COSA: Context-aware Output-Space Adapter for Test-Time Adaptation in Time Series Forecasting
Authors: Jeonghwan Im
Hyuk-Yoon Kwon
Venue: ICLR 2026 Poster (2026)
Keywords: Test-Time Adaptation
Time-Series Forecasting
Non-stationarity
Context-aware Adapter
Primary area: learning on time series and dynamical systems

Abstract: Deployed time-series forecasters suffer performance degradation under non-stationarity and distribution shifts.
Test-time adaptation (TTA) for time-series forecasting differs from vision TTA because ground truth becomes observable shortly after prediction. 
Existing time-series TTA methods typically employ dual input/output adapters that indirectly modify data distributions, making their effect on the frozen model difficult to analyze. 
We introduce the Context-aware Output-Space Adapter (COSA), a minimal, plug-and-play adapter that directly corrects predictions of a frozen base model.
COSA performs residual correction modulated by gating, utilizing the original prediction and a lightweight context vector that summarizes statistics from recently observed ground truth.
At test time, only the adapter parameters (linear layer and gating) are updated under a leakage-free protocol, using observed ground truth with an adaptive learning rate schedule for faster adaptation.
Across diverse scenarios, COSA demonstrates substantial performance gains versus baselines without TTA (13.91$\sim$17.03\%) and SOTA TTA methods (10.48$\sim$13.05\%), with particularly large improvements at long horizons, while adding a reasonable level of parameters and negligible computational overhead.
The simplicity of COSA makes it architecture-agnostic and deployment-friendly.
Source code: https://github.com/bigbases/COSA_ICLR2026

Published as a conference paper at ICLR 2026
COSA: CONTEXT-AWARE OUTPUT-SPACE ADAPTER FOR TEST- TIME ADAPTATION IN TIME SERIES FORE- CASTING
Jconghwan Im
Hyuk- Yook Kwon"
Department of Data Science Scoul National University of Science and Technology 2452001 www.ulech..a......
Department of Data Science Seoul National University of Science and Technology hyukyoon. kwwn@ tech. ac kr
ABSTRACT
Deployed time-series forecasters suffer performance degradation under non- stationarity and distribution shifts. Test-time adaptation (TTA) for time-series forecasting differs from vision TTA because ground truth becomes observable shortly after prediction. Existing time-series TTA methods typically employ dual input/output adapters that indirectly modify data distributions, making their ef- fect on the frozen model difficult to analyze. We introduce the Context-award Output-Space Adapter (COSA), minimal, plug-and-ple adapter that directly corrects predictions of a frozen base model. COSA performs residual correction modulated by gating, utilizing the original prediction and lightweight context vector that summarizes statistics from recently observed ground truth. At test time, only the adapter parameters (linear layer and gating) are updated under a ceakage-free protocol, using observed ground truth with an adaptive learning rate schedule for faster adaptation. Across diverse scenarios, COSA demonstrates substantial performance gains versus baselines without TTA (13.91~17.03%) and SOTA TTA methods (10.48~~3.055)) with particularly large improvements at long horizons, while adding reasonable level of parameters and negligible computational overhead. The simplicity of COSA makes it auchitecture-agnsste and deployment faaiioonmnnt-finnlll..... Source code: https: /tttpp://githee www.tt..tttt..ggggggg com com/bbibases// COSA ICLR2026
INTRODUCTION
Time-series forecasting serves as the foundation for critical decision-making across diverse do- mains, including finance (Chen et al. (023). supply chain management (Aamer et al., (2020). energy grids (Di Piazza al. 2021). and predictive maintenance (Makridis et al. al.]| 2020). Modern forecast- ing models, including Transformer-
architectures (Zhou et al. [202]] Liu et al. 2023 2022),
typically achieve high accuracy. However, they suffer performance degradation in real deployment settings due to non-stationarity and distribution shifts (Du et al.) [021] Chen et al.) (024a). Time series exhibit inherent non-stationarity, with changing temporal patterns and statistical characteris- tics over time, resulting in distributions at training that typically differ from those encountered after deployment.
To address this challenge, various approaches have been proposed, including online learning, tinual learning, and domain adaptation. Online and continual learning methods adapt by updating model parameters directly streaming data (Du et al. 2021 Zhang al. 2024 Kirkpatrick al.) 2017 Rolnick et al., 2019, Giannini et al.) 2023 Pham et al.] 2022). but these approaches incur additional computational costs, memory requirements, catastrophic forgetting issues, and plasticity. Furthermore, these methods typically require labeled data or explicit knowledge of task boundaries, making them unsuitable for scenarios where only unlabeled streaming data available during de- ployment. Domain adaptation methods learn robust representations by reducing source source-target target dis-
"Corresponding author: hyukyoon. kwon seoultech.ac.kt

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Published as a conference paper at ICLR 2026
COSA
Context Fector
Linear Layer
Gating
Adaps
Base Model
A
Contest Window
Inpot Leok--back Window
Prediction
Ground Truth
Base Model Prodiction
TTA Prediction
Adaptation
Figure I: Overview of COSA operation showing the context-awes aware gated linear adapter architecture with input processing, linear transformation, gating mechanism, and output correction for test-time adaptation.
tribution differences (Wilson et al. 2020 Jin et al. 2022), but they rely on explicit target domain data and boundary definitions.
Test-time adaptation (TTA) offers alternative approach that adapts to distribution changes by up- dating only lightweight modules using unlabeled test streams after deployment. TTA methods have evolved mainly in the vision domain through batch normalization coefficient optimization and en- tropy minimization (Wang et al.) 2020), seeffssuuuerviied//ontttttteee learning combined with pseudo- labeling g (Liang et [ Chen et al. 2022 Gong et al. (2025). single-sample multi- augmentation- based adaptation (Zhang et al. 2022). and long-term adaptation stabilization (Wang et al.) 2022).
Unlike vision tasks, time-series forecasting has unique characteristics that distinguish it from vision tasks: 1) employs normalization methods different from vision tasks to preserve periodicity and level information, and ground truth becomes sequentially observable after prediction with short delays, enabling the use of direct losses such as Mean Squared Error (MSE).
Time-series forecasting TTA is a recently evolving topic; to the best of our knowledge, only few methods (Kim et al. 2025 Medeiros et al., 2025 Grover & Etemad 2025) have been proposed. All of them adopted dual- dual-adapter architectures that place calibration modules both input and output ends of the base model. They map inputs to domains that the base model can handle more easily and restore outputs the original domain, controlling adaptation intensity through gating- However, these indirect distribution calibration methods involve design complexity and create un- certainty about the impact of imput transformations on internal model representations.
To this end, we propose Context-aware Output-Space Adapter (COSA), which offers direct output- space correction approach that operates with minimal computational overhead. Tigureppresent the overview of COSA. COSA takes the predictions from frozen base model and lightweight context vector, summarizes recent observation statistics as input, computes residuals through linear correc- tion, and controls correction strength using gating. At deployment, and update only a lightweight output adapter (i.e., linear correction with a learnable gate) under leakage-free streaming protocol: after each prediction, adaptation uses only previously revealed ground truth, never current or future labels. COSA is architecture-agnostic and demonstrates consis- tent performance improvements over existing state-of-the-a time-series forecasting TTA methods across various predictors and horizons.
freeze the base forecaster
The main contributions of this study are summarized follows:
1. Architecture-agnoste output adapter. Unlike existing time-series TTA methods that adopt dual input-output adapters, COSA consists of a single output adapter. COSA oper- ates independently in the output space, correcting predictions from any base model without changes to training pipelines or internal parameters. COSA also shows compatibility with SOTA normalizers, consistently reducing prediction error.
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Published as a conference paper at ICLR 2026
2. Context-aware linear residual with gating. A linear correction uses the base prediction and a lightweight context vector that summarizes statistics of recent observed ground truth, and learnable gate modulates correction strength.
3. Consistent accuracy gains. Across six benchmarks, four horizons, and six baseline chitectures, COSA improves test MSE over baselines (13.91~17 (3.03%) and SOTA TTA methods (10.48~13.0055 in particular, with the largest gains longer horizons.
4. Fast, efficient TTA. higher accuracy within a few adaptation steps. Specifically, COSA enables 88. 08.59~990.10% faster inference time against prior SOTA TTA methods.
Adaptive learning rate enables faster convergence of COSA, leading to
2 RELATED WORK
2.1 TIME-SERIES FORECASTING
To handle non-stationarity in time-series forecasting, existing methods typically employ 1) on- line learning, 2) continual learning, and 3) domain adaptation. Representative online learning, D3A (Zhang et al. 2024) narrows source-target gaps through z-score monitoring of loss distribu- tions and Gaussian noise injection, whereas Adarnn (Du al., 202I) reduces temporal distribution shifts using temporal distribution characterization and distribution matching. In continual learning, cPNN (Giannini al., 2023) grows temporal columns and transfers knowledge via lateral connec- tions, and FSNet (Pham et al. 2022) separates per-layer adapters for rapid adaptation from asso-
ciative memory for long-term retention to balance plasticity and stability. For domain adaptation, CoDATS (Wilson al. 2020) learns
features adversarially, and DAF (Jin et al.) 2022) shares attention with nomain-invariant queries/keys and domain-speciffi values. These fami- lies generally update the base model during training online operation, differing from TTA, which adapts lightweight modules on unlabeled test streams while keeping the base model frozen.
2.2 TEST-TIME ADAPTATION
Tent (Wang al. 2020) optimizes only batch-normalization affine parameters under entropy mini- mization, and SHOT (Liang et al. 202T) combines information maximization with self-supervised objectives to transfer source hypotheses to the target. AdaContrast (Chen al., 2022) constructs pseudo-labels via contrastive learning with a dynamic memory bank for gradual adaptation, while
MEMO (Zhang et al., 2022) applies multi-augmmenattion to a single test example minimize marginal output entropy, updating all weights. CoTTA (Wang et al. (2022) limits error accumulation via weight and stochastic restoration, and ACCUP (Gong et al. 2025) integrates adaptive clustering with pseudo-labeling, However, they are proposed for vision tasks. TTA for time-series forecasting requires different approaches from those for vision tasks due to its own characteristics.
2.3 TEST-TIME ADAPTATION FOR TIME-SERIES FORECASTING
Time-series forecasting TTA methods typically employ dual adapters that calibrate distributions both input and output. TAFAS (Kim et al. 2025) couples a calibration module to map inputs to a model-friendly domain and restores outputs to the original domain. uses gating to modulate the calibration strength and utilizes Periodicity-ANe
Adaptive Scheduling (PAAS) to adjust adaptation frequency using frequency patterns based on inputs. PETSA (Medeiros al. 2025) factorizes the calibration module with a low-rank structure and adopts combined loss for stable adaptation with fewer parameters. DynaTTA (Grover& Etemad 2025) adjusts the dynamic learning rate, based on local distribution shift, global distribution shift, loss z-score. Existing time-series forecasting TTA methods employ an indirect approach that bidirectionally calibrates distributions at the input and output sides of the base model. They entailed design complexity due to indirect calibration and difficulty in predicting the impact of input transformations on internal representations. In contrast, aim to utilize single output-space adapter that directly corrects predictions without requiring input calibration or bidirectional transformation, resulting in a simpler design and more predictable adaptation behavior.
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Table I: Adapter-specific notation. Basic sizes/indices are defined (W, L, B; k))
Symbol Meaning (shape)
Base (frozen) L-step prediction at time (R²).
Yime
True T-step target revealed after (RR)).
C.
Context vector from revealed batch statistics lis K, ,,..., Mr 11T (I
X
Input look-back window (IR
x
Adapter input [v]]] C.] (R)+
He
Linear residual W (aa + b (TR4).
Yr
Corrected output y + H. with a tanh(g) E (R²)
W.b,g
Adapter weights (R L x (L + K)). bias (R²), and gate parameter (R).
Operators: concatenation (a b]: || vector norm; || Frobenius.
X
Base Model
Context Buffer
C.
WX
Linear Layer
He
Gating tanh(g)
Batch
L ytrue
Learnable
Frozen
Figure 2: Detailed architecture of COSA illustrating the linear correction layer (weight matrix W and bias b), learnable gating parameter (g), and context vector (C) integration for output-space correction.
COSA:CONTEXT-AWARR OUTPUT-SPACE ADAPTER
3.1 NOTATION PROBLEM FORMULATION
Table shows the symbols necessary for COSA and their meanings.
This study targets univariate time-series forecasting, following the existing SOTA time-series fore- casting TTA methods (Kim et al.) 2025 Medeiros et al. 2025 Grover & Etemad (2025). For mul- tivariate time-series inputs, we decompose them into per-variable univariate forecasting tasks and perform the task iteratively for each variable. At time f, base model generates L-step original pre- dictions ( R. from input X, E W where W denotes the input look-back window length. COSA generates corrected predictions Y, E R from input x(") E L+KK where K denotes the length of the context vector. After making predictions, the ground truth for that interval becomes se- quentially observable following a short delay. Like other TTA approaches, we keep the base model completely frozen and perform only adapter adaptation at test time. Adaptation performed by col- lecting the most recent B prediction, ground truth pairs (batch index {1...., B} and context index & E (I....,K}}
3.2 OVERALL ARCHITECTURE
Figure illustrates the overall operation of COSA. COSA consists of single output adapter that directly corrects the predictions. The key components are: 1) linear layer composed of weight matrix W and bias variable b that computes correction values H. 2) learnable gating g that controls correction strength, and 3) context vector C that summarizes and stores recent trend information.
We choose a single linear layer for two key reasons: 1) Efficiency: Linear operations provide lower latency and higher throughput compared to nonlinear modules, making them suitable for fast adapta- tion. We confirmed that a single-layer adapter shows 34.95% faster wall-clock time on average than 2-layer MLP adapter. 2) CumpicityyPPeformmnt
balance: As reported in L.TSF-Linear (Zeng
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et al. 2023), linear layer sufficiently performs well in time-series forecasting, despite its simplic-
ity. We also verified that a single linear layer adapter showed 5.71 1% even better performance on average against 2-layer MLP adapter. These characteristics make the linear layer beneficial for TTA. Detailed results are provided in Appendix G.3
The streaming protocol for leakage prevention is follows (let the last adaptation performed t-1): 1):
1. Prediction: At time t, base model generates prediction Y from input X
2. Correction: Feed ! and context C2 into COSA to generate the corrected prediction Y,.
3. Observation: After delay A>0 0, values of ground truth of the prediction horizon Yirue sequentially observed.
4. Adaptation: Collect the most recent B prediction, ground truth pairs (Yo+i-1, Y and perform adaptation that updates COSA parameters (W, b.
3.3 OUTPUT-SPACE RESIDUAL CORRECTION
For time concatenate the original prediction of base model and context vector create the adapter input:
a
|| C.].
The residual is computed using a linear transformation:
H, W x b.
The correction magnitude is controlled through gating to compose the final output:
y tanh(g) H,-
The tanh activation stabilizes the correction magnitude.
3.4 CONTEXT CONSTRUCTION
To prevent information leakage, the context summarizes previously observed ground truth informa- tion. For time f, we compute batch-wise aggregation as:
J4 agg
true (i-(kB)+
1SisB) 1 S K.
where the aggregation function agg can use statistics such as mean, median, etc. We construct the context vector by stacking the most recent K aggregated values:
C, P2. Axx 1x]
This context vector summarizes level/scale changes and gradual drift patterns to help interpret the relative magnitude of the base prediction Y (reducing to single time-series values when B = 1).
3.5 ADAPTATION OBJECTIVE AND SCHEDULING
Because targets arrive with a delay, we employ a direct objective with weight decay:
B
Σ - yimi
-
X W
+ - +|g112)
When B forecast-target pairs have been enqueued, run S gradient steps the adapter parameters using a cosine-adaptive learning-rate schedule, simply CALR. We apply cosine annealing within the S steps.
SIT ( = Mmin + (17 7min) cos
S
and then adjust 7 online, based on short-horizon loss trends to encourage fast but stable convergence (decrease loss upticks; mildly increase on plateaus). When new batch arrives, it is always

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Published as a conference paper at ICLR 2026
initialized with the same learning rate, and thereafter the learning rate for the next step within the batch is determined through Equation according to the loss. Early stopping and gradient clip- ping are also implemented. The threshold values for learning rate adjustment are by balancing adaptation speed against stability. Conservative thresholds ensure convergence while aggressive values enable faster response to distribution shifts. Full pseudocode and thresholds given in Algorithm| D in Appendix
COSA targets TSF-TTA under non-stationary environments in which the distribution of time-series data changes over time, In such environments, the classical notion of convergence toward a fixed optimal point not well-defined. Instead, stable learning within each adaptation window is critical. CALR guarantees uniformly bounded wise updates through the following four mechanisms, which structurally prevent error amplification and thus ensure stability during adaptation.
1. Upper-bounded learning rate: The learning rate is constrained by S 7max limiting the maximum magnitude of single-step update.
2. Gradient clipping: At Line 18 of Algorithm I the gradient norm is adaptively bounded as |ggll| <- min II, max L)).
3. L2 regularization: The weight-decay term in Equation ! strains parameter magnitude.
A(I W + bb2 + +1g12), con-
4. Bounded gating: Because a = tanh(g) E {[1,, 1], the correction magnitude is structurally limited.
For every new batch, the learning rate reinitialized to max (Line of Algorithm D giving each batch equal opportunity for adaptation. The learning rate is then adapted according to the batch's ' loss behavior. When the loss spikes, we reduce the learning rate as 17 <- max(0.5m, Mmin), temporarily lowering update intensity. When the loss decreases stably, we increase it n <- min(1.17, M, strengthening adaptation. This enables stable learning even when short-term per- turbations anomalies appear in the input data, allowing rapid recovery.
4 EXPERIMENTS
4.1
EXPERIMENTAL SETTINGS
We evaluate COSA on six benchmark datasets (ETTh1/2, ETTm1/2, Exchange Rate, and Weather) with a fixed look-back window (W 96) and four prediction horizons E {96, 192, 336, 720)). We used six representative base models spanning different architectures: Transformer-based (iTrans- former (Liu et al. 2023), PStchTST (Nie et al., 2023)). linear-based (DLinear (Zeng et al. 2023
OLS Toner& & Darlow 2024)), and MLP--basdd (FreTS (Yi et al.) 2023). MICN (Wang al. 2023
By default, all input time series are treated as variable-wise univariate forecasting tasks, standard normalization is applied, and MSE serves as the performance comparison metric.
We compare COSA (our method) with Baseline (without TTA), TAFAS <Kim et al. 2025). and PETSA (Medeiros et al.) 2025). All experiments were conducted according to the official bench- mark library (Wang et al. 2024 The train:valdiation:eest ratio is 7:1:2 for all datasets.
Unless otherwise noted, we fix the adapter hyperparameters to K K=10 =10 and S=3, enabled CALR. We utilize the average as agg. Ablation studies for the variations of agg are provided in Appendix G.I
We report two variants for COSA: COSA-F, which uses fixed B=48 (half of the look-back), and COSA-P, which sets B online following the PAAS in TAFAS (Kim et al.) (025). Hyperparameters for comparative methods follow the settings reported in the original papers official code defaults. In tables, the best score is shown in bold and the second best is underlined.
We utilize Xavier uniform initializer (Glorot & Bengio 2010 with gain 0.1 for parameters of the weight matrix W. The bias and gating g are initialized to 0, and Adam optimizer is utilized.
In the case of DynaTTA Grover & Etemad 2025). there were reproducibility issues when we used the officially released source code. Therefore, we report the comparison results with them in the Appendix F.5 with the used detailed hyperparameters.

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Table 2: Prediction accuracy comparison. Standard deviations less than 0.001 are omitted.
Transformer--usel
Linear-based
MLP-based
iTrranformer
DLineur
F
Baseline TATAS PETSA COSA-FCOSM Baseline TAFAS PETSA
COSA.FCOAA Baseline TAFAS
PETSA
COSA.
96
.4507
A411
.3933
.3688
.4633
.6955
A618
4594
A574
.4482
.4462
A403
.4387
A384
.4711
.5078
.9988
.4949
.4961
.4919
-5213
-5117
.5066
.5050
.5022
.4922
.951
.4900
336
.5658
.5629
5640
.6611
.3300
.5659
.6004
.5177
.5288
.5466
.5544
.5521
.5227
.5467
.3511
.7038
.6612
.6596
.9588
.5638
.6820
.6743
.6107
.7182
.6446
6259
.5959
ETTm2 ETTml ETTh2
96
.2577
.2549
.2511
2504
.2433
.2123
.303
.2306
2300
.2281
.2884
.2367
2364
.2367
.2350
.3161
.3010
.3006
2983
.2447
.2842
.2827
.266
.2824
2824
336
.3545
.3552
.348
3241
.3339
.3252
3185
.184
.3050
3083
.3317
.3229
.233
.3031
3155
720
.4276
A0233
.0433
.3877
.3911
.4087
.3873
.3533
.3062
.3477
.4119
.3857
3360
.3169
3339
96
.3823
.3558
.3570
.347
.355
.3715
3497
.3524
.3456
.475
.3675
.3582
.3583
.3520
.2525
.4423
.1466
.1422
A124
.4438
.4666
.4778
.1133
.1122
.435
.4212
4150
.4212
336
.5093
A754
4751
A569
4643
5183
4799
4803
.4753
.8588
.5005
A827
.4789
1661
4775
720
.6065
.5562
.5553
.4773
5102
.5929
.5888
-5332
.4774
.4991
.5704
.5866
.5476
.4718
.4982
96
.1647
.1634
.1637
.1627
1632
.1998
.188
1584
.1583
.1566
.1581
.1572
.1572
.1568
15699
.2209
.2183
.2173
.2171
2173
1930
1913
.911
.1904
.9055
1923
.1909
.1988
.1905
1908
336
.2727
.2630
.2522
.2435
2535
.2324
.2899
.292
.2833
2242
.3200
.2288
.2289
.2098
.2111
720
.3451
.3305
.3332
.2477
2606
.3062
.2968
2963
.2215
2316
.3012
.2916
.2926
.2158
2314
Exchange
96 .0882
.0876
.8885
.8188
0837
.0933
.0885
.1878
.0812
.0334
.0828
.0799
.0803
.0744
.0766
Rate
192
.1811
.1686
.740
.1403
1479
.1277
.1760
.1730
.1459
.1199
.1734
.1665
16448
.1366
.499
336
.3428
.3079
3097
.0099
2624
.3277
2941
2420
.2039
2280
.3240
.2930
.2423
.2053
2461
720
.8540
.8322
8004
.3421
3460
.8833
8762
.8781
.3494
.4481
.868
.8273
.8067
.3352
.458
Weather
96
.1755
.1644
.1674
.1597
J612
.1954
.1796
.1823
.1773
.793
.1856
.1759
.1765
.1724
.1377
192
.2232
.2101
2128
.2077
2088
2403
.2244
.2554
.2216
2217
.2100
.2165
.2122
.2135
2189
336
.2800
.2614
.2665
.2003
2515
.2918
.2709
.2740
.2567
.2226
.2833
.2633
.2881
.2561
2587
720
.3571
3458
3459
.2480
2730
.3643
.3500
.347
.2581
.2788
.3599
.3400
3488
.2573
2692
PatchTST
OLS
MICN
Baseline TAFAS PETSA COSA-F COSA-P Baseline TAFAS
PETSA
COSA-F COSA-P
Baseline TAFAS
PETSA COSA-FCOSAL
ETTmZ ETTml ETTh2 Ennh
96
.4312
.4262
A2699
.4242
.4233
.4511
.4409
.4391
.4390
.4372
.5103
.4901
.4898
_4693
.4684
192
.4955
.8655
48544
.830
.4805
.5046
.4934
.4937
4915
.4986
.5954
.5617
.5620
.5372
.5328
336
.5559
.5478
.4755
.5438
.5320
.5510
.5440
.465
53885
.5320
.6615
.6387
.6420
5950
.5878
720
.7117
6860
6822
.6113
.5822
.6977
.6630
.6411
.569
.9333
8142
.8375
.7001
.6504
96
.2362
.2351
.2362
.2399
.2343
.2306
.2285
.2888
.2232
.2265
.2522
.2551
.2552
2292
.2485
192
.2826
.2758
.273
2665
.2008
.2839
.2844
2848
.2766
.2911
3282
.3179
3258
3049
3017
336
.3199
.3 3125
3132
.2971
.978
.2558
3182
3189
.3003
3043
.3722
.3482
.3497
.3211
3310
720
.4264
.4005
.4122
.3233
.3908
.3177
.4617
.3650
3885
96
.4024
.3894
3937
.3625
3626
.3110
3506
.3366
.3454
.3455
.4354
.3951
.3951
.3377
.331
.4372
.4133
.4250
A160
.4115
.8855
.5566
.4476
4514
336
.5081
.4905
.946
A568
4697
.1822
.7877
.792
.4788
.4449
.5556
.1008
.5082
.4832
5054
.5629
.5427
.5462
.6611
.5478
.4763
.6212
.225
96
.1584
.1881
15833
.1558
1562
1662
.15900
.5899
.1582
1586
.1710
.1711
.1700
.1702
.1704
.2059
.2036
2037
.2077
.1921
.1906
.2121
.2126
336
.2458
.2511
2452
2258
2352
.2311
2299
2302
.2131
2226
.2500
.2011
.2520
.2337
2351
720
.3268
.268
.2566
.2466
2645
3066
.2966
2971
.2171
2349
.3327
.3220
.3131
.2477
2643
Exchaange
96
.0867
.0843
.0837
.7665
07:88
.0844
.0792
07998
.0756
0773
.1151
.1087
.1146
.I955
1008
Rate
.1877
.1805
.1832
.1464
1570
.1658
.1393
.2150
1722
336
.3389
.375
3300
.1833
2445
.2266
2277
2898
.0020
2323
.950
.3447
.1000
.2119
2600
720
.8648
.8699
.6433
.3543
4662
.3666
.8188
8149
.3444
.4541
1.0259
.7191
.7805
.3871
.815
Weather
96
.1742
.1724
.143
.1624
1634
.1957
.1807
1795
.1772
.1803
.1757
.1853
.1970
.1636
.651
-2195
2117
2167
.2066
2108
.2404
.2244
2274
.2223
.2277
.2277
.2161
.2265
.2082
2120
336
.2766
22666
2201
.2451
2488
.2911
2214
2748
22511
2642
.2122
.2746
.2788
.2729
.2377
720
.3544
.3883
3442
.2590
2713
.3644
.3466
.393
.2579
.2708
.3508
.3573
.3681
.2582
.2855
All experiments were conducted on a machine with an Intel i7-7800X CPU and NVIDIA GeForce
RTX 3080 10GB.
4.2
MAIN RESULTS
4.2.1
COMPARISON WITH SOTA TIME-SERIES TTA METHODS
The proposed COSA achieves best performance in all scenarios, as shown in Table 2 The results reveal two key performance patterns:
1. Architecture-gnostt. benefits: strate that effectiveness of COSA is not dependent on specific model architectures. The average improvement ranges from 10.48% to 13.05%.
Consistent improvements across all base models demon-
2 All reported results averaged over 10 runs with different random seeds ensure statistical reliability.
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Bacclie+COSA
DON
DON+COSA
192
Figure 3: Prediction accuracy comparison with normalization methods.
2. Effectiveness in long-term forecasting: The largest performance improvements were ob- served at the 720 horizon, where COSA-F and COSA-P showed performance improve- ments of 32.24% and 26.33% compared to baseline, respectively, and 28.21 % and 21.96% compared to other methods. This trend suggests that COSA becomes increasingly valuable for longer prediction horizons.
These findings demonstrate that the COSA, which performs residual correction directly the output space, proves more effective than existing indirect dual-adapter approaches.
4.2.2 COMPARISON WITH NORMALIZATION METHODS
In this section, we analyze whether COSA serves as an alternative complementary role to existing normalizations, and demonstrate that COSA can work independently of normalizations and is com- patible with normalization mechanisms. Figure 3 shows performance comparison of COSA against two representative time-series normalizers, RevIN (Kim et al. 2021) and DDN (Dai et al. 2024) The results support two claims:
1. COSA its own generally outperforms explicit normalization, as demonstrated by the comparative analysis showing that using COSA with basic normalization achieves the low- est mean MSE across all experimental settings.
2. COSA is compatible with normalization and consistently improves accuracy within the same normalizer settings, with the addition of COSA reducing MSE by approximately 16.8~16.99.
COSA directly optimizes MSE on revealed targets and uses the context vector to encode recent level/scale, so the linear layer learns scale and level corrections from the error signal itself, Further analysis is provided in Appendix G.7
4.3 SENSITIVITY AND ABLATIONS
We probe the following four key design choices: 1) adaptation steps S, 2) context length K, 3) batch size B, and 4) adaptive learning rate CAARR.
We evaluated performance by varying each hyperparameter individually while keeping others fixed at the default settings. Figure shows MSE and wall-clock time according to each hyperparameter. Figure 4a shows changes according to the number of iterative learning steps S. COSA shows pattern where test MSE decreases S increases. However, while wall-clock time also increases with increasing S, even at the highest = 4 setting, showed time levels similar to PETSA.
Figure 4b examines the effect of context length K, which controls how much past information the adapter uses. Accuracy improves consistently with larger K, while wall-clock time remains unchanged. Since the adapter input concatenates base model's prediction with the context vector (dimensionality L + K). and L typically dominates, increasing K has negligible runtime impact. The context provides incremental but reliable gains by supplementing the level/scale information.
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Bantio
TARAS
PETSA
3-1
5-22
V 8-3
5-d
Bascine
TAPAS
FETSA
KM-
X-
0.6
066
0.5
0.5
4
0.3
0.2
96
192
336
730
192
55
720
(a) Average MSE and wall-clock time of different S.
(b) Average MSE and wall-clock time of different K.
Basellne
TARAS
FETSA
CALRR-Fole
CaL8-Ire
16
0.5
0.3
(c) Average MSE wall-clock time of different
(d) Average MSE and wall-clock time of CALR.
Figure 4: Hyperparameter analysis showing the trade-off between performance and efficiency. Charts display average test MSE (bars, left axis) and wall-clock time (lines, right axis, in seconds) across different parameter settings.
Figure 4c shows performance changes with batch size B. As described in Section 3.5 B determines the frequency of adaptation, collecting B (prediction, ground truth) pairs before each update. Even with B 96, COSA outperforms the baseline, with accuracy improving as B decreases due more frequent adaptation. This explains the superior performance of COSA-P over COSA-F on ETThl: the average B determined by PAAS for ETTh 1 is 24.55, while for other datasets the values are over 80. Detailed analysis is provided in Appendix C However, smaller B increases wall-clock time due both more adaptation calls and the computational cost of adaptation steps S.
Figure 4d performance with and without C'LRR (Section 3.5). CALR achieves up to 12.13% accuracy improvement as the window length increases and 21. 21.34% reduction in wall-clock time. This confirms that aggressive dynamic learning rate scheduling enhances performance within limited adaptation steps S while enabling early-stopping for computational efficiency.
Results for additional ablations (context aggregation methods and correction layer architecture) are provided in Appendix
4.4 COMPUTATIONAL OVERHEAD
Table 3: Computational overhead comparison of adapter methods.
Method
# Paramss J
Peak mem (MB) J
Sampleskee
Adaptation time/batch (ms)
Inference time/hatch
TAFAS
1,252.958
17.59
1,413.23 + 92.28
73.23 + 8.74
10.96 + 0.64
PETSA
58,334
36.09
987.91 78.67
88.46 7.08
12.63 4 0.37
COSA (Ours)
1,211.287
27.07
1080.70 80.66
80.12 4: 5.93
1.25 0.06
We report 1) observed additional parameters, 2) peak memory utilization, 3) throughput (samples per second), 4) wall-clock time per batch, and 5) inference time per batch.
All hyperparameters remain at default values. Table summarizes the average overhead across all datasets, base model, and horizons. COSA shows moderate overhead, falling between TAFAS and PETSA, while achieving the significantly fastest inference time. COSA performs adaptation repeat-

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edly for S steps, meaning that the throughput and adaptation time are dependent S. However, the single adapter structure and simplicity of COSA alleviate the overhead and improve the inference time, which is not affected by S. The computational complexity is OLL (L + K)) for the linear transformation plus (()) for the gating operation, resulting in quadratic scaling with respect to prediction horizon L. Further theoretical calculations included in Appendix
CONCLUSION
We introduced COSA, an archiitcture-agnootic TTA module that directly corrects the prediction of base model with a single linear layer guided by short-term context and a stabilizing gate. Across six benchmarks and diverse base models, COSA improves accuracy by 13.91% to 17.03% over baselines and by 10.48% to 13.05% over prior state-of-the-art TTA methods. These gains arise from the synergy trend-aware context, residual correction, and gated modulation.
While COSA shows strong empirical results, several areas offer room for refinement. The current adaptation relies on full ground truth, though extending to partial observations would enable real- time deployment. Performance varies with batch size B, and the fixed context length K may not be optimal for all temporal patterns. Additionally, linear corrections, while effective for many cases, could be enhanced for complex nonlinear shifts.
Future work will explore masked updates for real-time adaptation with partial targets, adaptive se- lection of K and / based on detected periodicity, and hybrid linear/nonlinear adapters for more complex distribution shifts. These extensions will broaden the applicability of the proposed method while maintaining its computational efficiency.
ACKNOWLEDGMENTS
This work was supported by the National Research Foundation of Korea(NRF) grant funded by Korea goVErnment(MSTTT (RS-2025-0052) 1452), and by the National Research Foundation of Korea(NRF) grant funded by the Korea goverament(MSIT) (RS-2025-1500298)
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A ADAPTATION ALGORITHM OF COSA
This section details the core adaptation algorithm COSA. This algorithm extends the optimizer mentioned in Equation 2 combining short-term loss trends, cosine annealing, and adaptive gradient clipping, batch-wise learning rate reset. We apply widely used values for the coefficients of CALRR and the threshold value of early stopping. The base model remains frozen, operating only adapter parameters = {W, J.
Purpose:
Performs rapid adaptation of linear adapters using direct loss, adaptive learning rate scheduling, and gradient clipping to improve prediction accuracy within few adaptation step S.
Algorithm COSA adaptation.
Require: Stream of batches (Y, Y!m!!) with length B, context vector C, steps S, 7mmin Mauax, weight decay X,
clip base e
Ensure: adapted predictions with improved accuracy the base model
I: for each hatch (Y, Y!mle in Data Stream do
I Loop over new batches
2: Initialize: 1) 7Jmax, loss history H 4-
Reset LRR for new batch
to do
b Main adaptation loop
4: Forward pass: form (a)
(
CJ. then H (W x (o)T +6)
5:
Gating: Y y + tanh(g)
2 H
6: MSE loss: L - - - X||p|1
7:
Learning rate adaptation:
if [[H] 2 then
9:
+ [[-1]
D Recent loss change D Loss increased reduce LR
10:
if
then
11:
7 maxx00.5 Mmmin)
12:
else if | 10- then
Converged increase LR for next batch
13:
77 <- min 17, 7mxx)
14:
end if
15:
end if
16:
Cosine annealing: 7) MJoin (1 Mimi cos( cos(())) ()))
Gradient computation: go +- v.C
18:
Adaptive clipping: || +- min (119 max(c, C))
19:
Parameter update: + yp 70p
20:
Early stopping: if > 2 and [H[-1] H[ 2]| 10 then break
21:
22:
23:
end
24:
end for
25:
end for
B COMPUTATIONAL COST
In this section, we report theoretical calculations of parameters, FLOPs, and memory footprint. For univariate time series, the number of parameters as follows:
Parameter count.
L(L+K)
L
# #params
(L(L+K)+ +L+1).
W
FLOPs per adaptation step (batch of size B). The dominant cost is the linear transform and residual composition:
(BI(L+K)) for WX(")) plus (BT.) for gating & residual add.
Memory footprint. Additional activations modest: the linear residual H IR Bx and the context vector K The total adaptation cost scales linearly with the number adaptation steps S and variables V.
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Table Average B of each dataset determined by PAAS.
Dataset
ETTh1
ETTh2
ETTm1
ETTm2
Exchange Rate
Weather
Average B
24.55
38.41
92.73
83.41
92.80
80.38
C BATCH SIZE ANALYSIS OF PAAS
Adaptive vs. Fixed Batch Strategy: While COSA-F shows the best performance in most cases, COSA-P generally performs better on the ETThl and ETTh2 datasets, revealing important insights about temporal adaptation strategies. The reason for this trend is that the size of B determined by PAAS is often smaller than 48 for these datasets, as shown in Table 4 enabling more frequent adaptation that better captures the higher-frequency patterns characteristic of these hourly datasets.
This differential performance validates the importance of dataset-specific adaptation scheduling: datasets with more complex temporal dynamics benefit from more frequent adaptation (smaller B), while datasets with smoother patterns can effectively use larger batch sizes for computational effi- ciency.
D BEHAVIOR ANALYSIS OF COSA
D. ANALYSIS BETWEEN GATING AND LINEAR RESIDUAL LAYER
In COSA, the gating is defined as gating = tanh(g) E [-1, IJ. where g is learnable parameter, and this bounded scalar modulates the correction strength by multiplying the output of the linear residual layer. If we proportionately large and unstable changes in the correction, making the adapter overly sensitive to noisy points. The tanh transform keeps the gating bounded, ensuring that changes in g reflected smoothly and gradually. When the residual magnitude spikes, the gate moves toward 0, as shown in Figure thereby attenuating the residual correction and stabilizing the adaptation process.
use g directly instead of tanh(g), small variations in g could induce dis-
Gating
Aug. Residual Magaitude
Gating Valuel After tunh)
300
Residual Magnitude
200
-0.075
-0.0150
-0.0225
20
30
40
50
68
70
100
110
120
138
140
150
Batch Index
Figure 5: Trajectory of average gating and average residual magnitude of batches over time.
D.2 ANALYSIS BETWEEN LEARNING RATE AND MSE
Figure 6 visualizes the trajectory of pre-adaptation loss and learning rate for the iTransformer- ETTml. T, = 96 case. As shown in Figure O when short-term loss spike occurs, CALR immedi- ately decreases the learning rate to minimize the impact of the perturbation, and once the loss enters stable decreasing phase, CALR increases the learning rate again to promote rapid re-adaptation. This control mechanism suppresses excessive parameter drift without requiring roll-back, enabling COSA to recover its correction performance instantly after perturbation. The interaction between the learning rate and loss shows that, in non-stationary environments with short-term perturbations, COSA can respond and recover performance stably.
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Adapt
Aag. Learning
1.2
3.28-04
M aN KAWN
MSE
Leurning
2.98-04
M MM w win
0.3
2.78-04
2.58:04
Batch Index
Figure 6: Trajectory initial MSE and average learning rate of batches over time.
Table 5: Average ERV and NAR across all benchmark datasets and base models.
TAFAS PETSA COSA
ERV + .0100 .0160 .0768
NAR 34.94% 36.34% 20.25%
E QUALITY OF TTA
To evaluate TTA quality, we measured Explained Residual Variance (ERV) and Negative Adaptation Rate (NAR) metrics across all datasets, base models, and forecasting horizons. ERV is defined in Equation where R represents residuals for TTA TTA-applied predictions and R(O) represents residuals for base model predictions. Specifically, ERV quantifies the extent to which TTA reduces the resid- ual variance the base model's predictions. Higher ERV values indicate greater residual variance reduction and correspondingly improved prediction performance through TTA.
Var Rt) Var R!O)
ERV
NAR is the ratio of prediction windows where the MSE worsened when TTA was applied, with smaller values indicating better performance.
N NAR
1 N
IMSE(Y.)) MSE(Y!"), where
[[[on]] = if con True
(4)
[[con]] otherwise
As shown in Table 5 COSA shows the highest ERV and the lowest NAR. This indicates that COSA provides effective TTA while decreasing the residual and improving accuracy average.
F FURTHER EXPERIMENTS
F. COMPARISON ON A LARGER DATASET
To demonstrate that COSA can achieve stable and substantial performance gains even larger-scale environments, we additionally conducted experiments on the Electricity dataset Lai et al. (2018); Godahewa et al. 2222I) We followed the same experimental setup as Section 4.] and used three representative base models, iTransformer, DLinear, and FreTS. Table/olis consistent with the findings in Section 4.2 COSA achieves either the best or second- best performance across all forecasting horizons L, and unlike other methods, which exhibit performance degradation compared to baselines in some cases, COSA improves their performances in every case. These results indicate that COSA remains robust and effective in large-scale environments.
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Table 6: Prediction accuracy comparison on Electricity dataset.
iTransformer
DLincar
PreTS
TTA TAFAS PETSA COSA-FCOSA-A No TTA TAFAS PETSA
COSA-FOOOO
TTA
TAFAS FOSAAEAFA
96
1663
.1568
.15%6
.1571
.1570
.2235
.2224
.2242
.2232
.2228
.1824
.1781
.1802
.8011
.1799
192
1794
1633
1664
.1631
.1631
.2242
.2153
.2152
.2146
.2143
.1794
.1894
.1781
.1780
.1779
336
.1743
.1741
.130
.333
.2247
.2226
.1905
.1885
.1879
720
2567
2316
.2011
2251
.2239
.279
2629
.2155
2557
.2511
.2044
.299
2287
2236
.2221
F.2
COMPARISON ON REAL DATASET
To validate that COSA performs well not only on benchmark datasets but also in real-world de- ployment environments exhibiting more extreme distribution shifts, we conducted a performance evaluation real-world dataset. The dataset consists of power generation data collected from actual solar power plant spanning from Jan. 24, 2024, 00:00 to Dec. 31, 2024, 23:59. comprises hourly active power sensor readings from 30 devices with missing values. The data was split into train, test, and validation sets at a ratio of 7:1:2. The dataset contains 8,232 rows, approximately 47.3% the size of ETTh1. We conducted experiments solely under the setting L 96, W 96, with all other configurations kept identical.
The experimental results demonstrate that, consistent with the benchmark findings, COSA achieves improved performance over existing methods regardless of B. This indicates that COSA can operate effectively even under more extreme distributional changes and can reliably calibrate forecasting performance on very small-scale datasets.
Table 7: Prediction accuracy comparison.
iransformer
DLincar
FreTS
Metric
TAFAS
COSA-P
TAFAS
No TTA
COSA-F
COSA-P
Arg. MSE
.9011
2879
.2730
2897
2832
.813
.2801
2803
.3133
.2933
.2944
2980
F.3 COMPARISON WITH VARYING INPUT/PREDICTIN SEQUENCE LENGTH
To further verify the performance of COSA across diverse scenarios, conducted experiments by varying both the input window W and the prediction horizon L. To examine short-term forecasting rather than long-term forecasting, mance under longer input windows, we additionally tested W = 192 with L E {192, 336, 720} and W 336 with L {336, 720]. Table summarizes the results across these different combinations of W and L. Consistent with Section 4.2] COSA achieves the best or second best performance in most cases, demonstrating
added the setting W 96, L {24, 48). To evaluate perfor-
ability to maintain high predictive accuracy across wide range of settings. Unlike other methods, which show performance degradation relative to baselines in several cases, COSA improves prediction accuracy over baselines in every case. contrast, TAFAS and PETSA, which adopt dual-adapter architectures that modify both the input and output of base model incur substantial additional complexity as increases, which likely contributes to their degraded performance. Since COSA operates solely in the output space of base model, it delivers consistent performance gains regardless of W.
F.4 COMPARISON WITH SOLID
SOLID (Chen et al. 2024b) is fine-tuning method of the prediction layer of the base model by detecting context drift. Its reconditioner estimates context drift based on the mutual information be- tween the model's 's residual and the input context. When drift is detected, SOLID selectively chooses samples and fine-tunes the model's prediction layer at the sample level. Like COSA, SOLID oper- ates in the output space of base model. However, unlike COSA, which keeps base model frozen and performs corrections through a lightweight adapter, SOLID directly updates the prediction layer of base model.
16

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Published as a conference paper at ICLR 2026
Table 8; Prediction accuracy comparison with different input/prediction sequence length.
iTranfformer
ineer
PieTS
Input
TTA
TAFAS
PETSA
COSA
COSA-P
No TTA
TAFAS
PETSA
COSA-F
COSA-P
No
TARAS
PETSA
COSA-F
COSA-P
96
.3669
.1254
.3299
.3105
.3098
.3437
.3751
.3765
-431
.3429
.2953
.3243
.3239
.2466
.2943
96
48
33322
3766
.3776
3353
.3527
.3838
.4177
.1165
-3226
.3820
.3424
.3770
.3751
3116
.3133
ET111
192
192
4459
50155
.4893
.475
.4120
.172
A967
4834
4157
.4411
.435
.999
4835
4207
4186
192
4729
-5700
-5422
4537
5362
4578
4489
539%
A577
4535
192
5885
6629
6687
5619
.5477
.5828
.504
6526
5660
6627
.6728
6651
.199
336
336
5354
61.39
36866
3209
.469
4392
.652
5174
4368
.4289
48.37
6114
.5444
4783
4674
336
720
6512
6673
66:35
6115
.5780
.5748
6.44
6443
5589
.5198
7265
6005
6773
6960
.225
96
.0337
.1277
.1666
.8122
.0812
.0622
.1217
.1218
.0661
0862
.0.12
.1180
.1178
.8866
0807
1047
1518
1520
1008
1081
.028
1050
.1422
.9966
J19%
R27122
192
192
1633
2272
.2800
1546
1563
.3444
.2155
2096
.1334
1338
1437
.2188
.2184
.1412
1420
192
336
1658
2541
2487
1551
1573
1474
2645
2394
.1400
1468
1556
.2944
.2460
.1519
1536
192
720
2197
3453
3192
2110
2158
1782
.1522
2962
.1762
1778
1945
.326]
.3086
.1892
1925
2986
3005
2012
2108
2366
2375
.1645
1695
336
3334
4253
A355
.3256
3134
1807
3101
3004
.1776
1798
1969
3130
.3144
.1920
1949
96
24
2543
.2359
2429
2405
2450
2578
.616
2599
.2533
2569
2494
2503
.241
.2449
2492
96
48
3305
3099
.1335
3115
3133
3105
3167
3151
.M335
3064
3191
.329
.3222
.3171
3172
192
192
3800
4006
.9611
.3991
3603
3694
4029
3942
3643
3648
355
.3663
.3815
.3524
33528
.4499
.4011
4149
A150
.4239
.6200
.436
4163
.3985
192
720
.992
5385
.5900
.4166
4718
.1797
.5766
5101
.6671
165
A631
.5.52
.1911
.4500
2550
336
336
4820
.4913
.4441
.449
4592
3981
A444
4244
3968
3977
4011
4380
.4255
.3975
4006
336
720
.2202
.4322
.1699
.678
.904
.4337
.5533
.852
.2256
4423
.407
.5046
.4877
.4261
.4397
0542
0600
0744
0601
.1561
.I561
96
48
.0735
.014
0988
0730
8732
.0677
.1027
.0155
.761
0762
0736
.992
.0987
.033
.0733
ET1m2
192
192
1035
1647
1601
1023
1022
1990
1451
1429
.9984
0965
0998
1480
.1156
.9922
0984
192
336
1343
2191
1970
1339
1335
1201
1791
1741
.1190
1195
1210
1863
.1781
.1200
.192
1628
2511
.164
1589
1518
.2291
2347
1498
1476
2337
.14%6
1446
1384
2250
1987
.122
1342
.1776
.1722
.7044
.1677
1174
1198
1815
.1760
.1172
1188
336
720
16455
2785
.2517
.1455
1604
.1456
.2338
2185
.1317
1446
.490
2309
.2255
.1289
1453
96
24
.318
0292
.273
0206
D306
0434
0397
0393
.434
0434
0283
0254
.0241
0283
0283
Exchange
0026
2015
.199
0542
2189
0449
2010
0516
0516
0606
0590
.0599
2024
.7144
0606
1715
0606
.081
0435
.0418
.4880
.6655
.481
.665
192
2963
3221
351
2019
2533
2878
3316
3484
2350
2875
2804
3129
3318
.2700
2802
192
720
8546
.713
8316
8120
9037
9593
9488
9016
9016
4506
8200
8315
A501
A501
336
336
4088
3390
420M
4036
4036
2753
3036
3323
2700
2751
3246
3219
3589
.3122
33445
1,7882
L0775
5274
.4233
.2633
.0026
.0166
.177
.077
.1007
.1151
.1151
.1000
.1183
.1183
96
48
1380
.1292
1310
1362
1363
.581
1499
.1475
.1590
1560
1530
.1435
1452
.1518
1510
Weather
192
192
2165
2102
2051
2075
2099
2393
2225
2214
2332
2354
2131
2058
20121
.0886
2108
192
336
2747
2588
.2549
2611
2653
.2044
2709
22611
2791
2829
2694
2547
.2531
.2604
.2637
192
3316
.390
.151
3211
.3426
3363
3446
3276
.360
.3188
.3205
336
336
2988
.2705
.7088
.2788
2278
.222
2633
2619
2627
2707
2526
2520
2174
.2444
.2501
336
720
3381
3423
3557
.8885
3340
3245
3247
3516
3742
3207
3129
3203
3229
26688
3088
Using the publicly available source codes, we evaluated SOLID on three base forecasting models: DLinear, FreTS, and iTransformer. The results are summarized in Table Across all settings, COSA achieves higher predictive accuracy compared to SOLID.
Moreover, COSA is significantly more efficient: it requires only 7.44 + 0.0488 seconds of wall-clock time on average, whereas SOLID incurs a much larger overhead with 306.55 + 2.6183 seconds. The substantial cost of SOLID arises from computing context drift and repeatedly updating the prediction layer of the base model, processes that are far heavier than COSA's 's lightweight updates. Because COSA freezes base model and updates only a compact output-space adapter, it offers a dramatically faster execution while maintaining higher accuracy.
F.5 COMPARISON WITH DYNATTA
This section presents complete bascline results of prediction accuracy comparison with various ex- isting methods. DynaTTA requires setting a total of 15 hyperparameters, and due to this complexity, report its performance using the best settings from our trials. The used hyperparameters of Dy- TTTAA are as follows:
HIDDEN.DIM-64 GATING BASE.LR= 0.005, SOUFFE RTAB SIZE-50, RDB SIZE-30, METRIC HISTORY SIZE-20, ALPHA 00000,000,, ALPHA MAX=0.01, KAPPA=2.0, ETA=0.1, EPS=le-8, WARMUP FACTOR=2, UP- BUWFEEEEEEEEERREEEEE
17

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Published as a conference paper at ICLR 2026
Table Comparison with SOLID
iTransformer
DLineur
FreTS
SOLID COSA-P SOLID COSA-P SOLID COSA-P
96
.4404
.4363
.4595
.4574
.4093
.4371
ETTm2 ETTml ETTh2 ETTh1
192
.435
.4919
.5063
.5066
.4701
.4440
336
.5420
.5300
.5602
.5528
.5254
.5467
720
.6523
.5638
.7107
.6107
.6980
.6259
96
.2480
.2493
.2315
.2281
.2354
.2350
192
.3061
.2947
.2824
.2819
.2830
.2972
336
.3339
.3339
.3103
.3083
.3248
.3153
720
.3701
.3591
.3366
.3477
.3667
.3399
.3353
.3455
.3634
.3456
.3121
.3525
192
.2266
.4140
.4336
.4222
.4299
.4212
336
.5019
.4443
.5071
.4858
.4915
.4775
720
.5986
.5102
.5821
.4991
.5612
.4982
96 .1641
.1632
.1590
.1583
.1574
.1569
192
.2291
.2133
.1910
.1943
.1933
.1934
336
.2525
.2555
.2138
.2222
.2288
.2211
720
.2704
26666
.2419
.2316
.2377
.2314
Weather Exchange
96 .0873
.0837
.0913
.0834
.0822
.0766
Rate
192
.1783
.1499
.1826
.1519
.1723
.499
336
.3294
.2624
.3276
.2480
.3218
.2461
720
.7531
.4460
.8872
.4481
.8325
.4458
96 .1753
.1617
.1954
.1793
.1849
.1377
192
.2231
.0888
.2433
.2277
.2009
.2189
336
.2801
.2515
.2918
.2626
.2843
.2587
720
.3450
.2730
.6433
.2708
.3561
.2692
Table 10: Prediction accuracy comparison with DynaTTA Grover Etemad 2025).
Prasformee-hhee
Linrar-uued
MI MLP-hoso
PaccFEST
DLincrr
hieTS
MICN
COSA DOO.FFFDOD.PTaTTTT.. COSA CO5.. DOS. COSS COS.TTAAAAOAOAOOOOPOOAP
96
.4233
4368
.3633
.371
4242
41.38
.4705
4574
.4482
.4485
4500
.4773
.4505
.1344
.4311
.5633
4663
.684
193
5175
.000
-8919
35405
11530
-8515
5121
.186
.555)
5135
2015
.8916
5139
.U51
.4900
57115
3372
.536
336
5874
5651
.300
-397
34388
5330
5792
5528
5456
5526
5385
5130
5540
.5467
5351
.6594
.950
5575
36.38
2107
6951
3600
2519
3017
1341
2971
2574
3180
3690
3005
3061
3624
3151
3341
331
720
.4545
3487
3591
.991
3333
3423
4325
3862
3477
4270
3177
345
4297
3169
3399
5229
3630
3585
k77m2 F.fll
96
4831
3353
.1244
3447
4140
5455
.2255
.258
3625
5636
4009
3514
.1133
3456
5473
3830
.115
3454
2118
3473
3723
4811
.150
.520
3525
4313
3331
A005
.476
3637
3831
1630
2508
155%
116
1500
1996
1164
1150
1100
2001
192
2597
2171
253
2714
2007
3022
3340
1994
1963
2115
1986
1967
2045
1995
1966
3349
1182
2120
196
1166
2835
M11
1534
.258
2014
2003
2761
2017
2151
2136
3776
2111
7986
.337
215
720
5344
2477
2006
.467
2446
2545
3765
2215
2316
A571
.171
3349
A020
3158
2314
5362
.2477
3543
Wouther Dadhange
0766
1005
344
3325
3421
999
3543
3612
3094
4181
8903
3446
356
J382
3520
.801
J815
96
1422
1197
1017
2117
.164
1634
1990
.1775
1985
1773
1903
1957
1124
110
2503
.666
1051
192
2575
2067
2063
2511
2006
2006
3311
.2216
2217
3024
2223
2257
2850
.1355
2180
3839
.2032
2120
2515
2851
248
4101
.2577
2536
2581
2542
3970
.161
2580
2130
2581
F.6 COMPARISON WITH VARIOUS BATCH SIZES
Table Haaaad and Table IT summarize the prediction accuracy and efficiency overhead under different batch sizes B. Thanks to CALR's stability-induced design, COSA adapts reliably even with very small batches, and the resulting increase in update frequency often leads to improved forecasting ac- curacy. Notably, even in extremely small settings such B 8, COSA maintains higher accuracy than existing TTA methods, demonstrating resilience against over-correction and short-term pertur- bations. On the other hand, smaller B inevitably increases the number of adaptation steps, leading
18

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Published as a conference paper at ICLR 2026
Table 11: Performance comparison with different batch sizes B.
(a) Prediction accuracy.
No ITA
TAFAS
PETSA
PAAS
8
16
24
48
96
96
0.2545
0.2471
0.2480
0.2409
0.1908
0.2202
0.2330
0.2398
0.2411
192
0.3144
0.3038
0.3046
0.2887
0.1900
0.2295
0.2524
0.2848
0.2946
336
0.3839
0.3653
0.3664
0.3280
0.1837
0.2292
0.2526
0.3013
0.3483
720
0.5539
0.5226
0.5232
0.3804
0.1811
0.2384
0.2672
0.3286
0.4158
(b)
Wall-clock time (Seconds).
TAFAS
PETSA
PAAS
8
16
24
48
96
96
5.9271
7.4129
7,0642
47,3922
25.6158
17.2297
9.6333
5.1258
192
6.0383
7,3675
7.1419
49.4422
25.1222
18.0969
9.4344
5,5133
6.1554
7.6588
7.4131
49.2211
25.1119
17.2906
9.5644
5,8081
6.5300
7.9867
8.1578
46.3711
24.4683
17.6253
10.3036
6.5397
higher adaptation time and clear computation- accuraac trade-off. Considering this trade-off, we adopt B = 48 for COSA-F in our main experiments, which provides a balanced choice between accuracy gains and computational efficiency.
G ADDITIONAL ABLATIONS
This section provides additional ablation studies on various design choices of COSA. Each ex- periment conducted to understand the impact of specific components and determine optimal hyperparameters. The default setting uses mean-base context aggregation with = 10 and = 3.
G.1 CONTEXT BUILDING METHODS COMPARISON
G.1.1 STATISTICAL METHODS
This experiment was conducted to evaluate the impact of different context construction methods on adapter performance. We compared three methods, i.e., Mean, Median, and Weighted Average (WA), to find the optimal context construction strategy. The weight of WA was designed to assign greater weight to recent values using exponential decay weighting. Table 12 presents comprehen- sive performance comparison of the three context construction methods.
Mean-based context construction demonstrated superior performance compared to median and weighted average approaches across most experimental configurations. While median-based ag- gregation provided robustness against outliers, it resulted in lower overall accuracy. The weighted average approach showed marginal improvements relative to its implementation complexity. These findings support the adoption of simple statistical aggregation for effective context summarization in COSA.
G.1.2 CONTEXT SELECTION STRATRGY
COSA aims not to model long-term time-series structure, but to perform fast and stable local resid- ual correction for output bias observed in the current window. non-stationary environments, the input distribution shifts continuously over time; thus, information from distant past windows may become misaligned with the current drift direction and deteriorate correction quality. For this reason, the default COSA employs lightweight context vector constructed solely from the most recently observed batches.
To examine the effects of longer-range temporal patterns, additionally implemented Selective Context mechanism. This approach stores all past context values in a buffer and computes impor- tance scores via attention between the current window and past contexts, selecting the top-K values
19

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Published as a conference paper at ICLR 2026
Table 12: Prediction accuracy comparison of diverse aggregation functions.
Transformer-basee
Linear-
Ml.--
Transformnrr
PatchTST
DLincar
OLS
FreTS
MICN
Mean Median
WA
Mean Median
Median
WA
Mean Median
Median
Mean
Median
WA
.4327
.4722
.4422 .0922
.4274
.4275 .6155
.4660
.4557 .4359
A463
4462
.4322
.449
.4440.4704
.4934
.4926
192 .4991
.8500
.4800
.422
.4778
.4770
.4869
.5090
.1111 .4932
4897
4894
.4671
.4893
.4954 .4769
.5567
.5688
336 .476
5301
.5317
A550
.5199
.2885
A6322
.3799
.378
.5188
.2088
.2099
4411
.5273
.5245
.4814
.3889
.5044
720 .4592
6237
.255
.4788
.3299
.635
.4777
.3588
.6166.5666
.243
6242
.755
.6439
.6428
.5230
.7196
7181
96 .2489
2532
2536
.2336
2346
22358
.233
.2522
2324 .2283
2300
2299
.2399
22799
.382
.2468
2266
2568
192 _3003
3012
.013 .2708
.2866
.2894
22622
.2846
.263 .2762
.2554
.2993
.2766
.2846
.2917
.2906
.3190
.1145
336 .3277
.6711
.3685
.2688
.1900
.3202
.2860
.3833
.3285 .2937
.3030
.025
.2889
.3214
.3205
.3088
.3429
.3466
720 ,3311
.4013
.403
.3091
.3737
.3737
.30016
.3358
.3358
.2992
.3415
33155
.2979
.3588
.3564
.3454
.4172
.4185
ETTm2 E11ml
96 .3428
.3687
3685
.3044
.3918
.3921
.3453
.3575
.3574
.3400
.3573
.3572
.3522
.3633
.3633
.3804
.4252
.4488
192 .4766
.407
.3004
A171
.398
.399
.4158
.266
.465
.4125
.265
4263
.473
.257
.266
.4002
.472
4740
336 _4663
.4930
.449
.4662
.4422
.4944
.4784
.5009
5005
.4700)
.4995
.000
.4711
.498
.4886
.4937
.5381
.3811
720 .4940
5614
.51555544
.7766
.5359
53116
.4928
.5640
5603
.4693
56.38
.5653
.4863
.5144
.5419
.5083
,5830
.8388
96 .1616
.1672
.153
.1552
.1911
.1595
.1578
1594
.1596
.1583
.196
.1600
.1556
.1592
.1594
.1710
.1712
.1723
192 .212
.2194
22240 .989
.0087
.2121
.1900
1959
.1957
.1919
1970
.1995 .1908
.1935
.1933
.2102
.2131
.132
336 .2402
.2700
.762
.2279
.2821
2543
.2135
22448
2561 .2066
2449
.277 .2158
.2353
.2420
.2354
.523
.246
720 .2550
3461
3463
.2397
.301
.3222
2357
.2855
.283
.2104
.3179
,2821 .2360
.2732
.2753
.2510
.3020
3084
Exchange
96. .O843
0852
0852
.I803
0814
0815
0843
0884
0885
.0728
.0787
(0787
.0790
.7785
.0785
0998
.065
1068
.140
1606
1607
.1480
1544
1546
1599
1653
.1654.11 .1335
1507
.1509 .1390
1500
1502.1827
1870
1872
336 .2588
.2544
.756
.2611
.2777
.2789
.566
.2918
.2220
.1833
.736
.2738
.2511
.2683
.6684.2660
.3140
3043
720 ,5039
5113
,5115
.937
.5066
.5078
.5001
.2677
.2700
.3349
.983
.986
.4789
.4777
.4980
.4815
.5806
5809
Weather
96 .1636
1726
.726611
.155
.731
.1735
.1738
1931
.931
.1748
.934
1934
.1758
.181
.1335
.1666
.1739
1738
.2073
.268
.2655
.2052
2162
.2162 .2217
.200
2520
.2144
2496
2490
.2151
.2346
.2347
.2060
.2208
2205
336 .2444
2707
.2007
.243
2668
22600
.2622
.2891
2885
.2428
.2111
2897
.2630
.2736
.2735
.2335
.2650
2648
720 .2907
3318
311
2662
3088
.3990
.2713
.3310
3325
.2487
.3377
3331
.2583
.3268
.3247
.2670
.3140
3094
Average .3121
.3450
.3458
.3032
.364
,3366
.3097
.3423
_3422
.2990
.3371
.3354
.3046
.3334
.3340
,3284
.3669
.3670
to form the context vector. Such a mechanism can leverage repeated phases or cycles in datasets with strong periodicity.
Table 13a compares COSA (the standard recent-context construction) with the dynamic context selection method. While the dynamic context selection method achieves clear improvements on datasets such as ETT, where the periodic structure is strong and easily detectable, the overall perfor- mance of the original COSA remains superior. Selective Context also introduces non-trivial over- head, since computing importance scores increases both adaptation time and inference time. More- over, in fully non-stationary settings where distributional characteristies change continuously, older contexts may become outdated and destabilize the correction process. Nonetheless, the observed gains on datasets with pronounced periodicity show the potential of Selective Context. We provide a more detailed discussion of these observations in Section H
G.1.3 COMPARISON WITH ENCODER-BASER CONTEXT
To compare with encoder-based context construction, we implemented an alternative approach that replaces the original statistics-based method in COSA with a temporal encoder that directly con- sumes the previously observed ground-truth sequence from the past 720 steps (the longest L). We added RNN- LSTM-, and Attention-based based encoders, each taking the past sequence in the form of [720, 1] as input and producing a [K, 1] context vector. The resulting context vector is concatenated with the base model's prediction output, just as in the original design, and then fed into the linear correction layer. The encoder is seamlessly integrated at the front of COSA, modifying only the context-generation stage while keeping the remaining components unchanged.
Table 14 shows that, except for few isolated cases, the original statistics-based context (0.3240) performs better than encoder-based alternatives (0.3254, 0.3260, 0.3278). Furthermore, the added architectural complexity increases both adaptation and inference overhead. In non-stationary TTA settings, where the input distribution shifts rapidly and adaptation steps are short, it is difficult for an encoder to learn stable temporal representations. Consequently, the generated embeddings may be- come misaligned with the current drift direction or overfit to outdated historical patterns, ultimately degrading correction performance.
20

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Published as a conference paper at ICLR 2026
Table 13: Prediction accuracy and overhead of selective context.
(a) Prediction accuracy.
Transformer-based
Lincar-based
MLP-based
Traansoommrr
PatchTST
DLineur
OLS
FreTS
MICN
Recent Selective Revent Selective Recent Selective Recent Selective Recent Selective Recent Selective
96
.4322
.2338
.4822
.4622
.4359
.4371
.6844
.4633
192
.4919
.4927
.4805
4848
.5050
.5088
.4906
.4933
.4940
.4965
.5328
.3368
336 .5300
.5367
-5320
.3310
.5466
.5541
.3320
.5368
.5351
.5505
.5878
.9666
720 .5638
.5671
.5822
.5881
.5996
6180
.5733
.6093
.5959
.6430
.6504
.7137
FT1m2 F11ml E1
.2494
.2343
.2281
.2258
.2262
.2485
192
.2947
.2942
.2608
22611
2819
.2813
.2791
2825
.2824
.2455
.3017
3027
336 .3339
.3367
2978
2949
3083
.3044
.3027
.3153
.3310
3328
720 .3591
3603
.3428
.3453
3477
.3462
.3453
.3199
.3399
.3509
.3885
3906
.1440
.3475
.3454
.3525
.831
.3815
192
.4140
.4128
.4258
.2788
4122
.4211
.4119
.4219
.4212
.4212
4514
4533
.4697
.857
.4755
.0544
.060
720 .5102
.5246
.8822
.8668
.4911
.0655
.5007
.5005
.4982
.4970
.5225
.5256
.1631
.1562
.1586
.1581
.1704
192
.2173
.2165
2022
2011
1905
.1930
.9077
.1522
1908
.1929
.2120
.2125
.2551
.2351
720 .2606
.2578
26445
2633
.2316
.2477
.2349
.368
.2314
.2373
.2643
.2764
Weather Exchange
.0773
.066
Rale
192 .1479
1516
.150
.1544
.1119
1544
.1457
1462
.1499
1514
.1722
.1770
.2633
.2480
.2361
.2660
.7322
720 ,4460
.4749
.4662
.4983
.4811
.4%4
.4541
.8335
.4458
.4914
.8855
.2255
96
.1616
.634
.1631
.1793
.1790
.1799
.1377
.1651
1654
192
.2088
.2056
.2108
21099
2217
.2181
.2377
.2222
.1899
.2187
.2120
.2134
.2524
.2488
.2626
2665
.2642
.2659
.2577
.237
.2813
720 .2730
.2798
.2713
.2798
.2708
.2729
.2708
.2211
.2622
.2332
.2855
.2900
(b) Overhead analysis.
Method # Params Adaptation time/batch (ms) 1. Inference time/batch (ms) | Average MSE +
Recent 1,211,287
80.12 + 13.58
1.25 + .0984
.3240
Selective 1,212,217
83.64 + 15.71
1.26 + .1039
.3287
These findings confirm that the statistics-based context remains the most robust and stable choice for non-stationary adaptation, while encoder-based context generation still demonstrates potential. We discuss these observations in greater detail in Section H
G.2 INPUT CALIBRATION EFFECTS
COSA performs residual correction directly in the output space, and demonstrated that output- only correction is often sufficient. However, in certain time series, we observe that input-level spikes or local noise degrade the base model's is predictions first, and this degradation subsequently propa- gates to the residual correction stage. To examine how such input perturbations influence the overall correction process, we conducted experiments combining COSA with the input-side GCM module from TAFAS. Table I5 reports the results.
In most cases, output-only correction achieves higher predictive accuracy. However, for datasets such as ETTh1, ETTh2, and ETTm2, where significant input noise is present, the combination with GCM produces improved results. In these cases, input GCM smooths the noisy input patterns, al- lowing the base model to generate more stable predictions, which in turn enhances the effectiveness of COSA.
Nevertheless, because GCM operates via distribution-shift normalization. it risks oversmoothing or removing meaningful drift signals when the input exhibits rapid or irregular changes. This behavior explains why, average (in terms of MSE), output-only correction remains more stable across diverse non-stationary scenarios. Overall, when input disturbances are not the primary source of prediction error, output-only correction is the most robust and reliable option.
21

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Published as a conference paper at ICLR 2026
Table 14: Prediction accuracy and overhead comparison with encoder-based context.
(a) Prediction accuracy.
Tramformer--ased
Linear-based
MLL--based
iTransformer
DLincar
FieTS
COSA
RNN
LSTM
Artn
COSA
RNN
1.TTM
Amm
COSA
RNN
1STM
Attn
96
.3363
.4163
.2338
.4234
.4882
A562
.4372
.4359
.477
4361
.4684
.4674
4919
.4227
4805
.4849
.0500
5088
.4005
.4933
.5940
.965
.5328
.368
.5320
.456
.5368
5505
.5878
.5667
720
-6638
.5672
.5822
.5881
.5896
6180
.5733
.6093
5959
.6430
.6504
7137
96
.2493
.2494
2343
2349
.2281
.258
2265
.2263
2350
.346
.2855
2486
2947
2042
2608
2661
2813
2791
.2825
.2244
2946
.0017
342
.978
.3028
3175
3328
720
.3911
.3603
.3228
3455
.3472
.3662
3355
.3619
.339
.3509
.3885
3906
96
3455
.3400
3626
.627
.475
.3566
.3755
.3544
3525
3522
.3831
3815
192
1140
.1228
.2588
.1788
.122
A221
4119
.2199
4212
.2122
.4511
A533
4697
.485%
1854
S160
720
.5102
.5346
4382
4368
.4551
5066
5007
.5005
.4922
4570
.5255
5256
ET
96
.1632
1631
.162
1561
.1566
1582
.15%6
.1581
1569
.1570
.1704
.1715
192
2173
2165
2022
2011
1905
1930
1907
.1952
1908
1929
.1220
.2125
2535
.352
2242
.212
2185
2555
720
3606
2645
2316
.2477
2349
2368
2314
2373
.2433
2764
Weather Exchange
96
.0837
I835
0788
.1799
JK34
II33
0773
0073
4766
0763
.008
1007
Rate
192
.1479
1517
1570
1554
.1519
1543
1457
1462
.149
1515
.1222
.171
336
.2624
2633
2445
.478
.2480
2481
2323
.2311
.461
2541
2660
.232
.4460
.662
.493
.9944
.4835
.4914
.4815
96
.1617
1617
.1644
.163
.1793
.1790
.183
.799
1732
.1711
.1651
.1654
192
2008
2056
21088
21099
.2217
2181
.2237
2232
2189
2157
.2120
2134
336
23155
2521
2118
2551
.2626
2665
.2642
.269
.2877
2614
.2737
2813
.2730
.213
.2708
2729
.2721
2260
.2855
PatchTST
OLS
MICN
COSA
RNN
LSTM
Alin
COSA
RNN
LSTM
Alln
COSA
RNN
LSTM
Alini
Rafe ET1m2 ETTml ET712 TT1
96
.4363
.4363
4813
A425
.4363
.4357
.4482
.0.50
A582
.4582
.5029
.4570
4371
4051
4375
.4378
.4322
.4928
.3000
.5319
.5118
5456
.5332
.576
.5620
5445
.487
720
5638
.5625
36:26
.5621
5896
.142
615L
.6120
.5959
6257
6252
6284
96
2493
.2507
2503
2511
.2281
.3044
2250
2278
2350
2349
.2350
2355
.238
2791
2981
3348
3337
.1833
.3004
3138
3186
720
.3891
.3551
3334
3555
.3477
.3495
3536
.343
3399
3314
.3484
3386
96
3455
3459
3459
3453
3415
3457
3457
.3455
35255
3529
.3529
.3519
.4140
4185
4183
.4131
41122
4234
4223
.237
4212
4215
.4215
.2166
.1613
.493
.858
2867
.1744
.178
.4761
720
5102
.5332
.5138
.142
.1911
7989
4962
.4133
.982
.513
.5033
.021
96
.1622
1612
.1611
.636
.1566
1585
1583
.1583
1569
.168
.1570
.1569
192
2173
2174
2175
21588
1905
1951
1939
.1932
1908
1938
.1338
.1922
.2355
.2211
2242
2216
2208
.2230
2217
.2214
2183
720
2606
2633
26-11
2653
2316
2284
2359
.383
2314
2296
.2280
2305
Weather Rochange
96
0837
0851
.0533
0862
.0844
0833
0837
.8119
.7666
0774
.779
.0789
192
.1479
1499
1544
1661
.1519
1550
1562
.1577
.149
1548
.1564
1605
.2624
2694
2700
.2400
.2455
2494
.5566
4450
.491
2486
.4735
.4478
.440
.735
96
.1617
1614
.1122
.616
.1793
1793
.193
.1807
.732
.1739
.1739
.1733
192
.2088
21066
2080
2126
.2177
2196
2158
2180
.2189
2161
2157
2169
336
.2515
2243
2592
2652
.2626
2613
2611
.690
.2587
2614
.6088
.242
.2730
2309
2754
2799
.2708
2700
.272
2692
3660
2665
(b) Overhead analysis.
Method
# Params J Adaptation time/batch (ms) + Inference time/batch (ms) | Average MSE +
COSA
1,211,287
80.12 = 13.58
1.25 + 0.0984
.3240
RNN 1,317,239
126.52 +. 22.88
1.66 1 0.2315
.3254
LSTM 1,466.615
134.29 1: 25.67
1.74 1:2 0.2778
.3260
Attention
1,647,735
175.72 +: 16.88
1.96 0.3183
3278
G.3 ADAPTER ARCHITECTURE COMPARISON
This experiment was conducted to compare the performance and computational efficiency of single linear adapters versus 2-layer MLP adapters with 64 hidden dimensions. We aimed to determine whether more complex architectures necessarily guarantee better performance. Table propiiss a comprehensive performance and efficiency comparison between linear and MLP adapters.
22

---

Published as a conference paper at ICLR 2026
Table 15: COSA with input GCM.
Transfomme- based
Linear hased
MLP- based
iTransformrr
PatchTST
DLincar
OLS
FreTS
MICN
COSA
w. Inpul
COSA
w. Inpul
COSA
w. In.nupl
COSA
w. Iupul
COSA
w. Inpul
COSA
w. Inpul
96
.4363
.4362
4238
.4209
4482
.4600
.4372
.4370
A371
.4343
.6684
.4852
Th2 Th
192
.9199
4821
4805
4790
5050
.4955
.4906
.4907
4940
.919
.5328
.5530
336
.5300
.386
-5200
.5216
5456
.3359
.3320
.5193
.351
.5286
.5878
.5533
720
.5638
.6287
.5822
.6386
.5896
.6513
.5733
.6500
.5959
.6726
.6504
.7509
96
.2493
.2001
.2343
.1845
.1819
.2265
.1033
.2350
.1849
.1995
192
.2947
.2384
.2688
.2287
.2819
.2277
.2791
2292
.2824
.2411
.3177
.2457
336
.3339
.978
.2405
.3833
.2506
.343
.2744
.2539
.2755
720
.3591
,3048
.3428
.2913
.3477
.2932
.3453
.2400
.3399
.2554
3385
.3111
.3455
.3676
.3626
.3903
.3475
.3518
.3516
.3596
.3831
.4216
192
.4140
.4273
4258
4396
4122
.4194
.1199
.4922
4212
.4200
4514
.442
336
.4643
.4963
.697
.4881
.858
.4749
.9266
.4775
.885
.5365
720
.5102
.5869
.8822
.3177
.491
.6778
.5007
.598
.4982
.5522
.5225
.5920
ETTm2
96
.1632
.1242
.1562
.1200
.1866
.1217
.1586
.1118
.1569
.1203
.1704
.1288
192
.173
.1673
.2022
.1551
1905
.1502
.1907
.1501
.1908
.1491
21200
.1618
336
.2535
.2017
22322
.1900
.2422
.8133
.2226
.1831
.2211
.1823
2351
1975
720
26066
.2554
26445
22668
.2316
22655
.2349
.2531
.2314
.2364
.2633
.2635
Exchange
96
.0837
.8599
.788
.0835
.0834
0883
.0773
.0789
.0766
.0798
.1008
.1005
Rate
192
.1479
.1706
.1570
.1754
.1519
1807
.1457
.1644
.1499
.1660
.1722
2083
336
.2624
.2974
.2445
3017
.2480
2986
.2323
29937
.2461
.2511
.2660
.358
720
.4460
.5884
.4662
.969
.4481
.1077
.4541
.5837
.4458
.5823
.8815
6885
Weather
96
.1617
.1723
.1634
.1728
.1793
.1924
.1803
.1927
.1737
.1822
.1651
.1741
.2088
.2108
.1881
.263
.2367
.2299
.2899
336
.2515
.2752
.2488
2809
.2626
2951
.2642
.9946
.2587
.2845
.2737
.2288
720
.2730
.3274
.2713
.3166
.3356
.2708
.3361
.3298
.3364
Table 16: Prediction accuracy comparison of single linear adapter and 2-layer MLP adapter.
Transfomer bused
Linear bused
MLP-based
Transormer-
Linear-bused
MLP--aased
TTrnsfemmer PatcTST
inear
01.5
FieTS
MICN
iTransfeemer
PaidTST
TM incar
OLS
FieTS
MICN
Lincar MLP
Lineur MLP Linear MLP
Linear MLP Linear MLP
Linear MLP
Linear MLP
Lincur MLP
Lincur
MLP
Lincur MLP
Linear
MLP
Linear
MLP
96 A3633
4376
.4238
4267
.482
4644
A372
4450
.371
4412
.684
4841
2.35
3.79
2.35
3.83
2.24
3.45
2.15
3.10
2.14
1.49
2.38
3.84
192
.9199
.968
.8005
.857
2450
1135
.996
.1980
.9480
.1577
.325
5496
1.39
3.73
2.44
3.85
2.25
3.49
2.21
3.42
2.16
3.47
2.59
3.83
336
5300
.5471
.320
.5244
5456
5501
5320
.5222
.351
.5346
.5878
6967
2.40
3.68
2.43
3.77
2.22
3.53
2.18
3.45
2.32
3.40
2,51
3.91
720 5638
6167
.5822
6350
.596
6498
5533
6351
.5959
6558
.504
7325
2.39
3,46
2.25
3.49
2.17
3.10
2.23
3.22
2.24
3.11
3.69
4.57
.2403
2345
336
2106
720 3391
3.48
3.19
4.62
96 .455
3352
.6.26
3680
3475
2505
3475
34889
3325
3371
3831
.914
8.49
14.08
3.56
14.24
8.14
11.50
8.17
13.16
8.23
13:22
8.33
14.38
192 41.00
.1103
425%
.4446
4122
41477
.119
4157
4212
.1168
4514
.4470
8.72
14.41
8.67
14.31
8.35
13.25
5.68
13.55
8.57
13.68
9.27
14.30
336 4643
.625
.4697
.709
4858
.6788
.17.89
4660
.7755
.1708
5054
.1784
9.07
14.62
9.03
12.04
8.72
13.59
8.86
13.31
8.87
14.17
10.86
15.26
720 5102
.4927
.4882
.4651
.991
.4763
51517
.4774
.9982
J1514
5225
.858
9.64
15.32
8.72
12.74
9.32
14,00
9.36
14.31
9.60
14.52
16.05
20.23
96 _1632
.163
.1522
1569
1586
4152
1556
1567
1559
1571
1704
.1703
8.51
11:73
8.72
14.41
8.34
13.23
8.06
13.04
8.45
9.13
8.25
14.35
192 2173
2012
1978
1905
11880
8.75
14.35
8.77
14.38
13.25
13.65
14.42
14.64
13.50
15:24
720
Exchange
96 .0837
.0788
0838
J776
1.99
1.79
1.20
1.77
1.26
2.00
192
1449
1730
.1570
1696
.1519
1761
.1457
1570
.1499
1600
1956
1.36
1.88
1.17
1.68
1.15
1.69
1.17
1.70
1.42
1.96
335 2624
.3103
2445
2941
2480
2872
2323
2856
2461
2410
2660
3359
1.26
1.30
1.32
1.81
1.09
1.57
1.10
1.58
1.10
1.62
1.48
1.50
720 4460
8059
.4662
3268
.481
3573
.541
7980
.455
7993
J815
9663
1.09
1.47
1.09
1.45
.91
1.24
.90
1.26
.93
1.27
1.46
1.76
Weather
96 .1617
1691
.1634
1691
.1793
1904
1883
1904
1737
1767
.161
1701
13,05
20
15.19
23.35
12.81
30.
34
12.76
18.41
12.84
20.90
12.88
20.56
192 2088
2045
2108
2012
1217
2285
1237
3224
2189
2120
2120
2270
13.33
20.79
15.33
23.72
13,10
20.43
12.89
20.55
13.13
20.72
13.93
20.44
336 2515
.2390
2488
1368
2626
2469
2642
2499
2557
2249
2757
73386
13,69
21.12
15.03
24.21
13.49
20.83
13.45
20.95
13.53
20.96
14.31
22.14
720 2730
2752
2713
2660
2708
2764
22708
2785
.2692
2737
28855
.2582
14.68
17.06
16.71
25.44
14.05
31,26
14.36
21.61
14.41
21.81
18.09
26.57
Average .3288
10.75
The comparative analysis reveals that single linear adapters achieve performance comparable to or superior to 2-layer MLP adapters while requiring significantly reduced computational resources. Although MLP adapters occasionally demonstrated slight performance improvements, the 1.5~2x computational overhead renders them impractical for real-time adaptation scenarios. These results validate the architectural design principle of COSA that emphasizes simplicity without compromis- ing effectiveness.
23

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Published as a conference paper at ICLR 2026
G.4 COMPARISON WITH VARIOUS LEARNING- RATE SCHEDULERS
To validate the effectiveness of CALR, we compared against several official PyTorch learning-rate schedulers: DossiiAAnnealinL.R ExponentialLR, POntace,ROnP,ateau,, StepLR, and a fixed learn- ing rate. All schedulers were configured with the same base learning rate of 0.005 for a fair compar- ison. One-Cycle, although widely used, was excluded because requires a predefined learning- rate schedule; in streaming TTA scenario where samples arrive continuously and the batch size changes dynamically under PAAS, such predefinition is not feasible.
As summarized in Table 17 each scheduler achieves improvements in some individual cases. How- ever, when results are averaged across all datasets and prediction lengths, the proposed CALR achieves the best or second-best accuracy in the vast majority of settings. These findings support CALR's stability-indee induced design and its suitability for non-stationary TTA environments.
G.5 EXTENTION TO MULTIVARIATE TIME-SERIES FORECASTING
COSA is originally introduced as an output-space residual correction module, treating each variable as an independent univariate forecasting task, for fair comparison with existing SOTA methods that assume univariate forecasting. However, in real multivariate time-series settings, correlations among variables may influence drift patterns, suggesting that modeling cross-variable interactions could potentially benefit COSA. Basically, COSA can be extended to multivariate forecasting; to examine this possibility, we implemented it.
We first incorporate Vassi-ar Context Attention, allowing the context of each variable to ref- erence information from other variables and thereby capture correlation-
contextual interac- tions. Additionally, we introduce a mixed structure composed of a low-rank shared component and variable-specific components: the shared component captures drift patterns common across variables in an efficient fow-dimensional form, while the specific components model idiosyneratic behavior unique to each variable. These two components are combined through a Icarnable mixing coefficient that automatically balances global and variable-specific contributions.
Table 18a presents the comparison results. For datasets where meaningful cross-variable dependen- cies exist, the multivariate structure achieves higher predictive accuracy than the univariate version of COSA. However, for datasets with weak inter-variable correlations, such as the Exchange Rate, the univariate structure remains more stable. In such cases, the shared component struggles to learn useful common patterns, which can lead to performance degradation. Moreover, as shown in Ta- ble 8&b the additional complexity leads to increased adaptation time and inference latency.
These results indicate that multivariate-based correlation modeling can indeed provide accuracy gains, but further design improvements are required for effective deployment under TTA constraints. We discuss these limitations and potential future directions in Section
G.6 EXTENSION TO VECTOR GATING
To evaluate whether finer-grained control over correction strength could provide additional benefits, we implemented an element-wise gating vector COSA. This vector shares the same dimensionality as the prediction length, allowing each time step within the prediction window to modulate its correction intensity independently. Such design is intended to handle scenarios where drift occurs in only a specific portion of the horizon.
extension of the scalar gating mechanism in
However, as shown in Table 19a vector gating yields degraded overall accuracy compared to the original scalar gating, and also exhibits reduced stability. We attribute this performance degradation to the propagation of local noise: noise spike at particular horizon position can influence the entire gating vector over successive adaptation steps, causing cumulative negative impact throughout the correction process. In contrast, scalar gating provides consistent batch-level modulation that effectively bounds the influence of noise and maintains stable behavior across adaptation windows.
G.7 VISUALIZATION OF NORMALIZATION
Figure 7 visualizes the learned weights of the linear layer in COSA with and without representative time-series normalization modules (RevIN (Kim et al. 2021) and DDN (Dai et al. 2024)). )
24

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Published as a conference paper at ICLR 2026
Table 17: Prediction accuracy comparison with various learning rate schedulers.
Transformer-base
Linear-based
MLP-based
iTranformer
DLincar
FreTS
CALR Cosine
Exp
Fixed Plateau Step
CALR
Cosine
Exp
Fixed Plateau Step
CALR Cosine
Exp
Fixed Plateau Step
96 .4363
4888
4961 .4848
.4848
.8885 .4482
.498
4556 .4513
.513
.437 .371
.400
.441 .439%
.439
.4055
192 .4919
5405
5613 5513
.5413
.426
.5050
5069
5183 55990
.5090
.5100
.940
.4914
5002 .4155
.915
.4311
336 .5300
.541
.9552
.5751
.5751
.5826
.5456
.5500
.5714 .5586
.5586
.5642
.5351
.5499
5570
.5422
.5422
.5494
720 ,5638
6216
6635
6163
.6663
.636
,5896
6033
.6511
5553
5953
.6166
,5959
6116
.699
6041
_6411
.6000
ETTm2 ETTml ETTh2
96 .2493
.2984
.302 .2984
.2984
.2877
.2281
.2008
.2877
.2321
.2321
.233
.2350
.2788
2359
.2766
.2376
.2372
192 .2947
.3866
3520 3399
3400
.394
.2199
2823
.2811 ,2836
.2836
.2845
.2824
.2377
7827
.234
.2834
.2831
336 ,3339
.3823
3992
3856
.3856
3802
.3833
.3078
.3093
.3104
,3105
.3081
.3153
3311
3151
.3311
.3131
.3087
720 .3591
4278
.4113
.4113
4070
.3477
.3490
.3562
.3462
.3463
.3488
.3799
.3421
.3524
.3391
,3389
.3387
96 .3455
.4006
4087
3978
.3978
.0448
.3475
.3501
.3610
3497
.3497
.3669
.3525
.3548
.3677
.3399
.3539
.3555
192 .4140
4650
4772
4630
.6630
4683
.4122
.1440
4283
.1446
.1466
.4191
.212
.236
A279
.231
.230
.2466
336 .4643
.5110
5286
51000
.1000
5160
.4858
.4828
5028
4838
4838
.4775
.775
.4740
4821
.4740
.4740
.4750
720
.5102
.5321
.5732
.5350
.5349
.5392
.4991
.4861
.1153
.4899
.4889
.4915
.4982
.4923
.5073
49550
.4550
.4951
96 .1632
.2138
22139
.2139
.133
1186
1621
1551
1629
.162
.1646
.1569
.1611
.1522
1604
.1604
.1606
192 .2173
.2697
.2005
2292
2693
2704
.1905
.1948
1916
1955
.1956
.1733
.1908
.1958
1921
1951
.1951
.1955
336 .2535
.3028
3122 .5047
.045
3305
.2242
.2305
2268
2310
.2310
.2324
.2211
.2285
2247
.276
.2276
.2278
720 ,2606
.3000
.3159
.2877
,9886
2966
.2316
.2369
2383
2405
.2405
2348
.2314
.2388
2397
22405
.2403
.2334
Exchunge
96 .0837
.1335
.1344. .1335
.1335
1333
.0334
.0865
08448
0883
.0873
.0886
.0766
.0800
.0775
.0794
.0794
.0792
Rafe
192 .1479
.961
2025 1960
.1960
1952
.1519
.523
1552,
1533
.153
.1522
.1499
.1518
1545 1513
.1513
1505
336 .2624
.3120
3395
,3116
.3117
3102
.2400
2521
2710
2528
.2577
.2535
.2461
.2501
.2735
.2491
.2492
2484
720 .4460
.4481
6622222242
.4498
.4460
.4448
.4481
.4185
.5919
.4164
.4622
.4179
.4558
.1288
.5679
.4072
.4063
.4068
Weather
96 .1617
.2118
2151
2215
22155
2123
.1793
.1824
.1277
.1277
.1827
.1858
.1737
.1770
.167 .1761
.1761
.1766
192 .2088
.2514
2592
2517
.2177
2517
.2117
.2266
.270
2232
.2322
.2559
.2189
.2011
2235
2191
.2192
.2044
336 .2515
2916
.3033
2249
2948
2920
2626
.2510
2622
2232
.2522
2541
.2877
.247
2606
2505
.2505
.2496
720 .2730
3230
3460
.225
3225
3267
.2708
2774
2965
2802
2802
22800
.2692
2726
2221 .2755
.2755
.2255
PatchTST
OLS
MICN
CALR Cosine
Exp Fixed Plateau Step
CALR Cosine
Exp
Fixed Platcau Step
CALR Cosine
Exp
Fixed Plateau Step
ETTm2 ETTml ETT12 E7Th1
96
.4238
.423
.294 .5723 .4923
.4232
.4372
.4375
4448
.4401
.4401
.4413
.4684
.4739
.904 .4708
.4708
.4769
192
.4805
5307
4958 6301
.5501
4838
.4966
4912
5041 .4944
.944
.4951 .5288
.5320
.5099 .5297
3298
.5900
336
.5320
.5851
.5535 6826
.6026
5396
.5320
.5342
.5155 .5844
.5384
.5424
.5878
.5864
6417 .5861
.5861
.5974
720
.5822
.4122
7330
.6533
6031
.5733
5582
.6371
5808
58088
.5987
.6504
.6266
82288
.6566
.6006
.6977
96
.2343
28800
2352
,3839
.3039
2345
.2265
.2255
2268
2301
.2000
.2266
22855
2499
.2499
.2521
.2521
.2466
192
.26088
.3114
.2611
.4092
.3292
2617
.2791
2804
2804
2828
.2228
.2823
.3077
2990
.307 .3025
.3026
.2960
336
.2978
.3514
3086
.4543
.3743
2993
.3043
.030
3064
.3063
.3033
.M029
.3310
3303
.3399 .3388
.3388
.3243
720
,3428
.3913
.3663
.951
A1111
3485
.3453
.387
33899
.3433
3472
.3476
3885
33665
4019
.3929
,3929
.3884
96 .3626
.4104
.3741
.5183
.4383
3655
.3475
.3487
.3008
.3495
.3495
.3552
.3831
.3912
.3982
,3900
.3900
.3913
192 .4258
4747
4427
55664
.4964
.315
.4119
4125
A283
.4142
.1422
.4174
.4514
.533
A641
.4524
.524
.4541
336
.4697
5149
4825
6203
.403
4700
.4749
.4706
4920
.728
.4728
.4751
.0554
5053
$249
.5048
.5048
5579
720 .4882
.5349
.5077
6391
.5550
.477
.5007
.4831
.5136
4873
.4873
.4882
.5225
.5152
.5443
.1888
.5188
.5185
96 .1562
.2065
1566
3064
.2265
1566
.1866
.1608
11500
.127
.1627
.1630
.1704
.1742
.709
.1622
.1763
.1709
192 .2022
2527
2056
3532
.232
2034
.1907
.1933
1914
1954
.1533
.1956
.2120
.1544
2138
.2180
.1800
.1222
336
.2352
2863
2367
.3863
.3063
2363
.2226
.2788
2256
2298
.2988
.2998
.2351
2383
2365
.2408
.2408
.2344
720 .2645
.3445
2692
.4114
.3314
.2619
.2349
.3900
2417
.2445
.2445
.2367
.2643
.2628
22622
2267
.2647
.2565
Exchanne
96 .0788
1278
0802
2278
.1478
.0776
.0733
.7899
0780
08009
.8809
.0808
.0088
.001
1027
.1051
.1051
.0994
Rate
192 1570
2051
1642
.3052
.2251
.1444
1452
.1452
1490
1474
.1473
.446
.1722
1715
11799.111 .1735
.1735
.1670
336
.2445
29666
.2780
.3962
.3164
2448
.223
.2311
2578
2349
.2348
.2334
.2660
.2300
.3114
.2745
.2745
.2675
720
4662
.743
.5724
.4923
.4218
.5411
.224
5806
4190
.190
.4189
.4815
.4155
.6597
.4488
.4511
.4460
Weather
96 .1634
.2144
1651
.3124
.2324
.1629
.1803
.1822
1840
1838
.1838
.1855
.1651
.1678
.1669
11695
.1685
.1644
192
.2108
2564
2122
3569
.2769
22065
.2277
.2332
2290
2250
.2250
.2263
22120
2096
.2105
.2109
.2109
.2050
336
.2488
.2924
2540
,3950
.3150
.2419
2642
2618
2743
2651
.2611
.2647
.2337
2545
2599
.2556
.2556
.2499
720
.2713
.3300
22913
.275
.3475
2737
.2708
2783
2987
.2824
.2824
.2817
.2855
2864
.3035
.2559
.2959
.2906
RevIN performs standard normalization on each input time series and then applies a correspond- ing denormalization step on the output. This procedure mitigates train-test distribution mismatch while restoring the information removed during normalization at the prediction stage, preventing degradation in forecasting performance.
DDN, in contrast, operates jointly in the time and frequency domains. It decomposes the input into low-frequency and high-frequency components and computes local statistics from each domain to remove non-stationarity. DDN then reconstructs non-stationary patterns in the predicted outputs using distribution statistics estimated from the model's predictions, enabling dynamic tracking of distribution drift.
25

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Published as a conference paper at ICLR 2026
Table 18: Prediction accuracy and overhead of multivariate consideration.
(a) Prediction accuracy.
Transformer-
Linear-based
MLP-based
iTrrnsformer
PatchTST
DLinear
OLS
FreTS
MICN
Indiv.
Corr.
Indiv.
Corr.
Indiv.
Corr.
Indiv.
Corr.
Indiv.
Corr.
Indiv.
Cor:
96
.3633
.4351
.2388
.4577
.4822
.4202
.4372
.4388
.4711
.4408
.6844
.4533
ETTm2 ETTml ETTh2 ETTh1
192
.4919
.4762
.8055
.4899
.5050
.4646
.4066
.8066
.4900
.4769
53288
.5039
336
5300
.4759
.320
.4798
5456
.4823
.5320
.4884
.5351
.4987
5878
.5105
720
-5638
.4371
.5822
.5244
.5896
.4695
.5733
.4600
.5959
.4954
.6504
.5314
96
.2493
.2453
.2343
.1836
.2281
.2342
.2265
.2249
.2350
.2311
.2485
.2411
192
.2947
.2871
.2608
.2172
.2819
.2578
.2791
.2770
.2824
.2922
.3077
.2923
336
.3339
.3341
.2361
.3083
.2866
.3043
.2911
.2971
.3310
.3122
720
.3591
.3306
.3428
.2638
.3477
.3094
.3453
.3399
.2979
.3885
.3441
96
.3455
.3186
.3626
.3595
.3475
.3335
.3475
.3330
.3525
.3381
.3831
.3385
192
.4140
.3988
.4258
.4159
.4122
.4058
.4119
.4125
.4212
.4133
.4514
.4188
.6433
.4491
.4697
.4739
.4858
.4561
.749
.4648
.4755
.4618
.5054
.4628
720
.5002
.4372
.4882
.4892
.4991
.4406
.5007
.4323
.4982
.4533
.5225
.4496
96
.1632
1633
.1562
.1195
.1586
.1557
.1586
.1574
.1569
.1560
.1704
.1697
192
.2173
.2111
.2022
.1526
.1905
.2005
.1907
.1935
.1908
.1921
.2120
.2097
336
.2355
.2347
.2352
.1783
.2242
.2235
.2266
.2145
.2211
.2149
.2351
.2429
720
.2606
.2100
.2645
.2162
.2316
.2295
.2349
.2066
.2314
.2022
.2643
.2265
Exchange
96
.0837
.0840
.0788
.0851
.8834
.0791
.0773
.0773
.0766
.0765
.1008
.0995
Rate
192
.1479
.1493
.1570
.1828
.1519
.1609
.1457
.1457
.1499
.1516
.1722
.1726
336
.2624
.2838
.2445
.3162
.2480
.2599
.2323
.2456
.2461
.2627
.2660
.2555
720
.4460
.5221
.4662
.7731
.4481
.5280
.4541
.5884
.4458
.5079
.4815
.5711
Weather
96
1667
.1547
.1634
.1656
.1793
.1566
.1803
.1731
.1737
.1673
.1651
.1591
192
.2088
.1338
.2108
.2033
.2217
.2003
.2237
.2158
.2189
.2095
.2120
.1979
336
.2155
.2300
.2488
.2339
.2626
.2321
.2622
.2461
.2587
.2331
.7377
.2565
720
.2730
.2236
.2713
.2668
.2708
.2254
.2708
.2122
.2692
.2165
.2855
.2420
(b) Overhead analysis.
Method
Params
Adaptation timc/batch (ms) 1
Inference timc/batch (ms)
Average MSE
Univariste
1,211,287
80.12 = 13,58
1.25 + .0984
.3240
Multivariate
1,214,851
+ 15.36
6.35
.3071
Each heatmap entry (i.j) shows the weight connecting the j-th imput to the i-th output; columns 1:L correspond to the original prediction of base model (0) and columns L+1:L+ K to the context vector C. The example taken from a single variable of ETThl with look-back W-96 and hori- zon L-96. Notably, the rightmost block (context columns) is strongly attenuated when RevIN or DDN is applied, whereas without a normalizer, the same block exhibits structured, non-negligible weights. This pattern indicates that explicit normalization reduces the marginal utility of the context (level/scale cucs are already standardized), while in the non-normalin normaazad COSA leverages C to per- form level-shift correction directly in the output sunce--upporting subsume normalization effects when needed and remain compatible with them when present.
claim that the adapter can
H DISCUSSION
Although COSA is built around simple output-space linear adapter, the extended experiments in the Appendix examined multiple alternative design choices. While low-rank adaptation, input-side calibration, vector gating, selective/encoder-baeee potential benefits in specific scenarios, our overall findings show that, considering average accuracy, stability, and latency, the architecture adopted in this paper remains the most consistent and robust choice for TSF-TTA.
context, and multivariate extensions each provide
The key observations summarized below:
26

---

Published as a conference paper at ICLR 2026
Table 19: Prediction accuracy and overhead of vector gating.
(a) Performance comparison.
Trannsormmr
Dinaa
FreTS
Scalar Vector Scalar Vector Scalar Vector
96 .4363 .4336
.574
.436
.4371
.4336
192 .4199
.4875
.5066
.4985
.4940
.4905
336 .5300 .5430
.5528
.5466
.5467
.5353
720 .5638 .6013
.6107
.6178
.6259
.6236
96 .2493 .1990
.2281
.1798
.2350
.1842
ETTml ETTh2
192 .2947
.2318
.2119
.2198
.2922 .2202
336 .3339
.2604
.3083
.2472
.3153 .2501
720 .3591
.3035
.3477
.2893
.3399
.2898
96 .3455
.3611
.3456
.3425
.3525
.3551
192 ,4140
.4119
.4222
.4068
.4212
.4137
336 .643
.4720
.4858
.4706
.4775
.4767
720 .5102
.5484
.4991
.5370
.4982
.5405
ETTm2
96 .1632
.1245
.1583
.1215
.1569
.1202
192 .2733
.1683
.1943
.1487
.1934
.1484
336 .255
.2010
.2242
.1798
.2211
.1795
720 .2666
.2488
.2316
.2319
.2314
.2280
Weather Exchange
96 .0837
.0875
.0834
.0903
.0766
.0818
Rate
192 .179
.1774
.1519
.1900
.1499
.1698
336 .264
.3258
.2480
.3344
.2461
.3044
720 .4460
.7649
.4481
.7904
.4458
.7500
96 .1617
.1718
.1793
.1908
.1737
.1825
192 -2088
.2176
.2217
.236
.2189
.2250
336 .2515
.776
.2626
.2888
.2587
.2745
720 .2730
.3559
.2708 .3418
.2692 .3378
(b) Overhead analysis.
Method
Params 4
Adaptation time/batch (ms)
Inference time/batch (ms)
Average MSE 1
Scalar
1,211,287
80.12 +: 13.58 96.34 + 12.48
1.25 : .0984
.3240
Vector
1,212,446
1.89 = .0745
.3287
Low-rank factorization. Despite its parameter-efffcienncy appeal, reducing representa- tional capacity can lead to unstable adaptation. A joint adapter that integrates low-rank structure without compromising stability is meaningful direction for future work.
Input-side calibration (GCM). Combining COSA with input GCM improves perfor- mance on datasets with strong input noise (e.g., ErTTh1/h2/m/1 by smoothing perturbations before prediction. However, for fast-drifting or irregular series, GCM may oversmooth im- portant variations and degrade performance, reaffirming that output-only correction is reasonable and stable default.
Gating and its variants. Although vector gating was expected to modulate drift at a finer temporal resolution, local noise propagated across the gating vector and reduced stability compared to scalar gating. Scalar gating's batch-level modulation limits the influence of noise and achieves more reliable behavior.
Context construction. Selective context (phase-aligned retrieval) and encoder-based con- text (RNN/LSTTM/Atee) suffered from outdated information, overfitting, or latency overhead in non-stationary set- tings. These results highlight that additional complexity does not guarantee better TTA per- formance unless paired with drift-aware representations and online update strategies. Fu- ture directions include sub-sequence vector gating, structure-aware context that explicitly
showed improvements in certain periodic datasets, but both
27

---

Published as a conference paper at ICLR 2026
only CGLA
0.06
16
Dlincar
FreTS
iTransformer
0.04
CGLA with DDN
0.02
0.00
Dlinear
FreTS
iTransfommer
-0.02
CGLA with RevIN
0.00
Dlincar
FreTS
iTransformer
Figure 7: Weight heatmaps of the COSA linear layer for one ETTHl variable (W=96, L=96). Columns 1:L are base-prediction inputs (()) columns L+1:L+K K are context inputs C. Each cell shows the weight from input j to output i. Color scales are kept identical across panels to allow magnitude comparison.
encodes trend and seasonality, and lightweight encoders capable of tracking drift without incurring high overhead.
Multivariate residual correction. While multivariate modeling with cross-variable atten- tion and shared components improved performance in most datasets, it degraded both aceu- racy and efficiency in datasets with weak inter-variable correlations (e.g., Exchange Rate). This suggests the need for selective correlation modeling or structural sparsity suppress unnecessary cross-variable interactions.
Taken together, the extended Appendix experiments reinforce that the proposed simple architecture particularly well-suited for TSF-TTA. They also indicate substantial room for generalizing COSA through carefully integrated low-rank structures, input calibration modules, selective or encoder- based context modeling, and vector gating, while preserving the efficiency and stability crucial for non-stationary test-time adaptation.
I CONFIDENCE INTERVAL OF MAIN RESULTS
Table 20 reports the 95% confidence intervals of the main accuracy comparison results over 10 independent runs for each method feethod-dttase---oe dataset-horizon combination. Overall, the intervals are narrow, indicating that the run-to-run variability of all methods is small, and COSA-IVP consistently retain their advantage over baselines even when accounting for this uncertainty.
THE USE OF LARGE LANGUAGE MODELS
Tool Version: Claude Somnet 4 (Anthropic, 2025-09) Research Stage: Not used.
28

---

Published as a conference paper at ICLR 2026
COSAF
4683
.200
.807
4856
-77
3274
3021
400
400
5530
400
2.400
309
1001
200
5901
-10
183
188
-000
COSA.F
5633
4.0
-000
68
-00
2000
300
-20
-004
45N
780
421
-80
-511
.701
-.70
200
210
250
69
156
-70
300
-55
968
-40
280
260
558
200
200
MICW
PETSA
A886
-910
640
422
8550
250
380
550
345
550
407
200
480
680
402
580
570
126
170
335
222
201
418
100
1923
320
990
532
800
196
150
355
290
360
350
TAPAS
400
4012
560
055
4006
527
240
360
390
368
150
468
400
560
385
480
157
400
510
170
150
200
210
260
250
324
105
110
200
230
120
181
550
188
180
291
300
30%
COSA
436
4379
474
130
510
4099
250
286
130
315
112
326
240
220
420
221
434
250
221
150
150
190
10
2NN
24
230
1406
140
412
270
120
120
218
234
33
360
200
COSA
252
565
246
222
850
290
38
300
300
214
336
350
467
455
480
409
466
476
190
150
190
180
210
43
820
140
380
390
471
120
23
3
280
250
FeTS
PETSA
5511
550
500
7067
230
212
26
530
130
360
780
250
430
200
476
440
5510
150
180
500
22
262
970
280
120
200
590
345
17
220
380
Table 20: 95% confidence interval of main accuracy comparision results
TARAS
4307
440
4015
5005
555
2678
7706
256
240
240
350
130
380
190
376
430
420
490
160
446
550
150
355
180
100
250
260
500
860
100
17
280
300
960
180
170
200
COSA
A3G
A37
5559
600
222
28
360
300
11
416
420
445
2.80
485
130
152
120
200
230
070
140
220
140
180
200
COSA
435
530
52
540
380
-003
2277
3000
110
4414
416
4358
420
400
467
180
184
1965
490
21
280
220
405
489
134
140
4US
531
355
11N
OLS
PETSA
J065
4977
566
545
1023
650
232
222
280
339
310
330
190
365
462
415
470
480
546
140
150
1405
190
200
240
390
475
600
160
185
30
38
100
150
22
Linarrlia hanee
TAPAS
.405
2411
520
540
1003
874
220
281
34
310
510
550
480
300
422
400
544
552
150
150
1906
162
226
21
375
4000
1796
1004
121
232
780
360
190
151
250
300
COSA
4671
4577
551
555
4809
4214
225
280
160
390
11
344
46
860
155
150
182
144
28
83
1812
1404
140
248
22
81
170
150
26
300
38
380
COX4E
47
5101
500
020
-3
2265
215
285
311
360
345
480
412
496
470
46
1557
150
150
1007
270
206
22
9809
1408
150
360
362
386
177
177
252
325
3M0
PETSA
4522
436
5557
560
555
161
652
284
240
322
100
36
180
362
48
406
442
550
150
300
100
500
867
900
267
120
580
322
900
931
145
51
500
361
355
TARNS
4666
463
5W6
560
0772
6908
296
280
316
362
700
360
456
475
400
480
445
150
150
150
29
2077
260
680
600
120
20
39
467
900
100
200
200
360
342
COSN
4322
4154
53
55
570
584
250
350
26
200
14
330
14
760
431
325
462
450
462
159
150
2013
201
250
25
57
610
1457
260
15
45
502
161
150
210
32
140
200
COSA
113
330
60
235
262
236
560
317
300
466
432
436
464
457
482
60
130
150
1988
200
2268
249
4756
677
18
284
358
36
162
102
120
380
250
39%
700
PailTTTT
PETSA
426
420
548
530
688
28
242
390
3088
310
390
460
922
360
400
460
48
800
585
150
130
180
200
280
265
330
660
080
122
100
325
361
860
12
120
78
362
<50
3309
340
Trandhrmmr-i hases
TANAS
433
561
512
680
1955
220
220
300
315
386
985
360
390
48
500
400
800
4
-50
550
150
1
200
266
240
345
460
600
478
180
286
222
900
422
122
26
25
3W0
355
COS
4361
A36
534
550
5612
5664
284
390
35
355
3867
35
41
110
461
200
162
160
400
207
201
350
262
600
180
140
220
230
555
436
16
10
280
200
23
COSAF
432
210
~50 550
JU0
580
252
245
200
280
301
136
340
284
41
41
422
46
46
491
162
145
JU0
277
242
360
290
400
462
136
244
3M6
3557
486
190
240
2015
Taansfrenc
PETSA
4000
-4
8937
586
584
A57O
~ 6622
290
2002
311
155
484
466
552
416
110
4117
425
500
1603
~ 264
100
210
2500
-22
310
4863
2007
1005
9.11 1717
116
728
620
462
300
200
261
200
300
351
~-
TAPAS
4411
4900
5580
5575
A551
~ 6655
2546
2997
3320
3184
3998
3556
350
4100
4153
4718
4793
5664
1630
~ 1655
1177
3189
2010
2644
3325
6073
0809
1665
177
3077
356
1683
1968
3978
236
3404
3512
96
192
336
720
96
192
336
730
192
336
730
96
192
336
96
192
336
720
96
192
336
730
29

---

Published as a conference paper at ICLR 2026
Writing Stage: Language editing of author-drafted text for clarity and conciseness.
Human Oversight: All outputs reviewed/edited by the authors; authors accept full responsibility for the content.
30


Reviews:
[{"review_id": "psVyvMP91V", "reviewer": "Reviewer_8Mzj", "summary": "This paper introduces COSA (Context-aware Output-Space Adapter), a Test-Time Adaptation (TTA) framework designed to address the performance degradation of time series forecasting models caused by distribution shifts after deployment. In contrast to existing TTA methods that often employ complex dual input-output adapters, COSA proposes a simpler and more direct strategy that operates solely in the output space. The core mechanism utilizes a lightweight context vector, which summarizes statistics from recently observed ground truth, along with the base model's original prediction. This information is fed through a linear layer, modulated by a gating mechanism, to compute a residual correction. During the test phase, only the adapter's parameters are updated, while the backbone model remains frozen. Extensive experiments demonstrate that COSA improves prediction accuracy while reducing inference latency.\n\n---", "questions": "1. **Design of the Context Vector:** The context vector C is constructed by aggregating the K most recent batches, which implicitly assumes temporal locality. However, this assumption may not always hold. For series with strong periodicity, data points from the same phase in previous cycles might be more informative contexts. Conversely, for series with abrupt concept drifts, a context vector based on recent history could provide outdated or even detrimental information. Is a design that relies solely on recent locality optimal, or would it be more robust to consider other relationships such as periodicity?\n2. **Clarification on Parameter Efficiency:** Given that COSA has far more parameters than PETSA, could the authors clarify the rationale behind choosing a linear layer with a relatively large parameterization (i.e., the weight W is L x (L+K))? Furthermore, could more parameter-efficient structures, such as low-rank factorization, be explored to potentially achieve similar performance while reducing the parameter count?\n3. **Practical Use of Adaptive Batch Size B in COSA-P:** The paper proposes COSA-P, which uses the PAAS strategy to adapt the batch size B, and shows its superiority on the ETTh1 dataset, while COSA-F performs better on others. In a real-world deployment without clear periodic patterns, the PAAS strategy may not be effective. This raises two practical questions: 1) How should we as practitioners choose between COSA-F (fixed B) and COSA-P for a new real-world dataset? 2) For COSA-F, are there any guidelines or heuristics for selecting an optimal fixed value for B?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1.  **Simplicity and Novelty:** The \"output-space-only\" design is a great innovation. It directly corrects predictions, offering a simpler, more intuitive, and safer alternative to complex dual-adapter methods that indirectly modify data distributions.\n2.  **Inference Efficiency:** The method is quite fast, achieving a nearly order-of-magnitude speedup in inference time compared to prior TTA methods. This high efficiency makes it well-suited for practical, low-latency deployment scenarios.\n3.  **Empirical Performance:** The method's effectiveness is validated by empirical results, where it consistently achieves best performance across six benchmark datasets and multiple backbone architectures, with particularly gains in long-horizon forecasting.\n4.  **Comprehensive Validation:** The paper includes a thorough experimental analysis, featuring detailed ablation studies and sensitivity analyses on key hyperparameters. This evaluation validates the method's design choices and strengthens the credibility of the findings.", "weaknesses": "1. **Unconventional Experimental Settings:** The experimental setup has some questionable aspects: (1) The lookback window of 96 is relatively short. Most contemporary work uses longer history windows, such as 336 or 512. Predicting a long horizon of 720 from a short 96-step history is a somewhat impractical scenario and may weaken the persuasiveness of the method's effectiveness. (2) For multivariate time series, the mainstream approach (even for channel-independent models) is to process all variates concurrently. Splitting multivariate series into univariate ones for individual forecasting is inefficient, especially for widely-used datasets with a large number of variates like Electricity and Traffic.\n2. **Missing Comparison with a Key Baseline and Motivation:** The authors motivate their work by claiming that existing TTA methods for time series forecasting use a dual-adapter architecture, and theirs is novel for being output-space-only. However, a recent paper, [SOLID](https://arxiv.org/abs/2310.14838), is also a TTA algorithm for time series that performs adaptation solely on the output prediction layer and involves an analysis of residuals. This paper is missing experimental comparison and analysis against SOLID, which weakens the novelty claim and leaves a gap in the evaluation.\n3. **Potential Risk of Over-Correction and Instability:** The paper mentions that the adaptive learning rate scheduler, CALR, adopts an \"aggressive\" strategy for fast convergence. While the tanh(g) gating mechanism bounds the correction, an aggressive learning policy, when faced with noisy or anomalous batches, could still lead the adapter to learn unstable or oscillating correction patterns. This over-correction might amplify noise in the short term rather than capturing the true distribution shift, especially with a small batch size B.", "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": "jDiwjjV9xJ", "reviewer": "Reviewer_hY4L", "summary": "The paper proposes a simple yet effective method to adapt time-series forecasting models under distribution shifts. Instead of dual adapters that modify both inputs and outputs, COSA introduces a single output-space adapter that directly corrects predictions from a frozen base model using a linear residual correction modulated by a learnable gate. The adapter leverages a lightweight context vector summarizing recent ground-truth statistics and updates only its parameters during inference under a leakage-free streaming protocol. COSA achieves consistent accuracy gains across six datasets and multiple model types, while remaining architecture-agnostic and computationally efficient for deployment.", "questions": "1. Can the authors clarify under which conditions an output-only adapter is sufficient, and when input-side calibration would still be necessary for stable adaptation?\n\n2. How sensitive is COSA to the construction of the context vector? Would richer temporal encodings or normalization statistics improve its robustness and generalization?\n\n3. Could the method be extended to jointly handle multivariate forecasting instead of decomposing into independent univariate tasks?\n\n4. How would COSA perform under partial label availability or delayed target feedback, which are common in real-world streaming scenarios?\n\n5. Would the proposed adaptive learning rate schedule still remain stable when applied to models with much longer adaptation windows or non-periodic datasets?\n\n6. Could you fix the code link? It seems to have expired.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper presents a clear and elegant solution to the problem of test-time adaptation in time-series forecasting through a single output-space adapter, offering originality by simplifying previous dual-adapter frameworks. The methodology is technically sound, with a well-motivated design and a careful leakage-free adaptation protocol. Empirical results are extensive, covering multiple architectures, horizons, and datasets, demonstrating consistent and significant improvements. The paper is well written, with strong clarity in the problem formulation and experimental design. Its simplicity, effectiveness, and deployment-friendliness make it a valuable contribution with practical and theoretical significance for the TTA and time-series communities.", "weaknesses": "The context construction relies on simple aggregation statistics, which may not capture complex temporal dependencies or handle irregular or missing data effectively. The experiments focus mainly on standard LTSF datasets without testing on more challenging non-stationary or real-world drift scenarios. The computational analysis could better clarify the trade-offs between adaptation time and inference latency. Additionally, statistical significance reporting or variance analysis would strengthen the reliability of the reported performance gains.", "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": "3k7HPcUvDD", "reviewer": "Reviewer_htEG", "summary": "This paper, titled “COSA: Context-Aware Output-Space Adapter for Test-Time Adaptation in Time Series Forecasting”, addresses the problem of distribution shifts and non-stationarity that cause performance degradation in deployed time-series forecasting models. The main objective is to develop a lightweight, architecture-agnostic test-time adaptation (TTA) mechanism that can improve model performance post-deployment without retraining the base model.\n\nThe proposed method, COSA, is a context-aware output-space adapter that performs direct residual correction on the model’s predictions. It introduces a linear correction layer modulated by a learnable gating mechanism and informed by a context vector summarizing recent ground-truth statistics. During deployment, the frozen base model’s predictions are corrected in real-time, and only the adapter parameters (weights, bias, and gate) are updated using an adaptive learning rate schedule under a leakage-free protocol.", "questions": "- The context vector $C_t$ is built from recent batch statistics (e.g., means) with fixed length $K$. Could a learned context encoder (e.g., lightweight RNN/SSM/attention) or an adaptive $K$ selected online (error-aware rather than rule-based) improve robustness across different periodicities and drift patterns without eroding the latency advantages? Please discuss the accuracy–overhead trade-off.\n\n- COSA applies a learnable gate $g$ with $\\tanh(g)$ to modulate correction. Do you observe interpretable gate trajectories during level shifts, scale drift, and seasonal phase changes (e.g., stronger gating when residuals spike)? Would horizon-specific or channel-specific gating improve control or stability relative to a single scalar gate?\n\n- Experiments decompose multivariate data into per-variable univariate tasks. In settings with strong cross-variable dependence, would COSA benefit from structured $W$ (e.g., block-sparse or low-rank shared components) or shared context to capture cross-covariances? What happens to parameter count, memory, and latency as dimensionality grows?\n\n- You describe a cosine–adaptive learning-rate schedule with thresholds motivated by stability. Can you provide formal reasoning or empirical evidence for convergence/safety (e.g., avoidance of error amplification) under short adaptation steps $S$, and comparisons against simpler schedules (fixed/one-cycle/standard AdamW) with statistical significance?\n\n- In cases where short-term perturbations revert (e.g., transient scale spikes), how quickly does COSA roll back adaptation?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- The paper tackles an important and timely problem—test-time adaptation for time-series forecasting—which has received comparatively less attention than its vision counterparts.\n- The proposed output-space-only adapter (COSA) is a conceptually clean and lightweight solution, addressing the design complexity and interpretability challenges of prior dual-adapter approaches.\n- The idea of context-aware residual correction, where recent ground-truth statistics inform a gating-based correction, is intuitive. It provides a plausible mechanism for leveraging the sequential observability unique to forecasting.", "weaknesses": "- Although the paper proposes a simplified, output-space-only adapter, the underlying idea of residual correction or adapter-based adaptation is not fundamentally new. Similar concepts—such as residual adapters, calibration layers, and lightweight correction modules—have appeared in various works.\n\n- While the simplicity of a linear output-space adapter is appealing, it may also limit the method’s expressive power, particularly under nonlinear or abrupt regime shifts.\n\n- The context vector construction relies on fixed aggregation (mean or median) and fixed length K, which might not generalize across datasets with different periodicities or nonstationary characteristics.\n\n- The paper positions the cosine–adaptive learning rate (CALR) as theoretically motivated but does not provide formal derivation or convergence analysis.", "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": "JcaZKkyjtn", "reviewer": "Reviewer_jjeA", "summary": "This paper introduces COSA (Context aware Output-Space Adapter), an adapter-based model that adjust predictions of a frozen base model. COSA achieves this via by learning a gated linear transformation on the original prediction and a context vector of summary statistics of the input. The model was tested on standard time series forecasting benchmarks and showed better performance with faster inference time. In addition, authors showed the utility of different components via an ablation study.", "questions": "Can you please comment on the performance of COSA-F (-P) with only a single update (S==1) either verbally and/or empirically?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- Although the idea is simple and one may argue that it is not novel per se, I think the empirical results show strong adequate performance gain in a much shorter inference time compared to the other baselines. \n\n- I think authors have done a good job in finding relevant (albeit recent) works.\n\n- Authors have reported hyper-parameters and also provided code. \n\nThe current results support the claims in the paper and look convincing to me and overall I am in favour of acceptance.", "weaknesses": "- The input of the gating mechanism and its transformation by parameters g is a bit unclear to me in the formulation and figures. I think authors should elaborate this part similar to other components. \n\n- Authors conducted experiments on the standard time series benchmarks. I think the message of the paper will be stronger if also test the method on the Monash benchmark [1]. Just to be clear, I do not expect authors to repeat all their experiments on this benchmark.  \n\n- The benefit of the proposed method is only visible in long-term forecasting which one may argue it is expected as in the current setup (including baselines) there is a delay period to observe some ground truth. I think the paper will be stronger if authors highlight the applicability domain of the work i.e., what problems COSA-F (-P) is the most suitable for? \n\n- Standard error or confidence interval for numerical results and error bars for the bar plots are not reported. Also, it would be nice to have average+se to summarize each method/dataset.  \n\n- The baseline normalization is not clearly defined in Section 4.2.2, overall this section seems a bit disconnected to the rest of the paper. \n\n- Looking at the reported results in TAFAS and PETSA paper, there are significant differences with those reported in this paper (Exchange, ETTm2, ETTh2 on iTransformer).  \n\n[1] Godahewa et al. 20221 https://arxiv.org/abs/2105.06643", "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)