CoRA: Boosting Time Series Foundation Models for Multivariate Forecasting through Correlation-aware Adapter
Authors: Hanyin Cheng
Xingjian Wu
Yang Shu
Zhongwen Rao
Lujia Pan
Bin Yang
Chenjuan Guo
Venue: ICLR 2026 Poster (2026)
Keywords: Multivariate Time Series Forecasting
Time Series Foundation Models
Correlation
Primary area: learning on time series and dynamical systems

Abstract: Most existing Time Series Foundation Models (TSFMs) use channel independent modeling and focus on capturing and generalizing temporal dependencies, while neglecting the correlations among channels or overlook the different aspects of correlations. However, these correlations play a vital role in Multivariate time series forecasting. To address this, we propose a Correlation-aware Adapter (**CoRA**), a lightweight plug-and-play method that requires only fine-tuning with TSFMs and is able to capture different types of correlations, so as to improve forecast performance. Specifically, to reduce complexity, we innovatively decompose the correlation matrix into low-rank Time-Varying and Time-Invariant components. For the Time-Varying component, we further design learnable polynomials to learn dynamic correlations by capturing trends or periodic patterns. To learn positive and negative correlations that appear only among some variables, we introduce a novel dual contrastive learning method that identifies correlations through projection layers, regulated by a Heterogeneous-Partial contrastive loss during training, without introducing additional complexity in the inference stage. Extensive experiments on 10 real-world datasets demonstrate that CoRA improves the state-of-the-art TSFMs in average forecast performance.

Published as a conference paper at ICLR 2026
CORA: BOOSTING TIME SERIES FOUNDATION MOD- ELS FOR MULTIVARIATE FORECASTING THROUGH CORRELATION- ADAPTER
Hanyin Cheng", Xingjian Wu', Yang Shu', Zhongwen Rao", Lujia Pan"
Bin Yang', Chenjuan Guo EEatt China Normal University
"Huawei Noahs Ark Lab
(hycheng, xjwu restu.ecnue edu. cn,
(raozhongwen, paniujial@euaeelll com, (yshu,byangh ejaug, (aceeagoooosseeeeeeeeeeee @dase. ecnu, edu. en,
ABSTRACT
Most existing Time Series Foundation Models (TSFMs) use channel indepen- dent modeling and focus capturing and generalizing temporal dependencies, while neglecting the correlations among channels or overlooking the different as- pects of correlations. However, these correlations play vital role in Multivariate time series forecasting. To address this, we propose CoRrelation-awan Adapter (CoRA), a lightweight plug-and aang-and-payy method that requires only fine-tuning with TSFMs and is able to capture different types of correlations, so as to improve forecast performance. Specifically,
reduce complexity, we innovatively de- compose the correlation matrix into low-rank l'meeVVryyng and Vime-Innarian components. For the Time- Varying component, we further design learnable poly- nomials to learn dynamic correlations by capturing trends periodic patterns. To learn positive and negative correlations that appear only among some channels, we introduce novel dual contrastive learning method that identifies correlations through projection layers, regulated by a Heterogeneous- Partial contrastive loss during training, without introducing additional complexity in the inference stage. Extensive experiments on 10 real-world datasets demonstrate that CoRA can im- prove TSFMs in multivariate forecasting performance.
INTRODUCTION
Time Series Foundation Models (TSFMs) that show strong generalization are proposed recently. Through pre-training large-scale time series data (Wang et all 2025d: Goswami all 2024 Lm all 2024g Wang et al), 2(253) or the use of large language models (Zhou et all 20233 Liu et all 2024107; [In ala 20244), these models maintain strong reasoning abilities when handling new or unseen data.
At the same time, multivariate time series forecasting, pivotal domain in data analysis, is widely applied in various industries (Quu el all 4025;;; Wu et all RIZA:: atultaal 20263; Qru el all, 202ATE Lunetall (0265; Wang et all, 20246: Quu all, 20256). Properly modeling and utilizing correlations in multivariate time series can significantly improve the performance of forecasting models (Zhang Yan, 2022 Lin all, 2024C; Wu et all, 2020). Based on different interaction characteristics among channels, as shown in Figure Пa, correlation can be summarized into three aspects: dynamic correlation (DCorr) describes the variation channel relationships over time (Zhao et al, 20233 Cistcc et al. 2( heterogeneous correlation (IICorr) focuses on how channels interact with each other by considering positive and negative correlations (Huang et all, 2022);; partial correlation (PCorr) emphasizes that correlation exists only among certain channels, and modeling interactions across all channels can easily introduce noise (Chen et all 2024: Quu et alj 20247 et 20248). Considering more comprehensive correlations provides richer information for the models.

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However, most existing TSFMs focus capturing and generalising temporal dependencies and ne- glect relationships among channels (Grssaam et all 2024; Ansar et all 2024 Liu et all 2024<h
Un et al, 2024: Shi et all 2023). Although some models like TTM (Ekambaram et al. 202210), UniTS (Gao et all 2024),, and Moirai (Won et all 2024) employ different methods to model the correlations among channels, they do not comprehensively consider multiple aspects of the correla- tions, For example, TTM employs an MLP-based channel mixing approach, but the MLP weights remain unchanged across different time steps, thereby failing to model DCorr while indiscriminately modelling interactions among all channels, and thus failing to capture HCorr and PCorr explicitly. While the attention mecha-
nisms used in UniTS and Moirai assign different atten- tion scores at different time points, they still interact all channels simultancously with- out considering HCorr and PCorr, thus leading to subopti- mal correlation modeling. Fur- thermore, due to the variations in correlations across different datasets, it is difficult to capture generalized correlations during the pre-training phase (Ekam-
Various Correlations
Pipeline
Legend
Dynamic Correlation (DCom)
E2EM Model TSFM
Strong
Multi-source
Single source
2
Tine Series
T8FM
EZEM CCM (C)
Foundation Model
Pre-train
CCM Cluster Naker
Heterogeneous Correlation (HCorr)
CCM (P)
CCM Projector
Positive
Negalive
Projector
CCM (P)
pre-train
Partial Correlation (PCom)
TSFM
E2EM CCM (C)
C-LORA E2EM 0
Dependent
Indapándent
Projector
CCM (P)
Projector
baram et all, 2024b).
Thus, it motivates us de- sign a plugin that can be fine-tuned alongside TSFMs, which avoids issues caused by correlation differences across datasets during the pre-training phase. Meanwhile, it possesses
Dependent
CoRA (ours)
C-LoRA
(a) Various Correlations
(b) Efficient Plugins for Learning Correlations
Figure 1: (a) Illustration of three different types of correlations, the formal definitions are provided in Appendix A (b) Compar- isons of different plugins for learning correlations
the ability to depict various correlations while also incorporating lightweight design. However, this faces a major challenge: balancing the complete modeling of various correlations with the lightweight design. It is intrinsically difficult to model all three correlations in unified manner. Although some models could address DCorr (Zhao et all 2023 Cirstea all 20211), HCorr (Huang atal 2023) and PCorr (Quu et all 2025d: etll (0243) individually, they struggle to effectively encompass various correlations simultaneously. Moreover, existing channel interaction methods of- ten rely on MLPs (Ekambaram et all, 2023: 20245), Transformers (Liu et all 2024:; [hang et all
2IZE etc., which have a time complexity of ((N'), where N denotes the number of channels. Some methods (Zhang & Yan, 2022: Chen M0zal Nie et all 2 have made efforts in reducing the complexity. However, end-to-end models such as Crossformer (Zhang & Yan, 2022) require modifying or redesigning the entire model structure, and thus cannot be directly used as plugins for TSFMs. Existing plugins are primarily designed for end-to-end forecasting models. CCM (Chen et all (0244) requires additional pre-training together with the end-to-end models before it can be plugged in. C-LoRA (Nie et all, 2024) is designed to be trained with an end-to-end backbone from scratch. Overall, there is lack of an efficient plugin specifically designed for downstream fine-tuning of TSFMs. More importantly, considering various correlations in these methods would lead to a higher complexity.
2023) and GNNs (Wl, 2020: Ca ata
To address this, we propose CoRA, a lightweight slug-and-play method that only requires training on few samples with TSFMs during the fine-tuning phase. By considering various correlations, CoRA utilises internal representations and original predictions from TSFMs to generate an enhanced prediction, shown in Figure Пb. To complete modeling the mentioned three types of correlation, we first propose the Dynamic Correlation Estimation (DCF) module which can learn dynamic correlation matrices. Then we design the Heterogeneous-Parre Partial Correlation Contrastive Learn- ing (HPCL) that uses the correlation matrices from DCE to learn HCоπ and PCorr adaptively. Specifically, achieve lightweight, we innovatively decompose the correlation matrices into two low-rank components: Time- Varying and
in DCE module. To better understand how DCor evolves, we propose learnable polynomial to capture trend periodic patterns within the DCorr effectively. Afterwards, to better distinguish of HCor,, we propose channel-aware projec-
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tions to map the representations into positive and negative correlation spaces. The projections guided by the novel Heterogeneous- Parttal Contrastive Loss during the training process, which en- ables adaptive learning of PCorr in the two HCorr spaces. As result, we capture the mentioned three types of correlations with linear complexity w.r.t. the number channels during inference. Our contributions are summarized follows:
We design a universal, lightweight plugin that allows TSFMs to capture the mentioned three types of correlations without re-pee--taaaiat-n pre-training the TSFMs.
We propose a lightweight Dynamic Correlation Estimation module that explicitly models the dynamic patterss of correlations in a lightweight manner.
We propose a novel Heterogeneous-Partee Correlation Contrastive Learning, which learns HCorr and PCorr through projection layers regulated by dual contrastive loss.
We conducted extensive experiments on 10 real-world datasets. The results show that CoRA effectively improves the performance of TSFMs in multivariate forecasting.
2 RELATED WORK
2.1 FOUNDATION MODELS FOR TIME SERIES FORECASTING
These methods leverage the strong representational capacity and sequential modeling capability of LLMs cap- ture complex patterns for time series modeling. Among them, GPT4TS (Zhou et all, (022) and CALF eLl (025) selectively modify certain parameters of LLMS enable the model adapt to time series data. On the other hand, UniTime(Lau et all, 2024h), 12IP-LLM (Pan et all 2024), L.MMixer (Kowsher all 2025), and Time-LLM (Imeetal all 2IZE)) focus creating prompts to trigger time series knowledge within LLMs. 2) Time Series Pre-trained Models: Pre-training on multi-domain time series equips these models with strong generalization capabilities. Among them, ROSE (Wang et all (0244) and Moment (Cioswami et all 2024) restore the features of time series data, enabling them to extract valuable information in an unsupervised manner. On the other hand, TimesFM (Das et all (DZE)) and Timer (Lm all 2022)), using autoregressive approach, em- ploy next-token prediction to learn time series representations. Generally speaking, most TSFMs based on channel -nneeeeneen strategies, with only few (Gao all 2024; Ekambaram et all 20221R cooll 2122)) modeling relatively simple inter-channel relationships. The effects of more complex correlations in TSFMs remain under-cxplored.
TSFMs for forecasting can be divided into two sections: 1) LLM-based Models:
2.2 CORRELATION OF CHANNELS IN TIME SERIES FORECASTING
Channel correlation plays a crucial role in enhancing the predictions(Quu et al. 2025a). They can be divided into specialized models and plugins from paradigm perspective. 1) Correlation Models: These models are typically based on foundational architectures such as ML.P (Ekambaram et all
2024a 2023), GNN (Shang et all 2021: Cai et all 2022),, and Transformer (Liu 2024c: Zhang & Yan (122). For example, ISMixer(Ekambaree
et all (2023) and TTM(Ekambaram at ()244)
directly mix all channels using MLP. MTGNN(WD et all (020) and Ada-MsHyper(Shangg et all 20228) treat different channels as distinct nodes, performing message passing to facilitate channel interactions. Furthermore, (Transformer(Liu all 20245) and Crossformer(Zhang
Yan. 2022)
treat different channels as distinct tokens and utilize transformers to realize channel interaction. 2) Correlation Plugins: Some plugins enhance the predictive capability of models by learning correlation (Cirstea et al. 2022: 202T). For example, LIFT (Zhao & Shen, 2024)) leverages locally relationships to extract correlations. CCM (Ch 2022)) further performs clustering and creates dedicated prediction heads for each cluster. However, the methods above either lack comprehensive correlation modeling capabilities or possess substantial complexity.
PRELIMINARIES
Time Series Forecasting. Given multivariate time series X, (x)- NNL with look-back window and N channels, the forecasting task aims to predict the future steps Ý, (&t 1 E N xFF corresponding to the ground truth Y, (x
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Correlation-Aware Adapter for Foundation Models. Consider pre-trained Time Series Founda- tion Model (TSFM), denoted by F. During the downstream fine-tuning phase, the model processes the input data X to generate initial predictions, formulated as Y F(X!"). Concurrently, the TSFM extracts the intermediate series representation, denoted as ft. Given the downstream input X its corresponding ground truth Y! the initial predictions Y and the latent represen- tations X correlation-aware adapter is to fine-tune the base model F to yield an adapted model F Here, J represents the foundation model augmented with the proposed adapter. During the inference phase, predictions unseen test data are generated via Y =F*(X) (X(est)
4
METHODOL.OGY
Estimation
DCorr Estimation
H-PCorr Contrastive Learning
paer Corr Matrix
Multivariate
Positive Correlation
Series
Rule-based Correlation
Heterogencous Division
Foundation
Model
M X
M
pox
Paira
Negative
H-PCorr Contrastive Learning
Learnable Correlation
Channel
Internal
X
Negative Correlation
Representation
Heterogeneous Fusion
Composition
Negative
Time-aware Polynomial
Pairs
Gated Add
Original Prediction
CoRA Architecture
Prediction
(a)
(b)
(c)
Figure 2: The framework of CoRA. (a) CoRA begins by learning DCorr in Dynamic Correlation Estimation module. Heterogeneous Division module projects representations into positive and neg- ative spaces for HCorr. Then CoRA conducts H-PCorr Contrastive Learning in each space to guide projection and capture PCorr. (b) The DCorr Estimation module estimates correlations by combin- ing Rule-based Correlations and Learnable Correlations, which are computed by Time-aware Poly- nomial and Time- Time-Varying and Time- Invarian (T-T) Composition. (c) H-PCorr contrastive learn- ing minimizes distances between strongly correlated channels and maximizes separation between weakly correlated channels in both positive and negative spaces.
In this work, we propose Corvelation-aware Adapter (CoRA), a lightweight plugin that allows the TSFMs to capture various correlations during the fine-tuning stage. The framework of CoRA is visualized in Figure 2 CoRA operates on input series, original predictions, and representations from TSFMs to enhance the prediction accuracy. Our method consists of four processes: (i) Dy- namic Correlation Estimation. This module utilize representations from TSFMs and input series to learn dynamic correlations and generate correlation matrices that guide subsequent contrastive learning. (fi) Heterogeneous Division. Some channels show dependencies on positive correlations, whereas some others show negative correlations. To better capture HCorr, we design the this module process the representations from the backbone and learn representations of positive and negative correlations separately. (iii) Heterogeneous Partial Correlation (H-PCorr) Contrastive Learn- ing. We propose H-PCorr Contrastive Learning within each representation of HCorr learn PCorr by clustering only correlated channels. (iv) Heterogeneous Fusion and Prediction. Finally, we fuse the representations after contrastive learning for positive and negative correlations in Hetero- geneous Fusion module and generate new predictions. Then, both original and new predictions are gated and added together.
4.1 DYNAMIC CORRELATION ESTIMATION
Channels exhibit both stable dependencies that do not change across time and fluctuations that change across time. Motivated by this, we introduce an innovative method that decomposes the leamable part of correlation matrix M R N'x N at time t into two low-rank components: Time- Varnin Q. E IR N and tion components, as illustrated in Figure Here, R E NNN denotes the rule-based correlation
V E IR MMM which can separate distinct correla-
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matrix which is added to the learnable part to incorporate more prior knowledge for enhancing correlation estimation. M is the hyperparameter for the destdpccomooiition rank, with M < N. This decomposition of the learnable part offers greater parameter efficiency, yet remains function- ally equivalent to conventional additive decomposition (Cirstea et all, 2021),, as formally proven in Theorem M1
We estimate the two components separately and then compose them back into the orig- inal correlation. The Time-Varying compo- nent represents the fluctuations in correlations across time. As time series data inherently have trends and periodic characteristics, the correla- tions that measure their dependencies also ex- hibit such variations across the entire time se- ries (Lm et all 2T22). Thus, propose Learnable Tame-aware Polynomials estimate the changes, polynomials can be effective in modeling temporal patterns by sharing a com- basis across different time steps. Based a global adaptive method, the Time-Invariant component aims to capture the stable depen-
Dynamic Correlation Estimation
Learnable Time-aware Polynomial
Q()) = Poly(t, q) = Ca. q C1 X +... Cup X q²
Time-Varying Time-Invariant Composition
R
Q
Time-Varying
Time-Invariant
All
Postlivate
Negalive
Figure 3: The details of DCorr Estimation
dencies among channels that do not change over time. Finally, we compute the correlation matrix Mf by composing learnable correlations and combining with the rule-based correlation R. This correlation matrix is then used for H-PCorr Contrastive Learning.
4.1.1 LEARNABLE TWAR- POLYNOMIALS
Most existing approaches (Shang et all 002E5 Crstca all 2021: Zhao eLaa (02%) struggle to accurately express the time-varying characteristics of DCorr due to the lack of explicit modeling of dynamic regularities.
In stationary time series, imate the fluctuations of the correlation. Considering that high-order polynomials provide better non-linear capacity than first-order ones, learnable polynomials estimate Q.. The proof of this approximation capability detailed in Theorem 2
well-behaved mathematical function to effectively approx-
We construct K-order Time-aware Polynomials with shared matrix basis:
K Q:
- D= Ga.g', (q' = ....0 i=0
(1)
limes
where Q E N denote the Time- Varying component time step L. Cie R is the i-th coefficient that varies time, while q NxM is the globally learnable basis, which represents the pattern of changes over time. We define q¹ as the i-times Hadamard product of the matrix q. where the operation @ is the element-wise Hadamard product.
For convenience, we define the collection of Ci,, as the matrix C, = (Co.,, (Co.,.-.CCk.))) E RRNK the dependency coefficient of each channel for pattern q' and exhibits different values at different times, determined by specific data. Therefore, we lear the mapping f between the representations of time series X, and coefficients C, to estimate it:
C, = =(xX)) E N
(2)
Since only the polynomial coefficients need to be estimated with f. rather than the entire varying component, we can use a simple MLP to implement
4.1.2 TIME-VARYIN AND TIME-INVARIANT COMPOSITION
Since the time-invariant part does not change over time, should be globally unique. Inspired by self-learned graphs (Shang el all 4Iz4F; Wi all (020), we use global learnalle vectors to capture the implicit stable dependencies among channels:
V Sigmoid(ReLL((,,
(3)
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where V E RM denote the Invariant component of DCor. E Eg RMxx are learnable vectors, de is used to expand the dimensions, thereby enhancing the representation capacity.
As the statistics-based Pearson coefficient can describe simple linear correlation, use it as the initialization for the final DComr and build upon to learn more complex correlations. The Pearson coefficient is calculated as follows:
E (24 2) - 7)
Ta.y Et x)² 1 D)²
(4)
where z, y are two variables in Xx; Fa,yy denotes the correlation coefficient among them, while 7 and the size of input series. We use R Nx to denote the collection of r. Overall, our DCorr includes rule-based correlation R. time-varying components Q. and time-ime inveriiaaiaant components V. The final estimated correlation is formulated as the sum of the learnable and rule- bale-baed parts in the following equation:
y indicate the mean values of and y, respectively,
M R + Q.VO'"
4.2 HETEROGENEOLS CORRELATION DIVISION
Positive and negative correlations affect the channels differently, and the proportion of their contri- bution also varies among different channels. Motivated by Sgueeze-and-Excitaae (Huetall 2018) (SE), we propose a channel-aware projector that adjusts the weights of channels based on contextual information during projection to better project the representations into positive and negative spaces and learn Heterogeneous Correlation (HCorr).
To distinguish the dependency of channels on Heterogeneous Correlation, we project the representa- tions into two spaces. Specifically, we use SE mechanism to aggregate contextual information over time and adaptively calculate projection weights among channels. The channel-aware projection layer P with X and X² is shown follows:
Proj MIP, (LayerNorm (!)) E PxNxd
(6)
W SoftMax (Layerrooa (X(")) E N
0 = X + Tr @ expand
(8)
where LayerNorm refers to the layer normalization operation, which enhances the model's gener- alisation ability; MLP, := Rd + IR is used for preliminary projection; MLP, == IgP + R. used to compute channel weights; denotes the number of patches; W denotes the adaptive channel weight, expand(-) denotes the dimension expansion operation.
We perform two identical projection transformations on X, to obtain the representations of the positive and negative latent spaces:
X = P, (X,, E (PxNxd)) X P (X,,) R(PxNxd))
where P1 and Po are the proposed channel-aware projection operations with distinct learned param- eters, and they are implemented as multi-layer architectures of X and X are representations projected into spaces of positive and negative correlations, respectively. They contain channel infor- mation with adaptive adjustments and will subsequently be used for contrastive learning.
It is noteworthy that the Heterogeneous Correlation Division module cannot directly accomplish the disentanglement of heterogeneous correlations. Instead, this separation achieved under the guidance of the contrastive learning framework detailed in the next section.
4.3 HETEROGENEOUS PARTIAL CORRELATION CONTRASTIVE LEARNING
To capture Partial Correlation, we design Partial Contrastive Learning, which uses the correlation matrix derived from Dynamic Correlation Estimation (DCE) and representations from Heteroge- neous Correlation Division (HD) to enable adaptive correlation learning.
We leverage Contrastive Learning's ' advantages for clustering to capture PCorr (Yang et al, 2023). Compared to existing methods (Chen et al. 2024 Quu et al, 20254). this approach facilitates the fine-grained interaction among channels. Moreover, it does not add an extra burden during inference.

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First based on the estimated correlation Mr define the heterogeneous correlations M and M, th to decouple the complex interactions among channels:
mit", corr > else
M, { ( if corr <-
M pus
(10)
(0,
10,
else
where mi is the element of Mr é is the learnable threshold. The following process is for the positive correlation in the positive latent space; the same operation performed on the negative latent spaces.
The matrix M is used to select positive and negative samples for each channel. In the designed contrastive learning if Mi O. it considered a negative pair; otherwise, it is considered positive pair. The loss for the positive correlation can be expressed as follows:
Σ log( 1-رر M 10xh [i, (sim X PUN [i] PoN LD)/T)
Lpss
(11)
Σ exp X p00 [
[B:))TT
where sim(-) represents the cosine similarity, and is the temperature coefficient used to control the degree of contrastive learning constraints. We do this for negative correlation in a similar way. The following equation gives the total auxiliary loss:
Laux
Epss + Lneg.
(12)
4.4 HETEROGENEOUS FUSION AND PREDICTION
Finally, we project the representations of the two heterogeneous latent spaces into shared space and then fuse them to perform prediction. Considering that some channels may require more correlation interaction while others may require more independence, conduct a convex combination:
X pos
pos
X. neg = (X, neg
(13)
Y Linear X
X _ (1 Y
(14)
where P3 and P4 consist of l2 projection layers like P, as given by equations (+)) Linear represents the linear prediction head, 3 E [0, 1 is a learning parameter denotes the gated weight.
4.5 COMPLEXITY ANALYSIS
The computational complexities are O(N2) for the DCorr Estimation (DCE, Section [ and H-
PCorr Contrastive learning (HPCL, Section [. and O(N) for HCorr Division (HD, Section A Most of the complexity arises from DCE and HPCL, which are only required during training. In the inference phase, since CoRA only includes HD modules, the time complexity is O(N).
Figure EI shows CoRA imposes only minimal additional time on TSFMs, during fine-tuning and inference. The details of complexity analysis are included in Appendix B
THEORETICAL ANALYSIS
5.1 THE SIGNIFICANCE OF TIME- VARYING AND TIME- COMPOSITION
straightforward approach to modeling dynamic correlations is to decompose the correlation matrix into the sum of time-varying matrix and time-invariant matrix (Cirstea et all 2021; Wi all 2019). However, this approach has parameter complexity. Our method can reduce the complexity while achieving the same effect.
Theorem When the time series is locally stationary, the Time- Varyina and Time-Invrrian De- composition allows Q: V to contain both time-varying and time-invariant information, like con- ventional additive decomposition.
Specifically, Q QT. can be expressed as the sum of a time invariant matrix M, and time-varying matrix M., as shown below:
Q.VQL =M, M.
(15)

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This indicates that our decomposition approach remains functionally equivalent to conventional ad- ditive decomposition. Notably, the expression Qe V Q? is the learnable component of the correlation matrix M as defined in Equation 5
5.2 THE FITTING ABILITY OF AWAE- POLYNOMIALS
Time-aware polynomials can model complex time-varying correlation relationships, and the error bound decreases the degree K of the polynomial increases.
Theorem
When the time series is locally stationary, we can approximate the underlying correla- tion matrix with high-order polynomial.
Specifically, assuming that the correlation is a smooth function of the basis q, the true correlation component Qi can be expressed F(g). The error bound can be formalized as follows.
(E)-1)(E)
Q -cl (K +1)! q² (K+1)
(16)
This indicates that by selecting appropriate K, we can strike an effective balance between model effectiveness and computational efficiency, thereby enabling the efficient estimation of dynamic correlations. We provide the proof of Theorems 1-2 in the Appendix C
6 EXPERIMENT
6.1 EXPERIMENTAL DETAILS
Datasets. To conduct comprehensive and fair comparisons for different models, conduct exper- iments on ten well-known forecasting benchmarks as the target datasets, including ETT (4 subsets), Electricity, Traffic, Solar, weather, AQShunyi and ZafNoo, which cover multiple domains. More details of the benchmark datasets are included in Table M of Appendix DJI.
Baselines and Implementation. We choose the latest trate-o--the-ee models serve as baselines, including Time Series LLM-bbsed models (GPT4TS, Auto AutoTTmms, UniTime) and 3 Time Series pre-trained models (Moment, Chronos, Timer). We utilize the TSFM- repository for unified evaluation. More implementation details are included in D To keep consis- tent with previous works, we adopt Mean Squared Error (MSE) and Mean Absolute Error (MAE) as evaluation metrics. We provide code http://tww...oooocooooo//l//////
(Lret all (025) code
6.2 MAIN RESULTS
Comprehensive forecasting results of TSFMs with and without using CoRA are listed in Table II. We have the following observations: i) Compared to fine-tuning without CoRA, fine-tuning with CoRA achieves better results in average results and results of different forecasting horizons (Table R and Table Z in Appendix E) for both L..M-based models and time series pre-trained models, even in 5% few-shot settings. ii) Sharing the same pre-trained parameters, TTM's Channel-Dependenn (CD) and (CI) versions differ only in their module configurations during downstream fine-tuning. We implement CI version of TTM, fine-tuned with CoRA and compare it with a CD version which is fine-tuned without CoRA. The better performance of the former demonstrates that considering the mentioned three types of correlations allows the model to better understand the inter-channels interaction.
Channel-Independee
6.3 COMPARISON WITH OTHER CORRELATION PLUGINS
To better validate the effectiveness of CoRA, we compare it with LIFT Zhao & Shen (2(22)) and C-LoRA Nie eLal (224).. We select GPT4TS, UniTime and Timer as the backbone and set H to 96. As shown in Figure El since LIFT and C-LoRA are not specifically designed for TSFMs, the limited training samples in the few-shot setting lead to degradation their performance, negatively im- pacting the effectiveness of the TSFMs. In contrast, CoRA. designed specifically for TSFMs, leams multiple correlations from the TSFMs' representations, allowing it to fully leverage their predictive capabilities. More comparisons with other fine-tuning setting are included in the Appendix ETT.
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Table 1: Multivariate forecasting results in the 5% few-shot setting with MSE are averaged across four different forecasting horizons H {96, 192, 336, 720).The better results are highlighted in bold. Full and MAE results are available in Appendix H
LLM--based
Pre-trained
Model
GPT4TS (2023)
CALF (2025)
UniTime (2024)
Moment (2024)
Timer (2024)
TTM (2024)
Plugin
ETTh1
0.468
0.456
0.443
0.434
0.739
0.714
0,550
0.543
0.444
0.432
0.405
0.397
ETTh2
0.375
0.362
0.373
0.399
0.386
0.370
0.365
0.356
0.350
0,343
0,340
ETTml
0.389
0.379
0.394
0.455
0.452
0.356
0.357
0.353
ETTm2
0,281
0.279
0.257
0,259
0.254
Electricity
0.208
0.201
0.201
0.195
0.202
0.200
0,241
0.236
0.179
0.177
Traffic
0.441
0,431
0,436
0.425
0.455
0,446
0,451
0.444
0,456
0.447
0,486
0,481
Solar
0.256
0.245
0.230
0.224
0.255
0.248
0.227
0.223
0.211
0.213
0.270
0.266
Weather
0.254
0.245
0,238
0.231
0.255
0.243
0.252
0.249
0.241
0.236
0.226
0.224
AQShmny
0.850
0.831
0.733
0.716
0.743
0.717
0.694
0.681
0.734
0.724
0.700
0.689
ZaiNoo
0.566
0,554
0,550
0,534
0,563
0.542
0.531
0.526
0.537
0.524
0.504
0.497
Reiative Change MSE (N)
vo done
Reletive Change MSE (9)
CaMA Dacctons Bucksens
Relative Change MSE (1)
Sactbore
Bacatons
Tiner
GF"NTS
Backbone
Backbone
ETTm2
(b) Weather
(c) Electricity
Figure 4: Correlation Plugins comparison in 5% few-shot fine-tuning setting.
6.4 ABLATION STUDIES
To investigate the effectiveness of CoRA, we conduct comprehensive experiments. In our work, the DCor Estimation (DCE) is used to learn DCorr and generate the labels required for H-PCor Contrastive Learning (HPCL), while HPCL utilizes these labels to guide the projectors in the Het- erogeneous Division (HD) module. Therefore, they cannot operate independently. We utilize naive implementations in place of the original modules within certain variants.
Table 2: The MSE results various variants.
Dataset
ETTm2
Electricity
DCorr Estimation
HCorr
H-PCorr Contrastive Learning
GPT4TS
UniTime
Timer
GPT4TS
UniTime
Timer
Dvision
1
X
X
0.279
0.292
0.262
0.208
0.201
0.241
2
0.277
0.287
0.261
0.206
0.199
0.239
3
0
/
0.274
0.285
0.260
0.204
0.197
0.239
0.273
0.283
0.260
0.205
0.198
0.238
5
0.269
0.281
0.257
0.201
0.195
0.236
X denotes module removed, / denotes module added, O denotes replace module with a naive implementation.
Specifically, we replace the DCE module with series-level Pearson correlation coefficient, which cannot model DCorr, and the HD module with single-branch projection layer, which unable to capture PCorr. The comparison between Row 1-2 demonstrates the effectiveness of HPCL; however, its performance is limited due to its inability to capture multiple types of correlations. In Rows 2- the addition of either the DCE HD module HPCL further enhances performance, which confirms the efficacy both modules. In Row 5, the combination all three modules achieves the best performance.

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Published as a conference paper at ICLR 2026
6.5 MODEL ANALYSIS
Efficiency Analysis Our proposed CoRA, as lightweight plugin for TSFMs, shows strong effi- ciency, particularly during the inference phase. Figure GI shows comparative analysis of the effi- ciency of TSFMs with and without the application of CoRA. We selected three datasets in ascending order of the number of channels: ETTm2 (N = 7), Weather (NV 21), and Electricity (NV 321). For the experiments, both the look-back window L and the forecasting horizon И were set to 96. Train time and Inference time refer to the duration of single training epoch and the total time re- quired to process all samples during inference, respectively. The results show that, compared to the backbone itself, the use of CoRA does not introduce significant additional time or parameter num- bers. Moreover, as the number of channels (N) increases from 7, 21, to 321, CoRA maintains its efficiency without noticeable degradation compared to the backbone, particularly during inference.
402
Parmiese [Racktane)
400
Paramene (iocksanee
400
Peramdte (Bucttrns
25
Peremzia
40
Parsminer (-CoRe)
500
200
Irleence Tims (laccosnar
Ieference CaRAI
Time CMPA)
20
Time
200-
500
Irference mh (Backtora)
Erferance (-CARA
Timg C4CUUA
200
300
Interonce toucktened
Inferance CHMA
Time ColA)
S
10
109
100-
10
100
100
GPT4TS
UniTmm mime
Moment
6P7475
UniTime Backbone
Momont
6P74TS
JIST-NG Backbone
Noneent
Backbone
(a) ETTm2 (N=7)
(b) Weather (N=21)
(c) Electricity (N=321)
Figure 5: Efficiency Analysis of TSFMs with and without the application of CoRA.
Data Analysis While the pre- vious results focused on the 5% fine-tuning setting, ex- pand the analysis to provide a more comprehensive view and to explicitly explore the impact of fine-tuning data volume on performance. Specifically, we fine-tune the TTM and CALF backbones on the ETTm2 and Weather datasets, using 3%, 5%, 10%, and 20% of the available training data. The MSE results summarized in the Table HL As the results indicate, CoRA still yields modest performance improvement even in a low-data regime using only 3% of the data.
Table 3: MSE results for different data percentage.
Dataset
ETTm2
Weather
Data
3%
5%
10%
20%
3%
5%
10%
20%
0.263
0.259
0.256
0.250
0.237
0.226
0.224
0.216
TTM
2:002
1:001
0,261
0.254
0,248
0.245
0.234
0.224
0.212
0,210
+
CoRA
1.004
2.002
4.001
4.001
1.003
4.001
4.001
0.285
0.272
0.268
0.261
0.251
0.238
0.230
0.224
CALF
#:005
=.003
4.004
+.008
5:004
4.008
4: 4:002
0,283
0.264
0.260
0.254
0.248
0.231
0.223
0.219
+ CoRA
2.0002
Sensitivity Analysis and Visualization The Data Sensitivity of CoRA in different few-shot setting are presented in Appendix [.I. The Prarmeter Sensitivity analyses for the polynomial's degree K, the decomposition size M, and the number of projection layers (, la are presented in Appendix E2 The Visualization of heterogeneous spaces are presented in Appendix
7 CONCLUSION
In this paper, we propose lightweight Corvelation-aware Adapter (CoRA) that enhances the pre- dictive performance of Time Series Foundation Models (TSFMs) by considering the mentioned three types of correlation relationships. We combine Time- Varying and Inve-anvariant Composi- tion with Learnable Time-aware Polynomials enable lightweight modelling of dynamic correla- tions exhibiting regular patterns. For Heterogeneous Correlation and Partial Correlation, we design Heterogeneous-Partee Partial Contrastive Learning. This approach decouples Heterogeneous Correlation while simultaneously achieving adaptive Partial Correlation learning among channels. Comprehen- sive experiments on real-world datasets demonstrate that CoRA can improve the forecast perfor- mance of TSFMs.
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Published as a conference paper at ICLR 2026
ACKNOWLEDGEMENTS
This work was partially supported by the National Natural Science Foundation of China (No. 62372179, No. 62472174) and the Fundamental Research Funds for the Central Universities, Chen- juan Guo is the corresponding author of the work.
ETHICS STATEMENT
Our work exclusively uses publicly available benchmark datasets that contain no personally identi- fiable information. The proposed adapter for Time Series Forecasting is designed for beneficial applications in system reliability and safety monitoring. No human subjects were involved in this research.
Series Foundation Models in Multivariate Time
REPRODUCIBILITY STATEMENT
The performance of CoRA and the datasets used in our work are real, and all experimental results can be reproduced. We have released our model code at: https///ttttc.coom/ccccoommnnntt
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A DEFINITIONS OF THE THREE CORRELATIONS
Definition (Correlation Martix) Given a multivariate time series X E RNX where N represents the number of channels and L the temporal length, the series is partitioned into set of K LL/T" non-overlapping segments using window of length T. For the k-th segment, we define the channel- wise correlation matrix as ( E IE N where E [1, kj. The element at the i-th row and j-th column of this matrix is denoted by Ci which represents the correlation between the i-th channel and the j-th channel.
Definition 2 (Dynamic Correlation) The Dynamic Correlation refers the case where the correla- tion martix (k E [1, K]) is not constant over the segments index k. Formally, this means there exist least two distinct segment indices m, n E [1, K] with # n, such that their corresponding correlation matrices are unequal: C((m) + C(a).
Definition 3 (Heterogeneous Correlation) The Heterogeneous Correlation refers to the case where there exists at least one temporal segment k E [1, K] in which some channels exhibit both positive and negative correlations with other channels. Formally, this means that for at least one correlation
matrix (*)) (A E [1, K]). there exist at least three distinct channel indices a, b, c E [1, N1. such that
the corresponding correlation matrix elements edb and (k) have opposite signs: cab Cac <.
(k) (k)
Definition 4 (Partial Correlation) The Partial Correlation refers to the case where, within at least temporal segment & Kj. there exists some pairs of channels with non-significant rela- tionship. Formally, given a predefined significance threshold c, this means there exists at least one matrix ((A (I E KJ) and at least one pair of distinct channel indices a, E [1, such that: (R)] lcab
<.
B COMPLEXITY ANALYSES
B. TRAINING PHASE
Dynamic Correlation Estimation This module consits of Learnable Time-aware Polynomials (LTP) and Time- Varying and Time-Invariant (T-T) Composition. The LTP have a computational complexity of O(PKNM M + PNdd) due to the polynomial operations and the MLP used to gen- erate C, and space complexity of O(d + MN) because of the basis q and the MLP used to generate C, Where P is the number of patches, .N denotes the number of channels, M is the second dimension of Q. KK' the degree of the polynomial and d the dimension of representations. The T-T Composition has computational complexity of O + N + MN2) ) due to the calcula- tion of the Pearson coefficient and the composition in Equation EL Where denotes the patch size. Heterogeneous Division This module has a computational complexity of O(N 22d2) and space complexity of ((d) due to the channel-aware projection. H-PCorr Contrastive Learning The time complexity of calculating loss in Equation [ is O(PdN3).
Since P. K, M, and I are much smaller than N and d, they will not be considered as the primary components in the complexity analysis. So the total computational complexity is O(d + N&)) and the total space complexity is Old + N). Most models cannot avoid having a computational complexity of (dd)) and a space complexity of Odd. Therefore, if we focus only on the complexity with respect to (N) in our discussion, our model has computational complexity of O(N2) and space complexity of O(N) during training.
B.2 INFERENCE PHASE
In inference Phase, CoRA only includes projectors in the Heterogeneous Division and Heteroge- neous Fusion modules, based on the above discussion, our model has a computational complexity of (NN) and a space complexity of O(1) during inference.
17

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Published as a conference paper at ICLR 2026
C THEORETICAL ANALYSES
C.I THE SIGNIFICANCE OF TIME- VARYING AND TIME-INVARIANT COMPOSITION
The channel correlation be expressed by combining long-term stable state with dynamic changes, We decompose the learnable correlation into two parts, Qe and V, as shown in Figure to fit the correlation relationship lightweightly.
Theorem When the time series is locally stationary, the Time- Varying and Time-Invarian De- composition allows Q Q.Q. to contain both time-varying and time iin-invaraant information, like con- ventional additive decomposition.
Specifically, Q.V can be expressed as the sum of time-invariant matrix M, and fime-varying matrix M., as shown below:
Q.Vo. M; + M.
(17)
Proof. Under the assumptions of locally stationary, Q: can be expressed as Q Q. where Q. represents the mean value and reeprseents the residual. Mnerefore,Moory can be expressed as:
Q.Vo' (Q. Q.) + Q.)
Q.V Q. + QQVQ. QQVĀē
(18)
=QQ.VQ)) (Q.V + +Q.QQ + QQVQ))
-M++M
where M, Q.V@? has the same value at different times, and M, Q.V Q.Vā? +
V?? has different values at different times.
C.2 THE FITTING ABILITY OF TIME-AWARE POLYNOMIALS
Since time series exhibit regular changes, such trends and seasonality, the dynamic correlation changes also have a certain regularity. To this end, we propose Time-aware Polynomials to fit the changing correlations better.
Theorem When the time series is locally stationary, we can approximate the underlying correla- tion matrix with high-order polynomial.
Specifically, assuming that the correlation is a smooth function to the basis the true correlation component Qi can be expressed as F(q). The fitting error of Time-aware Polynomials decreases as the highest degree K of the polynomial increases. The error can be formalized as follows:
F((K1)
q (K+1) 1,,+,,.E E Qi - Qel (K 11!
(19)
Proof. Given the true correlation F(q). Since F is sufficiently smooth to the basis we can perform Maclaurin expansion of around
F")
F(K)
F(n)
F(q) F(0)+
K! 9k
nl 9"
(20)
We construct auxiliary functions:
(t)
(t)
H(t) F(q) - (F(t) + F(t((a
2! (g t)² +
K! (q
(21)
G(t) (q t) (K+1)
(22)
Assume 0. Then, H and G are still continuously differentiable, and the following rules apply:
H(ty x(K-1)(
K! (q 1)²²
(23)
C(t) -KKK + 1)(9 - t) + 0.
(24)
18

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Published as a conference paper at ICLR 2026
Since H((q) G(q) 0. by the Cauchy Mean Value Theorem, _ E s.t.
H(0) H(0) - H(() H(O) H(q)) H² F(K+1)(E)
(25)
g()) ((0) ((g) g(0) ((q) ('(E) (K + +1)!
Therefore, we can derive the following equation:
F (0)
F(K) F(K+1)(E) K!
F(g) =(() F(0)
9k + (K 1
(k+1), _ (0.
21
(26)
Let C₁ F(o T. Then, have the following equation:
F(q) = Co. + C1 + C2 + ... + Ok.d + F()+))(E)
(K+1), , E [0.
(27)
(K + +1!
That is:
F()+))(E)
(((+1)) E 10.
F(g) Q.
(28)
(K 1]!
For all > 0 and < 0, we have the following equation:
(E)
[F(g) Qel
(K 1)! d (K (K+1), g [-|g]. lall
(29)
And that is:
(()
Q - Qel
(K + 1]! q (K+1) E E [-lgl.1g]
(30)
19

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Published as a conference paper at ICLR 2026
D EXPERIMENTAL DETAILS
D.I DATASETS
To conduct comprehensive and fair comparisons for different models, conduct experiments on ten well-known forecasting benchmarks as the target datasets, including: (I) ETT (Zhou all 2021) datasets contain variates collected from two different electric transformers from July 2016 to July 2018. It consists of four subsets, of which ETTh are recorded hourly, and ETTm l/ETTm2 are recorded every 15 minutes. (II) Electricity (Unndade, 2015) contains the electricity consump- tion of 321 customers from July 2016 to July 2019, recorded hourly. (III) Traffic et (02T) contains road occupancy rates measured by 862 sensors on freeways in the San Francisco Bay Area from 2015 to 2016, recorded hourly. (IV) Solar (Lai all 2018) records solar power generation from 137 PV plants in 2006, every 10 minutes. (V) Weather (Ww all (0ZT) collects 21 meteo- rological indicators, including temperature and barometric pressure, for Germany in 2020. recorded every 10 minutes. (VT) AQShunyi (Zhang ct all 201Z) is an air quality dataset from a mcasurement station, for 4 years. (VII) ZafNoo (Poyatos et all (020) is collected from the Sapflux data project and includes sap flow measurements and environmental variables. The details of the benchmark datasets are included in Table !
Table 4: Statistics of datasets.
Datazel
Domain
Frequency
Lengths
Dim
Split
Description
Electicityy
14,400
6:2:2
Power transformer comprising seven indicators such tomperature useful load
BTTh:
Electiitt
14,400
7
6:2:2
Power trnndoomer comprising seven indicators such temperature useful
ETTml
Electiiityy
15 mins
$7,600
7
6:2:2
Power transformer I, comptising seven indicators such as oil temperature and useful load
ETTm2
Electiiitty
15 mins
$7,600
7
6:2:2
Power transformer 2. comprising seven indicators such as oil temperature and useful load
Weather
Envinonment
mins
$2,695
7:1:2
Recorded every the whole year 2020, which contains 21 meteunolgiccal indications
Electricity
Electricity
26.304
321
7:1:2
Electricily records electricily consumption
every hour
2014
Solar
Energy
mins
$2,560
137
6:2:2
production records collected from 137 plants Alabama Rond occupancy rates meusured by 862 sensors on San Francisco Bay area freeways
Trallic
Traficc
hour
17,544
862
7:1:2
AQShumgi
Envinomment
hour
35,064
11
7:1:2
Air quality dutaset from messrement station, für 4 years
ZafNoo
Nature
30 mins
19,225
11
7:1:2
Sup flow menurements and environmental variables from the Sapflux data project
D.2 BASELINES
Remarkable achievements in deep learning have been witnessed across time series analysis (Wang Wang et all 20266; Cheng et all 2026:
al 20265; Tian et all 2026; Vu 20256:
Wang el all
2025c: Yu et all 2025a: Wang all 20256: Shang et all 2026: Wang et all 2025a; Shang el all
202215 Wang et all 2022; Chen at
20235) computer vision (M all, 20244 20255), and various
other domains et all 20251 Shao et all 002S [Tan all 2026: Wilet all 2026 Liet all 2026 Ma 2014). Existing literature indicates that features extracted automatically usually surpass human-designed ones in terms of performanceeMMa all, 2024; Wn et all 20256; Mt. 2025t
al 2025a; Lu
20267: Wang et al. 2026c Cheng et al, (022)).
In the realm of time series forecasting, numerous models have surfaced in recent years. We choose models with superior predictive performance in our benchmark, including the pre-trained time series models: Timer (Luu et all 2IZEE) TTM (Ekambaram el al) 20246) and Moment (Goswami all
2024):: The LLM- models: CALF Liuetall (025)), GPT4TS (Zhou ell (023), UniTime (Lm
all 20245); The specific descriptions for each of these models see Table
Table 5: Descriptions of time series forecasting models in experiment.
Models
Descriptions
Moment Conwermer (IM
Moment transfocmer system trained masked time series task. It reconstraces masked portions time senes taoks like forecssting, classification, anomaly detection, and imputation.
It based on ML. P-Mxer blocks with gated atteniinn and mult-resoluiion sampling It captures temporal polterns cross-channel correlations for time-sriis foreessting, optimized for sero/lewsshor learning with low computitional cost.
TTM 9 Som bog
Timer is a Gyylestlee autoregressive model for time series analysis, predicting the next token in single series sequences. It supports tasks like fonecasting, imputation, and anomaly detection acroes differens time series.
Timer Pam MUSS)
CALF emuss-mdall knowledge distillation framework that aligns time series data pre- tr-itrnnee LLMs levengingg both static and dynamic knowledge, achieving state-of batt--of-the-zt performance both long- and short-serm serm forecasting tasks with strong generalization abilitis.
CALF IITE mn MIKK
GPT-TS tine-tunes the limited parameters of LLM, which demonstrates competitive performance by transferrig know lodge from lapo--saale pre pe-ttaining text data.
GP
GPT4TS on kur.
UniTlme Co UIReI
UniTime designs domain instractions alige series modalities.
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Published as a conference paper at ICLR 2026
D.3 IMPLEMENTATION DETAILS
We utilize the TSFM-Bench (L. all ROZS) code repository for unified evaluation. Following the settings in TFB (Qiu et all (024)) and FMTS-BBench eLl 2025),, do not apply the Drop Last trick to ensure a fair comparison. All experiments of CoRA are conducted using PyTorch in Python 3.10 and executed on NVIDIA Tesla-A800 GPU. The MSE loss function guides the training process and employs the ADAM optimizer.
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Published as a conference paper at ICLR 2026
E FULL RESULTS
Table 6: The table reports MSE and MAE of LLM-based models for different forecasting horizons
F E (96, 192, 336, 720). The better results are highlighted in bold.
Model
GPT4TS (2023)
CALF (2025)
UniTime (2024)
Plugin
X
V
X
V
X
V
Metric
MSE
MAE
MSB
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
96
0.439
0.447
0.427
0.435
0.407
0.427
0.396
0.417
0.718
0.575
0.690
0,557
ETTh2 ETThl
192
0.461
0.458
0.449
0.448
0.429
0.443
0.420
0.433
0.750
0.592
0.723
0.573
336
0.464
0.468
0.451
0.458
0.443
0.456
0.433
0.446
0.723
0.592
0.702
0.582
720
0.509
0.512
0.497
0.496
0.495
0.495
0.487
0.484
0.767
0.623
0.739
0.606
96
0.331
0.382
0.318
0.369
0.303
0.364
0.297
0.356
0.360
0.391
0.351
0.383
192
0.370
0.408
0.356
0.393
0,386
0.402
0.378
0.391
0.388
0.430
0.376
0.417
336
0,380
0.422
0.369
0.413
0,387
0.419
0,382
0.408
0.393
0.436
0.382
0.427
720
0.419
0.452
0.405
0.441
0.417
0.449
0.409
0.458
0.455
0.473
0.437
0.458
96
0.344
0.381
0.333
0.372
0.319
0.366
0.309
0.361
0.358
0.385
0.345
0.377
ETTm2 ETTml
192
0.376
0.398
0.366
0.389
0.346
0.381
0.338
0.372
0.386
0.403
0.371
0.391
336
0.395
0.408
0.386
0.399
0.386
0.407
0.378
0.396
0.421
0.420
0,403
0.407
720
0.442
0.434
0.432
0.425
0.440
0.433
0.432
0.424
0.469
0.448
0.459
0.435
96
0.190
0.281
0.184
0.274
0.182
0.272
0.177
0.267
0.191
0.278
0.183
0.267
192
0.242
0.314
0.232
0.306
0.238
0.310
0.230
0.304
0.249
0.316
0.239
0.307
336
0.298
0.350
0.289
0.341
0.297
0.349
0.287
0.340
0.345
0.375
0.334
0.367
720
0.387
0,401
0,371
0.390
0.373
0.397
0,363
0.390
0,382
0.392
0,367
0.382
Electricity
96
0.180
0.295
0.173
0.288
0.142
0.241
0.139
0.236
0.174
0.283
0.168
0.277
192
0.194
0.308
0.186
0.302
0.158
0.254
0.152
0.248
0.186
0.292
0.181
0.285
336
0.209
0.319
0.204
0.314
0.175
0.272
0.169
0.263
0.201
0.305
0.195
0.300
720
0.248
0.349
0.241
0.340
0.218
0.307
0.214
0.299
0.242
0.337
0.233
0.325
96
0.440
0.323
0.429
0.314
0.407
0.299
0.395
0.291
0.424
0.311
0.414
0.303
Traffic
192
0.423
0,305
0.413
0.299
0.424
0.309
0.413
0.301
0.437
0.320
0.427
0.309
336
0.433
0.309
0.425
0.301
0.436
0.319
0.426
0.309
0.476
0.333
0.465
0.325
720
0.468
0.325
0.455
0.315
0.477
0.342
0.467
0.332
0.485
0.363
0.477
0.354
96
0.243
0.262
0.233
0.251
0.204
0.276
0.198
0.269
0.251
0,286
0.246
0.278
Solar
192
0.259
0.295
0.250
0.282
0.225
0.291
0.220
0.284
0,251
0.321
0.246
0.313
336
0.260
0.278
0.250
0.267
0.244
0.308
0.239
0.302
0.253
0.323
0.247
0.316
720
0.260
0.281
0.248
0.275
0.247
0.314
0.240
0.308
0.256
0.327
0.253
0.320
Weather
96
0.189
0.244
0.181
0.237
0.164
0.217
0.161
0.211
0.184
0.240
0.175
0.229
192
0.226
0.276
0.218
0.265
0,207
0.255
0.201
0.248
0.228
0.275
0.217
0.265
336
0.270
0.306
0,260
0.294
0,260
0.293
0.253
0.284
0.271
0.305
0.259
0.293
720
0.330
0.348
0.320
0.336
0.323
0.340
0,312
0.331
0.335
0.351
0.323
0.336
ZalNoo AQShunyi
96
0,800
0.536
0.786
0.526
0.691
0.510
0.675
0.501
0.691
0.513
0.667
0.496
192
0.846
0.550
0.824
0.538
0.722
0.517
0.701
0.503
0.738
0.523
0.712
0.509
336
0.855
0.557
0.832
0.545
0.736
0.526
0.719
0.517
0.748
0.542
0.721
0.528
720
0.897
0.574
0.884
0.559
0.785
0.552
0.771
0.539
0.797
0.565
0.767
0.544
96
0,515
0.486
0,505
0.479
0.471
0.434
0.457
0.426
0.473
0.448
0.458
0.435
192
0,552
0.505
0,542
0.495
0,532
0.476
0,517
0.464
0,547
0.482
0.526
0.465
336
0,583
0.516
0.574
0.507
0.569
0.494
0.554
0.483
0,571
0.496
0.553
0.484
720
0.612
0.532
0.594
0.517
0.629
0.522
0.610
0.509
0.659
0.538
0.633
0.522
22

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Published as a conference paper at ICLR 2026
Table 7: The table reports MSE and MAE of pre-trained models for different forecasting horizons F E (96, 192, 336, 720). The better results are highlighted in bold.
Model
Timer (2024)
Moment (2024)
TTM (2024)
CoRA
X
V
X
V
X
Metric
MSR
MAE
MSR
MAE
MSE
MAR
MSR
MAE
MSR
MAE
MSR
MAE
96
0.395
0,409
0.390
0.405
0.409
0.422
0.395
0.411
0.364
0.392
0.357
0.386
192
0.458
0,458
0.453
0.446
0.428
0,436
0.416
0.432
0.391
0,410
0.381
0.400
336
0.496
0,487
0.495
0.479
0.457
0,451
0.449
0.441
0,411
0,430
0.408
0.426
720
0.851
0.652
0.833
0.650
0,483
0,483
0.467
0.473
0.454
0.472
0.444
0.467
96
0.292
0.344
0.287
0.339
0.310
0.361
0.302
0.349
0.272
0.330
0.271
0.321
E7Th2
192
0.372
0.397
0.367
0.390
0.349
0.389
0.337
0.386
0.340
0.373
0.334
0.369
336
0.373
0.414
0.371
0.410
0.365
0.408
0.359
0.404
0.372
0,402
0.370
0.401
720
0.441
0.466
0.435
0.453
0.402
0.437
0.401
0.423
0.386
0.429
0.384
0.420
96
0,303
0.351
0,302
0.349
0,312
0.358
0,310
0.353
0.299
0.345
0.297
0.342
ErTml
192
0.364
0,390
0.360
0.384
0,342
0.375
0.339
0.371
0.341
0.367
0.341
0.361
336
0,405
0.414
0.400
0.408
0.368
0,391
0.367
0.379
0.367
0,383
0.359
0.378
720
0.750
0,560
0.747
0.549
0,416
0.417
0.407
0.403
0,422
0.413
0.413
0.411
ETTm2
96
0.168
0,250
0.166
0.243
0.177
0.265
0.173
0.257
0.164
0,250
0.160
0.247
192
0.238
0.303
0.236
0.297
0.228
0.298
0.226
0.296
0.223
0.291
0.218
0.287
336
0.323
0.362
0.315
0.353
0.278
0.334
0.274
0.330
0.283
0.331
0.278
0.323
720
0.386
0.415
0.384
0.411
0.364
0.389
0.357
0.384
0.365
0.381
0.356
0.372
Electricity
96
0,140
0.236
0.137
0.231
0,159
0.242
0.158
0.235
0,146
0.246
0.143
0.240
192
0.163
0.257
0.163
0.253
0.187
0.265
0.183
0.256
0.166
0.265
0.165
0.264
336
0,185
0.281
0.185
0.278
0,258
0.287
0.256
0.285
0.181
0.282
0.180
0.278
720
0.320
0.368
0.316
0.359
0.360
0.372
0.348
0.364
0.224
0,316
0.219
0.309
96
0.383
0.272
0.379
0.266
0.392
0.278
0.390
0.272
0.450
0.326
0.445
0.320
Traffic
192
0.414
0,286
0.411
0.280
0.444
0.297
0.429
0.287
0.467
0.331
0.459
0.324
336
0.436
0.299
0.426
0.294
0.436
0.302
0.429
0.293
0.493
0.346
0.489
0.341
720
0.571
0.484
0.559
0.484
0.552
0.494
0.540
0.478
0.534
0.366
0.530
0.358
96
0.170
0,219
0.169
0.216
0,203
0.270
0,201
0.268
0.255
0,208
0.251
0.206
Solar
192
0.197
0,248
0.196
0.241
0.215
0.276
0,209
0.274
0.271
0.241
0.269
0.241
336
0.203
0.255
0.198
0.254
0.225
0.282
0.224
0.272
0.274
0.239
0.274
0.239
720
0.336
0.337
0.328
0.335
0.225
0.281
0.218
0.281
0.278
0.237
0.271
0.235
Weather
96
0.150
0.200
0.148
0.195
0.170
0.227
0.164
0.224
0.149
0.196
0.149
0.194
192
0.215
0.264
0.214
0.259
0.211
0.260
0.208
0.260
0.195
0.239
0.193
0.237
336
0.283
0.317
0.278
0.312
0.256
0.293
0.251
0.283
0.245
0.278
0.240
0.274
720
0.360
0.375
0.356
0.366
0.327
0.343
0.323
0.337
0.315
0.330
0.313
0.322
ZalNoo AQShunyi
96
0.534
0.434
0.524
0.432
0.729
0.491
0.728
0.475
0.638
0.481
0.635
0.473
192
0.713
0.521
0.705
0.511
0.706
0.509
0.685
0.495
0.687
0.501
0.669
0.498
336
0.735
0.526
0.715
0.518
0.724
0.521
0.709
0.520
0.710
0.516
0.694
0.512
720
0.792
0.543
0.779
0.529
0.778
0.544
0.774
0.528
0.766
0.543
0.757
0.540
96
0.437
0.400
0.431
0.396
0.476
0.442
0.475
0.430
0.424
0.405
0.420
0.400
192
0.522
0.453
0.517
0.452
0.522
0.465
0.504
0.448
0.486
0.441
0.484
0.437
336
0.548
0.480
0.547
0.471
0.558
0.482
0.540
0.482
0.537
0.468
0.523
0.456
720
0.617
0.514
0.610
0.508
0.594
0.501
0.575
0.489
0.571
0.493
0.561
0.479
23

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Published as a conference paper at ICLR 2026
F MORE ANALYSIS ON CORA
F.1 COMPARISON IN DIFFERENT SAMPLING RATE
To further demonstrate the advantages of CoRA, we compared its performance with LIFT (Zha & Shen, 20Z)) and C-LoRA (Nie all BO2ED using TTM as the backbone and setting H to 96, under different sampling rates the few-shot setting. As shown in Table & CoRA consistently outperforms LIFT and C-LoRA, especially at lower sampling rates where LIFT and C-LoRA suffer from insufficient training data, leading to degraded performance. CoRA's superior performance is attributed to its comprehensive modeling of correlations and efficient utilization of TSFMs. As the sampling rate increases. LIFT and C-LoRA also improve TSFMs' performance, but at higher sampling rate will be a higher training cost.
Table The sampling rate set to (5%, 10%, 15%, 20%, 25%). Black: the best, Underline: the 2nd best.
Dataset
ETTm2
Electricity
Rate
5%
10%
15%
20%
25%
5%
10%
15%
20%
25%
TTM
0.164
|
0.162
0.163
0.160
0.157
0.146
0.143
0.145
0.141
0.142
+ LIFT
0.162
0.163
0.161
0.158
0.156
0.149
0.145
0.144
0.139
0.139
+ C-LoRA
0.166
0.163
0.162
0.159
0.155
0.148
0.146
0.147
0.140
0.141
0.160
0.158
0.159
0.157
0.153
0.143
0.141
0.142
0.138
0.135
+ CoRA
2000003
200002
+0.003
200001
=:0.002
1000003
100003
2:00002
4:00002
+0.001
F.2 HYPERPARAMETER SENSITIVITY
With TTM as the backbone and set to 96, we study the hyperparameter sensitivity of CoRA, including the Degree of Polynomial (K), the size of decomposition (M), the layers' number of projectors before and after HPCL. (71 and 12). Figure bz show that is a robust hyperparameter, common configurations. Figure 6F illustrates that the selection of M
and we often choose does not need to increase rapidly with the number of channels. Figure bdd and Figure bd show that too few layers may lead insufficient fitting capacity, while too many can diminish generalization ability. We often choose 3 or 5 as common configurations.
0370
Modker
Mack
0.300
0345
1340
6:30
6335
M
N2
N2
(a) Degree of Polynomial
(b) Decomposition Size
(c) Pi.Pa Layers
(d) Pa.Pa Layers
Figure 6: Parameter sensitivity of main
in CoRA.
F.3 VISUALIZATION OF HETEROGENEOUS SPACES.
To further demonstrate the effectivvness of CoRA in modeling the DCorr, HCorr and PCorr, we con- duct a visualization experiment. Specifically, by examining samples at time steps and channels in the Weather dataset, compare the similarities between representations in the heterogeneous space. The result is shown in Figure M Among them, Figure M illustrates the visualization of samples from the Weather dataset, with each time step comprising 64 time points. Figure 7B shows
24

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Published as a conference paper at ICLR 2026
the cosine similarity between the channel representations in positive and negative spaces. Based on observations, can be concluded that within the 0-64 time points, Channel and Channel 3 as well Channel 2 and Channel 4 exhibit significant positive correlations. Within the 64-128 time points,Channe, Channel and Channel show significant positíve correlations, while Channel demonstrates channel independence. Within the 128-192 time woints,Channir and Channel ex- hibit significant positive correlations, while they show significant negative correlations with Channel 2 and Channel 4. These findings align with the actual data, demonstrating that CoRA is capable of simultaneously capturing DCorr HCorr and PCorr.
Channel 1
Channel 2
Channel 3
Channel 4
192
Samples at time steps and 4 channels in Weather dataset.
Space
Space Step
Space Step
C1
C1
1.00
0.75
C3
C3
0.00
C1
C4
C1
C3
C4
Negative Space
Time Step
Negative Time
Negative Space
Time Step
1.00
0.75
C2
0.50
0.25
C4
G4-
C4
0.00
C4
(b) The similarity of representations in positive and negative spaces at 3 time steps.
Figure 7: Visualization of Heterogeneous Spaces
25

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Published as a conference paper at ICLR 2026
G THE USE OF LARGE LANGUAGE MODELS
The use of open-source Large Language Models (LLMs) this work was strietly limited to as- sisting with the translation of certain terms and polishing small portion of the text. LLMs did not contribute to the conceptual aspects of the research, including information retrieval, knowledge discovery, the ideation process.
26


Reviews:
[{"review_id": "tSMCHHs89l", "reviewer": "Reviewer_k2Aw", "summary": "This paper proposes CoRA (Correlation-aware Adapter), a lightweight, plug-and-play module designed to enhance existing Time Series Foundation Models (TSFMs) for multivariate forecasting. The central premise is that many TSFMs, while powerful in capturing temporal dependencies, neglect the complex inter-channel correlations that are vital for accurate multivariate prediction in downstream tasks. The main contributions of the paper can be summarized as follows:\n1. A Unified Framework for Complex Correlations: The paper provides a structured view by categorizing inter-channel relationships into three types: Dynamic (DCorr), Heterogeneous (HCorr), and Partial (PCorr) correlations.\n2. An Efficient and Effective Adapter Design: CoRA is designed as an efficient adapter that only requires fine-tuning. It models dynamic correlations (DCorr) by innovatively decomposing the correlation matrix into low-rank time-varying and time-invariant components.\n3. A Novel Contrastive Learning Method (HPCL): The core technical contribution is the HPCL module, which models HCorr by projecting representations into separate positive and negative latent spaces. Within each space, it then applies a guided contrastive loss to cluster strongly correlated channels, a process that elegantly captures PCorr.", "questions": "1. Regarding the Explicit Validation of Partial Correlation (PCorr): The paper's core thesis is the unified modeling of DCorr, HCorr, and PCorr. While the evidence for DCorr and HCorr is quite direct, the support for PCorr modeling appears more implicit. Could you provide a more direct piece of evidence to demonstrate that CoRA is effectively learning and leveraging partial correlations?\n2. Regarding the Optimization of the Learnable Threshold ε: Could you please clarify the specific mechanism that allows gradients to flow back toεduring the training process?\n3. Regarding Performance in Data-Rich Scenarios: The main experiments are conducted in a 5% few-shot setting. However, how does CoRA perform when fine-tuned on the full training dataset (100% data)? Does the performance gap between the baseline TSFM and TSFM+CoRA widen, narrow, or remain the same?", "limitations": "", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "This paper proposes CoRA, a novel correlation-aware adapter designed to enhance the multivariate forecasting capabilities of Time Series Foundation Models (TSFMs) on specific downstream tasks.\n1. Originality: The paper is the first to propose a unified framework that simultaneously addresses the dynamic, heterogeneous, and partial aspects of inter-channel correlations.\n2. Quality: The paper is of high quality, featuring a rigorous methodology, clear theoretical derivations, and practical efficiency.\n3. Clarity: The paper is well-written, with a complete logical flow and effective visualizations.\n4. Significance: This work is highly significant for the time series domain, particularly for fine-tuning TSFMs on downstream tasks.", "weaknesses": "This paper could be improved in the following areas:\n1. Lack of Direct Experimental Validation for Partial Correlation (PCorr): The paper claims to model three types of correlations: DCorr, HCorr, and PCorr. While experiments provide strong evidence for DCorr (e.g., Fig. 7) and HCorr (separation of positive/negative spaces), the validation for PCorr is less direct. The ablation study (Table 2) shows the overall benefit of the HPCL module but does not disentangle the specific contributions of modeling HCorr versus PCorr. The visualization in Fig. 7 implicitly shows PCorr through clustering but fails to highlight or analyze it separately.\n2. Omission of Experimental Details: The paper states that the thresholdεis a \"learnable\" parameter but does not detail how it is optimized. Furthermore, the main results in Table 1 are based solely on a 5% few-shot setting. It is suggested that the authors include experiments conducted with full-dataset fine-tuning.\n3. Confusing Notation: The authors use the standard and calligraphic forms of the same letter to represent two different concepts. It is recommended that the authors use distinct symbols and consider adding a notation table to the paper to ensure consistency and clarity.", "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": "hhItBSo2Mo", "reviewer": "Reviewer_iXBW", "summary": "This paper proposes a way to fine-tune multivariate time series foundation models as to better capture correlation between variables. Key ideas are to estimate a correlation matrix between features that has a time-dependent and time-invariant decomposition, and to screen for which variables to actually focus on in terms of positive or negative correlations via a contrastive learning strategy.", "questions": "Please see weaknesses (I raised a number of concerns there).", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "- I appreciate that the paper is trying to separately handle different types of correlation (DCorr, HCorr, PCorr)\n- I find the idea of using a time-varying and time-invariant decomposition to be valuable, along with the idea of finding pairs of features with strong enough positive or negative correlation\n- The experimental results appear to be very impressive (although as pointed out in weaknesses, I would like to see more baselines and some additional experiments)", "weaknesses": "- At least in how it is stated now, it's hard for me to see why Theorem 1 should hold since equation (15) in Theorem 1 disagrees with equation (5) and the decomposition showed earlier in Figure 3.\n- In stating theoretical guarantees, I would suggest also providing intuition for why the guarantee should hold (this intuition should be in the main paper and not in an appendix/supplemental material as it helps the reader understand/interpret the guarantee) and whether the proof uses any nontrivial ideas, or if it's largely just based on an existing result. Maybe I'm missing something but Theorem 2 seems to be a known result regarding polynomial approximation using a variant of the mean value theorem? If the result was not previously known, what are the closest known existing theoretical results (which can help provide the reader with point(s) of comparison as to what proof techniques/ideas are novel)? Also can you comment on the extent to which the assumption holds for real data?\n- Experiments: It would be helpful including more baselines, especially ones that already account for correlation structure (even if it doesn't do so as comprehensively as the proposed approach) such as UniTS and Moirai (both of which are mentioned in the paper but not actually compared against in the experiments).\n- Experiments: Right now Tables 1 and 2 are reported without error bars (such as standard deviation over experimental repeats with different random seeds). Please include error bars as to give a better sense of variability in results.\n- Experiments: It would be helpful seeing for the different datasets how the amount of data available for fine-tuning affects the performance of CoRA especially since I'd imagine that if one has somewhat limited data to fine-tune with, then the correlation matrix might be hard to estimate accurately.\n- Overall I find that the paper has many exposition issues and typos that altogether make it so that the paper has serious clarity problems. Here are a few issues (this list is not exhaustive):\n    - (minor) line ~17: since you're abbreviating \"**Cor**relation-aware **A**dapter\", shouldn't the abbreviation be \"CorA\" and not \"CoRA\" (i.e., why is the \"R\" capitalized)?\n    - line ~53 (last line of page 1 that actually is one line after line 53): the explanation here makes it clear why MLP doesn't handle DCorr but why precisely does it not model HCorr? Can an MLP not figure out positive or negative correlations? I'd imagine that the learned weights would be able to capture this sort of information?\n    - line ~122: \"LLMs enable\" should say \"LLMs to enable\"\n    - line ~153-154: \"$L$ length\" should say \"length $L$\"\n    - line ~153-154: please clearly define what $t$ is\n    - line ~161: \"pluged\" should say \"plugged\"\n    - line ~185: the comma after \"Figure 2\" should be a period\n    - lines ~205-206: please clearly state what $M$ is (the rank) and perhaps comment on how it is chosen (clearly it seems like we would want $M < N$ but is this a hyperparameter that is tuned later?)\n    - Figure 3: it would be helpful to better motivate the decomposition especially since the time-varying and time-invariant information is getting mixed together in the multiplication so that they're not decoupled (also Figure 3 seems to make it seem like $M_t^{corr} = Q_t V Q_t^T$ but then this isn't actually the case according to equation (5) or equation (15) later) -- yet somehow lines ~209-210 suggests that we can estimate $Q_t$ and $V$ separately and the text doesn't sufficiently provide intuition at this point for why this separate estimation should be possible\n    - Section 4.1.1: in modeling dynamic regularities, it would be helpful to better motivate why polynomials are particularly well-suited for the task vs alternative approaches (I'd imagine higher order polynomials become more susceptible to noise, for instance; for example, how does the proposed approach compare with a different strategy that amounts to just using a first-order polynomial but having multiple basis functions?)\n    - line ~231-232: \"i-th\" should say \"$i$-th\"\n    - line ~233-234 and also line ~236: inconsistent notation -> \"$q^i$\" should use a bold version of \"$q$\" to match equation (1); also I'd suggest stating clearly that \"$\\odot$\" stands for Hadamard product\n    - line ~235: \"we define the set of $C_{i,t}$\" should not use the word \"set\" here since what is being described is not what the word \"set\" means in math\n    - line ~250-251: \"Where\" should not be capitalized\"\n    - line ~261: \"L is the size of the input series\" -> \"L\" should be italicized (i.e., written as the math variable $L$)\n    - line ~261-262: \"$\\mathbf{R}\\in\\mathbb{R}^{N\\times N}$ to denote the set of $r$\" -> this is not the correct use of the word \"set\" in math\n    - equation (5) does not agree with equation (15) and also does not seem to agree with Figure 3\n    - line ~282: \"Where\" should not be capitalized\n    - line ~282: \"layerNorm\" should be capitalized (i.e., written as \"LayerNorm\") to match equations (6) and (7)\n    - line ~283: $\\text{MLP}_{\\alpha}=\\mathbb{R}^d\\rightarrow\\mathbb{R}^d$ ---- the equal sign \"$=$\" should be replaced by a colon \"$:$\" (a similar math typo shows up for the other MLP defined in this same line)\n    - does $\\beta$ in equation (7) and in equation (14) actually mean different things?", "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": "pQmtvufkH0", "reviewer": "Reviewer_bdjv", "summary": "To address the limitation that existing time series foundation models often overlook inter-channel modeling, this paper proposes a lightweight adapter, termed CoRA. CoRA innovatively decomposes the correlation matrix into time-varying and time-invariant components. It leverages learnable polynomials to capture dynamic patterns and introduces a novel dual contrastive learning mechanism to distinguish between positive and negative correlations. Optimized via a heterogeneous-local contrastive loss, CoRA incurs minimal computational overhead during the inference stage. Empirical results demonstrate that CoRA provides an effective solution for correlation modeling in multivariate time series forecasting.", "questions": "1. How does CoRA, as a plug-and-play module, accommodate the fundamental architectural differences between encoder-only and encoder-decoder models, particularly with respect to their distinct training objectives and inference processes?\n2. What is the underlying rationale for incorporating rule-based correlation relationships when the model is already designed to capture these dependencies through a learnable mechanism?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "1. The paper is well-motivated, addressing the critical challenge of modeling complex inter-channel dependencies in multivariate time series.\n2. The manuscript is well-written, featuring clear and consistent notation throughout.\n3. The empirical evaluation demonstrates that CoRA consistently surpasses state-of-the-art baselines across a diverse set of real-world datasets.", "weaknesses": "1. The projection layers are not much different from the related modeling methods in existing methods (such as TSMixer [1]), a more detailed clarification is needed.\n2. The set of baselines for comparison is not comprehensive, as it omits recent state-of-the-art foundation models like TimerXL [2].\t\n3. Discuss and comparison with classical baselines (e.g., PatchTST  [3], Leddam [4], iTransformer [5], Autoformer [6], DLinear [7]) is suggested.\n\n*[1] TSMixer: An All-MLP Architecture for Time Series Forecasting.*\n\n*[2] Timer-XL: Long-Context Transformers for Unified Time Series Forecasting.*\n\n*[3] A Time Series is Worth 64 Words: Long-term Forecasting with Transformers.*\n\n*[4] Revitalizing Multivariate Time Series Forecasting: Learnable Decomposition with Inter-Series Dependencies and Intra-Series Variations Modeling.*\n\n*[5] iTransformer: Inverted Transformers Are Effective for Time Series Forecasting.*\n\n*[6] Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting.*\n\n*[7] Are Transformers Effective for Time Series Forecasting?.*", "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": "et89TmFFlA", "reviewer": "Reviewer_TnwM", "summary": "This paper introduces CoRA, a lightweight and plug-and-play module designed to enhance Time-Series Foundation Models (TSFMs) by better modeling inter-channel correlations. CoRA employs a correlation decomposition mechanism combining global time-invariant matrices and learnable polynomial bases, capturing both static and dynamic dependencies. Importantly, CoRA does not require re-pretraining of the base TSFM and can be applied during few-shot fine-tuning, making it a practical adaptation method.", "questions": "1. Statistical Significance and Robustness:\nAre the improvements in Tables 1 and 2 statistically significant? Please report standard deviations, confidence intervals, or results across multiple random seeds to validate robustness.\n\n2. Adaptation in Nonstationary Environments:\nHow does CoRA behave under regime shifts or nonstationary dynamics where the global time-invariant assumption may break down? Could it be extended to support online updates or adaptive windowing?\n\n3. Scalability to Very High-Dimensional Settings:\nFor extremely large N (> 500), do global correlation matrices introduce memory or numerical bottlenecks? Any empirical or theoretical evidence on efficiency and convergence at that scale?\n\n4. Extensibility Beyond Forecasting:\nCould the proposed correlation decomposition framework generalize to other TSFM-based tasks—such as anomaly detection or temporal classification? What architectural adjustments would be required?\n\nA thorough response and additional evidence to the above points would influence my score adjustment.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "1. Clear Motivation and Positioning:\nThe paper clearly identifies a key limitation in existing TSFM-based forecasting—insufficient modeling of heterogeneous inter-channel correlations—and proposes a theoretically grounded yet efficient mechanism to address this.\n\n2. Lightweight and Practical Design:\nCoRA's plug-in design allows easy integration with existing TSFMs during fine-tuning without requiring re-pretraining. Its parameter efficiency and low inference overhead make it appealing to practitioners seeking post-hoc adaptation over full model retraining.\n\n3. Theoretical Depth and Interpretability:\nThe proposed correlation decomposition elegantly connects polynomial-based dynamic components with global invariant structures. Appendix provides a theoretical foundation and enhances interpretability of the correlation modeling process.", "weaknesses": "1. Limited Empirical Evaluation Scope:\nTable 1 focuses on few-shot MSE benchmarks using standard datasets but lacks evaluation under out-of-distribution shifts, missing channels, or nonstationary regimes—critical aspects for real-world TSFM deployment.\nFigure 4 presents relative MSE changes, which obscures absolute performance deltas; including absolute values alongside relative improvements (as in Table 1) would increase transparency.\n\n2. Assumption Boundaries Underexplored:\nTheoretical guarantees rely on local stationarity and bounded smoothness assumptions that may not hold in volatile domains (e.g., finance, IoT, environmental data). The paper does not examine edge cases such as abrupt regime shifts or high-noise inputs.\n\n3. Potential Overstatement of Generality:\nThe paper claims CoRA \"captures various correlations with O(N) inference complexity.\" While this is theoretically sound, real-world multivariate systems may involve nonlinear or hierarchical dependencies that exceed the current decomposition's expressiveness. The claim is reasonable but should avoid implying complete modeling capability.", "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)