level) underutilizes MAE'S decoder, which plays a crucial role in pixel prediction. Extensive experiments show that DMMV significantly outperforms both SOTA single-view methods and Time-VIAN -VLM, despite the latter incorporating an additional text encoder. To sum up, our contributions are as follows.
We distinguish MMVs in time series analysis from the broader notion in conventional multi-view learning and study the emergent yet underexplored problem of MMV-based LTSF.
We propose DMMV, novel MMV framework that is carefully designed to harness an inductive bias we identified in SOTA LVM-based forecasters, complemented by the strength of a numerical forecaster, with two technical variants DMMV-S and DMMV-A.
We conduct comprehensive experiments on benchmark datasets to evaluate DMMV, demonstrating its superior performance over 14 SOTA baselines and highlighting its potential as new paradigm for MMV-based time series learning.
2 Related Work
To the best of our knowledge, this is the first work to explore LVMs in decomposition- MMV framework for LTSF. Our work relates to LVbeba time series forecasting (TSF), Multi-modal TSF, and Decomposition-baseed TSF, which are discussed below.
LVM-based TSF. Various vision models, such as ResNet [13], VGG-Net [34], and ViT [7], have been applied to TSF [50, 47], with some studies exploring image-pretrained CNNs like ResNet [13], Inception-vi v1 [35], and VGG-19 [34] for LTSF [19]. The use of LVMs in this area is still emerging, with most efforts focused on time series classification (e.g.. AST [9] uses DeiT [37], ViTST [20] uses Swin [26]). In contrast, LVMs have seen limited use in TSF, likely due to their lower effectiveness on low-level (i.e., numerical-level) tasks. The most notable method is VisionTS [4]. which adapts MAE [12] for zero-shot and few-shot TSF. Another method, ViTime [47], trains ViT [7] from scratch on synthetic imaged time series but does not explore transferring knowledge from prengeepeeteaneed LVMs. Importantly, these approaches rely solely on vision models without incorporating other views or modalities.
Multi-modal TSF. Recently, large VLMs such as LLaVA [23], CLIP [33], and ViLT [16] have been explored for time series analysis [41, 56, 52]. The most relevant is Time- Mime-VLM| [52], which builds a forecaster on ViLT [16] to encode numerical and visual views, along with contextual texts. While integrating rich information with a large model, Time VLM demonstrates promising results in TSF.

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(a) DMMV-S (Simple Decomposition)
(b) DMMV-A (Adaptive Decomposition)
Trainable
MM
Transtomer Block
Freesing
Feed Forward
M
M
Add & Norm
Image
Image
Trand
Numerical Forecaster
W Visual Forecaster
Backcast
Forecast
Mult--Head Attn.
Transformer Linear model
Include
Numerical Forecaster
M&VVi Visual
MYNA
Decoder
Forecaster
LVM Encoder
Moving-Average
Decomposition Block
Projection
MAMMM
Patching
Figure 1: An overview DMMV framework. (a) DMMV-S uses moving- average to extract trend and seasonal components. (b) DMMV-A backcast-residual decomposition to automatically learn trend and seasonal components. In (b), the gray blocks are gray-scale images. "?" marks masks.
However, its fusion strategy closely follows the ViLT backbone and lacks sime-series-specifie design, leading to potentially suboptimal performance.
Decomposition-baset TSE. Decomposition is common technique in TSF, with seasonal-trend decomposition (STD) employed by models like Autoformer [44], FEDformer [54], and DLinear [49]. Recent work such as Leddam [48] replaces the traditional movingg-vverage kernel in STD with learnable one. Residual decomposition is another approach, used by N-BEATS [31] to reduce forecasting errors and later adopted by DEPTS [8] and CycleNet [21] for period-trend decomposition. While SparseTSF [22] predicts periods without explicit decomposition, SSCNN [6] introduces an attention-based method extract long-term, short-term, seasonal, and spatial components. However, none of these methods incorporate LVMs. In contrast, our proposed DMMV shares insights with residual decomposition but uniquely designed to exploit the inductive bias of LVMs for adaptive decomposition, setting it apart from prior works.
In summary, the proposed DMMV framework is distinct from existing approaches, yet integrates the strengths of pre-trained LVMs, the MMV framework, and decomposition techniques.
3 Decomposition-Based Multi-Modal View (DMMV) Framework
Problem Statement. Given a multivariate time series (MTS) = [x! XPIT RXT within look-back window of length T, where x E R² (1 < i D) is UTS of the i-th variate, the goal of LTSF is estimate the most likely values of the MTS at future H time steps, i.e., Y E IR DxH such that the difference between the estimation and the ground truth Y X7+1744 E R Dx is
minimized in terms of mean squared error (MSE), ie., D Eb DH | Y.
Preliminaries. Masked autoencoder (MAE) [12] is pre-trained self-supervisedly by reconstruct- ing masked image patches using ImageNet dataset [5]. To adapt it to LTSF, VisionTS [4] adopts period-based imaging technique in- troduced by TimesNet [43]. Specifically, each length- - UTS x" is segmented into [T/P] sub- sequences of length P. where P is set to be the period of x², which can obtained using Fast Fourier Transform (FFT) on x* [43] or from prior knowledge on sampling frequency. The subsequences are stacked form 2D image I' Px [T/P), After standard-deviation normaliza- tion, I' is duplicated 3 times to form a gray image of size P x [T/P] x 3, followed by a bilinear
Forecast
Mask
fLVM
History
Time
Timee
Temporally ordered segments
Temporally ordered segments
Figure 2:
An illustration of an LVM forecaster
interpolation resize it to image I' of size 224 224 x to fit the input requirement of MAE As Fig.

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2 shows, the forecast is achieved by reconstructing to the future horizon x'. The forecast y IR can be recovered from the reconstructed area by de-normalization and reverse transformation. The forecast of MTS X is achieved by forecasting over x², xD in parallel, following the channel-independence assumption [30].
masked area of corresponding
An Inductive Bias. Due to baaed imaging and the spatial consistency enforced during MAE'S pixel inference, VitionTS exhibits a strong bias toward inter-period consistency, often overshad- owing the global trend. Fig. 3 illustrates VisionTS's s forecasts on a synthetic sinusoidal time series with a period of 24. As shown in Fig. (d))-(d), where the segment length P varies from 24 to 48, forecasts alternate between accurate and inaccurate as P shifts from 1 1xperiod to 2 2epeiod, highlighting strong inductive bias toward periodicity. Notably, the forecasts aren't 't mere repetitions the decreasing intra-period amplitude indicates that LVMs can still capture local trends within each period. More quantitative results are deferred to Appendix D.2.
Look--back window
Forecast
Ground truth
00000000
Time
Time
Time
Time
(a) Segment length Pw24
(b) Segment length P=32
(c) Segment length P=40
(d) Segment length P=48
Figure 3: An illustration of LVM forecaster's inductive bias. The time series has period of 24, The vertical dashed lines mark the segment points. The example indicates a bias towards segment lengths that are multiples of the period in (a)(d) over other segment lengths in (b)(c).
Motivated by this observation, we design the DMMV framework leverage the inductive bias of LVMs while addressing their limitations. Specifically, the visual forecaster f-i (i.e., LVM) focuses on capturing periodic patterns from the visual view, while the numerical forecaster [num(-) models global trends from the numerical view, resulting in more balanced forecasting. Fig. presents the two DMMV variants- DMMV-S and DMMV-A within a decomposition- -ased architecture. Unlike prior approaches [44, 22, 6, 211, DMMV is explicitly designed to align with the inductive bias of LVMs.
3.1 DMMV with Simple Decomposition (DMMV-S)
DMMV-S adopts a simple moving-average (MOV) decomposition [44], which explicitly decomposes an input time series x' into a trend part and a seasonal (or periodic) part, reflecting the long-term progression and the seasonality of x respectively. Basically, MOV uses kernel (i.e., sliding window) of length 2 2/2] + 1 to extract the component with frequency lower than x" 's sampling frequency (i.e., 1/P), highlighting the global trend. The residual component is the seasonal part. This operation constitutes the decomposition block in Fig. I(a).
Xrend Moving-Averagee wwwpiigg-weergg(Paaadngg////""
X = x Xuendd IsiSD
(I)
where Padding(-) keeps the length of x" fixed.
The visual forecaster (vis(.) transforms the input x x into 224 x 224 x 3 image i scason and outputs the forecast D Season E RH for the seasonal component. For the numerical forecaster frum (-), rather than imposing a specialized inductive bias, we adopt a general-purper of capturing long-term dependencies. We investigate the feasibility of two options and leave other explorations as a future work: (1) A simple linear model motivated by the proven effectiveness of linear methods in LTSF [49, 22, 21], i.e., F'iend Snum (xfrens) W Wxtennd b, where W E HT and b E IR are weight and bias, respectively; and (2) A Transformer-based model inspired by PatchTST [30], which segments xirend into N length-L patches, where N = [T/L] + 1, to form the input X [ E BLLN and performs
architecture capable
Wppo X Gead + W
pcs 8 = Transformer (ieen)) + Fienn = Linear(Flatten/ (Xten)) (2)
Gend
pro
to achieve the forecast Firend "R for the trend part, where Wpoo pro E D'xL
L is the weight project the patches to D' D'ddimensional embeddings, W E D' x is a learnable positional encoding, Flatten(-) and Linear(-) are flatten and linear operators.
Finally, G Scason and firend are merged to produce the overall forecast 8 for the i-th variate. In particular, instead of using the regular commatioo--base merge, we design an adaptive merge function

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with light-weight gate sigmoid(wg) E [0, 1], where Wy is a learnable scalar parameter. To sum up, the overall process of DMMV-S as follows.
(1 - -9) Frend: where
y season f (T (Teesoo)::
Firend
mum (Xiena))
Remark, One limitation of DMMV-S the explicit trend-seasonal decomposition placed on the input x", which will enforce (-mm()) and fvis()) to fit pre-defined components extracted by certain kernel size. This is not flexible and may not fully leverage L.Ms' potential. To address it, we develop DMMV-A to have adaptive decomposition in the next.
3.2 DMMV with Adaptive Decomposition (DMMV-A)
Unlike DMMV-S, DMMV-A implicitly decomposes the imput x' into trend and seasonal components tailored to the strengths of the numerical and visual forecasters, respectively. This is achieved via sacckcast-residuue mechanism (Fig. I(b)) that leverages LVMs' bias toward periodic patterns. The input x² is first transformed into an image I' using period- imaging. Before forecasting, fvis() used to backcast the look-back window by reconstructing masked segments of T', An effective masking strategy must: (1) enable full-window reconstruction; (2) align with the forecasting setup (Fig. 2); and (3) minimize the usage of (-) to avoid computational overhead. To meet these criteria, propose efficient BackCast-Maskinn (BCMASK) strategy (Fig. 4), which applies two passes: masking and reconstructing the left and right halves of I', respectively.
i' Len Lightl with He fvis (Tigh)), Light fvis (Teen
(4)
where To right (o is the masked image with right (left) area unmasked, i (i (hight is the reconstructed left (right) area, I' is the reconstruction, or backcast, of I' by concatenating I and i Light
BCMASK satisfies all three criteria: (1) it enables full reconstruction of It; (2) it uses contiguous seg- ments in T nghi (Ten) to predict adjacent segments Rion (ight). mirroring the forecasting process in Fig. 2: and (3) it minimizes the use of fvis(.) only two passes are needed, as some unmasked regions of I' are required for prediction and must later be masked to complete the full reconstruction.
lnght (veelen))
hiun Sie (rean)))))
Backcast Mask
Backcast Mask
Forecast
Forecast
Time
Time
Notably, the backeast in image Í' is biased toward the periodic patterns in i', After de-normalization and reverse transformation, backcast time series
Look-back window
Look-back window
Figure 4: An illustration of BCMASK.
X E IR is recovered, reflecting periodic compo- nent in x². The residual Axt = x X therefore emphasizes the trend. As shown in Fig. 1(b), feed Ax' into frum( (-) to produce Virend E R analogous to its role in DMMV-S. Mcanwhile, fvis()) predicts from i', likely yielding the forecast of seasonal component &iesso RH Finally, Strend and y seuson are fused via the same gating mechanism as Eq. (3). In summary, this defines the overall process of DMMV-A A as follows.
8r g f season + (1 (1-9) g) z Frendd where ÿ season fvs (I'), G Frennd =f fmum (Ax')
(5)
Remark. Unlike DMMV-S, DMMV-A automatically learns decomposition of xf that optimally aligns fmm (.) and fvix()) with the forecasting task. As shown in $4.3, this adaptive decomposition effectively separates seasonal and trend components, leveraging the inductive bias of fvis() (-). Unlike the backcast in N- N-BEATS [31]- designed merely to extract predictive errors - our approach is specifically tailored exploit LVMs' bias toward periodic patterns, making fundamentally different.
3.3 Model Optimization
After obtaining Y [& PDT DDH, DMMV is trained by minimizing the MSE between Y and i.e,, D.H Ee1 while fvis (.) uses pre- pre-trained LVM weights with partial fine-tuning We find that fine-tuning only
E
EH Y Yallz. As shown Fig. 1, fmum(-) (-) is trained from scratch,
5

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the normalization layers yields the best performance, consistent with the findings in [55]. For the choice of LVM, we tested MAE [12] and SimMIM [45], both are supe-super pre-trained LVMs, in $4.2. MAE performs better and is set as the default. Training begins with fvic()) frozen while fnum() trained for number of epochs (e.g., ~30). Then, the norm layers of (-) are unfrozen and fine-tuned jointly with fnmm() until convergence or early stopping.
4 Experiments
In this section, we compare DMMV with the SOTA methods on LTSF benchmark datasets, and analyze its effectiveness with both quantitative and qualitative studies.
Datasets. We adopt 8 widely used MTS benchmarks: ETT (Electricity Transformer Temperature) [53], including ETTh1, ETTh2, ETTm1, ETTm2; Weather [44], Illness [44], Traffic [44], and Electricity [38]. Following standard protocols [44], we split the datasets chronologically into train- ing/validation/test sets using a 60%/20%/225 ratio for ETT and 70%/10%/20% for the others. The prediction horizon H is set to [24, 36, 48, 60) for Illness, and 196, 192. 336, 720) for the remaining datasets. By default, look-back window T 336. Full dataset details are provided in Appendix B.1.
The Compared Methods. We compare DMMV with the SOTA methods, including VLM-based multi- modal model: (1) TiMe [52]; LVM--ased model: (2) VisionTS [4]; LLM-based models: (3)
Time-LLM [15], (4) GPT4TS [55], (5) CALF [24]; Transformer-basee models: (6) PatchTST [30], (7)
FEDformer [54], (8) Autoformer [44], (9) Stationary [25], (10) ETSformer [42], (11) Informer
[53]; and non- Tran-rrasfrrmer models: (12) DLinear [49], (13) TimesNet [43], (14) CycleNet [21].
As we use the standard evaluation protocol, we collect results from prior works: Time-Vil VLM ([52)),
LLM-based models (reproduced by [36]), Transformer-basee models, PatchTST and TimesNet ([4]), and CycleNet ([2I). Since VisionTS in [4] originally uses dynamic look-back windows such as T = 1 1152 and T = 2304 for different datasets, we re-run it with T = 336. CycleNet's 's results on the Illness dataset is unavailable in [21]. Thus we run its official code on the Illness dataset.
We evaluate both DMMV variants DMMV-S and DMMV-A. A. A linear forecaster ($3.1) and MAE are set as the default in fmmm (-) and [vis()), respectively. Ablation studies (64.2) include variants with a Transformer- both VisionTS and DMMV is set based each dataset's sampling frequency (see Appendix B. Additional details on all compared methods are in Appendix B.2.
Snum (-) and SimMIM as (-)) Following [4], the imaging period P ($3) for
Evaluation. Following [30, 49, 36], we use Mean Squared Error (MSE) and Mean Absolute Error (MAE) to evaluate the LTSF performance of the compared methods.
4.1 Experimental Results
Table summarizes the LTSF performance of 10 representative methods across four categories: MMV-based, visual-view-based, full results for all 16 methods provided in Appendix D.1.
geguagg--ieewbbseee and numerical-view-beee approaches, with results on the Illness dataset are not reported in [52] and its code is unavailable at the time of this experiment, thus are marked by a_". For DMMV, the stronger variant, DMMV-A, is reported. In Table 1, several key insights emerge: (1) MMV and visual-vies methods generally outperform language-view view methods, underscoring the effectiveness of LVMs, particularly when integrated within MMV frameworks; (2) Numerical- view models such as PatchTST and CycleNet remain competitive, especially on datasets where VisionTS underperforms (e.g., ETTm2 and Electricity). highlighting their potential to complement visual models; (3) The strong results of CycleNet, a lightweight model with learnable decomposition, demonstrate the value of combining simplicity with structure in LTSF; (4) Notably, DMMV-A, which unifies visual and numerical views through a novel adaptive decomposition, outperforms the baselines in most cases, achieving 43 first-places and confirming its effectiivness; (5) Lastly, while VisionTs performs well on highly periodic datasets (e.g., ETTh1, ETTmI, Traffic) due to MAE'S inductive bias toward periodicity, DMMV-A alleviates this bias, resulting in more generalizable forecasts.
Fig. presents critical difference (CD) diagrams| [11] showing the average rank of all 16 methods based on MSE and MAE across prediction lengths and all datasets. DMMV-S ranks 4.5/16 in MSE and 7 in MAE, underscoring the benefit of the adaptive decomposition used in DMMV-A (Fig. ((b).. From Fig. 5, DMMV-S's comparable ranks to CycleNet indicate even with a simpler, fixed decomposition, DMMV-S exhibits an ability that a strong SOTA model with learnable decomposition has. In 84.3, detailed comparison between DMMV-S and DMMV-A is provided.

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Table I: LTSF performance comparison on the benchmark datasets. Lower MSE and MAE indicate better performance. Red values indicate the best MSE and MAE per row. Time- -VM's results on the Illness dataset are unavailable in [52] and its code was unavailable at the time of this experiment.
View
Mudti-Modal
Visual
Language
Numerical
Model
DA
Time- VLM
VIsionTS
GPT4TS
Time-LIM
PatchTST
CycleNet
TimesNet
DLinear
FEDformer
Metric
MSE
MAE|
MSB
MAE
MSE
MAE
MSE
MAE
MSB
MA
MSE
MAE
MSB
MAE
MSE
MAE|
MSE
MA
MSE
MAE
96
0.354
0.389
0.361
0.386
0.355
0.386
0.370
0.389
0.376
0.402
0,370
0.399
0.374
0.396
0,334
0.402
0.315
0.399
0.376
0,419
192
0.393
0.405
0.397
0.115
0.395
0.407
0.412
0.413
0.407
0.421
0.413
0:421
0.406
0.415
0.436
0.129
0.405
0.416
0.420
0,448
336
0.488
0,422
0:436
0.40
0.439
0,459
720
0.445
0.450
0.441
0.858
0.458
0.460
0.441
0.449
0.457
0.468
0.847
0.466
0.450
0.464
[.522
0.500
0.472
0.490
0.505
0.507
Aug.
0.395
0.414
0.405
0.420
0.407
0.419
0.418
0.421
0.418
0.432
0.413
0.431
0.415
0.426
0.458
0.450
0.423
0.430
0.440
0.460
0.204
0.274
0.336
0.770
0.34
0.789
0.351
0.35%
0.397
192
0,339
0.349
0.348
0.380
0.361
0.391
0.339
0.379
0.342
03385
0.402
0.414
0.388
0,418
0.429
336
0.322
0.384
0.357
0.406
0.364
0.39%
0.380
0.405
0.390
0.414
0.329
0.380
0.371
0.413
0.452
0.452
0.44%
0.465
0.49%
0.487
720
0.502
0.425
0.412
0.449
0.403
0.431
0.406
0.436
0.405
0.434
0.379
0.422
0.466
0.51
0.462
0:468
0.605
0.551
0,463
0.474
Avg.
0.3%
0.330
0.379
0.355
0.3%%
0.414
0.429
96
0.279
0,329
0.304
0.346
0.254
0.335
0.300
0.340
0.291
0.34
0.250
0.342
0.299
0.348
0.338
0.375
0.299
0.343
0.379
0,419
BTTa2 ETTmll
192
0.317
0.357
0.332
0.366
0.327
0.362
0.343
0.368
0.341
0.369
0,332
0.369
0.334
0.367
0,374
0.387
0.335
0.365
0.425
0.441
336
0.351
0,381
0,364
0.383
0.354
0.382
0,376
0.386
0.359
0.379
0.366
0.392
0.368
0.386
0.410
0.411
0.369
0.386
0.445
0.459
720
1140
0,415
0,402
0.431
0.415
0.419
0.416
0.420
0.417
0.414
0.47%
0.450
0.425
0.421
0.543
0.490
Avg.
0,340
0,371
0,351
0,376
0.344
0.573
0.363
0.378
0.356
0.377
0.351
0.381
0.355
0.379
0,400
0.405
0.357
0.379
0:448
0.452
96
0.172
0.200
0.160
0.250
0.174
0.202
0.163
0.249
0.162
01248
0.106
0.255
0.159
0.247
1.157
0.266
0.167
0.300
0.2005
0.287
193
0.227
0.504
0.250
0.214
0.2%6
0.324
0.328
336
0,772
0,277
0.70
0.325
0.281
0.537
0,273
0.327
0.380
0.330
0.274
0.329
0.369
0.322
0.321
0.351
0.2281
0.325
0.366
720
0.351
0.381
0,348
0.378
0.564
0.410
0.357
0.376
0.366
0.582
0,362
0.385
0.363
0.382
0,408
0.403
0.397
0.421
0.421
0.415
Avp.
0.256
0.317
0.248
0.111
0.267
0.527
0,254
0.311
0.361
0.316
0.255
0.315
0.251
0.309
0.201
0.333
0:7667
0.333
0.305
0.349
1613
1,89
0.507
1.319
0.754
2.255
2.317
2:215
3.225
1,260
36
1,290
0.745
1.316
0.750
1,853
0.854
1.833
0.833
1,430
0.854
2.121
0.980
1,972
0.920
1.963
0.903
2.679
1,080
48
1.499
0.810
1.548
0.818
1,886
0.855
2,269
1.012
1,553
0.815
2.187
1.007
2.238
0,940
2:130
1.021
2.622
1.078
1.428
0.773
1,50
1,470
0.788
2.185
2.368
1,096
1.157
Aug.
1.407
1,422
0.852
0.894
1,443
0.798
2.187
0.992
2.139
0.931
2.169
2.847
1.144
Truflic Weather Eleotriity
96
0.126
0.213
01142
0.445
0.127
0.217
0.141
0.239
0.137
0.233
0.129
0.222
0.128
0.223
0.168
0.272
0.140
0.237
0.193
0. 0.308
192
0.145
0,237
0.157
0. 0.660
0.148
0.237
0,158
0.253
0.152
0.247
0.157
0.240
0.144
0.237
0.184
0.289
0.153
0.249
0.201
0.315
0.267
0.160
0.254
0.196
0.214
0.329
720
0.197
0.286
0,214
0.308
0.199
0.293
0.207
0.293
0.200
0.290
0.197
0.290
0.198
0.287
0.220
0.320
0.203
0.301
0.246 0.365
Aug.
0.158
0.248
0.172
0.272
0.159
0,250
0,170
0.263
0. 166
0.259
0,162
0,253
0.158
0.250
0.193
0.295
0. 0.166
0.264
0,214
0.327
96
0,143
0,195
0.146
0.145
0.185
0.199
0.149
0.198
0.167
0:211
0.172
0.130
0.176
(123)
0.217
0,296
192
0,187
0,242
0.193
0.240
0.194
0.192
0.230
0.361
0.194
0.241
02112
0.258
0.219
0.261
0.220
0:276
0.336
336
0.237
0.273
0.245
0.281
0.243
0.275
0,246
0.273
0.251
0.279
0.245
0.282
0.260
0.293
0.280
0.305
0.265
0.319
0.339
0,380
720
0.362
0.315
0,312
0.332
0
0.325
0.320
0.328
0.345
0.342
0,314
0.334
0.328
0.329
0.365
0.359
0.333
0.362
0,403
0.428
Avg.
0.217
0.
0.255
0.270
0.226
0.264
0.242
0.278
0.259
0.249
0.360
96
0,344
0.257
0,393
0.290
0.346
0.232
0.396
0.264
0.392
0.267
0.360
0.349
0.397
0.378
0.503
0.321
0:410
0.287
0.587 0.366
192
0.363
0.219
0.405
0.296
0.376
0.245
0.412
0,268
0.409
0.271
0.379
0.256
0.411
0.283
0.617 0,336
0.423
0.287
0.504
0.373
336
0,387
0,256
0.120
0 10305000
0 0.389
0,252
0,421
0,273
0.434
0.296
0.392
0.264
0.424
0.289
0.629
0.356
0.436
0.296
0.621
0.383
0.432
0.256
0.450
0.640
0.626
0.382
Avg. 0.382
0.257
0.419
0.304
0.386
0.256
0.421
0.274
0.422
0.28
0.391
0.264
0.421
0.289
0.620
0.335
0.434
0.295
0.510
0.376
Wins
43
9
11
0
01
(a) MSE Ranking
(b) MAE Ranking
12 13 15 16
12
14
DHWN-A
Informer
DHNVAA
Informer
VisionTs
ETStormer
PatchTST
ETStormer
Timeshitt
GPT4TS
CALF
LiN
Diinsor
Figure 5: Critical difference (CD) diagram on the average rank of all 16 compared methods in terms of (a) MSE and (b) MAE over all benchmark datasets. The lower rank (left of the scale) is better.
4.2 Ablation Analysis
We validate the design of DMMV-A through ablation studies on four datasets; DMMV-S results are deferred to Appendix D.3 for brevity. Table 2 summarizes the analysis: (a) replaces the linear model in fmmm() with a PatchTTT-ssyyy Transformer (see $3.1); (b) swaps MAE with SiMMIM [45] as fvis fvss:); (c) replaces the gating fusion with a simple sum; (d) removes BCMASK, performing backcasting and forecasting on the full, unmasked look-back window; (e) substitutes BCMASK with random masking; (I) freezes the entire f-ix(-) instead of fine-tuning norm layers; and (g) removes the backcast-residual mechanism, feeding both fmum() (.) and (-) the same input x² and merging their outputs via gating.
Table 2 reveals key insights into DMMV-A'S 's design. In (a), replacing the linear numerical forecaster with a Transformer slightly degrades performance, likely due to the increased difficulty of jointly training Transformer with LVMs. In (b). MAE outperforms SiMMIM as fvi likely due to its ViT-based reconstruction decoder being better suited for pixel-level tasks like LTSF than SimMIM'S linear decoder, while both models share similar encoder architectures. In (c), gate-based fusion
7

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Table 2: Ablation analysis of DMMV-A. MSE and MAE averaged different prediction lengths.
Lower MSE and MAE are better. "Improvement" each ablation is relative to DMMV-A.
Dataset (-)
ETThl
ETTml
Illness
Weather
Method (Q)
Metrie (-+)
MSE
MAE
MSE
DMMV-A
0.395
0.414
0.340
0.371
1.407
0.771
0.217
0.256
Jun (-) Tranaformer
0.786
0.219
Improvement
-3.04%
-1.69%
+0.29%
-0.27%
-2.49%
-1.95%
-0.92%
-1.56%
(b) fii()) - SinMIM
0.407
0.415
0.345
0.377
1.649
0.814
0.227
0.261
Improvement
-3.04%
-0.24%
-1.47%
-1.62%
-17.20%
-5.58%
-4.61%
-1.95%
Gate Sum
0.414
0.427
0.352
0.383
1.606
0.863
0.233
0.278
Improvement
-481%
-3.14%
-3.53%
-3.23%
-14.14%
-11.93%
-7.37%
88.9%%
BUMASK-+ No mask
0.466
0.349
0.377
1.493
0.828
0.221
0.267
Improvement
-7.85%
-6.52%
-2.65%
-1.62%
-6.11%
-7.39%
-1.84%
-4. 4.30%
(c) BCMASK > Random mask
0.394
0,414
0.340
0.572
1.472
0.829
0,223
0.262
Improwment
0.25%
0.00%
0.00%
-0.27%
-4.62%
-7.52%
-2.76%
2.34%
(1) Freeze (+)())
0.431
0.428
0.358
0.380
1.442
0.773
0.246
0.288
Improvement
9.11%
-3.88%
5.29%
2.43%
2.49%
0.26%
13.36%
12.50%.
W/ decomposition
0,408
0.424
0,338
0.373
1.712
0.903
0.219
0,268
Improvement
-3.99%
-2.2%%
0.59%
0.54%
21.68%
17.12%
0.92%
4.69%
0.33
0.65
0.69
0.54
9.47
0.30
5.64
6.16
0.27
5.36
0.22
0.20
ETTh2
ETim1
ETTh2
ETTm2
weather
traffic
elactricity
illness
DMMV-A Visual
DMMV-A Numerical
DMMV-S Visual
DMMV-S Numerical
Figure 6: Comparing DMMV-S and DMMV-A w.t.. gate weights on visual and numerical forecasters.
outperforms simple summation, highlighting its adaptability to the distinct outputs of faum (.) and (-). (d) and (e) underscore the importance of BCMASK: removing it (i.e.. (d) "No mask") ") recovers the full look-back window as the backcasted seasonal component, diminishing the trend signal and weakening fnmm() (-), while "Random mask" (i.e., (e)) performs slightly worse due to poorer periodic pattern extraction, which leads to many fluctuations. In $4.3, we provide visual examples to compare these masking strategies. In (f), fine-tuning only the norm layers significantly improves performance over freezing, confirming the benefit of coordinated learning between forecasters, as described in $3.3. Finally, (g) shows that removing the backcast-residus mechanism causes major performance drop, affirming its role in effective decomposition. Overall, the LVM decoder, fusion strategy, masking method, training approach, and decomposition mechanism crucial to DMMV- A's success.
4.3 Performance Analysis
In this section, we perform in-depth analysis of DMMV using the same four datasets in $4.2.
The Difference between DMMV-S and DMMV-A. Fig. highlights DMMV-A's 's superiority over DMMV-S, largely due to its adaptive decomposition mechanism. A key advantage of the gate-based fusion is its interpretability. As shown in Fig. 6, which presents average gate weights across datasets, DMMV-A consistently places more weight on (vis while DMMV-S tends to balance both fnum (-) and (.) but leans toward f.)m()). In DMMV-A, A, these weights are learned based on forecasting performance, emphasizing [vis())'s importance. Notably, although fnum()) receives less weight, it remains essential - as evidenced by DMMV-A outperforming the visual-only bascline VisionTS in Table 1. In contrast, DMMV-S's weights are limited by its fixed moving-average decomposition, leading to a non-adaptive and suboptimal allocation of forecasting roles.
Fig. 7 provides example decompositions by DMMV-S and DMMV-A (additional cases in Appendix D.4). DMMV-A produces a smooth, clearly periodic component consistent with expectations, and trend component with some noises. In contrast, DMMV-S's moving- averrae yields smoother trend by absorbing fluctuations, pushing noise into the seasonal component. This makes forecasting harder for (.i)..). which is more sensitive to fluctuations than fnum (.), resulting in lower weights of (-) in Fig. 6. Since periodic patterns are crucial for long-term forecasting, as identified by [22, 21], the clearer period separation in DMMV-A leads to forecasts that better match the ground truth.
8

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Look-back window
Forecast (b) DMMV-S Seasonal
Ground truth
(a) DMMV-S Forecast
(c) DMMV-S Trend
6-00
6:90
0
2.7
212
/
204
95
152
200
384
-3.0
U97
304
(d) DMMV-A Forecast
(o) DMMV-A Seasonal
(f) DMMV-A Trend
6.50
-017
www.mmmmggg
-300
268
150
142
Figure 7: The decompositions of DMMV-S and DMMV-A on the same example in ETTh1: (a)(d) input time series and forecasts, (e) seasonal component, and (f)(f) trend component.
(a) Input Image
(b) Input Look-Back Window
(c) No Mask Image
fu (d) No Mask Backcast
200
288 226
(e) Rand. Mask Image
(f)
Mask Backcast
(g) Image
(h) BCMask
Tise
Figure 8: Comparison of different masking methods on the same example in ETTh1. (a) image of input look-back window; (g) are images of backcast output by DMMV-A: (c) uses "No mask"; (c) uses "Random mask"; (g) uses BCMASK. (b)()))((h) are their recovered time series, respectively.
PatchTST
DLinear
VisionTS
DMMV-A
(a) ETTh1
(b) ETTm1
[c) Weather
0.40
0.44
MAE
0.39
0.28
0.42
0:38
0.37
0.26
720
Context length
Context length
Context length
Figure 9: Average MAE comparison with varying look-back window (or context) lengths.
The Elfectiveness BCMASK. Fig. 8 compares the backeast results of DMMV-A using BCMASK, "No mask", and "Random mask" (as in Table 2) on a sample case; more examples are in Appendix D.5. BCMASK produces smooth image along the temporal (æ-axis) segments, effectively capturing clean periodic patterns. In contrast, "No mask" closely replicates the input, offering no meaningful decomposition. "Random mask" performs moderately well, resembling BCMASK but with less temporal smoothness, indicating less optimal decomposition.
Impact of Look-Back Window. Fig. 9 compares DMMV-A with visual forecaster (VisionTS) and two numerical forecasters (PatchTST, DLinear), which can serve as its single-view ablations. Illness dataset is excluded due its short time series (966 time steps). Using MAE metric (MSE results in Appendix D.6), we observe that DMMV-A and VisionTS benefit from longer look-back windows, while PatchTST and DLinear degrade beyond length of 336. Notably, DMMV-A outperforms VisionTS at length 1152, highlighting the advantage of explicitly modeling global trends.
5
Conclusion
This paper introduces DMMV, novel MMV framework that leverages LVMs and adaptive decomposi- tion to enhance LTSF. By addressing the inductive bias of LVMs toward periodicity through tailored backcast-residual decomposition, DMMV effectively integrates numerical and visual perspectives. Extensive experiments on benchmark datasets demonstrate that DMMV outperforms both single-view and SOTA multi-modal baselines, validating its effectiveness. This work highlights the potential of MMVs and LVMs in advancing LTSF, offering new direction for future research in this domain.

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[54] T. Zhou, Z. Ma, Q Wen, X. Wang, L. Sun, and R. Jin. Fedformer: Frequency enhanced decomposed transformer for long-ten term series forecasting. In ICML, 2022.
[55] T. Zhou, P. Niu, X. Wang. L. Sun, and R. Jin. One fits all: Power general time series analysis by pretrained LM. In NeurlPS, 2023.
[56] J. Zhuang, L. Yan, Z. Zhang, R. Wang, J. Zhang, and Y. Gu. See it, think it, sorted: Large multi- modal models are few-shot time series anomaly analyzers. arXiv preprint arXiv:4411.02465. 2024.
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A Limitation and Broader Impact
A.1 Discussion of Limitations
Adapting LVMs to LTSF is an emerging area of active research. This work serves pioncering effort in investigating LVMs within an MMV framework for LTSF, As an initial exploration, we acknowledge some limitations in this work. First, one limitation of the current best LVM forecaster (e.g., VisionTS) is its sensitivity to segment length used in image construction due to its inductive bias, as discussed in 33 (Fig. 3). By incorporating an additional numerical view for modeling the global trend, the proposed DMMV is expected to alleviate this sensitivity. In our further analysis in Appendix D.2, we observe DMMV-A is less sensitive to the change of segment lengths than VisionTS on some datasets, but cannot consistently enhance the robustness over different datasets, despite the improved overall forecasting performance. This may be caused by the higher weights automatically allocated to (-i than Foom (-) by the gate fusion mechanism (Fig. 6), which could make the model prone to inherit the behavior of the LVM used in fvis(-) to some extent, including its sensitivity to segment length, but with a less extent than a sole LVM. As such, a future work to improve DMMV is to reduce such sensitivity to an unnoticeable effect. Second, under our proposed BCMASK strategy, the vision backbone in (-i is reused three times during training and inference once for forecasting and twice for reconstructing different masked parts of the bock window. The triple use of (vis(-) could lead to non-trivial computational overhead. In this work, considering the remarkable performance improvement of B BCMASK over other masking strategies (Table 2) and its possibly minimum use of f.is()), as analyzed in 53.2, we take it the current solution. However, as a future work, we expect to further reduce the use of (-i and improve the efficiency, by methods such as joint backcasting and forecasting within a single forward pass or amortizing the use of LVMs across multiple time series samples. Finally, the proposed method shares a similar limitation of the existing LVM forecasters. The imaging process transforms an input time series into 2D image-like representation to fit pre-trained LVMs, which typically expect a high-resolution input of size such as 224 x 224 x 3. Therefore, upsampling is performed on a smaller image obtained from the patched time series to fit the input requirements of LVMs. While critical to compatibility, resizing may introduce subtle changes that may distort the original temporal structures to some extent. Thus an imaging process that can reflect the temporal patterns more accurately is in demand in future works.
A.2 Broader Impact
LTSF plays a vital role across various domains, including geoscience [1], neuroscience [3], energy [18). healthcare [28], and smart city [27]. This work proposes a novel MMV framework DMMV that integrates LVMs and a numerical forecaster, which could serve as a groundwork in the emerging area of LVM-based time series analysis and shed some lights on broader arcas that integrate LLMs, VLMs, and large multi-modal models (LMMs) for future research on multi-modal and agentic time series analysis. This work does not involve sensitive data, legal risks, ethical concerns. To the best of our knowledge, it does not adversely affect any specific population. The proposed method could serve a general-purpose time series forecasting technique with relatively broad applicability and social acceptability.
B Benchmark and Baseline
B.1 Benchmark Datasets
Following [53, 44, 30, 49, 36, 4], our experiments are conducted on 8 widely used LTSF benchmark datasets that cover a wide range of sampling frequencies, number of variates, levels of periodicity, and real-world domains. The four ETT datasets (ETTh1, ETTh2, ETTm1, ETTm2) record oil temperature from two electric transformers, sampled at 15-minute and hourly intervals. The Weather dataset collects measurements of meteorological indicators in Germany every 10 minutes. The Illness dataset keeps weekly counts of patients and the influenza-like illness ratio from the United States. The Traffic dataset measures hourly road occupancy rates from sensors on San Francisco freeways. The Electricity dataset records hourly electricity consumption of Portuguese clients. Table summarizes the statistics of the datasets.
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Table 3: Statistics of the benchmark datasets.
"Dataset Size" is organized in (Train, Validation, Test).
Dataset
# Variates
Series Length
Dataset Size
Frequency
ETTh1
7
17420
(8545, 2881, 2881)
Hourly
ETTh2
17420
(8545, 2881, 2881)
Hourly
ETTml
7
69680
(34465, 11521, 11521)
15 mins
ETTm2
69680
(34465, 11521, 11521)
15 mins
Weather
321
52696
(36792, 5271, 10540)
10 mins
Illness
7
966
(617, 74, 170) (12185, 1757, 3509)
Weekly
Traffic
862
17544
Hourly
Electricity
21
26304
(18317, 2633, 5261)
Hourly
B.2 Baselines
In the following, we provide a brief description for each baseline method involved in our experiments.
Time-Vil VLM [52] integrates time series data with visual views and contextual texts using pre-trained VLM, ViLT, to enhance forecasting performance.
VisionTS [4] reformulates time series forecasting as an image reconstruction problem using LVM, MAE, for zero/few/full-she forecasting.
Time-LLM [15] reprograms LLMs by aligning time series patches with text tokens, enabling time series forecasting without re-training LLMs.
GPT4TS [55] demonstrates that frozen pretrained LLMs, e.g., GPT, can be directly applied to a variety of time series tasks with strong performance.
CALF [24] adapts LLMs time series forecasting via cross-modal fine-tuning, bridging the distribution gap between textual and temporal data.
CycleNet [21] enhances LTSF by explicitly modeling the periodic patterns in time series through residual cycle forecasting technique.
PatchTST [30] introduces patching strategy and a Bhannel-independeee strategy for LTSF. uses patches time series the imput to Transformer to capture the temporal dependency of semantically meaningful tokens (i.e., patches).
TimesNet [43] transforms an input time series into a 2D image-like representation and models temporal variations in the image using inception-like blocks for time series analysis.
DLinear [49] decomposes input time series into trend and seasonal components, each of which modeled by linear layers for time series forecasting.
FEDfornod [54] incorporates firqueency-eni enhanceed attention mechanisms by combining
Fourier transforms with seasonal-tres -trnn decomposition in Transf ormer framework.
Autoformer [44] introduces an auto-correlation mechanism within Transformes archi- tecture to capture long-term dependencies in time series data.
Stationary [25] combines series stationarization and de-stationary attention mechanisms to solve the over-stationarization problem in time series forecasting.
ETSformer [42] decomposes an input time series into interpretable components with expo-
nential smoothing attention and frequency attention for time series forecasting.
Informer [53] proposes ProbSparse self-attention mechanism to reduce the computational complexity of LTSF with Transformer models.
C Implementation Details
C.1 Pre-trained LVM Checkpoints
As described in 83.3, fvi(-)) uses pre-trained LVMs. For MAE, we use the checkpoint released by Meta Research which was pretrained on 224 x 224 x 3 sized images from ImageNet-IK [5] with
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Stage 1 (Numerical forecaster training). In this stage, we freeze all parameters of fvis (-) and train frum (-) only. This warm-up step prevents (-) from updating with unstable gradients caused by the random representations from the under-trained fmmm()). this stage, Algorithm 1: The Training Algorithm of DMMV-A
Input: training dataset Dunin (X,, YiJis where X, E RXT is an MTS, Y, E DRD the ground truth of forecast Output: model parameters of DMMV-A
Load pre-trained (-is(-) and freeze its weights Randomly initialize [num() and the gating parameter g
/* stage 1: numerical forecaster training
3 for i &- to MaxEppoch do for (X, Y) in Dataloader(PPaii do
/* channel iiweell-dddeeedence strategy is applied in the following */
Xycasun; Y Yeeson fvis BCMASK) // backcast/forecast seasonal part // extract trend component // forecast trend with fnm(+) gate fusion // cal calaul MSE loss as specified in $3.3
Xtrend f- X Xxcaasn
Y Treend 4- Smmm! (Xerend)
Y 1-g0 9o Y Ysessn + (1 g) o Y trend
Calculate (MSE YY
10
Update model parameters of fmmm and g if Early stopping condition is TRUE then Break
11
12
13
end
14
end
15 end
/* stage 2: joint training */
Unfreeze the norm layers in f-ia())
17 for i 4- to MaxEpoch
for (X, Y) in Dataloader((naan)) do
/* Repeat lines 5-9 */
Update model parameters of f (-), norm layers in fvis(), and parameter g Early stopping condition is TRUE then
20
Break
22
end
23
end
end
ViT-Base Backbone. For SiMMIM, we adopt the checkpoint released by Microsoft', which has the same pretraining setting aforementioned for MAE. For these two LVM backbones, the base versions are adopted to balance the performance and computational costs.
C.2 Training Details
For training the proposed DMMV-S and DMMV-A models, we adopt Adam W optimizer throughout the experiments. The batch size is set to 64 for the ETT datasets and Illness dataset, and 8 for the other three datasets to balance training stability and memory consumption.
For both DMMV-S and DMMV-A, propose two-stage training scheme to facilitate effective integration of numerical and visual features:
learning rate is set to 0.01. The training runs up to maximum of 50 epochs the training set. Early stopping is applied with patience of 10 epochs.
httpp://githhbb http://ghh....ooo///coooott/////
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Stage 2 (Joint training). In this stage, we unfreeze the layer normalization parameter in (-) and jointly train them with (-mm() to enable deep fusion of visual and numerical views. The learning rate is reduced to 0.005 to preserve learned features and stabilize training. The training at this stage runs up to epochs. Early stopping applied with patience of 2 epochs.
The detailed training algorithm of DMMV-A is summarized in Algorithm 1.
C.3 Running Environment
The experiments are conducted on a Linux server (kernel 5.15.0-139) with 8x NVIDIA RTX 6000 Ada GPUs (48 GB each). The environment uses Python 3.12.8, PyTorch 2.5.1 with CUDA 12.4 and cuDNN 9.1. The key libraries include NumPy 2.1.3, Pandas 2.2.3, Matplotlib 3.10.0, SciPy 1.15.1, scikit-leam 1.6.1, and torchvision 0.20.1
D More Experimental Results
D.1 Comparison with All Baselines
Table 4 provides the full results of comparing DMMV-A and DMMV-S with all of the 14 baseline methods, which complements Table 1 in the paper. In Table 4, Time-Viii VLM's results on Illness dataset marked by "_" since its paper doesn't report the results and its code is not publicly available the time of this experiment. CycleNet's 's paper doesn't 't report its results on Illness dataset, so we run its code and reproduce its results on Illness dataset in Table 4.
From Table 4, we can observe that DMMV-A maintains a clear advantage when compared against all of the baseline methods. It achieves 41 first-place results, significantly surpassing the second- best method. Additionally, taking closer look at all compared methods, MMV-based methods LVM-based methods, and decomposition- based methods demonstrate superiority over other baseline methods. This suggests the synergy of MMV framework, LVMs, and decomposition strategy, which explored by the proposed DMMV model.
D.2 Further Analysis of The Inductive Bias
A contribution of our work lies in the in-depth analysis of an inductive bias of the current best LVM forecasters. In $3, we have discussed the impact of the alignment of the segment length and the period of time series on model performance. We find that the L.M exhibits a strong inter-period consistency when applied to synthetic data. The function of the synthetic time series is xtt) = A(t) sin ( (2st) where the period is set 24 and the amplitude function A(t) decreases linearly over time. The forecasts are more accurate when the segment length is multiple of the period (e.g.. 24, 48) than other values. This section provides detailed quantitative results on the synthetic data Table From Table 5, the fluctuations in MSES and MAEs across different segment lengths other than 24 and 48 support the findings of the inductive bias toward "forecasting periods".
In addition, we evaluate the performance of the proposed method DMMV-A and VisionTS w.r.f. varying segment lengths to compare their robustness to the change of segment length. Fig. 10 summarizes the results in terms of MSE on four benchmark datsets, where the segment length varies from P to GP and P period of the input time series. From Fig. 10, we have several observations. First, DMMV-A consistently outperforms VisionTS, validating the effectiveness of the proposed MMV framework. Second, in contrast to VisionTS, DMMV-A exhibits better robustness to the change of segment length on ETTh1 and Weather datasets, but has similar sensitivity to the change of segment length as VisionTS on ETTml and Illness datasets. This implies that by incorporating fmmm (-), DMMV-A A can alleviate f-is())ss sensitivity to the inductive bias to some extent. However, the current DMMV-A A does not fully mitigate this limitation, suggesting a future work for method development as discussed in Appendix A.
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Table 4: Full LTSF performance of the compared methods on the benchmark datasets, Lower MSE and MAE indicate better performance The best performance is highlighted in red. Time VLM results on the Illness dataset are unavailable in [52]. Its code was not publicly available at the time of this experiment. As such, its results on Illness dataset are marked by "_"
0.200
0.000
0.900
0.795
1.515
1961
1885
1.75
0,57
0.000
0.871
0
0.734
0.10
3.077
1:965
1.48
154
0.94
0.36
0.5M
0.430
0.355
0.354
0.54
0.44
0.80
0.370
0.425
0.471
0.416
Labonner
1.000
1.181
1.040
3755
560
4:21
360
4411
007
0.39
1,212
1.166
(1961
1.58
5379
1.40
5.704
4755
4708
520
51
0.2%
0
0.5
0353
0,511
030
6506
0528
0730
0.606
0.737
0164
01704
0.55
01521
055
0.500
0.39
0-000
0.99
440
0.288
1.45
1448
1420
100
6972
1806
1998
0.9
0250
03355
032
0.29
0300
655
0.5
0:50
0.30
0.390
0.29
MSE
0.550
0.574
0.50
0,54
0.34
0430
0488
0.09
055
0
0455
000
042
0100
025
9474
0250
235
265
230
240
2409
0100
0.10
025
0.35
0.0
0449
0200
990
020
0/00
0621
0622
060
0.5M
0.535
064
0.557
0.48
0.68
855
055
0.50
0.
0.60
620
1941
030
620
099
690
022
0.2
630
0.30
0.2%
0.233
025
055
0.3
0.308
0.55
0.550
0.585
0/64
0.570
0.466
01512
0552
0.562
0.535
80
0,00
0.005
955
03
000
2.50
185
2000
2175
0.02
888
0.222
0.295
0.73
110
8:32
1:38
0.633
0.585
PAS
0.40
0
0,512
0,477
0.388
0/522
0.00
0.000
0.455
0.006
0.55
9:0
0.52
630
0320
020
033
1.5
11
1899
12
10
025
0.6
0.33
0.38
030
6500
0.00
0.000
0,502
0.537
0:408
0.59
0.53
0.14
0495
0336
0455
066
051
050
855
262
0.59
425
250
922
3483
130
226
277
020
0225
9559
055
922
0556
280
055
000
0856
0989
0625
PhaMoone
0,465
0.50
0460
0.597
0.59
0:69
0424
0.40
0
0559
000
0.40
620
622
0359
1.500
1000
1028
13
1.44
0.0
035
035
0327
9229
0338
0300
0.00
0.000
0332
03355
0.5%
0420
0,49
0506
0440
0558
0429
0496
846
0437
055
0426
245
950
942
420
040
3528
289
220
235
410
950
052
3226
022
920
926
055
380
0102
94090
MAE
0.416
02000
0:30
035
0188
026
055
035
450
136
682
050
120
652
142
030
100
096
1124
140
166
655
850
152
680
834
023
126
080
150
155
033
122
10
1336
0.455
0.39
0422
0425
0250
0355
0468
0431
025
055
039
982
9237
922
032
930
2215
1948
23
239
2100
010
015
000
0308
01%
01
920
926
950
04
0223
0436
0.42
11000
8500
0-550
0.574
032
0.27
0555
880
641
120
1206
126
133
145
125
0004
050
000
122
850
150
0300
035
020
122
150
150
152
R33
0350
Tine
0.4%
0.801
051
0458
0.3
0.82
040
0.33
0.5%
052
9200
940
930
846
039
23
197
2228
200
2550
0.6
038
0220
839
017
920
850
650
050
0989
0.536
0.000
0.431
0.3%
0329
01200
0422
0.54
0:000
070
6:300
032
0:3
472
085
000
8:288
0.298
0.22
025
0.200
0.25
01196
920
0200
02
02200
0.256
0:00
61296
PALN
0443
0442
0440
0413
0224
0131
6379
6000
0.50
011
0305
040
0:51
4.45
022
635
025
13
14
155
147
144
015
015
010
8.99
0100
0140
024
625
0.000
033
0.500
64
0397
MAE
0.430
0.504
0-26
0.41
033
0413
0.5
0508
0507
035
051
055
424
0.2
130
R50
10F
690
180
290
990
025
635
055
038
025
022
1228
820
125
N22
023
12W
0220
CycleNe
0.61
0.05
0,15
0.79
03342
0-06
0.29
0.14
0.368
0407
0.355
830
02
225
212
238
2N
2.87
880
010
935
9.00
0142
0.44
0.50
0:11
0.024
0-90
0-421
0:436
0.400)
0.956
0:31
0,56
0.37
0.28
0.44
0.50
0326
0001
085R
0:91
625
051
030
055
0.70
0857
0290
220
0989
020
622
0280
0300
0300
620
030
050
652
022
023
0200
(N
0236
CALF
6.45
0.41
0.216
0452
0.24
0.35
0.91
0456
0.3
0.2
055
2411
076
9.596
412
0.62
950
1.500
575
1224
146
100
015
0255
0176
910
920
650
2250
075
MAF
0.511
0.400
0.421
0.35
0338
040
0:30
3:50
335
1100
0:
820
022
651
0.23
885
8288
8967
0.2
022
025
0506
0.50
0250
8488
R22
0200
6:000
055
FWW
GP1418
0.42
0.445
0.441
0.15
0.00
0.44
0406
0.54
0,505
0341
033
040
0.50
035
035
0254
1.00
1851
155
1577
157
014
0158
012
0307
0350
0148
010
655
0.9%
0312
0301
045
0421
Tiine LLM
MAE
0.438
0.28
0432
0.36
039
0114
0.50
030
150
055
155
8577
624
050
832
080
100
1925
080
025
034
450
020
025
015
920
650
6207
022
026
020
0251
0.600
0:457
0.48
0.256
033
0380
0425
035
8:31
335
0:055
9:386
610
1200
0.38
6:3
1.5
135
2300
2177
200
010
015
0100
0.300
0105
8155
922
0:52
0.000
0.054
0-551
6442
0.40
0.400
0.49
6,34
0.38
0.00
0.302
0.000
0382
0.533
840
0.27
055
8.34
081
030
0:29
0:317
0.25
0200
0.220
6.39
9.50
8:245
0:00
6.356
0.395
0.419
0.558
0.40
0.28
0.389
0.94
0.23
0.35
0.384
0327
0331
0:34
0.3
0.37
100
13166
1:54
1250
1.40
0.32
016
0.09
0.15
0.44
934
655
0.50
0.336
0.99
Time VLM
0.608
0.421
0.555
0373
866
0440
0.50
0.000
0353
4:00
933
820
920
0.555
0226
0.58
0272
9.20
828
0200
0.39
0305
095
0,430
0.441
0.405
0.267
0.33
0367
0.34
0.304
035
0362
0:00
0339
110
650
622
0.00
0354
0214
0372
0148
0100
620
620
0.00
0900
033
041
MAE:
0.430
0415
0.20
0426
0.500
0555
0.5%
0462
0.99
0300
0530
0398
0.52
035
0
0338
0355
9655
961
0.577
02%
056
0344
02%
0218
022
830
954
035
025
0200
0008
0.588
(1:58)
0.399
0.300
0:572
01:455
01288
0.300
333
1.296
0.322
0.309
1:34
150
163
173
PAC
1-122
15500
015
122
19
1220
0.385
0:30M
0:433
0.55
0.444
0.340
0.395
0.34
0.585
0.339
6,37
0.36
0415
6.37
0.5
0351
0.17
0:25
6745
6
9.75
4.71
4
0.37
0.24
6.5
0.248
0.95
0242
0.7%
0
0249
0.25
6:39
0:257
0.387
0.455
0.395
0.204
0.300
01222
0.992
0.39
0.279
0.377
0.351
0
8:34
0226
1.09
1-200
1-499
1-228
1.417
01:5
0162
01558
8.44
8387
R-237
0:364
03363
0.387
0.302
Model
102
336
230
96
192
516
720
AVE
AVE
A-E
236
730
96
192
216
ME
1
24

---

Table 5: Forecasting performance of an LVM w.t.t varying segment length on synthetic dataset. The function of the synthetic time series is xtt) A(t)- sin ( where the period P 24 and the amplitude function A(I) decreases linearly over time.
Segment Length
16
20
24
28
32
36
40
44
48
MSE
0.043
0.099
0.001
0.147
0.154
0.143
0.221
0.114
0.002
MAE
0.177
0.257
0.024
0.342
0.347
0.315
0.408
0.289
0.045
VisionTS
DMMV
ETTh1
ET1m1
Weather
llleess
0.23
MSE
0.38
1.80
0.36
0.23
1.50
Z/5P USP
3/P
4/5P
0.54
255
4/5p Segment Length
3MP
Li5e 2/5 2/5p
1.40
1/5
2/6P
S/5p
488 Sist
S/SP
Segment Length
Segment Length
Segment Length
Figure 10: MSE Performance of DMMV-A and VisionTS w.E.t varying segment length that is used in image construction. The r-axis indicates the segment length varies from 6 period to
6 period.
D.3 Ablation Study
In Table 2 (64.2). we provide ablation analyses for DMMV-A. Table 6 provides the ablation analysis for DMMV-S, where MSE and MAE are averaged over different prediction lengths. In addition, Tables 7 (Table 8) includes the full results for Table 2 (Table 6) with all prediction lengths.
In Table 6, from (a), replacing the linear numerical forecaster with PatchTST can slightly improve the performance of DMMV-S, likely because DMMV-S relies more on the predictions from the numerical view than visual view (Fig. 6). Therefore, in this case, increasing the complexity of the numerical model can improve the ability of fnum(-) and finally improve the overall performance. From (b), replacing MAE with SimMiM reduces the overall performance, this is the same as the findings in Table 2 for DMMV-A. From (c), bate-based fusion outperforms simple summation for DMMV-S, highlighting the effectiveness of gate fusion. From (d), fine-tuning the norm layers of fvis()) improves the performance for DMMV-S, suggesting the used fine-tuning strategy.
Table 6: Ablation analysis of DMMV-S. MSE and MAE are averaged over different prediction lengths. Lower MSE and MAE are better. "Improvement" of each ablation is relative to DMMV-S.
Dataset (-))
ETThl
ETTml
Illness
Weather
Method (3), (-tric(++)
MSB
MAE
MSE
DMMV-S
0.405
0.426
0.349
0.382
1.520
0.813
0.244
0.281
(-) TransCorner
0.402
0.423
0,342
0.376
1.544
0.841
0.229
0.264
Improvement
0.745
0.47%
2.01%
1.31%
-165%
-3.4%
6.15%
6.41%
(b) [ea(-] ] - SimNIH
0,415
0.423
0.355
0.382
1.810
0.875
0.233
0.272
Improvement
2.47%
0.47%
1,72%
0.00%
19.16%
7.633%
4.92%
3.20%
(c) Gate - Sum
0.419
0.435
0,355
0.379
1.453
0.790
0.256
0.297
Improvement
.3.46%
-2.24%
2.011%
0.52%
2.95%
-4.11%
Freeze fex(-)
0.436
0.442
0.368
0.386
2.125
0.969
0.251
0,288
Improvement
-7.4%%
-3.76%
-5.75%
-1.05%
-39.83%
-19.07%
-2.46%
-2.14%
D.4 Additional Visualizations on Decomposition
Fig. 11 and Fig. 12 several more examples the decomposed time series of DMMV-S and DMMV-A. Fig. 11 illustrates a case where the series has localized periodic anomaly at time step around 192, which poses challenge for detecting periodic patterns. In this case, DMMV-A effectively suppresses the influence of the anomaly and extracts clear periodic pattern from the time series series. In contrast, DMMV-S affected by the anomaly and fails to capture a smooth periodic pattern. Fig. 12 is an example with weak periodicity, where the periodic signal is either faint or overwhelmed by trend. In this case, DMMV-A is able to extract and utilize the underlying periodicity to produce reasonable forecasts, which is better than DMMV-S, suggesting the importance of the
25

---

Table 7: Full results of the ablation analysis of DMMV-A. Lower MSE and MAE are better. The Illness dataset uses prediction lengths of (24, 36, 48, 60) due its short time series (in total 966 time steps), which is different from the prediction lengths of other datasets.
Dataset -+)
ETTh
ETTml
Illness
Weather
MLthod(L), Metric(-))
Length
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
0.354
0.389
0.279
0.329
1.409
0.754
0.143
0.195
192
0.393
0.405
0.317
0.357
1.290
0.745
0.187
0,242
A
336
0.387
0.413
0.351
0.381
1.499
0.810
0.237
0.273
720
0,445
0,450
0.411
0.415
1.428
0.773
0.302
0.315
Avg.
0.395
0.414
0.340
0.371
1.407
0.771
0.217
0,256
96
0.357
0.389
0.279
0.329
1.604
0.823
0.145
0.193
192
0.407
0.318
0.359
1,250
0.742
0.187
0.239
(a) (-un()) Transformer
336
0.389
0.411
0.352
0.382
1.555
0.803
0.241
0.283
720
0.474
D.462
0.407
0.416
1.359
0.774
0.301
0,326
Avg.
0.407
0.421
0.339
0.372
1,442
0.786
0.219
0.260
0.301
1.729
0.832
0.145
0.194
192
0,405
0.41
0.325
0,363
1.643
0.734
0.192
0.242
(b) fra (-) - SinMiM
336
0.412
D.414
0.354
0.383
1.689
0.845
0.241
0.275
720
0.453
0.452
0.398
0.412
1.534
0.845
0.328
0.332
Avg.
0.407
0.415
0.345
0.377
1.649
0.814
0.227
0,261
96
0,373
0.400
0.286
0,339
1.728
0.845
0.156
0.214
192
U.414
D.424
0.329
0.369
1.423
0.795
0.214
0,261
Gate Sum
336
0.411
0.422
0.364
0,392
1.693
0.920
0.258
0.302
720
0.457
0.461
0.427
0.430
1,580
0.890
0.315
0.335
Avg.
0.414
0.427
0.352
0.383
1.606
0.863
0.233
0.278
96
0.384
0.402
0.288
0.342
1.628
0.840
0.145
0.198
192
0.413
0.440
0.325
0,363
1.325
0.796
0.191
0.244
(d)RCMASK > No mask
336
0.434
0.448
0.361
0.384
1.606
0.865
0.241
0,285
720
0.474
0.473
0.421
0.419
1.414
0.811
0.308
0.340
Avg.
0.426
0.441
0.349
0.377
1.493
0.828
0.221
0,267
96
0.348
0.384
0.279
0.329
1.618
0.859
0.146
0.197
192
0.388
0.405
0.318
0.360
1.318
0.798
0.189
0,240
BCMCM Random mask
336
0.383
0.404
0.350
0,381
1,560
0.858
0.243
0.282
720
0.458
0.462
0.414
0.418
1.392
0.800
0.312
0,328
Arg.
1.472
0.829
0.223
0.262
96
0.389
0.402
0.293
0.342
1.482
0.761
0.161
0,224
192
0.434
0.425
0.335
0,367
1,218
0.694
0.203
0.287
(f) Freeze (-)
336
0.431
0.428
0.372
0,389
1.58
0.82
0.285
0,302
0.468
0.431
0.422
1.489
0.815
0.335
0.338
Avg.
0.431
0.428
0.358
0,380
1,442
0.773
0.246
0,288
96
0.352
0.387
0.274
0.329
1.728
0.938
0.143
0.195
192
0.402
0.414
0.315
0.358
1.841
0.940
0.7
0,242
(g) decomposition
336
0.347
0.382
1.672
0.886
0.237
0.284
720
0.487
0.486
0.417
0.422
1.606
0.846
0.309
0.350
Avg.
0.408
0.424
0.338
0.373
1.712
0.903
0.219
0,268
proposed adaptive decomposition method. In summary, the results demonstrate that DMMV-A has strong modeling anomalous weakly periodic time series, validating its reliability and applicability across broad range of scenarios.
ability temporal structures and robustness to fluctuations even when dealing with
of
D.5
Additional Visualizations on Masking Strategies
Fig. 13 and Fig. 14 present additional examples of BCMASK in DMMV-A. Similar to $4.3, Fig. 13 and Fig. 14 compare different masking methods. From both figures, observe that BCMASK produces smooth patterns along the temporal (x-axis) dimension, effectively capturing periodic structures. Notably, when the input time series contains anomaly (e.g., Fig. 13, time steps 288-336), BCMASK can effectively extract the periodic patterns.
D.6 Impact of Look-Back Window
Fig. 15 provides the MSE results that compare DMMV-A with the other three models. Fig. 15 demonstrate similar trend as that of the MAE results in Fig. 9.
26

---

Table 8: Full results of the ablation analysis of DMMV-S. Lower MSE and MAE are better. The Illness dataset uses prediction lengths of (24, 36, 48, 60) due its short time series (in total 966 time steps), which is different from the prediction lengths of other datasets.
Dataset( ) Method U) Metrie(->)
Ilnsss
Weather
Length
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
0.350
0.388
0.296
0.349
1,688
0.838
0.168
0.218
192
0.399
0.420
0,328
0.370
1.323
0.753
0.220
0.259
DMMV-S
336
0.399
0.415
0.369
0.393
1.644
0.267
720
0.472
0.479
0.401
0.414
1.473
0.810
0.322
0.343
Avg.
0.405
0.426
0.349
0.382
1.520
0.813
0.244
0.281
96
0.352
0,387
0,286
0.339
1613
0.829
0.148
0.194
0.401
0.420
0.325
0.364
1.417
(2) (am(() + Transformer
336
0.395
0.415
0.354
0.387
1.610
0.853
0,246
0.280
720
0.460
0.471
0.401
0.414
1.536
0.858
0.330
0.341
Avg.
0,402
0.423
0.342
0.376
1.544
0.841
0.229
0.264
0.366
0.391
0.323
0.360
1,933
0.153
192
0.412
0.420
0.331
0.364
1.812
0.863
0.194
0.248
(b) fi(()) - SimMiN
336
0.419
0.420
0,361
0,386
1.793
0.854
0.245
0.279
720
0.464
0.461
0.404
0.416
1.712
0,883
0.339
0.352
Avg.
0.415
0.423
0.355
0.382
1.810
0.875
0.233
0.272
%
0.356
0.389
0,300
0.346
1,503
0.763
0,183
0.234
192
0.403
0.417
0,334
0.365
1,350
0.746
0.236
0.277
(c) Gale - Sun
336
0.414
0.426
0.362
0.385
1.530
0,820
0.271
0.308
720
0.504
0.506
0.424
0.420
1.429
0.830
0.333
0.369
Avg.
0.419
0.435
0.355
0.379
1,453
0.790
0,256
0.297
96
0.386
0,404
0,306
0,352
1,966
0.921
0.156
0.225
192
0.436
0.434
0.347
0.375
2,050
0.945
0,240
0.261
(d) Freeze f-i(()
336
0.436
0,440
0.377
0.392
2.223
0.999
0.271
0.312
720
0,484
0,488
0.443
0.424
2.259
1,009
0.335
0.353
Avg.
0.436
0.442
0,368
0.386
2.125
0.969
0.251
0.288
Look-back window
---- Forecast
Ground Iruth
(a) DMMV-S Forecast
(b) DMMV-S Seasonal
(c) DMMV-S Trend
5.00
M
-0.02
Time Stepe
Tave Steps
Steps
DMMV-A Forecast
(e) DMMV-A Seasonal
(f) DMMV-A Trend
3.00
M
-..m
192
Figure 11: The decompositions of DMMV-S and DMMV-A on the same example in ETTh1: (a)(d) input time series and forecasts, (b)(e) seasonal component, and (c)(f) trend component.
Look-back window
Forecast
Ground truth
(a) DMMV-S Forecast
(b) DMMV-S Seasonal
(c) DMMV-S Trend
6C0
2,000
2,003
0333
-1.800
-1333
-3 000
5,000
192
TIME
Three Steee
Stees
(d) DMMV-A Forecast
(e) DMMV-A Seasonal
(f) DMMV-A Trend
2000
0.33
-1553
-1300
Dagss
3000
152 Stezs
Stepo
Figure 12: The decompositions of DMMV-S and DMMV-A on the same example in ETTh2: (a) input time series and forecasts, (b)(c) seasonal component, and (f)(f) trend component.
D.7 Standard Deviations
To assess the uncertainty and stability of the forecasting performance, we report the standard devi- ations of DMMV-S and DMMV-A on the four benchmark datasets used in 64.2 and 54.3 in Table From Table 9, the relative standard deviations of the proposed models, which are calculated as
27

---

Input Image
(b) Input Look-Back Window
(c) No Mask Image
(d) No Mask Backcast
Rand. Mask Image
(f) Rand.
(g) BCMask Image
(h)
Time Seng
Time 546
Figure 13: Comparison of different masking methods the same example in ETThI. (a) image of input look-back window; (g) are images of backcast output by DMMV-A: (c) uses "No mask"; (e) uses "Random mask"; (g) uses BCMASK. (f)())(f((h) their recovered time series, respectively.
(a) Input Image
(b) Input Look-Back Window
(c) No Mask Image
(d) No Mask Backcast
w
M
(e) Rand. Mask Image
(i) Rand. Mask Backcast
(g) MCMask Image
(h) Mask Backcast
VVVVVV
Figure 14: Comparison of different masking methods on the same example in ETTh2. (a) image of input look-back window; (g) are images of backcast output by DMMV-A: (c) uses "No mask"; (e) uses "Random mask"; ; (g) uses BCMASK. (b)())(((() are their recovered time series, respectively.
PatchTST
DLincar
VisionTS
DMMV A
(a) ETTh1
(b) ETTml
[c] Weather
0.40
0.26
MSG
0.38
0.36
0.23
0.34
0.22
96
192
336
720
1152
96
152
336
720
1352
96
352
336
720
1152
Context length
Context length
Context length
Figure 15: Average MSE comparison with varying look-back window (or context) lengths.
Table 9: Standard Deviations of DMMV-S and DMMV-A in terms of MSE and MAE on four LTSF benchmark datasets.
Model
DMMV-A
DMMV
Metrie
MSE
MAE
MSE
MAE
96
0.354::
0.001
0.390= 0.001
0.350 + 0.001
0.388 + 0.002
0.393 0.001
0.405=
0.001
0.420
0.001
336
0.3874
0.001
0.413- 0.001
0.401 + 0.002
0.415 + 0.001
720
0.447:
0.002
0.411 0.001
0.472 = 0.001
0.480 + 0.002
ETTml
0,278:1
0.001
0.329 0.000
0.296
0.001
0.348 1 0.002
192
0.3174
0.001
0.358
0.001
0.328
0.001
0.368 + 0.002
336
0.3514
0.001
0.381 0.000
0.367
0.002
0,393 + 0.002
720
0.411: 0.000
0.415 0.000
0.002 0.401
0.415 1 0.003
Illness
24
1,409# 0.001
0.754=
0.001
1.638 0.003
0,842 + 0.005
36
1.291 0.002
0.742- 0.003
1.329 0.012
0.751 + 0.002
48
1.4991 0.002
0.810= 0.011
1.643 0.002
0,853 1 0.005
60
0.003 1,430+
0.774 0.001
1.473 0.002
0.810
0.002
Weather
96
0.1433
0.001
0.196 0.002
0.168
0.001
0.218 + 0.002
192
0,1874
0.001
0.245= 0.003
0.221 0.002
0.259 + 0.002
336
0.237+
0.001
0.272 0.003
0.267 0.002
0.305 + 0.001
720
0.300
0.002
0.318= 0.003
0.323 0.001
0.341 0.003
the ratio between standard deviation and mean, are all below 1.30% across different datasets and evaluation metries, demonstrating their stability and robustness over different runs.
28


Reviews:
[{"review_id": "loHWKAoF7q", "reviewer": "Reviewer_SJEM", "summary": "This paper presents DMMV, a novel framework for multi-modal long-term time series forecasting (LTSF) that integrates latent variable models (LVMs) with an adaptive decomposition strategy. To mitigate the periodicity bias inherent in LVMs, DMMV introduces a customized backcast-residual mechanism that enables effective fusion of numerical and visual modalities. Comprehensive experiments on standard benchmarks show that DMMV consistently outperforms both single-modal models and state-of-the-art multi-modal baselines, highlighting its robustness and effectiveness.", "questions": "Answer above Weaknesses.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n\nS1. The research presented in this paper is relatively novel, focusing on the application of large multimodal models to time series data.\n\nS2. This paper is technically strong and presents extensive experiments, bringing many new insights to the field.\n\n\n\n**Weaknesses**\n\nW1. Is the performance improvement achieved by the proposed method too incremental? A significance test may be necessary to validate its effectiveness.\n\nW2. Are visual models sensitive to the visual representation of time series data, such as line color, pixel conditions, the proportion of the time series line in the image, line smoothness, etc.?\n\nW3. Do multimodal models have potential applications in the spatiotemporal domain? Spatio-temporal data emphasizes the relationships between channels and may face many challenges. Can you bring more extended insights?", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer SJEM,\n\nThank you so much for the constructive feedback. We sincerely appreciate your valuable suggestions and questions. The following are our responses.\n\n**W1: Is the performance improvement achieved by the proposed method too incremental? A significance test may be necessary to validate its effectiveness.**\n\nThank you for highlighting this concern. Yes, the challenge of improving MSE and MAE over the SOTA methods on the widely used benchmark datasets may raise doubts about the significance of improvements. To address this concern, we ran our method three times with different seeds and calculated standard deviations. In our appendix, Table 9 reports the standard deviations of DMMV on the same four datasets used for ablation and performance analysis (section 4.2, 4.3). In the following, we summarize the comparison between DMMV-A and the most competitive baseline, VisionTS.\n\nFrom the results, both methods show small standard deviations across multiple runs, suggesting their stability and the reliability of the results. We ran two-sample t-tests for each dataset under different forecasting horizons (i.e., 96, 192, 336, 720). DMMV-A exhibits significant improvements over VisionTS in 13 out of 16 cases using MSE (p-value<0.05) and 9 out of 16 cases using MAE (p-value<0.05), totaling a majority of the cases. Also, considering the non-trivial difference in the overall numbers of wins between DMMV-A and VisionTS in Table 1, i.e., 43 and 9, we think the improvements are not a matter of randomness. We will extend this analysis to all datasets and add the results to a revised version of the appendix.\n\n| Datasets | Predicted length | DMMV-A(MSE) | DMMV-A(MAE) | VisionTS(MSE) | VisionTS(MAE) |\n| --- | --- | --- | --- | --- | --- |\n| ETTh1 | 96 | 0.354$\\pm$0.001 | 0.390$\\pm$0.001 | 0.355$\\pm$0.001 | 0.386$\\pm$0.001 |\n|  | 192 | 0.393$\\pm$0.001 | 0.405$\\pm$0.001 | 0.395$\\pm$0.003 | 0.407$\\pm$0.000 |\n|  | 336 | 0.387$\\pm$0.001 | 0.413$\\pm$0.001 | 0.419$\\pm$0.000 | 0.421$\\pm$0.000 |\n|  | 720 | 0.447$\\pm$0.002 | 0.451$\\pm$0.001 | 0.458$\\pm$0.002 | 0.460$\\pm$0.001 |\n| ETTm1 | 96 | 0.278$\\pm$0.001 | 0.329$\\pm$0.000 | 0.284$\\pm$0.001 | 0.332$\\pm$0.001 |\n|  | 192 | 0.317$\\pm$0.001 | 0.358$\\pm$0.001 | 0.327$\\pm$0.001 | 0.362$\\pm$0.001 |\n|  | 336 | 0.351$\\pm$0.001 | 0.381$\\pm$0.000 | 0.354$\\pm$0.001 | 0.382$\\pm$0.001 |\n|  | 720 | 0.411$\\pm$0.000 | 0.415$\\pm$0.000 | 0.411$\\pm$0.001 | 0.415$\\pm$0.000 |\n| illness | 24 | 1.409$\\pm$0.001 | 0.754$\\pm$0.001 | 1.613$\\pm$0.001 | 0.834$\\pm$0.000 |\n|  | 36 | 1.291$\\pm$0.002 | 0.742$\\pm$0.003 | 1.316$\\pm$0.002 | 0.750$\\pm$0.001 |\n|  | 48 | 1.499$\\pm$0.002 | 0.810$\\pm$0.011 | 1.548$\\pm$0.002 | 0.818$\\pm$0.001 |\n|  | 60 | 1.430$\\pm$0.003 | 0.774$\\pm$0.001 | 1.450$\\pm$0.001 | 0.783$\\pm$0.001 |\n| Weather | 96 | 0.143$\\pm$0.001 | 0.196$\\pm$0.002 | 0.146$\\pm$0.000 | 0.191$\\pm$0.000 |\n|  | 192 | 0.187$\\pm$0.001 | 0.245$\\pm$0.003 | 0.194$\\pm$0.001 | 0.238$\\pm$0.001 |\n|  | 336 | 0.237$\\pm$0.001 | 0.272$\\pm$0.003 | 0.243$\\pm$0.000 | 0.275$\\pm$0.000 |\n|  | 720 | 0.300$\\pm$0.002 | 0.318$\\pm$0.003 | 0.318$\\pm$0.004 | 0.328$\\pm$0.001 |\n\n\n**W2: Are visual models sensitive to the visual representation of time series data, such as line color, pixel conditions, the proportion of the time series line in the image, line smoothness, etc.?**\n\nThis is an interesting question. If time series is imaged by line plots, we saw a survey paper [*] discussed it (in its Section 3.1). Its conclusion is that there is no consensus on whether graphical components, such as lines, colors, legend, grids and tick labels, could provide extra benefits in any task.\n\nIn our method, since we didn't use line plots, our method can be think as not being influenced by graphical components. Section 3 (Preliminaries) describes our imaging method. Time series is segmented by period. The segments are stacked to form a matrix, which is resized to a 224x224x3 gray-scale image. The image is gray because the 3 channels are the same. This is intuitive because we don't have extra information to be encoded by color. The most informative pattern is the texture of the image, which is determined by time series values. As such, we think our method will not introduce sensitivity to graphical components to vision models.\n\n[*] J. Ni et al. \"Harnessing Vision Models for Time Series Analysis: A Survey\". In IJCAI, 2025.\n\n**W3: Do multimodal models have potential applications in the spatiotemporal domain?**\n\nWe are thankful to this great comment. We believe spatiotemporal data modeling is a notable direction to us for its wide applications in domains such as traffic, climate and neuroscience. One key challenge is modeling spatial dependency across channels together with their dynamics. In our humble opinion, our method can be extended to spatiotemporal data by introducing a spatial encoder, which could be a Transformer-like architecture that learns the attention among channels through intermediate embeddings. However, a bottleneck in computational cost may appear when there are hundreds or thousands of channels, which is worth further research. The key advantage of using multimodal view models, like ours, includes their capabilities in capturing complementary patterns across views and leveraging cross-modal knowledge transfer from LVMs, especially when task-specific data are scarce. We'd like to add this discussion to the revised appendix."}, {"review_id": "srRUZfVcE4", "reviewer": "Reviewer_srxJ", "summary": "The paper proposes a multi-model view framework (DMMV) that harnesses the inductive bias of LVM-based forecaster and the strength of numerical forecaster. Extensive experiments show that DMMV outperforms single-view and multi-modal view baselines, achieving good prediction results.", "questions": "1. For time series data with clear periodicity, DMMV leverages the inductive bias of vision models to capture such patterns effectively. However, this makes the model highly sensitive to the choice of segment length P; if P is not properly set, the performance may deteriorate significantly. \n\n2. Compared to DMMV-A, DMMV-S incorporates more complex designs, such as the backcast-residual mechanism. However, based on the results in Figure 5, DMMV-A outperforms DMMV-S. Does this suggest that these additional design components may be ineffective or unnecessary?\n\n3. Table 1 does not report the results for DMMV-S. Could the authors include them for completeness and comparison?\n\n4. On datasets with strong periodicity, such as Electricity and Traffic, the performance gains of DMMV-A over VisionTS are limited. Could the authors explain this limited improvement?\n\n5. According to Figure 6, the visual component's weight in DMMV-S is smaller than in DMMV-A. Would manually adjusting the gating value g in Equation (5) improve performance?\n\n6. Unlike VisionTS, DMMV-A cannot perform zero-shot forecasting and requires fine-tuning. Since fine-tuning latent variable models (LVMs) may incur additional computational costs, how can one balance these increased costs against the performance gains?", "limitations": "yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. The paper proposes a novel time series forecasting framework that combines the LVM-based forecaster and time series forecaster.\n\n2. DMMV-A achieves good forecasting results on some datasets, indicating its potential as a new paradigm for MMV-based time series forecasting.\n\nWeaknesses:\n\n1. The model's forecasting performance primarily relies on VisionTS (the visual forecaster). For DMMV-A, the authors only introduce a commonly used moving average decomposition mechanism, which limits the overall novelty of the framework.\n\n2. Compared to DMMV-A, DMMV-S involves a more complex design, yet its performance is actually worse, raising concerns about the effectiveness of the added complexity.\n\n3. DMMV-A appears to be well-suited for datasets with periodicity. However, it remains unclear how the model would perform on non-periodic datasets—would the forecasting accuracy of DMMV degrade significantly in such cases?", "was_revised": true, "final_justification": "Thank the authors for the response. The rebuttal and subsequent discussion have addressed some issues (e.g., the automatic selection of period P and the main results of DMMV-S). Several critical concerns remain unresolved:\n\n1. The authors claim in the motivation that vision-based models exhibit strong inductive bias toward period consistency, often overshadowing the global trend. Based on this,  DMMV-S (with simple decomposition), which combines the strengths of both vision-based and time series models, should theoretically outperform the pure vision model VisionTS. Furthermore, DMMV-A (with adaptive decomposition) would be expected to surpass DMMV-S. However, the reported results indicate that DMMV-S underperforms VisionTS, which appears inconsistent with the stated motivation.\n\n2. DMMV-A achieves remarkable results on the Weather and Electricity datasets, but the authors don’t clarify which specific designs contribute to this advantage. I believe that Figure 6, which analyzes the weights of the vision and time-series modules, is insufficient as evidence, since these weights are relatively similar across all datasets for DMMV-A.\n\n3. Regarding the comparison with VisionTS: since DMMV-A and DMMV-S are based on modifications to VisionTS, the experimental settings should align with VisionTS’s zero-shot setup (e.g., matching the input sequence length). Such alignment would provide a fairer and more convincing demonstration of the prediction improvements brought by the DMMV models.\n\nGiven these unresolved issues, I maintain my original rating.", "rebuttal": "Dear Reviewer srxJ,\n\nThank you so much for the constructive feedback. We sincerely appreciate your valuable suggestions and questions. The following are our responses.\n\n**W1: The model's forecasting performance primarily relies on VisionTS (the visual forecaster). For DMMV-A, the authors only introduce a commonly used moving average decomposition mechanism, which limits the overall novelty of the framework.**\n\nPlease let us clarify a misunderstanding in this comment. DMMV-A's decomposition is based on a backcast-residual mechanism with our proposed BCmask strategy, which is different from moving average decomposition. Specifically, in Section 3.1 and 3.2, we proposed two variants of DMMV, Figure 1(a) and (b) present their structures: (a) DMMV-S (simple decomposition) adopts moving average decomposition; (b) DMMV-A (adaptive decomposition) was designed with a learnable backcast-residual based decomposition, which is adaptive. By comparing them, we find DMMV-A is better in Figure 5 (also in Table 4 in appendix (supplementary files)), thus is more recommended.\n\nWe acknowledge the important role of LVMs in our method, and reflected it in the title of the paper. However, we'd like to highlight our contribution to explore multimodal views of time series by discovering and levarging a bias of the LVM-based forecaster, which could lay the groundwork for future multimodal models on time series. Also, we think the difference in the overall numbers of wins between DMMV-A and VisionTS in Table 1, i.e., 43 and 9, is remarkable, suggesting a non-trivial improvement. In particular, DMMV-A addresses VisionTS's bias toward periodic data, thus is generalizable to broader applications. As such, we hope our contributions could be fairly assessed.\n\n**W2: Compared to DMMV-A, DMMV-S involves a more complex design, yet its performance is actually worse, raising concerns about the effectiveness of the added complexity.**\n\nWe guess this question is caused by the same misunderstanding in Q1. We apologize for the confusion. From Figure 1, DMMV-A's is more crafted than DMMV-S by introducing a backcast-residual decomposition, which is more adaptive. From Figure 5 (and Table 4 in appendix), this design makes DMMV-A perform better than DMMV-S. In the following, we present the average performance comparison. The full results are in Table 4. Additionally, our ablation analysis in Table 2 validates the design choices of DMMV-A.\n\nAverage Performance of DMMV-A and DMMV-S across different datasets:\n| Dataset | DMMV-A(MSE) | DMMV-A(MAE) | DMMV-S(MSE) | DMMV-S(MAE) |\n| ------- | --- | --- | --- | --- |\n| ETTh1   | 0.395 | 0.414 | 0.405 | 0.426 |\n| ETTh2   | 0.337 | 0.388 | 0.339 | 0.397 |\n| ETTm1   | 0.340 | 0.371 | 0.349 | 0.382 |\n| ETTm2   | 0.256 | 0.317 | 0.254 | 0.318 |\n| illness | 1.407 | 0.771 | 1.520 | 0.813 |\n| Electricity | 0.158  | 0.248 | 0.192 | 0.296 |\n| Weather | 0.217 | 0.256 | 0.244 | 0.281 |\n| Traffic | 0.382 | 0.257 | 0.395 | 0.268 |\n\n**W3: DMMV-A appears to be well-suited for datasets with periodicity. However, it remains unclear how the model would perform on non-periodic datasets.**\n\nQuite the contrary, LVM-based forecaster alone, like VisionTS, is suited for datasets with periodicity, overlooking global trend to some extent. This is explained in our Section 3 (\"An Inductive Bias\"). In contrast, our method, DMMV-A, was designed to address this limitation and enhance LVM-based forecaster with multimodal views, thus is more suited for less periodic or non-periodic datasets such as **Weather** and **Illness**, as presented below.\n\nAverage Performance on Non-Periodic Datasets:\n| Dataset | DMMV-A (MSE) | VisionTS (MSE) | GPT4TS (MSE) | PatchTST (MSE) |\n| --- | --- | --- | --- | --- |\n| Illness | 1.407 | 1.482 | 1.871 | 1.443 |\n| Weather | 0.217 | 0.225 | 0.227 | 0.226 |\n\n\n**Q1: This makes the model highly sensitive to the choice of segment length P; if P is not properly set, the performance may deteriorate significantly.**\n\nIn fact, segment length $P$ can be set as a period by Fast Fourier Transform, releasing the burden of manual tuning. However, if $P$ is perturbed, LVM-based forecaster alone is more sensitive than our DMMV-A model since DMMV-A reduces reliance on period accuracy by adaptive decomposition. We did the following test: when the period $P$ is perturbed (i.e., varying by P/6, 2P/6, ..., P), VisionTS's performance drops more (e.g., ETTh1: 0.409 → 0.582 (42.3%)) than our model (e.g., ETTh1: 0.395 → 0.450 (13.9%)), suggesting the better robustness of our method.\n\n\n**Q2: Based on the results in Figure 5, DMMV-A outperforms DMMV-S. Does this suggest that additional design components of DMMV-S may be ineffective or unnecessary?**\n\nThis question is the same as W2. The response is summarized in the reponse to W2.\n\n\n**Q3: Table 1 does not report the results for DMMV-S. Could the authors include them for completeness and comparison?**\n\nYes. Currently, we put the results of DMMV-S in Table 4 in the appendix for keeping Table 1 succinct while highlighting salient methods. Now we are aware of the interests in DMMV-S, and we'd like to update Table 1 to include it in a revised version of the paper. Thank you for the suggestion.\n\n\n**Q4: On datasets with strong periodicity, such as Electricity and Traffic, the performance gains of DMMV-A over VisionTS are limited. Could the authors explain this limited improvement?**\n\nThis question relates to W3. In fact, VisionTS is suited for datasets with strong periodicity. On such datasets, VisionTS performs well, while modeling global trend may only bring small gains. This explains why DMMV-A's gain over VisionTS is limited. In contrast, on datasets with less periodicity, such as **Weather** and **Illness**, DMMV-A achieves more notable improvements over VisionTS, validating its effectiveness in addressing VisionTS's limitation. Considering both cases, periodic or non-periodic, DMMV-A is no less than VisionTS, indicating its broader applicability.\n\n\n**Q5: According to Figure 6, the visual component's weight in DMMV-S is smaller than in DMMV-A. Would manually adjust the gating value improve performance?**\n\nIn DMMV-A, $g$ is automatically learned to avoid human bias, allowing adaptive aggregation of the decomposed components. Manual tuning $g$ may be inefficient thus is not recommended.\n\nTo check whether manual tuning $g$ works for DMMV-S, we set the visual weight as same as DMMV-A for DMMV-S. The following table compares the results. As can be seen, manual weights lead to performance drop. This is because the imposed manual $g$ cannot align with other parts of the model, which are aligned with the leared $g$ during model training. We'd like include this result in a revised version of the appendix.\n\n| Dataset | DMMV-S(MSE) | DMMV-S(MAE) | Manual Weight(MSE) | Manual Weight(MAE) |\n| --- | --- | --- | --- | --- |\n| ETTh1 | 0.405 | 0.426 | 0.433 | 0.452 |\n| ETTm1 | 0.349 | 0.382 | 0.376 | 0.422 |\n| illness | 1.520 | 0.813 | 1.964 | 1.313 |\n| Weather | 0.244 | 0.281 | 0.265 | 0.296 |\n\n\n**Q6: Unlike VisionTS, DMMV-A cannot perform zero-shot forecasting and requires fine-tuning. Since fine-tuning latent variable models (LVMs) may incur additional computational costs, how can one balance these increased costs against the performance gains?**\n\nAlthough VisionTS can be used for zero-shot forecasting, we wanted to highlight its performance is limited. The following table presents its zero-shot performance, which is even inferior to baslines DLinear, Time-LLM, PatchTST, etc. (Table 1). Thus fine-tuning is still important for VisionTS to perform optimally, like DMMV-A.\n\nOn the other hand, DMMV-A allows freezing LVMs while fine-tuning other weights -- a light-weight numerical forecaster (0.2% of total weights) -- in the model, thus can be efficient. However, to reach optimal performance, fine-tuning is still recommended and it only incurs a negligible overhead compared to VisionTS, as indicated in the second table below. Consider the benefits of DMMV-A, we think the small cost overhead is paid off.\n\nVisionTS zero-shot averaged performance\n| Dataset | MSE | MAE |\n| --- | --- | --- |\n| ETTh1 | 0.4325 | 0.4178 |\n| ETTm1 | 0.4198 | 0.3945 |\n| illness | 2.312 | 1.543 |\n| Weather | 0.3195 | 0.3125 |\n\nModel size and training time\n| Model | Parameters | Training Time / Epoch |\n| --- | --- | --- |\n| DMMV-A | 112.1M | 158s |\n| VisionTS | 111.9M | 133s |"}, {"review_id": "xO9UtRKU8h", "reviewer": "Reviewer_KH6N", "summary": "The authors propose an approach for long-horizon forecasting using large vision models. In their approach, the authors use a pre-trained large vision model to model the periodic components of a time series, and another architecture to model its trend components. The authors show that large vision models have inductive biases which allow them to model periodic components well. Their approach outperforms compared long-horizon forecasting models on a widely-used benchmark.", "questions": "I do not have any other questions beyond the ones I have asked in the previous section.", "limitations": "The authors have a section on the limitations of their in the appendix. I would encourage the authors to reflect on the efficiency of your method.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Strengths\n1. The approach is interesting, and performs well in comparison to the compared methods. \n2. The paper is well-written and fairly easy to follow. \n3. The related work is well written and organized. \n\n## Weaknesses\n1. **Comparison on the GIFT-Eval benchmark:** The datasets that the authors have used to evaluate their methods have know issues. The GIFT-Eval forecasting benchmark was released to fix some of these issues. I would encourage the authors to compare their model on the GIFT-Eval benchmark. \n2. **SoTA compared methods:** The model is not compared against SoTA forecasting methods such as N-HITs, iTransformer etc., and foundation models such as TimesFM, MOMENT, MOIRAI, Chronos, LagLlama, etc. \n3. **Efficiency:** The method is not efficient, and there should be research on \n4. **Value of multimodality:** The value of multimodality is non immediately clear to me. How does the model do without explicitly modeling the linear components (only using the vision model), versus only using a transformer / linear component, versus model decomposed time series with a linear model (DLinear) or a transformer (say decomposition + PatchTST)? \n5. Why is 336 chosen as the look back window? In most recent studies, lookback windows are either 512 (e.g., MOMENT, PatchTST), or 96 (e.g., iTransformer).", "was_revised": true, "final_justification": "I have read the authors' rebuttal and have responded to them. \n\nI believe that my current score reflects my assessment of the paper in its current form. The datasets need to be improved and the authors are running experiments to this end. I also do not immediately see the practical value of the method, with the baselines that the model is compared against. That said I do think it is an interesting direction of work.", "rebuttal": "Dear Reviewer KH6N,\n\nThank you so much for the constructive feedback. We sincerely appreciate your valuable suggestions and questions. The following are our responses.\n\n**Q1: Comparison on the GIFT-Eval benchmark: I would encourage the authors to compare their model on the GIFT-Eval benchmark.**\n\nThank you for this valuable suggestion. We acknowledge the limitations of the widely used eight benchmark datasets. We used them mainly for their widespread adoption in related works, so as to ensure fair comparison and reproducibility. While our method is not intended as a large-scale foundation model and was therefore not initially pre-trained on datasets like GIFT-Eval or Time-MMD, we fully agree that evaluating on standardized and diverse benchmarks such as GIFT-Eval is helpful for demonstrating generalization and robustness.\n\nDue to time constraints, we have currently finished running the solar dataset from GIFT-Eval. We present the performance of DMMV-A and compare it with VisionTS on this dataset in the table below, which demonstrates the superiority of DMMV-A. We'd like to extend the results to more GIFT-Eval datasets and include them in a revised version of the paper.\n\n| model        | DMMV-A |      |      |      | VisionTS |      |      |      |\n| ------------ | ------ | ---- | ---- | ---- | -------- | ---- | ---- | ---- |\n| Input Length | MSE    | MAE  | MAPE | CRPS | MSE      | MAE  | MAPE | CRPS |\n| 96           | 0.187  | 0.243| 1.996| 0.415| 0.190    | 0.245| 2.081| 0.475|\n| 192          | 0.201  | 0.252| 2.013| 0.434| 0.206    | 0.257| 2.165| 0.492|\n| 336          | 0.205  | 0.253| 2.158| 0.508| 0.214    | 0.265| 2.231| 0.512|\n| 720          | 0.210  | 0.257| 2.162| 0.512| 0.235    | 0.299| 2.342| 0.532|\n| Avg.         | 0.201  | 0.251| 2.082| 0.467| 0.211    | 0.267| 2.204| 0.502|\n\n\n**Q2: SoTA compared methods: The model is not compared against SoTA forecasting methods such as N-HITs, iTransformer, etc., and foundation models such as TimesFM, MOMENT, MOIRAI, Chronos, LagLlama, etc.**\n\nThank you for raising this concern. Our baseline selection aimed to cover diverse models by categories (Table 4 in appendix): (1) multimodal (Time-VLM), (2) vision-based (VisionTS), (3) language-based (GPT4TS, Time-LLM, CALF), (4) numerical methods (PatchTST, CycleNet, FEDformer, etc.).\n\nModels like **N-HiTS** and **iTransformer** were not included because they belong to numerical methods similar to baselines reported in that category (e.g., PatchTST), which empirically perform no better than the cross-modal baselines[*]. Time series foundation models (TimesFM, MOMENT, Moirai, Chronos, Lag-Llama) rely on pre-training on large-scale time series datasets, which differs fundamentally from our experimental setting that didn't use time series pre-training data, which may lead to unfair comparisons.\n\nAveraged Results for N-HiTS\n| Dataset | MSE | MAE |\n| --- | --- | --- |\n| ETTh1 | 0.473 | 0.462 |\n| ETTm1 | 0.395 | 0.412 |\n| illness | 2.997 | 1.171 |\n| Weather | 0.235 | 0.286 |\n\n[*] M. Jin et al. \"Time-LLM: Time Series Forecasting by Reprogramming Large Language Models\". In ICLR, 2024.\n\n**Q3: Efficiency: The method is not efficient, and there should be research on.**\n\nWe agee with the reviewer that our method is not designed to be the most efficient but rather to balance performance and complexity. The additional numerical forecaster in DMMV-A is lightweight (0.2% of total weights) and adds only a small number of parameters compared to the LVM backbone. The table below compares the total parameters and training time per epoch on the ETTh1 dataset.\n\nIn practice, our method only incurs a negligible overhead compared to VisionTS, making the it suited for real-world applications while still delivering significant performance gains, especially when dealing with non-periodic datasets or cases where the predefined period P is inaccurate. Consider the benefits, we think the small cost overhead is paid off. We'd like to include this discussion in the revised draft.\n\n| Model | Parameters | Training Time / Epoch |\n| --- | --- | --- |\n| DMMV-A | 112.1M | 158s |\n| VisionTS | 111.9M | 133s |\n\n**Q4: Value of multimodality: How does the model do without explicitly modeling the linear components (only using the vision model), versus only using a transformer / linear component, versus model decomposed time series with a linear model (DLinear) or a transformer (say decomposition + PatchTST)?**\n\nYes, we agree with the reviewer that comparing with the suggested ablations will help understand the advantage of multimodal views. \n\nFor \"model only using the vision model\", the VisionTS baseline in Table 1 serves for this purpose since DMMV-A's visual forecater alone is similar to VisionTS. For \"model only using a transformer / linear component\", the PatchTST and DLinear in Table 1 serve for this purpose since DMMV-A's numerical forecaster alone is similar to either of them. However, please let us clarify that DMMV-A's technical novelty lies in the multimodal view fusion framework, i.e., the backcast-residual mechanism in Figure 1(b), by leveraging the inductive bias of the visual forecaster.\n\nFrom Table 1, DMMV-A outperforms the aforementioned baselines, suggesting multimodal fusion brings complementary advantages.\n\nFor \"model decomposed time series with a linear model or a transformer\", we replaced the visual forecaster in DMMV-A with a linear model, and report the results in the following. As can be seen, the original DMMV-A outperforms the variants, suggesting the effectiveness of visual forecasters.\n\n| Dataset | DMMV-A (MSE) | DMMV-A (MAE) | DMMV-Linear (MSE)     | DMMV-Linear     (MAE) |\n|---------|-------------|---------------|---------------------------|---------------------------|\n| ETTh1   | 0.395       | 0.414         | 0.436                     | 0.448                     |\n| ETTm1   | 0.340       | 0.371         | 0.365                     | 0.389                     |\n| Illness | 1.407       | 0.771         | 2.378                     | 1.105                     |\n| Weather | 0.217       | 0.256         | 0.250                     | 0.306                     |\n\n\n**Q5: Why is 336 chosen as the look-back window? In most recent studies, lookback windows are either 512 (e.g., MOMENT, PatchTST), or 96 (e.g., iTransformer).**\n\nWe appreciate the opportunity to clarify this point. While 512 and 96 are commonly used look-back lengths, 336 is also a standard choice adopted by models such as PatchTST (PatchTST/42 version), DLinear, CycleNet, ETSformer. The key reason for adopting 336 is that we tried to follow the standard evaluation protocol of our baselines as specified in [1][2][3]. This facilitates fair comparisons and reproducibility.\n\nTo validate robustness, we conducted experiments with multiple window sizes (Illness: {104, 156, 208, 312, 416}). The averaged MSE results in the table below indicates DMMV-A outperforms the baseline in most cases. Also, in Figure 9 of the paper and Figure 15 of the appendix, our method consistently outperforms baselines under various input windows, confirming its robustness to look-back length.\n\nModels Averaged performance under different look-back windows:\n\n| Model | Dataset | 96 | 192 | 336 | 720 | 1152 |\n| --- | --- | --- | --- | --- | --- | --- |\n| VisionTS | ETTh1 | 0.428 | 0.424 | 0.407 | 0.394 | 0.392 |\n|  | ETTm1 | 0.380 | 0.358 | 0.351 | 0.340 | 0.348 |\n|  | weather | 0.252 | 0.232 | 0.225 | 0.222 | 0.225 |\n|  | Illness | 1.482 | 1.429 | 1.523 | 1.729 | 2.112 |\n| DMMV-A | ETTh1 | 0.419 | 0.412 | 0.395 | 0.389 | 0.386 |\n|  | ETTm1 | 0.372 | 0.349 | 0.340 | 0.342 | 0.344 |\n|  | weather | 0.238 | 0.229 | 0.217 | 0.221 | 0.222 |\n|  | Illness | 1.407 | 1.389 | 1.497 | 1.575 | 1.494 |\n\n\n[1] M. Tan et al. \"Are Language Models Actually Useful for Time Series Forecasting?\". In NeurIPS, 2024.\n\n[2] A. Zeng et al. \"Are Transformers Effective for Time Series Forecasting?\". In AAAI, 2023.\n\n[3] S. Lin et al. \"CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns\". In NeurIPS, 2024.\n\n**Q6 in Limitations:  The authors have a section on the limitations of their in the appendix. I would encourage the authors to reflect on the efficiency of your method.**\n\nThis question is related to Q3. The response is summarized in the reponse to Q3. We'd like to follow the suggestion and include it the discussion of limitation in Appendix A."}, {"review_id": "Q4YgGEiwd9", "reviewer": "Reviewer_Ymur", "summary": "The authors propose a decomposition-based long-term time series forecasting model where seasonal-like patterns are captured by a pretrained large vision model and trend signals are learned by a linear module. The components are merged using a lightweight gate function.", "questions": "Questions are listed above.", "limitations": "As the authors acknowledge,  the triple usage of LVMs could cause some computational overhead, though they present it as the best solution available at the time of submission.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strength:\n1. The use of LVMs is well-motivated due to the structural similarity between continuous images and time series data.\n2. They propose a backcast-residual mechanism to achieve more robust time series decomposition rather than relying on pre-defined components.\n\nWeakness:\n1. The claim that “applying LVMs to LTSF poses an inductive bias towards forecasting periods” is unclear. In my understanding, Fig. 3 shows that the LVMs do well when the segment length aligns with the true period of the time series. While I agree that preprocessing alignment in period-based transformation is important for LVMs, I am not convinced that this evidence supports the direct conclusion that LVMs are inherently good at seasonal modeling. \n2. The sources of baseline results are inconsistent, and the authors do not explain why some baseline results differ from their original papers or whether they reproduced the methods themselves. It appears that the results for Time-LLM and GPT4TS are copied from VisionTS, while VisionTS results differ from the original paper. It would be better if the author could explain their selective use of results, as an inconsistent comparison setting may be unfair and may not reflect the performance gains. \n3. Compared to the most competitive baseline VisionTS, the performance gains are marginal, with a maximum average gain is ~0.014. On ETTm1, Electricity, and Traffic datasets, the MSE improvements are less than 0.005. It could reflect that the multi-modal view of the TS plays a lesser role in forecasting than expected. I would suggest conducting a statistical significance test or providing the standard deviation for both methods to better understand the performance gap. \n4. Another concern is about the cost-efficiency. The authors do not compare against the most competitive numerical methods like TimeMixer. As shown in their paper, TimeMixer with a larger window length could produce very strong results, which raises questions about whether LVMs are necessary in the decomposition-based setting. I am curious about the results if seasonal modeling is replaced by other numerical methods, like linear module used in TimeMixer. Would there still be significant gains from the usage of LVMs?", "was_revised": true, "final_justification": "Based on the rebuttals, the authors addressed most concerns through statistical significance testing and technical clarifications. While performance gains are incremental, the work demonstrates some contributions through its adaptive decomposition framework and insights into periodicity bias in LVM-based time series forecasting.", "rebuttal": "Dear Reviewer Ymur,\n\nThank you so much for the constructive feedback. We sincerely appreciate your valuable suggestions and questions. The following are our responses.\n\n**Q1: The claim that \"applying LVMs to LTSF poses an inductive bias towards forecasting periods\" is unclear. I am not convinced that LVMs are inherently good at seasonal modeling.**\n\nThank you for pointing it out. By re-reading the draft, we became aware of this non-rigorous wording. Yes, we shouldn't say \"LVMs poses an inductive bias towards forecasting periods\", which may cause confusion since LVMs are not inherently designed for seasonal modeling. Instead, the bias comes from the period-based imaging method. We will clarify this difference in a revised version of the draft and emphasize the source of the bias is the period-based imaging method.\n\n**Q2: The sources of baseline results are inconsistent. It appears that the results for Time-LLM and GPT4TS are copied from VisionTS, while VisionTS results differ from the original paper. It would be better if the author could explain their selective use of results.**\n\nYes, we'd like to clarify our criteria of reporting results. For Time-LLM and GPT4TS, we collected the results reproduced by the work in [*], which uses the standard evaluation protocol and re-implement the methods to confirm their reported results, adding confidence to the reliability of the results. Also, we have re-run both methods on selected datasets (ETT, Illness) and observed <1% differences, confirming consistency. For VisionTS, since it didn't use the standard evaluation protocol (its look-back window length varies, e.g., 1152 and 2304), we implemented it following the protocol (fixed look-back winodow as 336) for fair comparison. For CycleNet, we collected its results from its paper which uses the standard evaluation protocol. For other methods, we collected their results reproduced by [**] under the same protocol, which are generally better than those reported by their original papers. Since CycleNet didn't report results on Illness, we run it and report it below, which will be added to a revised version of the paper. Time-VLM didn't use Illness as well and released code recently. We will run it on Illness and add the results to the paper.\n\nCycleNet performance in Illness datasets:\n\n| Length | MSE   | MAE   |\n| ------ | ----- | ----- |\n| 24     | 2.255 | 1.017 |\n| 36     | 2.121 | 0.950 |\n| 48     | 2.187 | 1.007 |\n| 60     | 2.185 | 0.997 |\n| Avg.   | 2.187 | 0.992 |\n\n[*] M. Tan et al. \"Are Language Models Actually Useful for Time Series Forecasting?\". In NeurIPS, 2024.\n[**] M. Chen et al. \"VisionTS: Visual Masked Autoencoders Are Free-Lunch Zero-Shot Time Series Forecasters\". In ICML, 2025.\n\n**Q3: Compared to the most competitive baseline VisionTS, the performance gains are marginal. I would suggest conducting a statistical significance test or providing the standard deviation for both methods to better understand the performance gap.**\n\nThank you for highlighting this concern. Yes, the challenge of improving MSE and MAE over the SOTA methods on the widely used benchmark datasets may raise doubts about the significance of improvements. To address this concern, we ran our method five times with different seeds and calculated standard deviations. In our appendix, Table 9 reports the standard deviations of DMMV on the same four datasets used for ablation and performance analysis (section 4.2, 4.3). In the following, we summarize the comparison between DMMV-A and the most competitive baseline, VisionTS.\n\nFrom the results, both methods show small standard deviations across multiple runs, suggesting their stability and the reliability of the results. We ran two-sample t-tests for each dataset under different forecasting horizons (i.e., 96, 192, 336, 720). DMMV-A exhibits significant improvements over VisionTS in 13 out of 16 cases using MSE (p-value<0.05) and 9 out of 16 cases using MAE (p-value<0.05), totaling a majority of the cases. Also, considering the non-trivial difference in the overall number of wins between DMMV-A and VisionTS in Table 1, i.e., 43 and 9, we think the improvements are not a matter of randomness. We will extend this analysis to all datasets and add the results to a revised version of the appendix.\n\n| Datasets | Predicted length | DMMV-A(MSE) | DMMV-A(MAE) | VisionTS(MSE) | VisionTS(MAE) |\n| --- | --- | --- | --- | --- | --- |\n| ETTh1 | 96 | 0.354$\\pm$0.001 | 0.390$\\pm$0.001 | 0.355$\\pm$0.001 | 0.386$\\pm$0.001 |\n|  | 192 | 0.393$\\pm$0.001 | 0.405$\\pm$0.001 | 0.395$\\pm$0.003 | 0.407$\\pm$0.000 |\n|  | 336 | 0.387$\\pm$0.001 | 0.413$\\pm$0.001 | 0.419$\\pm$0.000 | 0.421$\\pm$0.000 |\n|  | 720 | 0.447$\\pm$0.002 | 0.451$\\pm$0.001 | 0.458$\\pm$0.002 | 0.460$\\pm$0.001 |\n| ETTm1 | 96 | 0.278$\\pm$0.001 | 0.329$\\pm$0.000 | 0.284$\\pm$0.001 | 0.332$\\pm$0.001 |\n|  | 192 | 0.317$\\pm$0.001 | 0.358$\\pm$0.001 | 0.327$\\pm$0.001 | 0.362$\\pm$0.001 |\n|  | 336 | 0.351$\\pm$0.001 | 0.381$\\pm$0.000 | 0.354$\\pm$0.001 | 0.382$\\pm$0.001 |\n|  | 720 | 0.411$\\pm$0.000 | 0.415$\\pm$0.000 | 0.411$\\pm$0.001 | 0.415$\\pm$0.000 |\n| illness | 24 | 1.409$\\pm$0.001 | 0.754$\\pm$0.001 | 1.613$\\pm$0.001 | 0.834$\\pm$0.000 |\n|  | 36 | 1.291$\\pm$0.002 | 0.742$\\pm$0.003 | 1.316$\\pm$0.002 | 0.750$\\pm$0.001 |\n|  | 48 | 1.499$\\pm$0.002 | 0.810$\\pm$0.011 | 1.548$\\pm$0.002 | 0.818$\\pm$0.001 |\n|  | 60 | 1.430$\\pm$0.003 | 0.774$\\pm$0.001 | 1.450$\\pm$0.001 | 0.783$\\pm$0.001 |\n| Weather | 96 | 0.143$\\pm$0.001 | 0.196$\\pm$0.002 | 0.146$\\pm$0.000 | 0.191$\\pm$0.000 |\n|  | 192 | 0.187$\\pm$0.001 | 0.245$\\pm$0.003 | 0.194$\\pm$0.001 | 0.238$\\pm$0.001 |\n|  | 336 | 0.237$\\pm$0.001 | 0.272$\\pm$0.003 | 0.243$\\pm$0.000 | 0.275$\\pm$0.000 |\n|  | 720 | 0.300$\\pm$0.002 | 0.318$\\pm$0.003 | 0.318$\\pm$0.004 | 0.328$\\pm$0.001 |\n\nAdditionally, we'd like to highlight another advantage of introducing TS view by our method: It alleviates the sensitivity to period estimation. When the period $P$ is perturbed (i.e., varying by P/6, 2P/6, ..., P), VisionTS's performance drops more (e.g., ETTh1: 0.409 → 0.582 (42.3%)) than our model (e.g., ETTh1: 0.395 → 0.450 (13.9%)), suggesting the better robustness of our method.\n\n**Q4: I am curious about the results if seasonal modeling is replaced by other numerical methods, like linear module used in TimeMixer. Would there still be significant gains from the usage of LVMs?**\n\nThis is an interesting question, which can help validate the effectiveness of LVMs in our framework. We performed an ablation by replacing the LVM in DMMV-A (Figure 1(b)) with the seasonal mixing module of TimeMixer [*]. Specifically, we use this module to extract seasonal components from the look-back window and use DMMV-A's numerical forecaster to model the residual component. The forecasts from the numerical forecaster and the seaonal mixing module are aggrated by the gate function. The ablation results are summarized as following. As can be seen, the original DMMV-A outperforms the variants, suggesting the effectiveness of visual forecasters.\n\n| Dataset | DMMV-A (MSE) | DMMV-A (MAE) | Seasonal mixing (MSE)     | Seasonal mixing     (MAE) |\n|---------|-------------|---------------|---------------------------|---------------------------|\n| ETTh1   | 0.395       | 0.414         | 0.436                     | 0.448                     |\n| ETTm1   | 0.340       | 0.371         | 0.365                     | 0.389                     |\n| Illness | 1.407       | 0.771         | 2.378                     | 1.105                     |\n| Weather | 0.217       | 0.256         | 0.250                     | 0.306                     |\n\n[*] S. Wang et al. \"TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting\". In ICLR, 2024.\n\n**Q5 in Limitations: As the authors acknowledge, the triple usage of LVMs could cause some computational overhead, though they present it as the best solution available at the time of submission.**\n\nYes, we acknowledged this limitation in our appendix A. The triple usage includes two passes of LVMs for backcasting and one pass for forecasting. At the time of submission, we thought two passes were possibily the minimum usage of LVM for backcasting. Compared to other LVM-based models, which include at least one pass for forecasting, our method adds two backcast passes. In the following, we compared the inference time of our method and VisionTS. From the results, the computational overhead of DMMV-A looks practically acceptable. We will add these results and the discussion to a revised version of the paper. Moreover, we'd like to improve the model by optimizing the backcast-forecast mechanism using LVMs. Some thoughts are provided in appendix A.\n\nThe Averaged inference time for each sample in ETTh1:\n| Model | Inference time  |\n| --- | --- |\n| DMMV-A | 0.213 ms |\n| VisionTS | 0.165 ms|"}]

Author rebuttal:

Meta-review: Most reviews are positive, specifically from BA, BA, BA, and BR. The majority of reviewers recognize the merits of the proposed work, including the findings on the bias of the SOTA LVM-based forecaster, the effective solution to address limitations through a backcast-residual based adaptive decomposition framework, the comprehensive experiments involving 14 SOTA baselines categorized by vision, language, multimodal, and numerical methods, and the potential to inspire future research on LVM-based forecasters.
The authors have made substantial efforts to address the concerns raised by the reviewers, and most of these concerns have been resolved. Reviewers SJEM, KH6N, and Ymur have no further concerns. The authors have also provided detailed responses to the questions posed by Reviewer srxJ, and I believe the remaining questions have been adequately addressed.
Therefore, I recommend the acceptance of this submission. Additionally, I expect that the authors will incorporate the suggested modifications from the rebuttal phase into the final version.
Decision: Accept (poster)