Bridging Past and Future: Distribution-Aware Alignment for Time Series Forecasting
Authors: Yifan Hu
Jie Yang
Tian Zhou
Peiyuan Liu
Yujin Tang
Rong Jin
Liang Sun
Venue: ICLR 2026 Poster (2026)
Keywords: Time Series Forecasting
Representation Learning
Alignment
Primary area: learning on time series and dynamical systems
TL;DR: TimeAlign is a lightweight, plug-and-play framework that bridges the distributional gap in time series forecasting by aligning past and future representations through a reconstruction-based alignment task.

Abstract: Although contrastive and other representation-learning methods have long been explored in vision and NLP, their adoption in modern time series forecasters remains limited. We believe they hold strong promise for this domain. To unlock this potential, we explicitly align past and future representations, thereby bridging the distributional gap between input histories and future targets. To this end, we introduce TimaAlign, a lightweight, plug-and-play framework that establishes a new representation paradigm, distinct from contrastive learning, by aligning auxiliary features via a simple reconstruction task and feeding them back into any base forecaster. Extensive experiments across eight benchmarks verify its superior performance. Further studies indicate that the gains arise primarily from correcting frequency mismatches between historical inputs and future outputs. Additionally, we provide two theoretical justifications for how reconstruction improves forecasting generalization and how alignment increases the mutual information between learned representations and predicted targets. Code is in available at https://github.com/TROUBADOUR000/TimeAlign.

Published as a conference paper at ICLR 2026
BRIDGING PAST AND FUTURE: DISTRIBUTION- AWARE ALIGNMENT FOR TIME SERIES FORECASTING
Yifan : Yang".', Tian Zhou Peiyuan Liu', Yujin Tang', Rong Jin", Liang Sun TTsinghua University 2DAMO Academy, Alibaba Group University of Illinois Chicago *Dartmouth College
[huyf0122 yangjii ii. workmail, peiyuan i edu, tangyujinngn ji02275 @mmail gemail.com com (tian. zt, liang. , sun S @alibaba ibaba inc.com
ABSTRACT
Although contrastive and other representation-leamiin methods have long been explored in vision and NLP, their adoption in modern time series forecasters re- mains limited. We believe they hold strong promise for this domain. To unlock this potential, we explicitly align past and future representations. thereby bridging the distributional gap between input histories and future targets. To this end, we introduce TimeAlign, a lightweight, plug-and-play framework that establishes a new representation paradigm, distinct from contrastive learning, by aligning aux- iliary features via simple reconstruction task and feeding them back into any base forecaster. Extensive experiments across eight benchmarks verify its superior per- formance. Further studies indicate that the gains arise primarily from correcting frequency mismatches between historical inputs and future outputs. Addition- ally, we provide two theoretical justifications for how reconstruction improves forecasting generalization and how alignment increases the mutual information between learned representations and predicted targets. Code is in available at https::/githi:n cowm//TTOOADDOOOOOOTTCCa.o
INTRODUCTION
Representation learning techniques have been widely explored for time series forecasting (TSF) (uue
al. 2022 Eldele et al. 2024 Liu & Chen 2024 Yang et al.) (2225)), inspired by their success in vision (Chen & He 2021 Yu et al.] 2025] Yao et al. 2025) and language tasks (Liu et al. 2023b Dong et al.) 2024). They enable forecasters to gain deeper understanding of the underlying pat- terns by automatically deriving efficient representations from time series data. However, for the forecasting task, mapping embeddings extracted from history to future distributions is inherently challenging under distribution shift. Consequently, models often rely on simplistic direct predictive mappings rather than cultivating richer iuture-aligned representations, leaving the potential of rep- resentation learning largely underexploited in modern forecasters. We argue that this discrepancy is not merely an implementation issue, but rather stems from a fundamental limitation of the prevailing forecasting paradigm as shown in Fig. a). Below, we thoroughly analyze several failure modes in modern forecasting and propose a novel prediction- rec.onorrooooootitiiiooiooo www.oostttuiiiiioliliannenn solution.
A shortcut through low-frequency periodicity. We find that models often exploit this by overem- phasizing low-frequency periodic components (Huang et al. 2025 Cai et al. 2024). When repre- sentation embeddings are optimized solely under error-driven objectives, such mean squared error (MSE) or mean absolute error (MAF), the resulting predictions tend to oscillate around the learned mean, following dominant periodic patterns (see Fig. aa)). Besides, the similarity within the pre- dicted patches is so high that indicates the forecast is just repetition of the low-frequency periodic signals extracted from the past (see Fig. [b)). Furthermore, as Fig. 2 c), our empirical analysis across multiple datasets reveals that high-frequency components in the true values are significant, as they reflect abrupt variations beyond simple periodic repetition and are indispensable for robust forecasting. However, these fighffrequency signals are often underestimated in the predictions.
"Equal contribution
Project lead
Corresponding author

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Figure 1: Comparison among history, ground truth, forecast with and without alignment using dif- ferent visualization perspectives. (a) Time Series Visualization. (b) Token (Patch)-wise Cosine Similarity. (c) Spectrogram Map. (d) t-SNE Embedding Space. More examples are in Appendix
Distributional mismatch between past and future. As illustrated in Fig. [d), the distribution of learned, -igensiienii representations often differs from the distribution of predicted tar- gets (Kim et al. 2022). In practice, these embeddings tend to favour the statistical characteristics of the past over the future. This discrepancy arises from the inherent shift in distribution between historical sequences and the signals to be forecasted (Fan et al. 2023). Consequently, mapping em- beddings extracted from history directly to the target distribution becomes challenging (Dai al.) 2024b Liu et al. 2023a). To overcome this issue, the representation learning process requires addi- tional constraints ensure that the learned embeddings faithfully capture historical patterns and are also informative for future prediction.
Structural Flaw of the Unidirectional Paradigm. Most prevailing prediction paradigm (Fig. 2 a)) is fundamentally unidirectional, mapping historical input solely to the prediction target. This struc- tural constraint inherently limits the model's ability retain crucial target information. Conse- quently, as representations are sequentially encoded through deep layers, the process inadvertently acts like a frequency smoother, discarding subtle frequency structures. And these fine-grained details often encode sudden variations triggered by time- varying external events. After being smoothed out, such information cannot be exploited during forecasting, resulting in a consistently low frequency correlation between predictions and ground truth (see Fig- d)).. Therefore, modeling fine- ine-grained dynamics effectively is essential for enhancing robustness against abrupt fluctuations.
Collectively, these three observations underscore fundamental limitations of the current paradigm and thus prompt the following question: is it possible to design a forecasting framework that can bridge the gap between the past and the future, mitigating distributional shifts while faithfully capturing multi-frequency dynamics?
To this end, we introduce Aigga which forecasts with an auxiliary reconstruction branch for guidance, as shown in Fig. (b), illustrating the poefictio-rrcoonsuuutttoaaaiiiii
pipeline. The intuition behind reconstruction is twofold. Firstly, unlike forecasting, reconstruction embeddings are naturally aligned with the target distribution since the reconstruction task involves recovering inputs from themselves. Secondly, to faithfully recover signals, reconstruction encourages attention to spectral details, retaining both coarse periodic structures and fine-grained, high-frequency varia- tions. Furthermore, we demonstrate that representations optimized under reconstruction loss exhibit stronger forecasting generalization (see the proof in Appendix BB. Consequently, by jointly training the predict and reconstruct branches and aligning their intermediate embeddings, we constrain the predictive representations be distribution-avv aware and detail eettil-preserringg
As for alignment, TimeAlign employs two complementary mechanisms. Global alignment reduces the distributional discrepancy between prediction and reconstruction representations, while local alignment enforces fine- -raiined consistency at the token level. Together, these modules enrich the predictive representation space, enabling the forecaster capture both periodic low-frequency sig-
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Figure 2: (a) The original paradigm of deep learning forecasters. Distributions are extracted from history and mapped to the prediction space, (b) The paradigm of TimeAlign. Joint optimization of the predict and reconstruct branches provides distributional alignment. (c) High-frequeng energy ratio. For different datasets, the threshold between high- and low-frequency bands is determined adaptively via knee-point detection of the cumulative energy distribution. (d) High-frequency sim- ilarity. Pearson correlations are computed on the high-frequency components between the ground truth and the history, the forecast with and without alignment. IMP. means improvement.
nals and fegeffreyeency dynamics. Importantly, alignment reflects a deeper principle. Predictive representations inherently contain mutual information with future targets, yet conventional objec- tives underutilize it. Our analyses confirm that TimeAlign acts as an implicit mutual information en- hancer, aligning predictive representations more closely with targets (see the proof in Appendix C
Extensive experiments demonstrate TimeAlign effectively bridges past and future and delivers more reliable forecasts across diverse datasets. In nutshell, our contributions are summarized as follows:
① Paradigm Shift. We revisit the representation learning in the current dominant forecasting paradigm and reveal its key limitations. It overemphasizes low-frequency periodicity, suffers from distribution mismatch, and discards informative fine-graine pneegraiied components. To fill these gaps, we introduce new paradigm incorporating alignment between prediction and reconstruction.
Technical Contribution. We present TimeAlign, a dual-branch framework that consists of a predict branch and reconstruct branch, distribution-awarl aligning their latent representations through global and local objectives to bridge the past and future effectively.
In Theory and In Practice. We provide two theoretical guarantees: (i) reconstruction improves the forecasting generalization, and (ii) alignment enhances the mutual information between predictive representations and future targets. Extensive experiments across diverse benchmarks further vali- date these insights, establishing tfate-of-the-ar performance in both accuracy and robustness.
RELATED WORKS
2.1 DEEP LEARNING IN TIME SERIES FORECASTING
Recently, deep learning has become the dominant paradigm for TSF, with a variety of neural archi- tectures including CNN (Donghao Xue 2024
Wu et al. 2023 Wang et al. 2022). Linear (Huang
et al., 2025 Hu et al. 2023c Si et al., 2025). Transformer (Liu et al.) 2024b 2025 Dai et al.)
2024a), GNN (Hu al. 2025d Wu al. 2020), etc. Despite architectural diversity, these methods generally follow an encoder decoder paradigm: they embed historical sequences into latent repre- sentations and map them to predictive targets (see Fig. aa). However, as shown Fig. T this paradigm tends to overemphasize low-frequency patterns while neglecting fine-grained structures, and it suffers from distribution mismatch between history and future. To address these limitations, propose Alig,, which jointly optimizes predict and reconstruct branches and aligns their embeddings, thereby bridging the gap between the past and the future more effectively.
2.2 REPRESENTATION LEARNING
Representation learning is crucial for enabling models capture meaningful and transferable fea- tures. Across domains, it has been used to introduce inductive biases that extend beyond task- specific objectives. For instance, in diffusion models, learned representations serve as structured noise priors that improve sample quality and stability (Yang et al.) [202cc] Yu et al.] [025] Jiang et al. 2025), while in vision and language, aligning task-specific embeddings with pre-trained
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enriches feature spaces and boosts downstream performance Yao et al. 2025 Leng et al. 2025
However, in TSF, error-driven training often yields biased embeddings that smooth away subtle but critical dynamics Yue et al. 2022); ; Eldele et al. (2024), limiting their predictive value. We argue that auxiliary mechanisms are needed to enforce consistency between predictive and reconstructive signals, thereby preserving fne-grained temporal cues and alleviating distribution mismatch.
METHOD
3.1 PROBLEM DEFINITION
In TSF task, let X {21, .2.. (2. CC be the history input series, where C' denotes the number of channels and L denotes the look-back horizon. R represents one of the channels.
The objective is to construct model Fo(-) that predicts the future sequences Y peed RCXT, where T denotes the forecasting horizon. The forecasting process is given by Y peed Fx(X). A lower error between Y pred and ground truth Y indicates stronger forecasting capability of the model Fo(.). However, X and Y often exhibit distribution shift. Instead of predicting patterns in Y using learnable statistics derived from X, our focus is to leverage direct constraint from Y to guide model optimization, thereby achieving robust and efficient distribution alignment between peed and Y. To this end, introduce auxiliary reconstruction task. Specifically, the reconstruction model is defined as Go(-) that directly maps to its reconstruction Y recon G& (Y). Here, Go(+) learns compact representation of the target distribution without relying on past inputs, and the reconstruct representation Hy serves guidance for aligning the latent space H. of Fo()).
3.2 STRUCTURE OVERVIEW
As illustrated in Fig. 3 our proposed TimeAlign consists of four components: (i) Predict Branch employs a backbone encoder to map X to Y preas active in both training and inference. The backbone is plug-and-plle and replaceable by any forecasting architecture. In our default setup, it shares the same lightweight encoder as the Reconstruct Branch to highlight the effect alignment. (ii) Recon- struct Branch leverages a lightweight encoder to reconstruct recon from Y, thereby capturing compact representation aligned with the target distribution. This branch is used only during training. (iii) Distribution-Aware Aligmment explicitly aligns H, and H, via global and local mechanisms, providing distributional constraint for optimization. (iv) A Simple Encoder serves the minimal yet effective design for the Reconstruct Branch and default Predict Branch.
3.3 PREDICT BRANCH
The predict branch follows the standard deep learning paradigm for TSF, extracting temporal rep- resentations from historical input and mapping them into the future horizon. In TimeAlign, we deliberately adopt a minimal encoder design to demonstrate that the improvements stem from align- ment rather than architectural complexity. Importantly, the encoder here can be replaced by more sophisticated backbones, enabling TimeAlign to serve as a plug-and-pll and-play module.
Given the history input X E RCxL, we first divide into patches and project them onto embeddings X, Linear(Patching (X))h E E(C-N))D where N is the number of patches and the Reconstruct Branch share the same N with the Predict Branch. X, is then processed by an M M-layer encoder, where each layer consists
innearacctivationn linear block with residual connection:
H -
H
1-1 Linear (a (Linear(H(*-)))
- I, M
with H Xp and is an activation function. Finally, a prediction head projects the latent repre- sentation into the forecasting results Y predd = Linear(H.M)
3.4 RECONSTRUCT BRANCH
The reconstruct branch provides explicit constraint from the target distribution by reconstructing the ground truth from itself. This design captures the intrinsic structure of Y, thereby offering reliable
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Figure 3: Overall architecture of Aigen (i) Predict Branch maps history to forecasts (both training and inference), with replaceable backbone. (ii) Reconstruct Branch reconstructs targets to capture the distribution (training-only) (iii) Distribution-Awarc Alignment aligns predict and reconstruct representations via global and local mechanisms. (iv) Simple Encoder the default lightweight design in Reconstruct Branch and default Predict Branch.
distributional Hy reference for alignment. Unlike the predict branch, the reconstruct branch is only active during training and discarded inference.
Similarly, given the future sequence Y RRXX,, we embed in the same way of patch embedding Y, = Sinear(Patching (Y) (CC It then encoded by the same M M-layer encoder:
H = H Linear (a (Linear(HH,,)))
1= M
(2)
with H Yp- Finally, a reconstruction head then maps the latent representation back into the target space Y reccon Linear(H
The hidden representations H2 and H, are structured by deep transformations and normalization layers. In the spirit of the Central Limit Theorem (CLT), these compounding effects typically enforce the distribution of H2 and H, to be approximately Gaussian. This structured property is key to the theoretical generalization advantages discussed in Appendix
3.5 DISTRIBUTION-AWAN ALIGNMENT
Although the predict and reconstruct branches encode their respective inputs independently. the latent spaces still diverge due to distributional shift between the history X and the target Y. To explicitly bridge this gap, we introduce a distribution-awarr alignment module that aligns the repre- sentations two branches each layer. We consider the i-th layer as an example below.
Alignment with an Additional Mapping. Instead of aligning the raw hidden states directly, we introduce an additional linear mapping applied to the predict branch before alignment:
H Linear(HH) (CCNN)D
This mapping layer, implemented as lightweight Linear layer, serves to temporally reposition and normalize the highly abstracted features of the predict branch, making them more compatible with the representations from the reconstruct branch. Importantly, gradients from the alignment loss are only propagated to the predict branch via this Linear layer, leaving the reconstruct branch unaffected (Chen & He 2021). This asymmetric gradient flow ensures that the reconstruct branch provides a stable supervisory signal without being distorted by the alignment procedure.
Local Global Complementarity. To ensure fine- fine-grained fidelity and distributional consis- tency, we introduce two complementary objectives, including local alignment to capture patch- wise similarity and global alignment to capture relational structure (Yao al. 2025 Yang et al. 2025b).
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Local alignment ensures that individual patch-level features capture similar semanties, while global alignment enforces consistency in the overall relational structure representations (Yang et al., (026). Specifically, local alignment preserves fine-grained similarity between correspond- ing patches, which is crucial for capturing sharp transitions and high-frequency details. Notably, such similarity measures spectral energy projection, thereby leveraging nulti-frreuency informa- tion. h is the j-th item in H and
NL:
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Meanwhile, global alignment aims to make the relative distance matrices within the features as similar as possible, ensuring that large-scale temporal dependencies and low-frequency dynamics are also aligned. means the transpose. We subtract margins dioc and ōgto to relax the constraint:
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These margins used to relax the constraint, which is common technique in metric learning. They create a "buffer" where, two representations are already close enough, the loss becomes zero. This prevents the model from overfitting easy samples and focuses its optimization effort on harder-to-align pairs, leading to more stable training.
Weight-Based Dynamic Loss.
Finally, the overall alignment objective is weighted fusion
Lalign
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We adopt an adaptive scheme to prevent domination of either objective and stabilizes optimization across different datasets and regimes. The dynamic weights a and B are computed as
Liocal + Lglobal
Llocal + Cglobal
B
Liocal
Lggohal
Combining local and global alignment under an asymmetric mapping design encourages the predict branch to capture detailed, patch-level similarities while respecting global relational structures. This dual alignment, guided by the stable target distribution from the reconstruct branch, enhances the robustness and fidelity of the forecasting process.
3.6 OPTIMIZATION OBJECTIVE
The full optimization combines the prediction loss, reconstruction loss, and alignment loss:
C Lpedd + Crecon + >.Calign
where Lpred and Freaon error-based MAE objectives and À is scaling weight. This joint training paradigm enables the predict branch to benefit directly from distributional constraint provided by the reconstruct branch.
4
THEORETICAL ANALYSIS
4.1 IMPROVE GENERALIZATION WITH RECONSTRUCTION ERROR MINIMIZATION
The following theorem characterizes the advantage of reconstruction-gun guided estimation. Let M be the optimal forecasting solution, Mi the empirical estimator obtained from the training examples, and M2 the estimator derived from the one-dimensional representation via reconstruction error minimization. Given the concentration bounds, the reconstruction- based estimator M2 achieves strictly tighter approximation to M than Mi. The proof can be found in Appendix
M22 -M.FF
M1 M.lF
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|M-FF
|M,lF
where denotes the Frobenius norm.

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4.2 TIMEALIGN IS AN IMPLICIT MUTUAL INFORMATION ENHANCER
To understand the mechanism of Lalign from structural perspective, we reformulate the role of our dual loss objectives through the lens of Mutual Information Maximization (MIM).The conven- tional prediction loss, fpred, provides a variational lower bound on the mutual information T(Y; Hz,), implicitly guiding the representation learning. Our core alignment of TigeAlign acts as comple- mentary mechanism, ensuring that the predictive representation H (ha) is explicitly enriched by maximizing its mutual information with the ground truth (yy) This effectively enhances the total information flow used for forecasting. The mutual information is formulated as:
ply, hz) p(haa) p(y)
I(Y; Hz) Ep(x.ha)
log
(10)
MIM in Prediction Loss. Following the derivations introduced in previous IB-relevant works (Choi & Lee 2023] Alemi et al. 2016), we can obtain a lower bound for the informative term, which aims maximize the mutual information between H. and Y (see full derivation in Appendix C.TI:
Fo(u(ha) p(y)
+ f p(hz)
I(Y: H.) = Ep(.A2)) log
dh
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def Spred,
where the incquality holds due to the non-negativity of the KL divergence and entropy.
MIM in Alignment Loss. To further enhance the mutual information, we introduce a comple- mentary formulation that explicitly targets the mutual information between H₂ and Y. Inspired by 2018), we derive an alternative lower the InfoNCE objective from contrastive learning (Oord et al.
bound of 7 7(Y; Hz)) (see the full derivation in Appendix C.2 Furthermore, instead of predicting directly, we model a density ratio [y, kx) = exp(proj (t Gv(v) that preserves mutual infor-
mation [(;; Z). it proportional p(g)
plyl=), This yields the following Alignment loss.
p(y) NN) log N A P(p() log p(y()))))
log ply)
ply hz)) x) (12)
T(Y; H.) =
= -Pp(y. [exp (proj(tez)
T (o(v))] del -allign-
In summary, jointly optimizing Spee and Lalign effectively maximizes the mutual information (Y:HH)) thereby enabling accurate and robust representation learning. To further refine falign. we adopt the complementary local and glohal strategies discussed in Sec. 3.5 which together ensure both fine-grained fidelity and distributional consistency.
EXPERIMENT
In this section, we conduct extensive experiments to validate the superiority of our TimeAlign in effective forecasting performance, plug-and-play capability, and competitive efficiency. More experimental details can be found in Appendix DDand Appendix
5.1 EXPERIMENT SETUP
Datasets. We conduct experiments on eight widely used real-world datasets, including the Electric- ity Transformer Temperature (ETT) dataset with four subsets (ETTh1, ETTh2, ETTml, ETTm2), as well as Weather, Electricity, Traffic, and Solar (Miao al. 2025 datasets are shown Appendix [.2)
2024). The statistics of the
Baselines. We compare TimeAlign with several SOTA baselines representing the latest advances in TSF, including TimeMixer (Wang et al. (202)). iTransformer (Liu et al. 2024b). PatchTST (Nie al. 2023), Crossformer (Zhang & Yan 2023), TVNet (Li et al. (025), ) ModemnCN (Donghao & Xue 2024). TimesNet (Wu et al. 2003), and lightweight methods like DLinear (Zeng et al. 2023),
CMoS (Si al. 2025). TimeBase (Huang al. 2025 and Leddam (Yu et al. 2024).

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Models
TimeAlign (Oun)
CMuS
Timellaee
TVNet
iTrnndomme
TimeMixer
Leokum
ModeraTCN
PacchTST
Croesformer
TimesNet
DLinear
Bo5d
205r
Nert
[003
Metric
MAR
[T7ml
10.340
0.379j0.35
0.360 |0.348 0.379 0.362 0.391 [0.355
0.380/0.354
0.353 0.38/j0.20 0.435004400 0,406 (0.156 0.378
m77m2
10.243
0,302
0.259
2,316
0,314
10.251
0.311
0.269
0.329
(0.257 0,318 (o.11s0.000. 265 0.320 0,253 0.314
0.256 0,31700,518 518 0.501 10.292 0.330
0.124
ETTh1
[0,406
0,420
0.403
0.41d
0.414
J0.407
0,421 (0449 0.448
(0.427 0,441 (o 41. 0,430 0,404 0.420 0.418 0.43/ju.440
0.463 ju.4s8 0.450/0.424 0.439
ETTh2
[0,356
0,382 0.331
0.303jo.345
0,357
10:22
0.377
0,314 0,406 [0.549 0,390 10.345 0.391 0.322
paazy 0.351 0.404j0.009 0.65a |0.50 0.427 (u431 (1447
Weather
[0.214
0.230
(0211
0,263
10.221
0.261 (0233 0.271 [0.226 0.264 to 226 0,264 0,224 0.264 0.226 0.264jo.225 0.287 (0.299 0.257 (0.242 0.293
Elecniciy|0.154
0.344 0.158
0.0.255
10.165
0.254 0.164 0,261 [0.185 0.254 1616 0.256 0.150 0,253 0.159 0.253j0.151 0.279/0.192
0.295 jo.06 0.264
Tratfic
[0.378
0.270/0.417
0.278 10.296
0.208
0,397
0.282 (0.409 0.279/0.452 0.283 0,396 0.270 0,397 0.275|0.523 1224400.600 0.336
(0.418 0.287
Solar [0.192 0.214 0.200 0.257|0.256 0,270 J0.288 0.277 0.202 0.248 192192 0.26440..25 0.264 0.228 0.281 0.194 0.25500.205 0.232 |0.24 0.334 (0.224 0.226
Table 1: Long-term forecasting results. The input length L is searched from (336, 512, 720} and
the results are averaged across four forecasting horizons T E {96, 192, 336, 720). The best and
second-best results are highlighted in bold and underlined, respectively. See Tab. 6 for full results.
Local Align
Global Align
ETTml
ETTm2
Wcather
Electricity
Traffic
Case
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
0.349
0.370
0.252
0.308
0.225
0.254
0.159
0.248
0.390
0.249
X
0.344
0.372
0.245
0.305
0.220
0.249
0.157
0,247
0.383
0.244
0.342
0.369
0.244
0.303
0.218
0.242
0.157
0.246
0.383
0.245
(
0.340
0.367
0.243
0.302
0.214
0.244
0.154
0.244
0.378
0.240
Table 2: Full results of ablation on the effect of removing alignment in local and global perspective. V indicates the use of alignment, while x means alignment is retained.
Implementation Details. All experiments are performed on one NVIDIA V100 32GB GPU. We select two common metrics in TSF: MAE and MSE. Moreover, a grid search is conducted on the look-back length of (96, 192, 336, 512, 720}. For each setting, the results are averaged over three runs with random seeds. For additional details on hyperparameters, please refer to Appendix (D3
5.2 FORECSATING PERFORMANCE
As shown in Tab. D Align delivers effective forecasting performance across most datasets. The only exceptions are E and ETTh2, yet its performance remains highly competitive. Most notably, on the ETTml and ETTm2 datasets known for severe distribution shifts (Qiu et al. 2024). TimeAlign substantially outperforms current SOTA methods. Owing to the Distribution-Awarc Alignment Module, Aime aligns predict representations with evolving distributions, thereby enabling more detailed modeling of the target and further boosting accuracy. Overall, compared to the second best method TVNet, Aige reduces MSE/MAE by 3.27% /5.20% with a Wilcoxon test p-value of 1.37e confirming significance at 99% confidence. The full error bars are in Tab.
5.3 ABLATION STUDIES
We validate the effectiveness of each architectural design in TimeAlign through the following abla- tion studies: O w/o Align signifies the Predict Branch alone without alignment. w/ Local only denotes the Local Alignment is retained. @ w/ Global only denotes only the Global Alignment is retained. ④ w/ Align encompasses both Local and Global Alignment mechanisms.
The results in Tab. 2 reveal that the combination of Local and Global Aligmment is essential for accurately reconciling the predict representations with the target distribution, yielding the best per- formance. Interestingly, Global Alignment alone outperforms I. Local Alignment alone; the former provides a coarse-graine grained distribution-level pull that is more effective at high-level representation calibration, while the latter focuses on fine-graines point-wise corrections. As expected, removing both alignment strategies results in the worst accuracy. Furthermore, we observe that w/o Align is already SOTA-level Baseline, showing that TimeAlign achieves consistent performance improve- ments on top of the Atready-SOTA-BRe trick that only works SOTA-level architecture and make it even better.
baseline. This proves that our TimeAlign module is not a weak baseline. It is powerful module that can take strong, efficient,
Additionally, the effectiveness of Reconstruct can be found in Appendix H.5
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Published as a conference paper at ICLR 2026
Models
iTransformeer
+TimeAlign
DLincar
-TimeAlign
Metrie
MSE
MAE
SIM
MSE
MAE
SIM
AIMP
MSB
MAB
SIM
MSB
MAB
SIM
AIM
ETTml
1
0,362
0.391
0.862
0.355
0.384
0.865
+1.80%
| 0,356
0.378
0.869
0.352
0,373
0.872
+1.05%
ETTm2
0,269
0.329
0.970
0.260
0.317
0,974
+3.44%
0.259
0.324
0.973
0.252
0.311
0.976
+2.61%
ETTh
|
0,439
0.448
0.825
0.428
0.448
0.828
+2.45%
0.424
0.439
0.841
0.414
0.433
0.840
+2.41%
ETTh2
| 0.374
0.406
0.958
0.363
0.402
0.962
+2.87%
| 0.431
0.447
0.960
0.418
0.431
0.960
+3.07%
Weather
0.233
0.271
0.777
0.240
0.274
0.777
-3.00%
0.242
0.293
0.778
0.238
0,280
0.775
+1.55%
Electricity
0..16
0,261
0.914
0.163
0.255
0,916
+-0.76%
0.166
0.264
0.912
0.164
0,260
0.916
+1.20%
Traffic
|
0.397
0.282
0.845
0.390
0,260
0.848
+1 +1.5%%
| 0.418
0.287
0.832
0.418
0,285
0.833
+0..19%
Solar
0,202
0.248
0.852
0.204
0.243
0.87%
0.224
0.226
0.848
0.214
0.219
0.852
+-1.15%
Table 3: Full results of long-term forecasting with TimeAlign as plugin. All results are averaged across four different prediction lengths: O E {96, 192, 336, 720). AMP denotes TimeAlsgn's
performance gain, either positive or negative.
ECL
Distribution Mismatch
Tiuutigs (Dard)
Hiseyry
Altty
Hunery Mover
MAE-0.187
MAA-00200 MAE-0.200
MAE-0.207 MAE--0198
-22
Traffic
(ii Distribution Calibration
Poture
Treelige (Dems
TTranformer
History
Honey trae
Hinery
Hatty
7,
60
46
8.0
MAE:0.190
-22
-10
-25
MAE10.216
ETTm1
(ii) Distribution Absence
Port
TieeAige (Dun)
10 Treestareer
OLieer
Brondhrath
MAE:0244
M.AEHO
-30
T-SNE
P-ONE Dan
T-
Figure 4: The t-SNE visualization illustrates the distribution of the history, the ground truth and the forecasts produced by TimeAlign, iTrrnsffrmer (Liu et al. (2024b). DLinear [eng et al.] 2002), iTransformer+ Alne and Timellnn on the ECL, Traffic, and ETTml datasets. The Aige forecasts almost perfectly overlap with the ground truth manifold, whereas the predic- tions from vanilla iTransformer and DLinear exhibit obvious distributional divergence. Plugging in TimeAlign visibly collapses this gap, steering backbones toward the target distribution.
5.4 PLUG-AND-PLAY EXPERIMENT
TimeAlign can be seamlessly integrated into diverse forecasting backbones. For encoder-based models, the encoder first maps the history X into latent embedding X' via patch embedding (Nie) ct al. 2023), value-wise convolution (Liu et al. 2024b) Wu et al. 202I), or linear projection (Huang et al. 2025 A parallel reconstruct branch with the same architecture projects the target Y into the same space Y', enabling alignment between prediction and reconstruction representations. This guides the backbone beyond point-win wise error minimization toward representations more informative of the target. To verify the plug-and-play capability. we augment both iTransformer (Liu et all 2024b) and DLinear (Zeng et al. 2023) and further quantify distributional discrepancy using cosine
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Published as a conference paper at ICLR 2026
ETTRZ (Ceput-220 -700
0.17
[Tgut-72D-fradct--00
Traffic
0.19
SOSNA Plec
1O0Twe 175mg
(M3)
maneforer
manetorar--ll
0.79
S06R6 5Tme
200AMB 43wa
66466 27tas
STONS 27na
1000
5000
0.40
0.37
TTreref sigefinnerrAggnn
7320MB
ModE
MOE
CCOEMO L0btea
1610ND 4ima
3607246 oddeo
ITaanformer 6672MB 142Ms
1902NO Mena
1450AR
0.16
4LOMB 10ma
(000)
1500
0.4G
0.30
198
DIONS 13
PRGMB
53me
15602M0
4000
(ms/iter)
Traiiing
Traning Iteration
Figure 5: Left: Model efficiency comparison under ETTm2 and ECL datasets. Right: Training iteration vs. MSE plot. Model training becomes more efficient and effective.
similarity (SIM), and ensure a fair comparison by searching the input length I. as Sec. 5.1 As shown in Tab. B TimeAlign consistently improves forecasting accuracy by 1%-4% across most benchmarks, while increasing cosine similarity between predictions and ground truth. This dual benefit of low error and high distributional similarity enhances forecast reliability. Performance dips on Weather and Solar datasets are caused by extreme outliers and zero-imputed values, which distort the learned distribution, inflate alignment loss and impair local alignment, respectively. Moreover, these excessively complex architectures hinder the alignment module from effectively correcting the hierarchically extracted representations, leading to inferior performance compared TimeAlign.
Furthermore, Fig. (right) visualizes the training trajectories of the vanilla and Time.Align- augmented iTransformer. With the plug-in, TimeAlign guides the encoder towards distributionally coherent minima, slightly increasing GPU memory usage, preserving the original per-iteration la- tency, and greatly accelerating convergence. On the Traffic dataset, the augmented one reaches the same validation loss 3,000 iterations earlier than the vanilla TTransformer.
5.5 ANALYSIS OF DISTRIBUTION AWARE AWARE ALIGNMENT
Fig. 4 presents t-SNE visualizations of the distributions of the history X. ground truth Y, and fore- casts from various methods on ECI., Traffic, and ETTm1. (a) X and Y exhibit a clear distribution shift with partial overlap. (b) Our Y pred bridge this gap, matching Y's range and fine-grained struc- ture, including peripheral outlier clusters, highlighting the effectiveness of TimeAlign. (c) and (d) TingAlign-uggmented
contrast the vanilla and TimeAlign augmented I'Transfommer and DLinear, respectively.
Furthermore, we categorize the discrepancies between Y and Y into three patterns. (i) Distribution Mismatch: resembles X more than Y; (ii) Distribution Calibration: global shapes align but local modes diverge; (iii) Distribution Absence: Y misses some modes of Y. Incorporating TimeAlign markedly reduces all three artifacts. On ECI., DLinear's forecasts shift from X's skew to Y's man- ifold; on Traffic, both I'Transfrmer's s and DLinear's predictions recenter around Y's true mean; on ETTm absent regions are recovered, yielding almost identical distributions Y. These qualitative results confirm Align is a robust plug-in for distribution alignment across backbones.
5.6 EFFECTIVENESS AND EFFICIENCY
Another key advantage of Align lies its competitive efficiency, delivering superior perfor- mance with few time cost. Using official configurations and the same batch size, Fig. shows that as a purely Linear architecture, TimeAlign surpasses all Transformer- and CNN-based methods in both speed and memory usage, while achieving SOTA training times among Linear-basee models.
6 CONCLUSION
This paper introduces TimeAlign, distribution-awar alignment framework for time series fore- casting. By coupling prediction and reconstruction with global and local alignment, TimeAlign effectively bridges the gap between past and future, preserving critical frequency components and boosting forecasting accuracy. Theoretical evidence demonstrates that reconstruction improves fore- casting generalization, while aligmment increases the mutual information between learned represen- tations and predicted targets. Extensive experiments validate the effectiveness of Time across diverse benchmarks. We believe that our findings open up promising avenues for reconsidering representation learning in time series forecasting.
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Published as a conference paper at ICLR 2026
7 ETHICS STATEMENT
As our work only focuses on the time series forecasting problem, there no potential ethical risk.
REPRODUCIBILITY STATEMENT
In the main text, we have formally defined the model architecture with equations. All the implemen- tation details, including dataset descriptions, metrics, and experiment configurations, are provided the manuscript.
ACKNOWLEDDMENTTS
This work was supported by DAMO Academy through DAMO Academy Research Intern Program.
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A
LLM USAGE
We used Large Language Models (LLMs) as auxiliary tools to assist with the writing process. They were used solely to polish the language and improve readability, with no influence over the research design, experimental implementation or analysis. We conceived and executed all methodological contributions, experiments, and conclusions independently.
B IMPROVE GENERALIZATION WITH RECONSTRUCTION ERROR MINIMIZATION
In this section, we discuss how the representation derived from the minimization of reconstruction error can be used to improve the generalization error. Let (z;, Vz). i = 1,..., be the set of training examples, where the latent input pattern 2; E IR. sampled from an Gaussian distribution (0, Ia) and the output vector y/ (1 Vi.d) R is constructed as follows:
Vi.
(0)
W x
(13)
We consider learning a linear regression model to map the input x output y. It is clear that the optimal solution is given by
M. = e1w The empirical estimator learned from the training examples (1r;, Ui) Wi) is given by
(14)
M =
T
aiy =we +
Σ
(15)
where 1 0 and 25,j Uo for j [2.....dl d]. Using the matrix concentration inequality, we have, with a probability 28
n
6d
d =
S
log
ca
(16)
0
i=1
2
Since
2
n
20
2 2
(m(d-1)
(17)
we have, with a probability
1-d d
2
n
3
Σ
n(d - 1 1
log
(18)
V
n(d - 1)
F
As a result, with a probability at least 1 - 35, we have
Mi - MalMal
1
T
24
M.M]
[Ma
72
71
i=1
i=1
-1
σ
6d
d
1
3
log 1 8
(19)
+
log
[
n
V
n
n(d 1)
Ω
10
Our second approach is to first learn one dimension representation for each yi by minimizing the reconstruction error, and then learn a linear regression model from the derived one dimension repre- sentation. The one dimension representation is derived by minimizing the following reconstruction еттor:
min wER", RvER
Y
vu
2
(20)
15

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Published as a conference paper at ICLR 2026
where Y (y1,.... Moo E Rdx", Evidently, and are the left and right singular vectors of Y with the largest singular value. We first write YYT as
Yy
(w a;)
erei
1
Σ
2
(21)
n1
Using the Davis-Kahan sin 0 theorem, we have
sin sin((u,e1) $
(22)
1, - (wT x2,)
Using the matrix concentration inequality, we have, with a probability 1 25,
6d
1
2
T
0
1 +
log
x
(23)
1=1
2
Since
n
(w
5;
~ |w Xm
(24)
have, with probability 1- 5
1 Σ
- w T x;;)²
log
1w0
(25)
As result, with a probability least 1 -25,
0² +
log
sin (2) S
m
(26)
Iw|2
log
As result, the one dimension representation
(u1 Un)
Y u. where each u, is given by
U v 1/4 w x; + (v eT)TT y/
(27)
Using the one dimension representation u, we obtain a new estimator M2 given by
1
MI =
Iunt' T = (o (TTe wwo T +
Tizi ve T
i=1
i=1
(28)
First, we have, with probability 1
(v e1)weT weil F I || - v eil [el + wllle eil
[1 11-- cos (w, + sin? 011, e1) + (1 - cos ((u,e))) |w]
2 cos 0(v, e1)) |wl = (snn A(v, e1)
((v,e1)
-11- 0o) V2
+ sin
[w] (29)
2
2
log
$ 44
n
w
log
Second, since
1
(30)
i=1
i=1
using the matrix concentration inequality, we have, with a probability
28,
4 log
n log
2
d
V
+
log
(31)
n
3n
n
16

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Published as a conference paper at ICLR 2026
Hence, with probability 1 - 36, we have
-1
222 0v
S
6d
log
d
4
1/2
log
3/2
d
+
log d
72
n
3n
8
n
(32)
Finally, with a probability
3d, we have
M22 MalF
log
6d
log
d
-1
1
log
3/2
2
log
d
IM.l.
|w]
1
log
m
3n
n
5
o²
22
|w/2
(33)
where
denotes the Frobenius norm. And when
(34)
n
have
MM M.LE
M1-M.l
-
(35)
M.Ir
I.MIr
Therefore, under the stated assumptions, the reconstruction-baseed estimator M2 achieves a strictly tighter approximation M than MM
C DETAILED DERIVATION OF MUTUAL. INFORMATION MAXIMIZATION
This section provides detailed derivation showing that our proposed method, TimeAlign, is grounded in the principle of Mutual Information Maximization (MIM). We demonstrate that our loss functions, Lped and Calign. are formulated to maximize the mutual information between the representation H. and the ground truth Y.
C.1 DERIVATION OF PREDICTION Loss LERED
Here, we illustrate the entire derivation of the mutual information (Y;; in Eq. We begin by deriving the prediction loss, Epred- presented Eq. TT this loss is directly related the mutual information term I I(;; H.). Using variational inference, we establish a lower bound for this term:
log P(y. hz)
I I(Y H.) Ep(y.h))
p(y) p(hx)
log plyl p(y]kz)) l1z) p(hx))
Ep(y.h.)
p(y) p(hz)
log p(yl hxz)
Ep(y.h))
(36)
p(y)
log plylhz) hx) Fo(u(h)))
Ep(y.h
p(y) Fo Fo hz)
log (u
p(y hz))
-Ep(y.h.))
+ Replan
log Foly hr))
p(y)
The second term is the Kullback-Leibe (KL) divergence between the true posterior p(yl hz) and the variational approximation Fo (...)) The equation can thus be rewritten as follows:
log Fo (t.)
[ / ply. hw,) log p(y)ha) Fo(y(ha)
IY; = Ep(y.he)
+
dy dh
p(v)
log Fo
/ plultw) (ailhh))p(h))))))))))))))))))))) log Fo(y(h.)
ply) dy dhas (37)
Eply.he)
p(y)
ho
log Fo(y)ha)
-Epy.hh))
+ p(te))
dha-
p(v)
17

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Published as a conference paper at ICLR 2026
Since the KL divergence term is non-negative (DKLHII) 0), can establish a lower bound for the mutual information as follows:
log Fo (km))
+ / hr
I(Y; H.) Ep((.he)
p(hx)) bww.Daaaleeeaaaalllll//a.... dha-
ply)
(ox)
log p(y)
(38)
B)(
llgg Fb())(z)) B(). [log p(y)),
2 Ep(v.A.) [log ht()) def Lped
As we assume that prediction errors follow Laplace distribution with fixed scale parameter b:
+ c, where ~ (1)
T
|c 1l--011 011
exp
(39)
26
Therefore, Folu h1a) ( 26 exp (- [iv==lle) ). The derived prediction loss can be further simpli-
fied to the form MAE loss:
Cpedd = -Bp(y.h.))
-T (ogo((26)
1 f1ll +1| x Bp(x.h.) [lly U|l1],
(40)
where ý denotes the predict results generated by the model, and T is the forecasting horizon.
C.2 DERIVATION OF ALIGNMENT Loss LALIGN
In addition to the prediction loss, we introduce an alignment loss, Latigns to further maximize the mutual information between the representation H2 and the ground truth Y. Inspired by contrastive learning, we derive an alternative lower bound for [Y: H.) based on the InfoNCE objective (Oord
al. 2018):
plu) p((tx))) )
p(y. he)
I(Y; H2) Ep(y.h2)
log
p(u(tu p(hex)
Bp(y
log
p(y) p(ha))
p(y(hw) p(y)
Ep(y.hz)
log
p(y)
-Ep(y.ha)
log
p(ylhx)
p(y) N
Ep(y.ha)
log
log N
p(y)ha) p(y) N ]
Eply.ha)
log
p(ylhm)
(41)
1+ p(y)
(N (N- - 1) 1).1)) 1
E p((,
log
p(y(he)
p(y)
p(es (hw) p(v))
)
Ep(y.h.)
log
1+ plulhe hew)
(N 1) Ep(ss)
ply (bre P())
-p(y.hz)
log
plylha p(3)
+
Σ
ply, PA.) (...) p(U.)
f(y.hw)
= Ep(y.hw)
log
[(y. hm) +
Σ
Mui ha))
18

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Published as a conference paper at ICLR 2026
Here, fly, hw) (hx T Go(y)) is a density ratio that is proportional to common practice (Choi Lee 2023), we use in-batch negative sampling strategy, where negative samples are drawn from other instances in the same mini-batch.
pla plul
p()) Following
Furthermore, inspired by recent advances in contrastive learning (He al. 2020 we simplify Eq. 41 as follows:
Chen & He
202
HY; ~ -Bp (f, hz)],
(42)
= -p(), [exp (proj(h2) ( def Callggn
Therefore, we get simpler alignment loss in Eq. 12 which further enhances the mutual information between the representation H₂ and the ground truth Y.
D EXPERIMENT DETAILS
D.1 METRIC DETAILS
We Mean Squared Error (MSE) and Mean Absolute Error (MAB) evaluation metries. Given the ground truth values Y; and the predicted values Y,, these metries are defined as follows:
1 Σ Y. Y.), MSE
MAE
Y,
Y
(43)
N
where N is the total number of predictions.
D.2 DATASETS
Time series forecasting is fundamental problem with wide range of applications in areas such as climate modeling (Niu et al.) 2025 Liu et al. 2024a). finance analysis (Hu et al. 2025a b), traffic flow prediction (Shu et al. [021] Miao al. 2024 Qiu et al., (025) and
From these areas, we choose several widely sidely-usedd used time series datasets and conduct extensive experiments on TSF. We report the statistics in Tab. Detailed descriptions of these datasets
follows:
(I) ETT (Electricity Transformer Temperature) dataset (Zhou et al., 2021 encompasses temperature and power load data from electricity transformers in two regions of China, spanning from 2016 2018. This dataset has two granularity levels: ETTh (hourly) and ETTm (15 minutes).
(2) Weather dataset (Wu al. 2023) captures distinct meteorological indicators Germany, meticulously recorded at 10-minute intervals throughout 2020. Key indicators in this dataset include air temperature, visibility, among others, offering comprehensive view of the weather dynamics.
(3) Electricity dataset ( (Wu et al. 2023 features hourly electricity consumption records in kilowatt- hours (kWh) for 321 clients. Sourced from the UCL Machine Learning Repository, this dataset covers the period from 2012 to 2014, providing valuable insights into consumer electricity usage patterns.
(4) Traffic dataset (Wu et 2023) includes data on hourly road occupancy rates, gathered by 862 detectors across the freeways of the San Francisco Bay area. This dataset, covering the years 2015 to 2016, offers a detailed snapshot of traffic flow and congestion.
(5) Solar-Energy dataset (Liu et al.) (024b) contains solar power production data recorded every 10 minutes throughout 2006 from 137 photovoltaic (PV) plants in Alabama.
D.3 IMPLEMENTATION DETAILS
All experiments are implemented in PyTorch (aaske et al. 2019) and conducted on one NVIDIA V100 32GB GPU. We use the Adam optimizer (Kingma 2014) with learning rate selected from (1e"3, 5e 1, 1e The batch size set to 16 for the Electricity and Traffic datasets, and 32 for all other datasets. Tab. 5 provides detailed hyperparameter settings for each dataset.
19

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Published as a conference paper at ICLR 2026
Dataset
Dim
Prediction Length
Dataset Size
Frequency
ETTml
7
{96, 192, 336, 720)
(34465, 11521, I 11521)
15 min
ETTm2
7
[96, 336,70) 720)
(34465, 11521, 11521)
15 min
ETThl
7
{96, 192, 336, 720)
(8545, 28811,
hour
ETTh2
7
{96, 192, 336, 720)
18545,2881) 2881)
hour
Electricity
321
{96, 3336, 720)
(18317, 2633, 5261)
hour
Traffic
862
{96, 192, 336, 720)
(12185, 1757, 3509)
hour
Weather
21
{96, 192, 336, 720)
(36792, 5271, 10540)
10 min
Solar-Energy 137
{96, 192, 336, 720)
(36601, 5161, 10417) 10 min
Table 4: Dataset detailed descriptions. "Dataset Size" denotes the total number of time points in (Train, Validation, Test) split respectively. "Prediction Length" denotes the future time points to be predicted. "Frequency" denotes the sampling interval of time points.
Tasks
Dataset
e_layers
Ir
d_model
d.ff
Num. of Patches
Num. of Epochs
ETTml
le-4
128
10
ETTm2
le-4
12
ETThl
5e-4
24
Long-term ETTh2
5e-4
48
Forecasting
Weather
1e-4
128
48
10
Electricity
2
5e-4
512
2048
10
Traffic
2
1e-3
512
2048
1
30
Solar Energy
2
5e-4
256
256
1
10
Table 5: Hyperparameter settings for different datasets. "e layers" denotes the number of graph block. "Ir" denotes the learning rate. "d model" and "d fP" denote the model dimension of attention layers and feed-forward layers, respectively.
E FULL RESULTS
E.1 MAIN EXPERIMENTS
Tab. Blnd Fig. pressent the full results for long-term forecasting, where the results obtained through hyperparameter search. The look-back horizons searched from {192, 336, 512, 720). TimeAlign consistently achieves the best performance, demon- strating its effectiveness and robustness.
ETTm2
ETTm1
0.243
0.340
0.154
0.192
E.2 ERROR BARS
ECL
Solar
In this paper, repeat all the experiments three times. Here we report the standard deviation of proposed TimeAlign and the second best model TVNet (Li et al. 2025), as well as the statistical sig- nificance test in Tab. We perform the Wilcoxon test with TVNet (Li al. 2025) and obtain the p- value of 1.37e indicating sigmificant improve- ment at the 99% confidence level.
Avg. IMP:4,75%
0.214
0.378
Weather
Traffic
TimeAlige
CMoS
iTronsformar
PatchTST
TVNet
TimeBose
Figure 6: MSE Performance of TimeAlign.
E.3 ABLATION STUDIES
Tab. presents the full results of the ablation studies discussed in the main text. @ w/o A Align signifies the
20

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Published as a conference paper at ICLR 2026
Predict Branch alone, with both Local and Global
Aligmment removed. @ w/ Local only denotes the Local Alignment module is retained to refine point-to-poine point similarity, while Global Alignment is disabled. @ w/ Global only denotes only the Global Alignment is retained to coarsely align the embedding distributions, while Local Alignment is omitted. ④ w/ Align encompasses both Local and Global Alignment mechanisms.
E.4 PLUG-AND-PLAY EXPERIMENT
presents the full results for Plug-and-Play experiment. TimeAlign enhances forecasting ac- curacy across diverse benchmarks while improving alignment between predicted and ground-truth sequences in the representation space. This combined improvement in predictive precision and dis- tributional consistency results in more reliable forecasts.
Tab.
E.5 EXTRA ANALYSIS OF RECONSTRUCTION
To validate the effect of reconstruction, we visualize the patch-wise similarity of history. ground truth, reconstructed series, and forecasts with and without alignment on the ETTml, ECL, and
Models
TimeAliga
CMo5
Timellase perg
TYNet
iTrassfomer
TimeMiser
Leddam
ModernTCNN
PaccTTST
Crosslomer
Times/et
DLinear
Metric
MSF
MXB
MBR
MAR
MAS
MBB
MAR
MSF
MAR
MSB
MAH
MSB
MAR
MSB
MAR
MAN
MSR
MAR
MSR
MAll
MSR
MAR
0.279
0.330
0.292
0,345
0,311
0.351
0.288
0.343
0,300
0.353
0.293
0,345
0.294
0.347
0.292
0.346
0.203
0,346
0,310
0,561
0,338
0.375
0,300
0.345
0.322
0.366
0.314
0.365
0.388
0.326
0.367
0.345
0.382
0.315
0.372
0.334
0.370
0.330
0.368
0.333
0.370
0.363
0.402
0.311
0:887
0.396
0.366
356
0.350
0.375
0.366
0.385
0.364
0.386
0,365
0.391
0,374
0,398
0.368
0.385
0.392
0.425
0,365
0.391
0,369
0.369
0.389
0.430
0:410
0.413
0.367
0.386
0.407
0.413
0.413
0:419
0:412
0.547
0.478
0:480
Ave
0.340
0.367
0.354
0,375
0.357
0.380
00,355
0.379
0.262
0,291
0.355
0,380
0.355
0.381
0.3251
0,381
0.225
0,382
0.420
0.435
0.400
0.405
[0.356 0,372
[0.155
0.341
[0.167
0.257
0.162
0.256
[..66]
0.254
0.175
0.266
0.165
0.256
0.114
0.260
0.166
0.256
0.166
0.256
0.263
0.359
0.189
0.365
[0.164 0.255
192
0.210
0,280
0.228
0.299
0.218
0.203
0.220
0.292
0.222
0,312
0.225
0.298
0.231
0.301
0.222
0.203
0.223
0.296
0.345
0.400
0.254
0,310
0.124
0,304
0.263
0.315
0.275
0.325
0.270
0.326
0,272
0,316
0,282
0,340
0.277
0.332
0.288
0.336
0.272
0.324
0.274
0.329
0.409
0.696
0,313
0.345
0.277
0.357
720
0.343
0.372
0.367
0,385
0,352
0.560
0.340
0.370
0.395 0.378
0.360
0.387
0.368
0.386
0.351
0.361
0.362
0.385
0.096
0.750
0.413
0.402
0.377 0.401
Arg
0.243
0.302
(1259
0,316
0,750
0.314
10225
0:311
0:000
[.227
0.M1
00000
0:330
0:253
0.314
0.256
0:317
0.518
0.501
0.202
0.390
10:880
0.334
96
0.332
0,347
0,361
0,383
0,349
0.384
0,371
0.400
0,296
0,405
0.372
0.401
0.377
0.394
0.268
1.394
0,377
0.397
0,386
0.426
0,384
0.402
0,403
ETThl
0.800
0.412
0.005
0.409
0.387
0.410
0,409
0,424
0,400
01413
0,430
0.405
0,427
0:415
0,413
0.409
0.429
0,413
0.642
0.557
0:436
0.400
0,419
336
0.424
0.430
0.412
0.420
0.405
0.418
0.40]
0.409
0.449
0.460
0.438
0.450
0.424
0.437
0.391
0.412
0.451
0.444
0.440
0.461
0L491
0.469
0.440
0.440
0.433
0.451
0.439
0.487
0.451
0.405
0.457
0.477
01519
0.524
0.521
0,500
00477
0,483
Avg
0.406
0.420
0.403
0.415
0.396
0.414
10.007
0.421
00.430
0.445
[.427
0.441
0.415
0.430
0.404
0.420
0.418
0:436
0.440
0.465
0.458
0.450
(0.424 0.430
10200
0.528
0.2274
0,341
0,202
0:339
0:200
0.345
002281
0.351
0.283
0.345
0,303
0,332
0:274
0.337
0.611
0.587
0.334
0,370
10.389
0.353
190
0.330
0.372
0.538
0.983
0.389
0.587
0.319
1L372
0.371
0.409
0.949
0.387
0.390
0.381
0.330
0.37d
0.348
0.364
0.709
0.634
0.404
0.415
0.383
0.418
0:300
0.399
0.542
0.384
0.358
0.410
0,311
0,373
0.404
0.428
0.366
0.413
0.366
0.405
0.313
0.376
0.377
0.466
03877
0.675
0,349
0.435
00:448
0.416
0.678
0.354
0.423
0.400
0.448
0.401
0.454
0:434
0.464
0
0.495
0
0.4%
0.190
0.439
0.406
0.441
1.094
0.775
0.434
0.445
00005
0.551
Ava.
0.336
0,382
0.331
0,383
0,345
0.397
0.324
0.377
0.374
0.406
0.349
0.397
0.345
0
0.332
0.379
0.35L
0.404
0.809
0.638
0,390
0.427
[0.43] 0.447
96
10.400
6.179
0.144
0.193
0.146
0.108
10.147
0.108
00.000
0.208
0.147
0.105
0.140
0.200
0.140
0.200
0.140
0.198
0.146
0.212
0.172
0.220
10.100 0.250
Woatee
0.182
0.220
0.186
0.237
0.185
0.241
0.194
0.238
0.200
0.245
0.192
0.243
0.193
0.240
0.196
0.245
0.194
0.241
0.195
0.261
0.219
0.261
0.316
1.232
0.362
0.240
0:081
0.286
0.281
0:235
0.272
0.359
0.389
0.244
0:284
0:341
0.279
0.238
0.272
0.345
0.262
0.252
0.311
0.240
0.106
0.055
0.307
720
0.307
0.317
0.311
0.332
0,309
0.331
0.308
0.331
0.321
0.358
0.318
0.330
0.324
0.338
0.314
0.334
0.314
0.334
0,318
0.565
0.365
0,359
0.323
0.362
|Arx
00:314
6.344
0,200
0.261
0.319
0.263
10:221
01261
002255
0:271
[0:226
0.204
10.205
02264
0:224
01264
012200
01264
112000
0.287
00.299
0.280
|0:343 0.293
00.126
0.216
0.120
0,223
0.139
0.231
0.342
0.223
0.138
0.237
0.142
0.247
0.134
0.228
0.129
0.226
0.129
0,222
0.135
0.237
0.168
0.272
00.140 0.237
Bleensity
152
0.163
0.235
0.143
0,233
0.153
0.345
0.105
0.241
0.157
0.250
0.108
0.209
0.155
0.248
0.161
11239
0.147
0.240
0.160
0.202
0.18:
0.289
0.152
0.249
336
0.155
0.349
0.161
0.254
0,169
0.362
0.164
0.269
0.167
0,264
0.171
0,260
0.173
0.268
0.161
0.259
0.163
0.259
0.182
0.292
0.198
0,300
0,170
0.267
0.159
0.378
0.200
0.285
0.207
0.294
0.190
0.254
0.194
0.286
0.209
0,313
0.186
0.252
0.191
0.266
0.197
0.290
0.246
0.337
0.220
0.320
0.203
0.301
AAg
[0.154
0.344
1.1
0,250
0.167
0.0.55
00.165
0.254
0.116
0.261
0.185
0.284
0.162
0.256
0.1.6
0.253
0.1.0
0.253
0.181
0.279
0.192
0.295
(0.166
0.264
10,39
0.225
0.357
0.256
0,394
01267
00.667
01252
0.3003
0.200
0.309
0.257
0.415
0.204
0.304
01255
0.370
01262
0.512
0.283
0.595
0.321
10.395
0.275
Tailfic
192
0.365
0.233
0,370
0.261
0.403
0.271
0.381
0.262
0,385
0.273
0.400
0.272
0.445
0.277
0.379
0.261
0.396
0,269
1.501
0.275
0.607
0.336
0.407
0.290
0.377
0.340
0.397
0.270
0.417
0.278
0.345
0.208
0.296
0.277
0.907
0.272
0.461
0.286
0,297
0.270
0.246
0.275
0.507
0.279
0.629
0.336
0.417
0.296
720
0.422
0,263
(1442
0.295
0,486
0.298
00.442
0.200
0.465
0.308
[ 0.316
0.489
0.300
0.440
0.290
0.29%
0.571
0.901
0.640
0,550
0.454
0.300
Arg
8.340
0.320
0:417
10:005
0.300
0:300
0.081
[0
0.279
004452
0:283
0.210
0.309
0.275
0.523
0.284
0.600
0:396
(0441 0.387
96
[..12
0.300
18188
0.341
0,320
0.369
00:204
0.260
0.188
0:333
0.179
0.283
0.197
0.341
0.300
0.263
0.178
0.239
0.183
0.208
[.219
0,314
(0.197 0.210
0.189
0.215
0.207
0.256
0.232
0.266
0.227
0.272
0.193
0.248
0.201
0.259
0.231
0:264
0:223
0.219
0.089
0.246
0.208
0.226
0.231
0.322
0:211 0.222
836
(1204
6.219
(.219
0.363
0.347
0.294
0.344
0.968
0.307
0:340
0.190
0.286
0.216
0.272
0:341
0.209
01108
0.349
1.212
0.219
0.246
0.389
(0:384
0:231
0.202
0.224
0.222
0.269
0.247
0.242
0:223
0.261
0.261
0.250
0.281
0:247
0.292
0.209
0.256
0.215
0.256
0.250
0,362
00:443
0.241
Arg.
0.192
8.214
0.200
0,257 0,236
0.270
[0.228
0.277
0.200
0.345
0.103
0.364
(0.223
0.264
0.228
0.281
0..04
0.245
0.205
0.230
0.244
0.334
(0.224 0.226
Table 6: Full results of long-term forecasting of hyperparameter scarching. All results are averaged across four different prediction lengths: O E [96, 192, 336, 720). The best and second-bes results are highlighted in bold and underlined, respectively.
21

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Published as a conference paper at ICLR 2026
Model
TimeAlign
TVNet 2025
Confidence
Dataset
MSE
MAE
MSE
MAE
Interval
ETTml
0.340 + 0.011
0.367 = 0.008
0.348
0.009
0.379 = 0.007
99%
ETTm2
0.243 + 0.006
0.302 - 0.006
1.250+00 0.004
0.311 + 0.005
99%
ETThl
0.406 + 0.009
0.420 = 0.007
0.407 0.010
0.421 + 0.009
99%
ETTh2
0.336 + 0.014
0.382 = 0.012
0.024
0.377 = 0.015
99%
Weather
0.214 0.009
0.214 0.007
0.221 0.008
0.261 = 0.008
99%
Electricity
0.154:10.00
0.244 = 0.008
0.008
0.254 + 0.006
99%
Traffic
0.378 0.010
0.240 0.011
0.396
0.268 0.013
99%
Solar
0.192 + 0.012
0.214 = 0.013
0.228 0.0011
0.277 = 0.009
99%
Table 7: Standard deviation and statistical tests for TimeAlign and second-best method (TVNet) on ETT, Weather, Electricity, Traffic and Solar datasets.
Local Align
Global Align
ETTml
ETTm2
Weather
Electricity
Traffic
w/
Length
MSE
MAE
MSE
MAE
MSB
MAE
MSE
MAE
MSR
MAR
96
0.289
0.333
0.162
0.246
0.151
0.191
0.129
0.219
0.358
0.235
192
0.328
0.358
0.221
0.287
0.193
0.231
0.146
0.235
0.377
0.245
336
0.359
0.377
0.275
0.324
0,243
0.272
0.162
0.252
0.393
0.253
720
0,420
0.412
0.349
0.375
0.314
0.323
0,200
0.284
0.431
0.273
Aug.
0,349
0,370
0.252
0.308
0,225
0.254
0.159
0.248
0.390
0.249
96
0.284
0.335
0.158
0,243
0.145
0.184
0.129
0.219
0.352
0.230
192
0.324
0.359
0.212
0,282
0,188
0.226
0.145
0.235
0.372
0.239
x
336
0,356
0,380
0.265
0.318
0,236
0.267
0.160
0.251
0.385
0.244
720
0.414
0.415
0.345
0.375
0.310
0.319
0.196
0.282
0.425
0.265
Avg.
0.344
0,372
0.245
0,305
0,220
0.249
0.157
0.247
0.383
0.244
96
0.282
0.332
0.157
0.242
0.142
0.180
0.128
0.218
0.354
0.232
192
0.325
0.358
0.211
0,281
0.184
0,223
0.146
0.234
0.369
0.236
336
0.353
0.378
0.265
0,318
0.235
0.265
0.161
0.251
0.383
0.245
720
0.409
0.410
0.343
0.371
0,311
0.320
0.193
0,280
0.424
0.265
Avg.
0.342
0.369
0.244
0.303
0.218
0.247
0.157
0.246
0.383
0.245
96
0.279
0.330
0.155
0.241
0,140
0.179
0.126
0.216
0.349
0.225
192
0.322
0.356
0.210
0.280
0.182
0.220
0.143
0.233
0.365
0.233
336
0.350
0.375
0.263
0.315
0,232
0.262
0.158
0.249
0.377
0.240
720
0.407
0.406
0.343
0.372
0.307
0.317
0.189
0.278
0.422
0.263
Avg.
0.340
0.367
0.243
0.302
0.214
0.244
0.154
0.244
0.378
0.240
Table 8: Full results of ablation on the effect of removing alignment in local and global perspective.
V indicates the use of alignment, while x means alignment is retained.
Traffic datasets as in Fig. 8 The similarity maps of the ground truth and the reconstructed series are almost identical, with reconstruction errors approaching zero. This demonstrates that reconstruction effectively captures multi-frequenc information, including both low-frequency periodic patterns and high-frequency variations, thereby assisting the forecaster in making more accurate predictions.
E.6 ROBUSTNESS ANALYSIS
For robustness against abrupt fluctuations, we also include experiments on high-volatility Stock Market data. It is well known that stock market data is extremely non-stationary, exhibiting evolv- ing dynamics, abrupt regime changes, and distributional instability over time. To further evaluate robustness under distribution shifts, we conducted additional experiments on the two stock datasets (NASDAQ and NYSE) released by TFB (Qiu et al. 2024). As shown in Tab. I0 TimeAlign consis- tently achieves the best forecasting performance, outperforming all baselines across all prediction horizons. These findings further validate that our distilled "future prior" behaves reliably under distribution shifts, non-stationary temporal patterns, and evolving dynamics.
22

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Published as a conference paper at ICLR 2026
(6) ETTh2
(b) ETTml
(6) EdL
(d) Traffic
0.40
0.40
0.12
0.42
96
0.36
0.30
0.40
336
192
0.34
0.38
720
0.32
0.33
0.32
0.30
0.30
0.54
0.36
0.28
0.0
0.2
0.4
0.6
0.5
1.0
0.0
0.2
0.4
0.5
0.6
1.0
0.0
0.2
0.4
0.5
0.6
1.0
0.0
0.2
0.4
0.5
0.6
1.0
Algnment Weight
Algrment Weight
Algmment Weight
Algmment Weight
Figure 7: Effect of alignment loss weight across ETTh2, ETTml, ECL and Traffic.
Models
iTransformer
-TimeAlign
DLineur
ATimeAlign
Metric
MSE
MAE
SIM
MSE
MAE
SIM
AMP
MSE
MAB
SIM
MSE
MAB
SIM
JJMP
0.300
0.353
0.850
0.302
0.352
0.883
-0.67%
0.345
0.887
0.300
0.888
+-000%%
192
0.345
0.382
0.870
0.337
0.374
0.872
12.32%
0.336
0.366
0.878
0.332
0.361
0.880
11.19%
336
0.374
0.398
0.859
0.364
0.389
0.863
+2.67%
0.367
0.386
0.863
0.362
0.380
0.867
+1.36%
720
0.429
0:430
0.840
0.119
0:421
0.843
+2.33%
0.419
0:416
0,848
0,413
0.409
0.853
+1.43%
Aug.
0.362
0.391
0.862
0.355
+1.0%
0.356
0.378
0.869
0.352
0.872
+ +1.0%
0.175
0.266
0.980
0.170
0,984
+2 86%
0.255
0,982
0.162
0.985
+1.22%
ETTm2
192
0.242
0.312
0.974
0.234
0.298
0.979
13.31%
0.224
0.304
0.977
0.218
0.287
0.979
1 2.68%
336
0,282
0.340
0.969
0.278
0.332
0.972
+1.42%
0.277
0.337
0.971
0.270
0.325
0.975
+2.53%
720
0.378
0.398
0.956
0.358
0.381
0
+5.299
0,371
0:401
0,960
0,359
0.385
0,963
+3.23%
Aug.
0.329
0.970
0,260
0.974
+3.44%%
0.259
0.324
0.973
0.252
1..61%
0.386
0.405
0.849
0.382
+1 0.0%
0.403
0.862
0.367
0.394
0.861
+3.117%
192
0.424
0.440
0,833
0.420
0.439
0.836
1 10.94%
0.408
0.419
0.848
0.406
0.416
0.846
0..49%
336
0.449
0.460
0.823
0.447
0.458
0.825
+0.45%%
0.440
0.440
0.338
0.432
0.440
0.835
+1.22%
720
0.495
0.487
0.795
0.162
0.482
0.799
+6.67%
0.471
0.493
0.816
0,452
0.480
0.819
+1.03%
Aug.
0.825
0.428
0.448
+.2.45%
0.424
0.439
0.841
0.414
0.840
12.41%
0.297
0.967
0.288
0.349
0.971
+3. 03.
0.289
0.353
0.970
0.283
0.344
+2.08%
192
0,371
0.403
0.959
0.361
0,395
0.963
+2 70%
0,383
0.418
0.962
0.362
0.396
0.962
+5.48%
336
0.404
0.428
0.954
0.394
0.421
0.959
+2.48%
0.448
0.465
0.956
0.420
0.439
0.957
+-536%
720
0.424
0.444
0.950
0.110
0.442
0.953
+3.30%
0.605
0.551
0.950
0.607
0.545
0.951
-0.33%
Aug.
0.406
0.958
0.363
0.402
0.962
22.87%
0.431
0.447
0.960
0.418
0.960
1.300%
0.159
0.208
0.852
0.160
0.203
-0. 0.63%
0.170
0.230
0.848
0.169
0.223
0.845
+-0.59%
Weather
192
0,200
0.248
0.798
0,209
0,248
0,809
-4 5.50%
0.216
0.273
0.805
0,210
0.256
0.805
+2.78%
336
0,253
0.269
0.751
0.258
0.294
0.758
.99%%
0.258
0.307
0.760
0.255
0.294
0.758
+1.16%
720
0.321
0.338
0.706
0.334
0.350
0.682
-1.5%
0.323
0.362
0.698
0,318
0.346
0.692
+1.35%
Aug.
0.271
0.777
0.240
0.274
3.00%
0.242
0.293
0.778
0.238
0.280
0.775
1.55%
0.237
0.932
0.132
0.225
0.936
+4 35%
0.237
0.927
0.137
0.234
0.932
+2.144%
Elecnriity
192
0.157
0.256
0.920
0.154
0,247
0.923
+1.91%
0.152
0.249
0.919
0,151
0.247
0.923
+0.66%
336
0.167
0.264
0.908
0.169
0,262
0.910
1.20%
0.169
0.267
0.911
0.167
0.263
0.914
+1.1
720
0.194
0.286
0.895
0.196
0.284
0.893
- -1.08%
0,203
0.301
0.891
0,201
0.295
0.893
+0.99%
Aug.
0.164
0,261
0.914
0.163
0.916
1 10.66%
0.166
0.264
0.912
0.164
0.260
0.916
1.20%
0.363
0.265
0.854
0.354
+2. 48%
0.275
0.838
0.397
0.837
-0.51%
Traffic
192
0,385
0,273
0.848
0.377
0,255
0.852
+2.055 08%
0.407
0.280
0.836
0.106
0.278
0.535
+0.25%
0.396
0.277
0.845
0.399
0.264
-0. 766
0.286
0.834
0.416
4-0.24%
720
0.445
0.308
0.831
0.128
0.279
0.837
+3.82%
0.154
0.308
0.821
0,452
0.302
0.822
+0.44%
Avg.
0.397
0.282
0.845
0.390
0.260
1 1.95%
0.418
0.287
0.832
0.418
1.21
0.232
0.860
0.181
+3.72%
0.854
0.190
0.858
+3.35%
192
0.193
0.248
0.852
0.205
0,249
0.851
-6.25 22%
0,218
0.222
0.849
0.212
0.217
0.854
+2.75%
0.203
0.850
0.218
0.250
7 7999
0:234
0:231
0.846
0.224
4-1.27%
720
0.223
0.261
0.845
0.210
0.244
0.847
+3.83%
0.243
0.241
0.844
0.229
0.253
0.846
+5.76%
Avg.
0.202
0.248
0.852
0.204
0.243
0.853
-0.87%
0.224
0.226
0.848
0.214
0.219
0.852
15.
Table 9: Full results of long-term forecasting with Time as a plugin. All results are averaged across four different prediction lengths: O E (96, 192, 336, 720). A/MP denotes TimeAlign's performance gain, either positive or negative.
23

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Published as a conference paper at ICLR 2026
History
GroundTruth
Reconstruct
w/ Align
w/o Align
(a) ECL
History
GroundTruth
Reconstruct
w/ Align
w/o Align
(b) ETTml
Coslee Similority
0,7
History
GroundTruth
Reconstruct
w/ Align
w/o Align
(c) Traffic
Visualization of patch-wiss wise similarity of history, ground truth, reconstructed series, fore- cast with and without alignment from ETTml, ECL and Traffic. The similarity maps of the ground truth and the reconstructed series are almost identical, with reconstruction errors approaching zero.
Figure 8:
TimeAlign
PatchTST
Crossformer
DLinear
NLinear
MICN
TimesNet
FEDformer
Models
(Ours)
2023
2025)
2023
2023
2022
X22
Metric
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
NASDAQ 0.649 0.879 0.717
0.977 0.999 1.752 0.889
1.503
0.682
0.926
0.884
1.530 0.697
0.996 0.694
0.900
NYSE
00.885
0,388 0.427 0.471 (0.913 0.988
0.556
0.582
0.401 0.402 0.639 0.737 00.45 0.509 0.422 0.407
Table 10: Long-tern forecasting results on stock market data.
E.7 HIGH FREQUENCY ANALYSIS
To directly validate TimeAlign's 's capability to capture rapid temporal dynamies, introduce the Hrihh-Frquencyy Mean Squared Error (CHF-MsE). This metric quantifies the error between the pre- dicted (Y") and true (Y) series the frequency domain, focusing only on the high-frequency band (Snigh) identified via knee-point detection. Calculation of HF-MSE:TH metric is computed by per-
forming the Discrete Fourier Transform (DFT) on Y and Ý and calculating the mean squared mag- nitude difference the isolated high-frequency components:
LHE-MSF
Σ Thigh AE
(Yrre))s (Frre))a
where Thigh is the count of components in Snigh- Tab. 11 summarizes the improvement in HF-MSE datasets and presents results various datasets, demonstrating the superior robustness of TimeAlign on abrupt, fine- mne-grained temporal dynamics.
E.8 EXTRA ANALYSIS OF DISTRIBUTION-AW.N ALIGNMENT
Influence of Alignment Loss Weight. We further investigate the influence of the key hyperparam- eter, the weight of alignment loss X, sweeping À (0.0, 0.2, 0.4, 0.6, 0.8, 1.0] across four datasets. Fig. 7 shows that ETTh2 and ETTml are highly sensitive to X, whereas ECL and Traffic remain relatively stable. In essence, À controls the trade-off between distribution matching and point-wise enror minimization. As increases, the model increasingly emphasizes aligning the predictive and target distributions, strategy that generally reduces error, since better distribution overlap typically
24

---

Published as a conference paper at ICLR 2026
Models
ETTh1
ETTml
Weather
ECL
Traffic
Metric
HE-MSE HF-MAF
HF-MSE
HE-MAR
HF-MSE
HF-MAE
HF-MSE
HF-MAF
HE-ME
HF-MAE
TimeAlign
2.86
1.27
2.54
1.19
3.51
1.35
40.60
5.09
253.71
10.64
w/o Align
2.97
1.36
2.73
1.35
3.66
1.50
42.75
5.44
261.43
11.56
Table 11: Long-term forecasting results with HI-MSE/HT-MAE metrics.
Sample
Somple
SSmple
-0.70
-1.9
-0.72
Volce
-1.0
-1.3
Timestomp
Sample
Sample
Samplc
-3.1
1.5
-1.3
Videe
2.5
-..
Timestenp
Timeshonp
Figure 9: Visualization predictions from ETTm1, ETTm2, ECL, Solar and Traffic.
implies lower error. However, excessively high À may cause the model to highlight minority modes, particularly outliers, thereby degrading performance. Therefore, selecting an appropriate for each dataset amounts to carefully balancing these two optimization objectives to maximize the overall predictive capability.
F VISUALIZATION
In order to facilitate a clear comparison between with and without alignment, we present supplemen- tary prediction examples for four datasets, ETTm1, ETTm2, Weather, ECL, Solar, and Traffic in Fig. 9 respectively. The book-back horizon and the forecasting horizon T are both 720 for all four datasets.
25


Reviews:
[{"review_id": "PP9LMsmVdp", "reviewer": "Reviewer_tnT5", "summary": "This paper proposes TimeAlign, a lightweight and plug-and-play framework for time-series forecasting that aims to mitigate the distributional bias between historical inputs (Past) and future targets (Future). The authors observe that existing models tend to over-rely on low-frequency periodic patterns, lose high-frequency details, and suffer from representational misalignment between past and future features. To address this, TimeAlign introduces an auxiliary Reconstruction Branch and employs both global and local distribution-aware alignment mechanisms to constrain the main Prediction Branch, enabling representations that are simultaneously distribution-aware and detail-preserving. The method is theoretically analyzed through mutual information and empirically improves forecasting performance across multiple benchmarks and backbones.", "questions": "1. Could the authors provide more evidence that the model learns meaningful high-frequency dynamics rather than merely amplifying spectral noise? For instance, have the authors considered phase-level or band-wise validation (e.g., coherence with ground-truth signals) to confirm that the reconstructed high-frequency components are temporally aligned?\n\n2. How does this prior behave under distribution shifts or evolving dynamics where future statistics differ from training? It would be informative to test this explicitly. For example, simulate mismatched future distributions or evaluate on real-world datasets with non-stationary temporal patterns to verify whether the learned alignment remains adaptive.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 4, "presentation": 2, "contribution": 4, "strengths": "S1: The paper explicitly attributes forecasting errors in time series forecasting models to the distributional misalignment between past and future representations, and quantifies this mismatch through cosine-similarity analysis and visualization.\n\nS2: The method is simple and modular. A reconstruction branch could be added to any backbone model, and the prediction branch is constrained through dual alignment. Both alignment formulations, relaxation terms, and the adaptive weighting factors (α/β) are well defined, and the overall objective adds only one alignment loss term to the original training loss, making the module fully plug-and-play.\n\nS3: The paper provides formal analysis showing that reconstruction-based alignment can tighten generalization bounds and implicitly enhance the mutual information between model representations and targets. This gives the method a stronger theoretical foundation than most empirical time series forecasting approaches.\n\nS4: The proposed module is tested on several representative time series forecasting architectures (e.g., iTransformer, DLinear) and achieves consistent improvements across benchmarks. It also demonstrates faster convergence during training, with negligible additional overhead.", "weaknesses": "W1. Although the paper motivates TimeAlign through the problem of frequency smoothing, the proposed method does not explicitly model spectral information. Its improvement on high-frequency dynamics is achieved only implicitly via reconstruction and alignment. The frequency analysis is limited to the high-frequency energy ratio and spectrogram visualization, which measure the amount of high-frequency content but not its correctness or temporal alignment with the ground truth. Without band-wise or phase-level validation, it remains unclear whether the model truly learns meaningful high-frequency dynamics or merely amplifies spectral noise.\n\nW2: The reconstruction branch provides strong supervision from the future target distribution during training, but is discarded entirely at inference. This raises a potential train-test inconsistency: predictive representations are optimized under guidance unavailable during deployment. The paper does not evaluate whether removing the reconstruction branch alters representation stability or performance, leaving uncertainty about the robustness of TimeAlign under distribution shift or domain generalization.\n\nW3: The alignment mechanism may implicitly push the prediction branch to form a collapsed representation resembling a static “future prior.” Since the reconstruction branch (which observes future data) is only available during training, the learned “future-like” latent space might represent a statistical prior distilled from past futures rather than the true evolving future distribution. This is not necessarily harmful, but it remains unclear whether such a prior actually helps mitigate distribution mismatch at inference, especially when future dynamics deviate from the training regime.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "sfu7emYbMV", "reviewer": "Reviewer_FFNQ", "summary": "This paper proposes a representation learning framework for time series data based on reconstruction objectives.", "questions": "I wrote these questions based on the priority.\n\n1. Provide a clear and theoretically grounded explanation of why reconstruction is beneficial for time series forecasting. (Related to W1)\n\n2. Re-examine the performance of the Predict Branch in the ablation studies and explain why it outperforms many baselines. Ensure that the experimental setup and baseline implementations are described in sufficient detail to guarantee fair comparison. (Related to W5)\n\n3. Offer a solid rationale for the Gaussian and linearity assumptions introduced in Eq. 9 and Appendix B, and discuss their practical relevance to real-world time series data. (Related to W3)\n\n4. Clearly articulate how and why reconstruction provides explicit advantages within the Mutual Information Maximization (MIM) framework, compared to other existing MIM-based approaches. (Related to W4)\n\n5. Provide reasoning or empirical evidence supporting key design decisions - such as the use of margin terms, GELU activation, and dynamic loss weighting. (Related to W2)", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "1. The empirical results are generally strong; the reported evaluation metrics outperform or are on par with existing baselines, although some results appear potentially inconsistent and merit further verification.", "weaknesses": "Major Weaknesses\n\n1. **Lack of rationale for reconstruction:**\nThe motivation for using reconstruction as the core learning principle is not clearly articulated. The paper claims that reconstruction aligns representations with the target distribution because it “recovers inputs from themselves,” but this statement simply restates the definition of reconstruction. It does not provide a conceptual or theoretical justification for why reconstruction should yield better representations. Similarly, the claim that reconstruction emphasizes high-frequency details is asserted but never explained or supported by analysis.\n\n2. **Unclear methodological details:**\nSeveral methodological choices are insufficiently justified or analyzed.\n- Why are the margin terms ($\\delta_{loc}$, $\\delta_{glo}$) necessary?\n- What is the rationale for using the GELU activation function specifically?\n- What motivates the introduction of a weight-based dynamic loss?\n\n3. **Abnormal assumptions in Eq. 9 and Appendix B:**\nThe theoretical analysis assumes that patterns are drawn from a Gaussian distribution and that outputs follow a linear transformation only at the first time step, with Gaussian noise thereafter. These assumptions are highly unrealistic for time series data. Consequently, the claim that an optimal estimator exists in a linear form is not meaningful in practice. The proof and theorem therefore have limited - if any - practical relevance.\n\n4. **Weak justification of claims in Section 4.2:**\nThe discussion on mutual information maximization (MIM) lacks substance. Prior works such as MINE (Belghazi et al., ICML 2018) and other MIM-based methods have already shown that deep models implicitly maximize mutual information through their layers. The paper does not provide convincing evidence that reconstruction is strictly better than other MIM approaches.\n\n5. **Inconsistent ablation results:**\nIn the ablation study, the variant using only the “Predict Branch” (i.e., without reconstruction) outperforms most state-of-the-art baselines. This raises concerns about the fairness of the experimental setup and the actual contribution of the proposed reconstruction mechanism. Further clarification or additional controlled experiments are needed.\n\nMinor Weaknesses\n\n6. The Introduction lacks clear structure. The first and third observations are redundant and should be merged or rephrased.\n\n7. The figures are visually cluttered; they attempt to convey too much information at once, which makes them hard to interpret.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "pgXgWt8hCb", "reviewer": "Reviewer_Daur", "summary": "The paper presents TimeAlign, a framework for time series forecasting that bridges the gap between past and future data. It uses a dual-branch architecture, with a Predict Branch for forecasting and a Reconstruct Branch for target reconstruction. TimeAlign employs distribution-aware alignment, combining local and global objectives to preserve fine-grained details and enhance forecasting accuracy. Experiments show it outperforms existing methods, with theoretical analysis highlighting its ability to improve generalization and increase mutual information between learned representations and future targets.", "questions": "Please see the weaknesses.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper is easy to follow, with clear and thorough writing. The motivation highlights three key limitations in current time series forecasting, which are well-justified.\n\n2. The experiments are solid. The main experiments demonstrate that TimeAlign outperforms other SOTA methods, and the ablation studies validate the effectiveness of its components.\n\n3. I appreciate the theoretical analysis provided in Section 4, Appendix A, and Appendix B, which enhances the theoretical contribution of the paper and explains the underlying reasons for the method's effectiveness.\n\n4. TimeAlign can also serve as a plug-and-play module, making it easy to integrate with other mainstream methods.", "weaknesses": "1. Equation 8 in Line 292 is slightly inconsistent with Figure 3. One version includes both $\\lambda_1$ and $\\lambda_2$, while the other has only $\\lambda$. It seems the version you're using is the one with a single $\\lambda$, so the formula in the figure should be updated. Also, Figure 6 analyzes the impact of different $\\lambda$ on performance. If following the formula in the figure with both $\\lambda_1$ and $\\lambda_2$, what would be their effect? I would appreciate a more detailed analysis of the loss function's behavior.\n\n2. In the Weather/Solar plug-in experiments, author attributes performance differences to outliers and zero-padding issues. However, more concrete quantitative evidence is needed to support this claim.\n\n3. The knee-point detection used to separate high/low frequencies (Figure 2) may be sensitive to noise and window selection, which could affect the reliability of the high-frequency energy/similarity analysis.\n\n4. I find Figure 4 (right) quite interesting, but in Lines 453-457, it seems you are merely describing an experimental result. What is the underlying reason for iTransformer+Align converging faster than iTransformer? Also, do other architectures, such as CNN-based or Linear-based models, show similar behavior?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "krh9v05o9p", "reviewer": "Reviewer_adVR", "summary": "This paper proposes TimeAlign, a lightweight framework that enhances time series forecasting by introducing a reconstruction branch and aligning its representations with those of the prediction branch at multiple layers. Theoretically, the authors justify that (1) the reconstruction branch improves generalization, and (2) the alignment loss strengthens the mutual information between historical and future representations. Extensive experiments on eight benchmark datasets and multiple backbones demonstrate consistent performance gains.", "questions": "1. The authors conducted plugin experiments on iTransformer and DLinear. So, which types of backbones (e.g., Transformers, MLPs, CNNs, etc.) benefit the most from being combined with TimeAlign?\n\n2. What is the computational and memory scaling of the global alignment loss as sequence length and channel dimension grow?\n\n3. In the NIPS 2024 workshop[1], some researchers pointed out that current methods sometimes use the \"drop-last\" trick [2] to improve performance. Therefore, It is recommended that you clarify whether the \"drop - last\" operation was used in your paper in the implementation details section of your paper for transparency.\n\n[1] Fundamental limitations of foundational forecasting models: The need for multimodality and rigorous evaluation\n\n[2] TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods", "limitations": "", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "1. The motivation is clear and intuitive. The paper explicitly identifies three limitations of current forecasting paradigms and addresses them directly through reconstruction and alignment. \n\n2. The method requires only a lightweight reconstruction branch during training, and introduces no additional parameters at inference.\n\n3. The paper presents two theoretical analyses: reconstruction-guided generalization based on the assumption of a linear model, and an approach based on mutual information for alignment, which aligns well with empirical observations.\n\n4. The effectiveness of TimeAlign has been validated on eight widely used benchmarks.", "weaknesses": "1. It seems important to stop the gradients from the alignment loss to the reconstruction branch, but the justification for this is insufficient, as it lacks a comparison with symmetric gradient flow.\n\n2. The overall loss function combines three terms, but the paper does not analyze sensitivity to the hyperparameter margins $\\delta_{loc}, \\delta_{glo}$.\n\n3. It is unclear whether all the baselines were retuned under identical conditions with regard to the look-back window and learning rate. As TimeAlign is a plug-in, consistent hyperparameter settings across backbones are required for a fair comparison.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)