Language in the Flow of Time: Time-Series-Paired Texts Weaved into a Unified Temporal Narrative
Authors: Zihao Li
Xiao Lin
Zhining Liu
Jiaru Zou
Ziwei Wu
Lecheng Zheng
Dongqi Fu
Yada Zhu
Hendrik Hamann
Hanghang Tong
Jingrui He
Venue: ICLR 2026 Poster (2026)
Keywords: Time Series Modeling
Multimodal Learning
Time Series Forecasting
Primary area: learning on time series and dynamical systems

Abstract: While many advances in time series models focus exclusively on numerical data, research on multimodal time series, particularly those involving contextual textual information, remains in its infancy. With recent progress in large language models and time series learning, we revisit the integration of paired texts with time series through the Platonic Representation Hypothesis, which posits that representations of different modalities converge to shared spaces. In this context, we identify that time-series-paired texts may naturally exhibit periodic properties that closely mirror those of the original time series. Building on this insight, we propose a novel framework, Texts as Time Series (TaTS), which considers the time-series-paired texts to be auxiliary variables of the time series. TaTS can be plugged into any existing numerical-only time series models and effectively enable them to handle time series data with paired texts. Through extensive experiments on both multimodal time series forecasting and imputation tasks across benchmark datasets with various existing time series models, we demonstrate that TaTS can enhance multimodal predictive performance without modifying model architectures. Our Code is available at https://github.com/iDEA-iSAIL-Lab-UIUC/TaTS

Published as a conference paper at ICLR 2026
LANGUAGE IN THE FLOW OF TIME: TIME-SERIES- PAIRED TEXTS WEAVED INTO A UNIFIED TEMPORAL NARRATIVE
Zihao Li', Xiao Lin', Zhining L Jiaru Zou', Ziwei Wu', Lecheng Zheng', Dongqi Fu²
Yada Zhu Hendrik Hamann', Hanghang Tong', Jingrui Jingrui He University of Illinois Urbana-Champaige MMtta, 3BB Research
ABSTRACT
While many advances time series models focus exclusively on numerical data, research on multimodal time series, particularly those involving contextual textual information, remains in its infancy. With recent progress in large language models and time series learning, we revisit the integration of paired texts with time series through the Platonic Representation Hypothesis (Huh et al., 2024), which posits that representations of different modalities converge to shared spaces. In this context, we identify that time-series parrees-pireddd texts may naturally exhibit periodic properties that closely mirror those of the original time series. Building insight, we propose a novel framework, Texts as Time Series (TáTS), which considers the time-series-paire TaTS can be plugged into any existing numerical-only time series models and effectively enable them handle time series data with paired texts. Through extensive experiments on both multimodal time series forecasting and imputation tasks across benchmark datasets with various existing time series models, we demonstrate that TaTS can enhance multimodal predictive performance without modifying model architectures. Our Code is available at https: //g. tuu. com/ LDE/DDDAA--AAA SSAI-- Lab- CAAAL-----CUUC/TTTSS
this
texts to be auxiliary variables of the time series.
INTRODUCTION
Time series modeling plays an important role in a wide range of real- world applications, including finance (Sezer et al., 2020), healthcare (Zhang al., 2024b), climate (Fu et al., 2024), and energy systems (Kotzur et al., 2017; Li et al., 2015). While extensive research has focused on approaches that rely solely on the numerical values of time series (Zhou et al., 2021; Liu et al., 2024c; Wu al., 2023b; Wang et al., 2024c), real-world scenarios often involve additional modalities that co-occur with the time series and can provide valuable complementary information (De Baets & Harvey, 2023; Rai et al., 2023; Kyei & Antwi, 2017; Wang al., 2024d).
Astrerite
In scenarios like pandemic policymaking, economic planning, or investment strategies, textual information can provide explanations. updates, or external factors that influence the underlying numerical patterns. However. research on effectively leveraging data from other modalities paired with time series remains in its early stages. In this work, we focus on time-series paired with texts at each timestamp, a common data format where textual descriptions are associated with time series at each timestamp in a parallel manner, as illustrated in Figure 3 (left). For instance, during a pandemic, infection rates are often accompanied by government announcements and news reports in real- time (Cinelli et al., 2020). On the one hand, numerical-only models overlook valuable contextual information that may influence or explain the patterns in the time series. On the other hand, the current state-of-tt th- approach (Liu et al., 2024a) disregards the unique positional characteristics that sime-series-painee texts may inherently possess. Such limitations raise a pivotal question:
Figure 1: Mean Square Error of modeling frameworks of time series with paired texts. Full results in Appendix E.2.

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Published as a conference paper at ICLR 2026
What unique attributes may characterize tine-series-patie paired texts, and how can they be systematically integrated to improve time series modeling and predictions?
In this paper, motivated by the Platonic Representation Hypothesis (PRH) (Huh et al., 2024), we pioneer the exploration of effectively leveraging paired texts to enrich time series analysis. We identify an intriguing phenomenon, which we term "Chronological Textual Resonance" (CTR): texts may exhibit periodic patterns that closely reflect
depending on data quality, the temporal dynamics of their corresponding numerical time series. More specifically, despite variations in expressions, the hidden representations of two periodicity-lagger texts associated with time series may demonstrate high similarities, revealing deeper alignment between textual and numerical modalities. We attribute this phenomenon to the fact that the paired texts inherently evolve in response to the dynamics of the time series itself. Further, we introduce TT- W'sssssres new metric designed to measure the level of CTR and quantify alignment quality.
Building on these insights, we propose Texts as Time Series (TaTS), a simple yet effective framework for integrating paired texts to enhance multimodal time series modeling. Previous studies have shown that different variables in one multivariate time series exhibit similar periodicity properties (Zhang & Yan, 2023; Wang et al., 2024d; Yi et al., 2024), and CTR suggests that time-series-painee texts follow a similar pattern. This observation implies that paired texts can be considered as special auxiliary variables to augment the original time series. Motivated by this, TaTS first transforms the paired textual information into a lower-dimensional representation, then combines the original time series with the textual representations new variables to form an augmented time series. This augmented time series is subsequently fed into existing time series models, allowing them to capture both numerical and textual dynamics. TaTS offers two key benefits: (i) it effectively captures the evolving positional characteristies of texts paired with a time series; and (ii) it functions as a plug-in module, maintaining compatibility with existing time series models. Empirically, the proposed TaTS achieves tfate-of-the-arr the-art performance on both forecasting and imputation tasks. Notably, we observe that higher CTR level (i.e., a lower (assessrstt)ii) correlates with greater improvements compared to numerical-only modeling. In summary, our contributions are:
We revisit multimodal time series with the PRH and uncover a previously overlooked phenomenon, termed Chronological Textual Resonance (CTR), that time-series-paired texts may exhibit periodic patterns closely aligned with their corresponding numerical time series. Further, we propose TT- Wasserstein to quantify the level of CTR and the aligmment quality.
Based on this phenomenon, we propose a plug-and-pla multimodal time series forecasting framework, Texts as Time Series (TaTS), which transforms text representations into auxiliary variables, seamlessly integrating them into existing time series models.
Experiments on diverse benchmark datasets and multiple time series models demonstrate TaTS's superior performance without requiring modifications to model architectures.
2 PRELIMINARY
We use calligraphic letters (e.g., AA for sets and bold capital letters for matrices (e.g., A). For matrix indices, ji] denotes the entry in the 1hh row and the j"h column. For a vector v, e/i : 5l represents the sub-vector sliced from the jth to the jMh position, inclusively. A :i, returns the zth row in and A|: returns the first rows of A. In this paper, we focus on both forecasting and imputation.
Time Series Forecasting. A time series denoted as X [x1, X2. ..)) E T where T represents the number of time steps and N denotes the number of variables. x, is the time series sequence of the tthh variable. When N > 1, the time series is referred to as a multivariate time series. Let X..b represent the time slice of the series from timestamp a to b, i.c., Xash = {x1[a= : 6). x2(a ......,xyla b]}. The task of time series forecasting is to predict the future H steps:
Å = F
1:7; 1x::; Oroooass E R HxN
where FF denotes the mapping function, and Oforseast denotes the learnable parameters of F.
Time Series Imputation. The goal of imputation is to estimate missing values in the time series X, where the missing entries are denoted by a binary mask M E {0, 1) 7xN, Specifically, M = 1 indicates X,, being observed, M,,,, = 0 indicates Xt,x being missing. Formally,
X Imputed
g (X c M. M; Oampate) E T'N
(2)
2

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Published as a conference paper at ICLR 2026
5000
(a) Economy
(b) Social Good
(c) Traffic
Figure 2: By overlaying the top frequencies of paired texts (vertical dashed lines) onto the amplitude spectrum of the time series, it is observed that the time-series-paiiee texts exhibit similar periodic properties that closely mirror those of the original time series. We term this phenomenon Chronologi- cal Textual Resonance. More Details are provided in Appendix A.
where X Imputed represents the imputed time series, G denotes the imputation function, Oimpute denotes its learnable parameters, and @ represents the element-wiss multiplication. The imputation process aims to recover the missing entries such that X Imputed = X with respect to the actual X values.
Extending Time Series with Paired Texts. In addition to the numerical time series X RTTN, the dataset D = (X, S} includes textual information S {si, $2, ........ }T). where each 8, represents the text timestamp Each 8, string that be tokenized into a sequence of tokens, i.e., Tokenize(s) = [w,,1, Wr.2, Wr,,. ). where L, denotes the number of tokens in the text at time t. The textual data can be transformed into numerical representations using textual encoder Heeti
e, Haea sr; rexx)) E 12
(3)
where e; is the encoded text representation at time t, diext is text embedding dimension, and 6 are encoder parameters. In this work, we leverage pre-trained large language models to encode the texts.
CHRONOLOGICAL TEXTUAL RESONANCE (CTR)
The association of time series at each timestamp may imbue time-series- sime-series-paired texts with unique characteristics that can be effectively harnessed through an appropriate design.
The Platonic Representation Hypothesis. PRH (Huh et al., 2024) posits that different modalities describing the same object converge towards shared, latent representation. Extending this hypothesis, if time series and paired text both describe the same changing event, their representations are dynamic projections from a common underlying source, and should exhibit similar periodic properties.
To illustrate this hypothesis for time series with paired texts, analyze three real-world datasets (Liu et al., 2024a), including (i) Economy: The time series represents trade data the U.S., while the texts describe the general economic conditions of the country. (ii) Social Good: The time series captures the unemployment rate in the U.S., and the texts include detailed unemployment reports. (iii) Traffic: The time series reflects monthly travel volume trends from the U.S. Department of Transportation, with corresponding texts derived from traffic volume reports issued by the same department.
For each dataset D SX employ Fourier Transform (Nussbaumer, 1982; Sneddon, 1995) analyze the frequency components of time series data and identify its dominant periodic components, illustrated by the blue curves in Figure To examine the periodicity of texts, we embed each s, S to obtain the text embedding at timestamp t. Then, we compute their lag-similarity, defined as d E, cos(es, L)+ where I. is the lag and cos(;,) represents the cosine similarity. the text embeddings exhibit a significant periodic pattern, the lag-similarity dj will also fluctuate periodically as the lag increases (proof in Proposition A. Finally, we identify major frequencies (with the largest amplitudes) of the texts by applying FFT to text lag-similarity, and mark them with red dashed lines, as shown in Figure 2. Detailed process is provided in Appendix A. We find that the major frequencies of the paired texts closely match those of the time series. Specifically, the paired texts also show periodicity 12 (frequency 0.083) for monthly sampled time series, indicating that the paired texts exhibit periodicity that is strongly aligned with the temporal dynamics of the time series.
3

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Published as a conference paper at ICLR 2026
Numerical Sequence
Time Stries
Model
Prodiction
Text as Bag-of-texts
Output alighmant
Bag
Encoder Vigh
Layar
Temportt Modeling
Time Ser serwe, Statii
Modeling for Toxts
Paired Test Sequesse
Suquence
Sequence
derins Model
Prediction
Time-Series
Multi-modal Time-Serios
Temporal Hodwling for Both Serles Teats
Figure 3: Texts as Time Series (TaTS) framework. As paired texts may exhibit behaviors similar to accompanying variables in a time series, TaTS transforms the paired texts into auxiliary variables. These variables augment the numerical sequence, forming a unified multimodal sequence that can be seamlessly integrated into any existing time series model.
Why may CTR happen? We present three key reasons for the observed alignment in periodicity between time series and their paired texts: (i) Shared External Drivers: Both the time series and their paired texts are often influenced by common external factors, such as seasonal changes, recurring events, or societal and economic cycles. These shared drivers naturally induce periodicity in both modalities. (ii) Inftuence of Time Series on Texts: Paired texts often serve contextual reflections of the underlying time series, adapting and evolving in response to numerical trends. For articles government reports accompanying economic indicators are frequently updated in response to the numerical trends. (iii) Texts Contain Additional Variables with Aligned Periodicity: Paired texts often include additional variables that are closely related the time series. For example, if the time series represents economic GDP data, the accompanying texts may reference related variables such as stock market indices inflation rates. These related variables often exhibit periodicity patterns aligned with the time series and affect the periodicity of the paired texts.
instance,
Table 1: TasSessestenin measure of Time-MMD (Liu et al., 2024a) datasets and their random shuffle.
Mombly Sampled
Weekly Sumpled Energy
Daily Sumpled Faivironment
Agriculture
Climate
Feonomy
Security
Glood
Original
0,26
0.025
0.022
0.049
0.027
0.055
0.307
0.233
0. 0.302
TS shuffee
0,088
0.032
0.098
0.044
0.069
0.102
0.320
0.268
0.358
Text shufited
0.106
0,037
0.053
0.072
0.104
0.312
0.364
Quantifying CTR level. Of course we cannot expect every time series with paired texts at each timestamp to exhibit periodicity similarity. In some cases, texts aligned with timestamps may not provide meaningful or complementary information, for example, daily lottery winning numbers. To this end, we propose new metric for CTR, TT- Wasserstein, defined as the Wasserstein distance between the normalized spectra of time series and texts. Formally, based on Wasserstein distance (P,, Q) (Kantorovich, 1960), for time series with paired texts dataset D (X, after computing normalized frequencies and amplitudes f fis. drexts C...
72
m
TT- Wasserstein(D) = W Ps) = inf (EIT(Pa..PP)
Vig
7(8) texts
i=1
Subject to
70 2 0,
Σ j=1
Rú = T
Intuitively, TT- (T-Wasserstein(2) quantifies the discrepancy between the spectral distributions of paired texts and time series data. By design, a lower value of TT- Wasserssstt (D) should indicate a higher alignment between the textual and numerical modalities. To validate this, compute our TT- Wasserstein measure Time-MMD (Liu et al., 2024a) datasets, whose web-retrieved texts are filtered, disentangled, and summarized for relevance and alignment. We also compute TT- WTssesserttein
4

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Published as a conference paper at ICLR 2026
time-series-shuffiee text-shuffled versions of the datasets to disrupt alignment. As shown in Table 1, the corrupted Time-MMD datasets yield much larger Wasserstein distances compared to the original datasets. This finding suggests that TT-Wasserstein the alignment hetween modalities and a gauge of dataset quality. In Section 5, we will show that TT- TT-Sesserstein can even predict the potential effectiveness of proposed framework. Additionally, because TT WT-Sasserntein is an empirical statistical metric, we further analyze its sensitivity and estimation stability in Appendix A.I.
indicator for
TEXTS AS TIME SERIES
An overview of the proposed Texts as Time Series (TaTS) is illustrated in Figure 3.
Concurrent Texts are Secretly Auxiliary Variables. As we elucidated in Section 3, the properties of concurrent texts closely align with those of variables in multivariate time series: similar numerical variables, concurrent texts are influenced by shared external drivers and interact dynamically with the time series. Furthermore, mapping concurrent texts structured variables enables capturing hidden variables embedded within the concurrent texts.
1r)) 1). TaTS first embed the texts using a text encoder Hie to obtain text embeddings E = {E1. {e1.e2,.... C2,..... er E IR ReOXT, Since the text embedding dimension chext is typically much larger than the number of variables in the time series, we reduce the dimensionality of the text embeddings by applying Multi-Layer Perceptron (MLP), mapping them into lover-dimensional space of reduced dimensionality dmapped-
Given the dataset D fX (x1, x...... X. {s1. $2...., ST
MLP((e; 0MLP) E dugees
(5)
Unifying by Plugging-in Time Series Model. The resulting mapped embeddings Z {z1, ø2..... ........... (TT) E Roqquttt are then treated auxiliary variables in the time series. Specifi- cally, Z is concatenated with X to form a unified multimodal sequence:
U = [ ZT dim=l E (NN
The unified sequence U then passed into an existing time series model for downstream tasks. Here, we formulate the example of forecasting the next H steps of the time series
X XT+1T+# F 1::;; (iseaas)) [: N] "
where F(:; (rorcaast denotes the time series forecasting model with parameters Broccast and N] extracts the first N variables corresponding the original time series.
Finally, we joint train the time series model fforeentt well as the mapping MLP OLP using the Mean Squared Error (MSE) loss.
T+ Σ (=T+1
Lrorecast X,
Σ X
H
where X., and X,, represent the ground truth and predicted values of the 7thh variable time step respectively. TaTS for imputation follows similar process and is omitted here due to space constraints. Detailed algorithms for both forecasting and imputation are provided in Appendix C.
To conclude this section, we note that while some existing literatures make similar but limited attempts to model covariates in multivariate time series or multiple time series. Our TaTS framework differentiates from those approaches by unifying multi-modality using deep learning architectures. In Section 5, we compare TaTS with these existing approaches.
EXPERIMENT
In this section, we empirically validate the effectiveness of the proposed TaTS framework. In particular, GPT2 (Radford et al., 2019) encoder to embed the paired texts. We also validate the performance of TaTS with other text encoders across different datasets section 5.2 and Appendix E.7. Implementation details are provided in Appendix D.4.
5

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Published as a conference paper at ICLR 2026
Table 2: Time-series forecasting performance. Compared to numerical-only unimodal modeling and MM-TSFLib, TaTS consistently and significantly enhances existing time series models to effectively handle paired texts. The results are averaged across all prediction lengths. Full results reported in Appendix E.3. Promotion (positive or negative) denotes the percentage reduction (or increase) in MSE or MAE achieved by TaTS compared to the best-perfon perfoormfg baseline.
Mides
(21043
PaccINT (2023)
Croedeena (2023)
DLiner (2023)
(2023))
(20221)
RLL
Astofience (2121)
Inferrec (30211
Translomer
(2017)
Maric
MSB
MAll
MSS
MAIl
MSR
MAII
MSR
MAR
MSE
MAR:
MAR:
MSR
MAR
MAR.
MSB
Uni-modal
0.122
0.251
0.120
0.267
0.523
0.406
0.223
0.354
0.158
0.286
0.139
0.256
0.158
0.297
0.599
0,610
0.154
0.434
Auriculture
MMC-15PLB
TaTS (eund)
0.009
0.112
08.00
0.224
0.114
0.114
08.33
0.235
0.312
0.215
0.313
0.312
0.314
0.218
0L355
0.351
0.151
0.151
1U375
0.377
0.135
0.140
0.358
0.251
0.158
01125
0.288
0.266
0.313
0.255
0.416
0.348
2.349
01191
0.352
0.313
Uniamodal
L183
0.671
1,230
0.595
1.124
0.857
1,900
0.872
1,92
0.893
1,270
0:911
1.351
0.965
3,310
0.341
1,092
0.339
Clinate
MMG-T5PLb
TaTS (eumo
1.05
11844
0.800
01894
11004
1,000
0..00
017945
01913
1,002
0.772
11775
11991
1.104
0.857
01719
1.011
1966
0.397
01760
1,170
0.571
(1900)
1,053
0.827
0.789
0.510
3.501
0.792
0.716
0.783
Uni-modal
0.014
0.00%
0.017
0.115
0.758
0.825
0.008
0,192
0.062
0.166
0.025
0.129
0.071
0.207
1.325
0.130
0.58L
0.711
Boarony
MM.TSFLB
Tal8 (suno
0.011
0.005
0.000
0.007
0.014
010009
0..0%
0.079
01250
0.219
0.458
0.419
0.004
0.001
0.180
0.117
0.085
0.015
0.555
0.101
0.000
0.006
0.129
0.058
0.024
0.192
0.121
01452
0.399
0.618
0.512
0.315
5009
0.46
Prosotion
Uni-modal
0.369
0.375
0.369
0.370
11203
0.006
0.261
0.396
0.340
0.351
0.378
0.385
0.319
0.475
0.319
0:425
0:297
0.805
Farrg
MM-TSFLB
TaTS (surs)
0.367
01.77
11271
01.28
0.372
0.371
11291
0.229
0.00
0.3955
0.388
0.258
0.35%
0.379
0.271
0.385
0.379
0.314
0.320
0.478
0.410
0.301
0.384
0.413
0.295
0
Procodion
Dni-maaal
0:641
11:061
11:547
01557
11.41
0.961
11555
0.191
0.501
11.19
0.577
0.965
0.119
0.996
0.159
0.112
3-800
6.51
Envicement
XM.-SFLL
TaTS (eurs)
0.421
0.478
0..99
0.501
0.371
0.427
0.485
0.425
0,500
0.423
0.466
0.478
0.400
0.371
0.452
0.500
0.357
0.424
0.450
0.406
04255
0.81
0.397
Promotion
Um-mmcaa
1.507
01:17
1,632
1.535
06827
1.757
0.848
1.196
1,982
1,005
1.562
8,001
1.375
0:715
1.318
0.776
Hedli
MM.TsFLb
TaTS (eurs)
1.486
0.816
1.547
1.273
0.744
1.541
0.800
1,252
0.790
1,675
0:549
1.454
0.887
1.315
0.740
1.218
0.248
Promution
9.19
0.11%
3.99
6.255
Uni-meaal
115.04
5,600
112.85
5.371
128:56
6.277
109.11
4.711
114-46
5.158
115.55
5-467
115:27
5.118
131.76
6.625
131.35
6.582
Securit
MM-TSPLI h
(sumo)
116
5,557
80
1,183
10K.00
4.713
1.007
10
113:44
4.975
178.05
6.415
178.0
6.77
Promution
1,4%
2.8%
0.4%
0.7%
7.855
2.74
3.715
1.8%
3.01%
Uni-madal
1.212
01:887
1.007
01:095
01467
1.151
0.712
11.90
01476
1.761
5.664
1.375
0.701
0.871
0.504
5/310
0-484
Social Good
MMM-SFFLL
1997
01.500
1.071
01515
01877
1.061
01875
1.987
04152
1:256
0.575
0,510
0.457
0.356
Promusion
17.5%
9.4%
6.1%
6.9%
-3.5%
7.1%
7.2%
6.9%
10.75
0.0%
2.8%
0.55%
3.5%
-0.4%
5.7%
9:15
Unp-madal
0.213
01225
01188
01362
8.214
0.326
01250
01355
0.215
11266
01215
0.314
01212
0.206
0.200
0:355
0,200
0.346
Tralic
MMM-TFFL.h
(suns)
0.711
Promution
5.0%
8.8
3.4%
9.15
10.85
15.45
10.05
9.1%
10.45
10.95
15.0%
17.15
18.5%
15.85
4.7%
6.555
1.55
7.155
Datasets. We evaluate our framework on 18 real-world datasets from Time-MMD (Liu et al., 2024a), FNSPID Dong et al. (2024), and FNF Wang et al. (2024b). The datasets span diverse domains with sample frequencies ranging from daily to weekly and monthly. More details are in Appendix D.I.
Time Series Models and Baselines. To demonstrate the compatibility of TaTS with existing time series models, we integrate TaTS with 9 widely used models across different categories, including (i) Transformer-bee basso models: iTransformer (Liu et al., 2024c), PatchTST (Nie et al., 2023), Crossformer (Zhang& & Yan, 2023), Autoformer (Wu et al., 2021), 1), Informer (Zhou et al., 2021) and Transformer (Vaswani et al., 2017). (ii) Linear models: DLinear (Zeng et al., 2023). (iii) Frequency- based models: FEDformer (Zhou et al., 2022b), FiLM (Zhou et al., 2022a).
We compare our TaTS framework with wide array of baselines, including (a) numerical-onty uni- modal modeling, which ignores the paired texts and utilizes only the numerical time series with the given time series model; (b) MM-TsFLib (Liu et al., 2024a), a recently library proposed together with Time-MMD datasets for multimodal time series forecasting; (c) covariate- methods: N-BEATS (Oreshkin et al., 2020), N-HiTS (Challu et al., 2022); (d) convolution- method TCN (Bai et al., 2018); (e) a recent multimodal time series foundation model Chat'Time (Wang et al., 2025).
Metrics. We evaluate the performance of multimodal time series modeling using MSE, MAE, RMSE, MAPE, and MSPE. Due to space constraints, we report only the MSE and MAE results in the main paper, while the results for the other metrics are provided in Appendix E.
5.1 MAIN RESULTS
Improved Forecasting over Uni-modal Modeling and MM-TSFLib. Table 2 presents the per- formance results for the time series forecasting task on Time-MMD datasets. For each dataset and time series model, we report the average performance across four different prediction lengths, and

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Published as a conference paper at ICLR 2026
Table 4: TaTS compared with several baselines on a variety of datasets, Best results are bolded and best results are underlined. Full results in Table 28.
Metlods
TaTT (ouas)
TaTS (OMR3)
TaTS (0X33)
N-BEATS
N-HITS (21071y
Chaflise
CPT4MIS
Dntascts
MSE
MAAE
MSE
MAA
MSE
MAE
MSE
MAE
MIS
MAAE
MSE
MAE
MSS
MAE
MSE
MAB
Agricaitue
0.11
0.235
0.804
0.945
0.712
1,095
1.303
1.998
1.565
1.019
1.127
0.573
Time MMD.
Maliiasial
Tire Serios
Enrkoceeen
Escearmy
Ezengy
Health
0.28
6/66
8.267
0
0
0.744
0.369
01200
0.215
8.258
1,333
0.11
0.371
0.271
0.009
0.23
1.41
0.880
0335
0.319
0.111
6.329
0.518
1,310
0.923
0.573
0.424
0.664
0,572
0.533
1.886
0.584
0.453
0.583
0.430
0.854
1.938
5.546
0.970
0.713
2.599
0.512
0.040
0.335
0.580
18853
0.417
0.000
8.166
1.591
0.014
0.345
0.263
1.265
0.085
0.825
01422
0.576
Good
0497
0.452
0.972
1.300
0866
1,273
1.314
0896)
1.364
01657
1.414
0.559
Traffle
0157
0.717
0,172
0.309
0.176
0.348
0.347
01:04
0.208
0.382
0.708
0.704
0.367
0.524
0.185
0.346
Deta Aitiass (DML.)
0.152
8.886
0.192
0.05
0.201
0.286
0.641
0.236
0.379
0.33
0.665
0.094
0.312
01913
0.301
FNSPID:
(BBM)
0.910
0,900
2.513
1.419
3.426
Steck Price
NVIILA (SVDA)
6/943
0.541
5:48
0.15
0.50
0.134
0,222
0.434
0.122
0.262
0.433
0.574
0.033
0.161
0.054
0.199
(1004)
Pfive (PPT))
0.336
0.416
0.448
044T
0.676
0.573
11524
0665
0.678
0.500
0.005
0.677
0.369
01:34
Toda (TSI.A)
01142
0.781
0.707
0,310
0.266
0.188
0.532
0.251
0.416
3426
1851
0.158
01300
0.181
0.303
Bacoun
Poeecatt with News
Trufflc
17.244
3.712
17
1453
23.333
23,365
31.636
3.62
20.764
3.999
19:20
2,27
(20244)
Bledraiity Demuad
0.260
0.39h
0.254
0.35%
0.266
0.377
0416
0.495
0.364
0.458
0.516
0.564
0.532
0.565
0.295
0.305
the full results for each prediction length are provided in Appendix E. For datasets with relatively few samples, we perform short-term forecasting with prediction lengths of {6, 8, 10, 12). In contrast, for datasets with a larger number of samples, we perform long-term forecasting with prediction lengths of {48, 96, 192, 336}. From the results, compared to uni-modal modeling or MM-TSFLib, our TaTS consistently achieves the best performance across all datasets. Notably, by plugging in TaTS to various existing time series models, it achieves average performance improvement of over 5% on out of datasets and delivers a remarkable performance boost of over 30% on the largest dataset, Environment. The results also demonstrate that TaTS is highly compatible with a wide range of existing time series forecasting models, consistently delivering performance improvements across all of them in both long-term forecasting and short-term forecasting tasks. We provide a visualization of the performance boost in Appendix E.2, showcasing the improvements achieved by different time series models on each dataset.
Improved Time Series Imputation. We evaluate the performance of our TaTS framework on the imputation task using the Climate, Economy, and Traffic datasets, each with an imputation length of 24. Though MM- TSFLib only supports forecasting tasks, we extend it to serve as an imputation baseline by applying a similar linear interpolation. We select one representative time series model from each category and present the results in Table 3. The results demonstrate that TaTS consis- tently enhances the imputation capabilities of existing time series models, achieving improvements of up to 30% compared to baseline methods.
Table 3: Imputation task performance. Full
results in Appendix F.4. Promotion: per- centage reduction by TaTS over the best- performing baseline.
PichTST
DLisees (2021)
Meticc
MSSH
MAR
MSE
MAE
MSB
MAE
Uni modal
1.113
0.866
0.969
0.801
1,123
0,829
Climate
MSS-TSFLB
TaTS touns)
0.77%
0.730
0.821
0.912
0.961
0.757
03300
1.130
0.718
Promotion
12.3%
5.3%
27,09
13.4%
Uni-stdal
0.029
0.138
0.067
0.190
0,077
0,209
Boonony
MIN-TSRI ib
TxTS (nuno)
0.17
8.06
0.945
0.137
0.061
0.045
0.171
1956
0.554
0.074
0.301
0.168
From the above results, effectively leveraging the text modality provides significant benefits when paired texts are available, and our TaTS framework achieves notable improvements over baseline methods that disregard po-
Premation
34.55
67.755
31.0%
11.2%
78.05
17.2%
Uni
Traffic
TML-TSFLB
1aTS tommo
0.341
01348
0.170
0.154
0.335
0.287
Prometion
30.7%
36.8%
25.1%
11.3%
18.95
16:0%
sitional information in time- wew-ss-eeiiieeeee texts.
TaTS Benefits from Better Alignment (i.e., lower TT- "T--asser)ttiin. We compute the average forecasting improvement of TaTS compared numerical-only modeling, as well as the ratio of Wa-Sasserstein between original and shuffled Time-MMD datasets. The results, shown in Table 5, reveal that, within the same sampling frequency, lower TasSesserntnin original-shuffled ratios tend to correlate with larger performance gains from TaTS (except for Climate). In other words, for paired time series and texts that have stronger CTR, i.c., more relevant, our TaTS could improve performance more. Thus, TT- Wasserstein can indicate the usefulness of paired texts and the potential effectiveness of TaTS when text quality and cross-modal alignment are uncertain.
Comparison beyond Uni-modal Modeling and MM-TSFLib. Besides numerical-only time series models and the MM-TSFLib framework, we compare our TaTS with several other baselines on three dataset sources, including Time-MMD (Liu et al., 2024a), FNSPID (Dong al., 2024), and
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Table 5: TaTS Improvements positively correlated with TT-Wasserstein measure of Time-MMD (Liu et al., 2024a) datasets. "Original-Shuffles TT Ratio" means the ratio of TT- Iasssssserttiin on the original dataset to TT-Wasserstein on the shuffled dataset. "TaTS Improvement" means the average improvement of TaTS over uni-modal time series modeling.
Monihly Sumpled
Weekly Sampled Enengy
Duily Sampled Envinoment
Dataset
Agriculture
Climate
Feonomy
Security
Social Good
Traffic
Health
Original Shufflle Ratio TaT'S Improvement (1%)
26.8
72.4
91.5
20.70
18.03
64.80
4,05
19.51
36.00
FNF (Wang et al., 2024b). Although N-BEATS, N-HiTS and TCN are not specifically designed for time series with paired texts, we adapt them by feeding both time series and text embeddings to them. We also include several baselines that explicitly incorporate multimodal information.. For ChatTime, we concatenate all paired texts into a single long text and perform zero-shot inference. For GPT4MTS, we convert the datasets we used into their prescribed input format and directly apply their pipeline. The results averaged from multiple prediction lengths are shown in Table 4, with full results in Table 28. The results show that covariate-basee and convolution- perform comparably or worse than iTransformer, and consistently underperform compared to our TaTS, Although ChatTime achieves competitive results even in zero-shot setting, highlighting the value of integrating texts when high-quality texts are available, our TaTS outperforms it through supervised learning. We further compare TaTS with several multimodal methods from concurrent preprints that also evaluate on Time-MMD. Using their reported results (Table 12), we find that TaTS elevates standard time-series backbones into highly competitive models, rivaling recent approaches with substantially more complex designs.
models
5.2 FURTHER ANALYSIS
Hyperparameter Sensitivity. We perform hyperparameter studies to evaluate the impact of (i) the learning rate and (ii) dmmpped. the dimension to which high-dimensional text embeddings are projected by the MLP, as defined in Equation 5. The results are presented in Figure 4, subfigures (a) and (b), with full results available in Appendix E.5 and Appendix E.6. The findings indicate that TaTS maintains robust performance across different choices of the learning rate and the text projection dimension dmmpped-
Ablation with Different Text Encoders in TaTS. While GPT-2 was used as the primary text encoder in main experiments to demonstrate the effectivvness of TaTS, we further evaluate the performance of TaTS with different text encoders, including BERT (Devlin et al., 2019), GPT-2 (Radford et al., 2019), and LLaMA2 (Touvron et al., 2023). We utilize the official implementations available on Hugging Face and present the results in Figure 4, with full results provided in Appendix E.7. The results show that TaTS remains robust across different text encoders and consistently outperforms both the uni-modal and MM-TSFLib baselines. Notably, as the size of the language models used in TaTS increases from 110M (BERT) to 1.5B (GPT-2) and further to 7B (LLaMA2), we observe a slight improvement in performance. Investigating the relationship between the text encoder size and TaTS's effectiveness remains an open direction for future research.
Ablation with Other Design Choices to Com- bine Modalities. In our main experiments, TaTS transforms the paired texts into auxiliary variables through embedding, projection and concatenation. Our TaTS framework is readily extensible other fusion design choices. We evaluate two alternative architectures that replace the MLP projection with:
Table 6: TaTS Ablation on Alternative Modality Fusion Architectures.
Deanect
Cliradc
Scortte
Trlfic
A Pussstes
74775 Settigg
MSE
MAR
MBE
MAE
NBE
MAE
Flacz
Tital
peodectiion Onigindd
254
0027
6330065
MMM
0192
000 T3M
996
0.118
10333
W0-11
6431003
(a) a gated residual and (b) cross-attention module between the time series and text embeddings. We report the average MSE and MAE across TaTS with iTransformer, PatchTST, and FiLM in Table 6. From the results, these alternative mechanisms achieve similar performance to the MLP-based design. One possible explanation is that linear projections are already highly competitive for time-series representation learning, especially when paired with strong backbone forecasters that account for the majority of the model parameters. We leave the exploration of more fine-grained multimodal fusion designs as an interesting direction for future work.
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1.10
0.23
Time dehu Node 101
5.22
0.33
0.59
Learrin Rale
Mereciann Fennerr oerere bois
(b)
(c)
(d)
Figure 4: Further analysis of our TaTS framework. (a) Learning rate sensitivity: TaTS maintains stable performance across different learning rates (full results in Appendix E.5). (b) Text Projection
Dimension sensitivity: TaTS remains robust across varying dnupped (full results in Appendix E.6). (c)
Varying text encoder: TaTS consistently outperforms baselines across different text encoders (full results in Appendix E.7). (d) Efficiency: TaTS introduces only minor parameter increase (~ 1%)
but significantly improves the performance according to Table 2.
Ablation on Corrupted Datasets. To validate that the performance gains stem from useful tex- tual cues, we conduct corruption experiments where the textual information was randomly shuf- fled across timestamps. All other settings are un- changed, and the results are in Table 7. When
Table 7: TaTS Ablation on text- iext-shufflld datasets.
Dstect
Ciiaacc
Searty
Thtalic
Settings
MSR
MAlI
MS.
MAR.
MSB
Trooefoo TTTT origital dat
083
112.05
5151
0.187
TTstafomus TxIS commapes
1242
0.855
11782
5.067
0.225
0.265
ilsusslomer uni-snedd - seigind data
1,885
0.71
115.44
5660
0.13
0.23
textual alignment is destroyed, the performance drops significantly to matching or even being worse than the uni-modal baseline. This is expected, as randomly shuffled text acts as noise rather than a meaningful signal. Yet our TaTS stays relatively robust because it can learn to assign small weight to textual information during optimization as a mitigation to noisy texts.
Ablation Text- Text-Randomly-Dne Randomly-Dropped Datasets. Similar to corruption ablations, we conduct ex- periments with randomly dropped texts. Dropped texts are filled with "no information available." The results are in Table 8. While performance de- grades slightly as more text is randomly dropped, TaTS remains effective, performing comparably to MM-TSF Lib even with 25% of the text missing. This experiment shows that whenever textual information is available, our TaTS could benefit from it to improve time series modeling.
Table 8: TaTS Ablation on text-dropped datasets.
Duaedt
Clinaec
Securiy
Trilic
Scoings
MSR
TIITS orggnaal dato
1
113.05
5,181
0,187
0.317
TATS 10% text randonll dooped
1.02
0
112.54
5,372
0,194
0.239
TETS 2518 sesi undombl dropped
1.056
O818
114.99
5231
0.001
0.354
Mitigating Negative Effects of Extremely Noisy Texts. Our ablation on corrupted datasets shows that highly noisy text can cause TaTS to even slightly underperform numerical-only modeling. To address this, we evaluate a simple mitigation strategy: randomly dropping a portion of the noisy texts and replacing them with "no information available." " We test drop rates of 40% and 80%. As shown in Table 9, dropping noisy texts allows TaTS to recover performance close to the unimodal baseline, demonstrating the effectiveness of this strategy in handling unreliable text. Practitioners can refer to Appendix B.2 for how TaTS can adapt to scenarios with low-quality texts.
Table 9: Dropping extremely noisy texts miti- gates negative effects from them.
Dantseet
Glimate
Security
Traffic
Settings
MSB
MAE
MSE
MAE
MSB
MAB
TiTSS comupted data
1,242
0.895
117.52
5,767
0.223
0.265
TaT'' corupted
0.879
11743
5,730
0.215
0.260
TITT 299 comuped
0.878
116.88
5711
0.255
uni modal original
0.871
115.4
3.600
Computational Overhead vs. Performance Gain, We also evaluate the efficiency of our proposed TaTS by measuring the training time per epoch and the total number of model parameters. Figure 4 (d) presents the total number of parameters for the best-performing models in our forecasting experiments. TaTS introduces only lightweight three-layer MIPP to project high-dimensional text embeddings into wwwer-dimensional space, adding minimal number of parameters compared to the original time series models. As a result, the overall parameter count increases by only about 1%.
Due to the inclusion of augmented time series with auxiliary variables from paired texts, the training time per epoch increases slightly, as shown in Figure 5, with average performance of each framework indicated by cross markers. Full results for all datasets are provided in Appendix E.8. Notably, this marginal efficiency trade-off (~ 1% in terms of number of learnable parameters and ~ 8% in terms of training time) leads to significant improvements (~ 14%) in forecasting performance.

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Published as a conference paper at ICLR 2026
6 RELATED WORK
Numerical-only Time Series Modeling, Recently, various deep learning models have been developed for time series anal- ysis, which can be broadly categorized into three categories. (I) Patch-based models. PatchTST (Nie et al., 2023) seg- ments time series into subseries-level patches to capture depen- dencies, while Crossformer (Zhang & Yan, 2023) employs a two-stage attention mechanism to model both cross-time and cross-variable dependencies efficiently. Autoformer (Wu et al., 2021) introduces decomposition blocks separate seasonal and trend-cyclical components. (2) Global representation models. iTransformer (Liu et al., 2024c) utilizes attention over global series representations to capture multivariate correlations. In- former (Zhou al., 2021) reduces self-attention complexity using ProbSparse self-attention for improved efficiency. Dlinear (Zeng et al., 2023) demonstrates that simple linear regression in the raw space can perform competitively on MTS tasks. (3) Frequency-awarr models. FEDformer (Zhou et al., 2022b) represents series through randomly selected Fourier components, while FiLM (Zhou et al., 2022a) enhances representations with rrequency-basee layers to reduce noise and accelerate training. In this work, our proposed TaTS is compatible with all of the models listed above.
0.7
Uni-modal MM-TSFLib
TTS
Mean Square Error
0.6
0.4
0.3
Training Time for Each Epoch
Figure 5: While TaTS incurs a slight increase in training time due to augmented auxiliary variables, significantly improves forecasting. Full results in Appendix E.8.
Time Series with other data sources. In the financial domain, several early works have explored integrating time series with textual data, albeit not in a timestamp-aligned manner, or often leveraging general machine learning models rather than time series-specific architectures. For example, StockNet (Xu & Cohen, 2018) uses VAB-like model for chaotic stock-text data, while (Rodrigues al., 2019) fuses time series with a single event-related document. BoEC (Farimani et al., 2021) applies seg-of--conomiccconcepe
approach, and Dandelion (Zhou et al., 2020) leverages multimodal attention for feature aggregation from multiple text sources. Some works also explored time series with vision information (Liu & Cai,, 2012; Gerard et al., 2023; Lütjens et al., 2024) for spatio-temporal analysis. Recently, MMD (Liu et al., 2024a) constructs a dataset of time series paired with parallel text, covering nultiple domains, which we used our main experiments.
Large Language Models on Time Series. The rapid advancement of Large Language Models (LLMs) has inspired a new line of research that transforms time series into natural language represen- tations, enabling LLMs to perform downstream tasks (Zhang et al., 2024c). While these approaches demonstrate strong generalization capabilities due to the power of LLMs (Gruver et al., 2023; Cao al., 2024; Jin et al., 2024; Xue & Salim, 2024), they also inherit limitations such hallucination (Huang et al., 2023) and context length constraints (Wang et al., 2024a; Liu et al., 2024b). Notably, a recent work (Tan et al., 2024) suggests that replacing complex LLM architectures with basic attention layers does not necessarily degrade the performance. Another emerging line of work focuses on generating texts from time series, with applications in temporal reasoning and time-series question answering (Chang et al., 2025). MTBench (Chen et al., 2025) provides a comprehensive evaluation framework for assessing whether LLMs can jointly reason over structured numerical trends and unstructured textual narratives. TSAIA (Ye et al., 2025) benchmarks LLMs' multi-step temporal reasoning capabilities. TimeXL (Jiang et al., 2025) further introduces collaborating LLM agents to generate interpretable natural-language explanations alongside time-series forecasts. One notable future direction is to enable latent communications (Zou et al., 2025a;b) between the time series model and language model to build general time series intelligence.
7 CONCLUSION
Real-world time series data often comes with textual descriptions, yet prior studies have largely overlooked this modality. We identify Chronological Textual Resonance, where text embeddings exhibit periodic patterns similar their paired time series. To leverage this insight, we propose plug-and-play framework that transforms text representations into auxiliary variables, seamlessly integrating them into existing time series models. Extensive experiments across various forecasting models and real-world datasets demonstrate the sfate-of-the thr-----rtttt performance of our approach.
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ACKNOWLEDGEMENT
This work is supported by NSF 2433308, IBM-IIlinois Discovery Accelerator Institute, and MIT- IBM Watson AI Lab. The content of the information this document does not necessarily reflect the position or the policy of the Government, and no official endorsement should be inferred. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation here on.
STATEMENTS
ETHICS STATEMENT
Our work solely focused on the technical challenge multimodal time series and does not involve any elements that could pose ethical risks.
REPRODUCIBILITY STATEMENT
We provide our full experiment code in the supplementary materials, accompanied by detailed README facilitate reproduction. The experimental environment is described Appendix D, including hardware and software configurations. All benchmark datasets used in this work are publicly available. Comprehensive experiment details, including dataset specifications, hyperparameters, and optimizer settings, also documented in Appendix D. Reported results averaged across multiple prediction lengths. Furthermore, Section presents hyperparameter studies, demonstrating the robustness of proposed TaTS framework.
LARGE LANGUAGE MODEL USAGE STATEMENT
Large Language Models did not play significant role in research ideation and/or writing to the extent that they could regarded as contributor. They were used only for minor refinement of writing and as components within our proposed TaTS framework for handling the text modality.
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Appendix
Roadmap. In this appendix, we provide detailed overview of our methodology and experimental setup. Appendix A outlines the complete process of frequency analysis for both time series and paired texts. Appendix B discusses of preprints that are related this work. Appendix C illustrattes the TaTS algorithms for time series forecasting and imputation. Appendix includes details on datasets, hyperparameters, evaluation metrics, and additional implementation specifics. Due to space constraints in the main text. Appendix E presents the full experimental results. including comprehensive forecasting and imputation outcomes, hyperparameter and ablation studies, efficiency evaluations, and visualizations. The table of contents is provided below for reference.
TABLE OF CONTENTS
Detailed Frequency Analysis Process of Time Series with Paired Texts
A.1
Estimation Stability of TT-Wasserstein
22
Further Discussion
24
B.1 Concurrent Works
24
B.2 Limitations
24
B.3 Ethical Impact Statement
25
C
Algorithms
26
C.I Pseudo Code
26
C.2 Incremental Complexity Introduced by the Text Modality
26
Experiment Details
28
D.1 Dataset Statistics and Details
28
................................
D.2 Hyperparameters
D.3 Metrics
29
D.4
Implementation Details
30
E
Full Experiment Results
32
E.1
Why should we leverage CTR?
32
E.2
Full Forecasting Performance Comparison Visualization
32
E.3
Full Forecasting Results
32
E.4
Full Imputation Results
44
E.5
Full Hyperparameter Study Results of Learning Rate
45
E.6
Full Hyperparameter Study Results of Text Embedding Dimension
46
E.7
Full Ablation Study Results Using Different Text Encoders
47
E.8
Full Efficiency Results: Computational Overhead vs. Performance Gain Trade-offs
48
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A DETAILED FREQUENCY ANALYSIS PROCESS OF TIME SERIES WITH PAIRED TEXTS
Here, provide detailed explanation of the frequency analysis process for both the time series and their paired texts. In Proposition A.1 and A.2, we simplify the proof by analyzing each periodic component individually
single cosine. This without loss of generality, as the operations involved are linear. Therefore, the conclusions naturally extend to signals composed of multiple periodic components through linear superposition.
Proposition A.1. The computation of lag similarity preserves the original periodicities of the data.
Proof. Let S = {8x represent the paired texts or data sequence, where each 8; corresponds to time step f. Define the lag similarity at lag as:
k sim St4R);
LagSim(k)) = T
(9)
where sim(.,)) is a similarity measure (c.g., cosine similarity).
Now, consider the periodic component of the data sequence S, which can be represented as:
2Tl +
A cos
(10)
where A is the amplitude, P is the period, and é is the phase.
For two points separated by lag k, the similarity sim(st. St4R) depends on the relative difference between their phases:
Sitk cos
( k)) P
+b) ④5) = A cos
2xt
2T P
(11)
p
The lag similarity is then computed as:
LagSim(k) T
1
T k
Σ
sim
cos
2tt P 0) A
2nt P P + ④b +)))
+
2nk
(12)
Since the cosine function is periodic with period P, the similarity sim(st, 81++k) also inherits this periodicity. Therefore, the overall lag similarity LagSim(k) retains the periodicities of original sequence S.
Thus, the computation lag similarity preserves the original periodicities of the data.
Proposition A.2. The stabilization of a data sequence using first-order differentiation preserves its original periodicities.
Proof. Let = {s represent a data sequence, where &; is the value at time step f. The first-order differentiation of the sequence defined
As, 8141
St: t = 1. . - 1.
(13)
Suppose the sequence exhibits periodic behavior with period P and can be represented as:
2nt
=
cos
P + t
(14)
where is the amplitude, P is the period, and Φ is the phase. The first-order difference of is:
2T + 1)
2nt
As; = 8141 84 = A cos
+ + - A cos
+
(15)
P
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Compute Avarage Text Similarty ty for Each Log At
Time Series with Concurrent
up Wllaammn
Stabilizalion Fourier Transform and Mam-maa Suppression
Stabiliztion and Founter Transform
5
Ampiltaae Spectrum Time Seroe Eoorctry
Anrdiiade Spettrur of Thee Sente Eowenn
Aaplituce Spectran Concarmet Tedts Ccaneny
60000
e10000
5ow0r
30000
30008
Top-Amplitude Frequencies Spectrum
Figure 6: Illustration of the frequency analysis process for time series with paired texts in the Economy dataset. Step D: Compute the average text similarity for each lag k. Step 2: Stabilize the time series using first-order differentiation, apply Fourier Transform, and perform Mon-Maximum Suppression (NMS) to obtain the amplitude spectrum. Step @: Visualize the lag similarity of paired texts. Step 4 Stabilize the paired texts, compute the Fourier Transform, and visualize the amplitude spectrum. Step @ Overlay the top-/ (here (=4) frequencies of paired texts onto the time series amplitude spectrum to highlight shared periodic patterns. All the data transformation operations in this process are periodicity
sepodicityypeserviing preserving according to Proposition A.1 and Proposition A.2.
Using the trigonometric identity for the difference of cosines:
cos( (r + y) - cos(æ) sin
y sin
x +
y/
(16)
we set x P
2nt + and y = 25 giving:
Ast 22A sin
sin
2xll p
o
m p
(17)
The first term, sin (T), , a constant dependent the period P. The second term, sin 2gt + の $). retains the periodicity of P, as it is sinusoidal function with the same frequency as the original sequence.
Thus, the first-order difference Ast preserves the periodicity P of the original data sequence.
The overall process of frequency analysis for the time series X (x1, X2,.. XN) E RTxV and paired texts S = {s1. ... sT] in the Economy dataset D Deconomy = (X, is illustrated in Figure In this process, starting from the original dataset (subfigure ()) the time series and paired texts
are analyzed independently. For the time series X (x1, x., xv), we perform standard frequency analysis, stabilizing the data through first-order differentiation.
AX, = X - X,, for =
(18)
where AX, represents the first-order difference of the time series. This step removes long-tern trends and ensures that the data is stationary, allowing for a more accurate analysis its frequency components.
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Then, compute the Fourier Transform (Nussbaumer, 1982; Sneddon, 1995) of AX to analyze its frequency components. The Fourier Transform of AX defined as:
T-1 1
Fax
Σ AX 127ft
(19)
t=1
where f represents the frequency, AX, is the first-order difference of the time series time t, and i the imaginary unit. The resulting (fx provides the amplitude and phase information of each frequency component present in the time series.
The magnitude spectrum, which represents the amplitude of each frequency component, is computed
[Fax where Re(Fax (f)) and Im(Fax(f)) are the real and imaginary parts of (f), respectively.
Im(xxx(()
(20)
By analyzing [Fax(f),. we identify the dominant frequencies in the time series, which reveal its periodic patterns. To further highlight the dominant frequencies, we apply Mon-Maximum Suppression (NMS) to the magnitude spectrum Fax (-) [a)( NMS ensures that only the most prominent frequencies are retained while suppressing nearby less significant frequencies. The NMS operation is defined as follows:
Fax(f)),
if > |FAx(f)lVf' EN()).
N() 0.
(21)
otherwise,
where (f)) represents a local neighborhood around the frequency f. The operation compares the magnitude of Fax( with those of neighboring frequencies and retains only the largest value within the neighborhood. Frequencies that do not satisfy the condition are set to zero
After applying NMS, the remaining frequencies represent the dominant periodic components of the time series, making it easier to identify significant periodic patterns. This process eliminates noise and reduces the influence of minor frequency components, enhancing the interpretability of the spectrum. The final visualization of the amplitude spectrum of the time series is shown in Figure 6, subfigure ②.
For the paired texts S = {s1, $2, ST}. we first embed each st using the text encoder Heeti
Haxx (st; bexx)) E R4,,,
(22)
where 6x represents the parameters of the text encoder, and e is the resulting text embedding at timestamp t.
Since the text embeddings are typically close in the embedding space, leading similar cosine similarity values, we normalize the embeddings by centering them around their mean to improve numerical stability and enhance sensitivity differences. Specifically, we compute the mean embedding:
emean
e
(23)
T
and shift all embeddings by subtracting the mean:
e e Cmeans
(24)
where of represents the centered (shifted) embeddings.
Next, compute the average text similarity for each lag l E [1,7 1} as:
Sim(k
sim(e', e(+x).
(25)
T-k
where sim(e), e(+x) denotes the similarity measure (e.g., cosine similarity) between the centered embeddings at time t and + k, defined as:
c. 6/
sim(e,, e(+x))
(26)
||< [T</|lll//+.11
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We visualize the lag similarity of paired texts, Sim(k), in Figure 6, subfigure 3 Subsequently, stabilize the data by applying first-order differentiation and perform a Fourier Transform, following a similar process previously described for the time series frequency analysis. The final visualization of the amplitude spectrum of the paired texts is presented in Figure 6, subfigure A
Then, compute the frequencies with the top-l amplitudes from the lag similarity Sim(k). We apply the Fourier Transform to Sim(
Frex(() Σ
12mft
(27)
where f is the frequency, and Ff) represents the complex Fourier coefficients corresponding to each frequency f.
Next, we compute the amplitude spectrum as:
[Feu(f)== / ((e(F (f(Fiex()))²
(28)
where (e)Fiet(f)) and Im(Fiex(()) the real and imaginary parts of (f), respectively.
We then identify the top-l dominant frequencies by selecting the frequencies corresponding to the largest amplitudes:
Fop (G [fie among the top-l largest amplitudes).
(29)
These top-/ frequencies represent the most significant periodic components of the paired texts, revealing their dominant temporal patterns. we overlay the top-/ (in the Economy dataset I=4) frequencies of the paired texts onto the amplitude spectrum of the time series, as illustrated in Figure 6, subfigure 5
We also visualize the frequency analysis process in the Social Good dataset and Traffic dataset respectively in Figure 7 and Figure 8.
3
Cimilrrty Concument SocaaGoed
Computa Avarage Text Similaity Each
TUNE D.GD MC
To Ber
Time Concurrent Texts
300
200
30
500
Stabilization, Fourier Traistorm and Nor-Maximum Suporession
Stabilization Fourier Transfor
Are cate Sp leve Servic: alooodl
Ampiiaale Spectrar of Coecurent butt: socillood
Ny
Mark Texts' Top Amplitudd Frequencies Time Series Spectrum
Figure 7: Illustration of the frequency analysis process for time series with paired texts in the Social Good dataset. In Step 5 overlay the top-9 frequencies of paired texts onto the time series amplitude spectrum.
A.1 ESTIMATION STABILITY OF TT- WASSERSTEIN
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025
Compute Average Text Similarity for Each Lag k
Time Series with Concurrent Texts
300
200
500
Stablizzaton, Fourter Transform and Maximam Suppression
Stablizztton and Founerr Transtorm
5
Arpiituuee Spectuur Time Tafic
Spectru Doneurent Todts
03-
02
5O
Top-Ampinude Frequencies Time Series Spectrum
Figure 8: Illustration of the frequency analysis process for time series with paired texts in the Traffic dataset. In Step a we overlay the top-7 frequencies of paired texts onto the time series amplitude spectrum.
As TT-Sssserstein is an empirically estimated statistical metric, we provide detailed sensitivity and robustness analysis in this appendix. Our default configuration uses a rectangular window, & e--normalization of spectral amplitudes, and frequency grid determined by the full length of the time series (native FFT resolution). To assess the stability of TTTT-assersteein we perform ablations that vary each of these components: windowing schemes, normalization strategies, and frequency resolutions, while keeping all other settings fixed. The results are summarized in Table 10, where each row reflects the effect of a single deviation from the default configuration. From the results, our TT-Wasserstein is stable across various configuration choices. We also implemented block bootstrap with a bootstrap sample size 10 for time series and texts to compute the confidence intervals for the default settings in Table 11.
Table 10: Wassessennn measure of Time-MMD (Liu et al., 2024a) datasets. Our TT- Wasserstein is generally stable on different frequency computation configurations.
Dataset
Asriculure
Clinase
Ecosomy
Montlyy
Sampled
Security
Social Good
Tratlic
Woekly Sumpled Energy
Health
Daily Sumpled Eavinoament
Defoolt
0.026
0.025
0.022
0.049
0.027
0.035
0.307
0.233
0.302
Ham: Window
0.081
[1029
0.016
0.041
0.040
0.057
0.304
0.243
0.306
Hamming Window
0.064
0.055
0.016
0.04]
0.037
0.966
0.305
0.242
0.305
Blockman Window
0.061
0.029
0.000
0.036
0.043
0.85
0.297
0.245
0.296
Minnus Nonuaization
0.032
B.035
0.025
0.043
0.031
0.049
0.345
0.201
0.332
Log Nomulization
0,016
81000
0.066
0.049
0.050
0.048
0.267
0.170
0.286
Zero podded frequency resolation (2x)
0,046
0.058
0.52
0.051
0.028
0.050
0.200
0.187
0.292
Dewn-smplod frequency resoutionn ()))
0.011
0.026
0.039
0.090
0.051
0.025
0.250
0.197
0.298
Table 11: Standard deviation of default TT- TT-Ssssersteiin measure of Time-MMD (Liu et al., 2024a)
datasets by block bootstrap.
Moothly Sampled
Weekly Sampled Energy
Daily Sampled
Dataset
Agriculture
Climate
Economy
Security
Social Good
Traffic
Health
Favironment
Default
40.06
+0.04
+0.03
+0.03
+0.04
+0.06
+0.21
40.16
+0012
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B FURTHER DISCUSSION
B.1 CONCURRENT WORKS
We discuss concurrent preprints available online that relate to this research, providing a comprehensive understanding of existing works and ongoing efforts to integrate texts into time series modeling.
more
(Williams et al., 2024) introduces benchmark (CiK) for time-series forecasting that integrates both numerical data and textual context. While both (Williams et al., 2024) and our work emphasize the integration of textual context into time series forecasting, the textual contexts in (Williams et al., 2024) are descriptions regarding the time series itself, but in our work, we do not have such a constraint.
(Kim et al., 2024) develops hybrid forecaster that jointly predicts both time series and textual data by projecting time series to the language space and fine-tuning the pre-trained LLM. Their assumption is that though LLMs originally for language but not for time series, they be fine-tuned to adapt to time series.
(Zhang al., 2024a) introduces a dual-adapter model for time series and textual data, but their data format is similar to (Wang et al., 2025), where the whole time series is paired with one text.
(Xie et al., 2024) proposes novel multimodal LLM framework (T'S-MLLMM that treats time series as modality akin to images. But they are using synthetic generation and focus on NLP tasks rather than time series forecasting.
Comparison with Concurrent Multimodal Time Series Forecasting Methods. Several concurrent works also explore incorporating multimodal information to enhance time series forecasting and report results on the Time-MMD benchmark (Liu et al., 2024a). TFHTS (Zhou et al., 2025) adopts a dual-tower architecture to fuse time series and textual signals, followed by large language models for forecasting. MCD-TSF (Su et al., 2025a) proposes a multimodal-conditione adaptively aligns textual context with temporal dynamics. TeR-TSF (Su al., 2025b) introduces text reinforcement, generating augmented textual descriptions improve downstream prediction.
diffusion model that
For a fair comparison, we follow their evaluation protocol and exclude datasets that exhibit substantial performance gaps, suggesting that their preprocessing pipelines may differ from ours. we report aver- aged performance over prediction lengths 6, 12, and 18 for wonthly-frequence datasets (Agriculture, Climate, Social Good); 12, 24, and 36 for rrekkl-ffreqeenc datasets (Energy, Hcalth); and 48, 96, and 192 for the daily-frequency Environment dataset. Note that, unlike our main experiments, we use historical window of 36 steps for monthly, 96 for weekly, and 192 for daily datasets. The results are summarized in Table 12. From the results, TaTS achieves the best or second- best performance on out of the 12 metrics. To provide an overall comparison, we compute an average ranking as follows: for each dataset, we assign each method a rank from I to 4 for both MSE and MAE (with lower values indicating better performance), average the two ranks to obtain a per-dataset score, and then average these scores across all datasets. Under this ranking scheme, TaTS obtains the smallest average ranking, indicating the best overall performance among concurrent multimodal time series forecasting methods.
B.2 LIMITATIONS
This work focuses on revealing and quantifying Chronological Textual Resonance (CTR) and de- signing the TaTS framework to leverage it. However, several limitations remain. First, we do not thoroughly investigate the data construction processes that may induce CTR, such biases introduced during text collection or the choice of contextual information. Understanding how these factors affect CTR would provide deeper insights into the robustness and generalizability of our approach. Second, we do not analyze how text embeddings are utilized at the neural level within the TaTS framework. more detailed study on how the model learns temporal patterns from paired texts could inform improvements in architecture design. Third, the effectiveness of TaTS is influenced by the quality and relevance of paired texts. While we study cases where texts are randomly shuffled, real-world texts could have different patterns, and the model's performance may degrade. Future work could explore methods to assess and enhance text quality or develop more robust models to handle noisy input. Lastly, while TaTS demonstrates strong empirical performance across benchmark datasets,
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Table 12: TaTS compared with several concurrent works that have been evaluated Time-MMD. We use the reported performance in the concurrent works for comparison. Best results are bolded and second-best best results are underlined. Full results in Table 28.
TaTS (Ours)
TEHTS (2025)
MCD-TSF (2025a)
TeR-TSF (2025b)
Methods
iTransformer
Datasets
MSE
MAE
MSE
MAE
MSE
MAB
MSE
MAE
Agriculture
0.201
0.321
0.571
0.564
0.222
0.322
0.338
0.402
Time-MMD:
Climate
1.227
0.890
1.782
0.948
1.583
0.971
1.348
0.874
Multimodal
Energy
0.214
0.321
0.290
0.403
0.153
0.293
0.202
0.324
Time Series
Environment
0.267
0.374
0.262
0.368
0.275
0.379
0.251
0.346
(2024a)
Health
1.372
0.763
1.514
0.809
1.496
0.811
1.384
0.756
Social Good
1.146
0.558
1.352
0.677
1.035
0.569
1.199
0.587
Average Ranking
1.83
3.5
2.58
2.08
its generalization to other types of multimodal time series or domains with fundamentally different patterns remains untested, for example, time series with paired images audio. We leave these investigations and improvements for future work.
Regarding our third limitation on text quality, we briefly clarify how TaTS may adapt under imperfect textual inputs. When texts are missing at some timestamps, TaTS can simply use placeholder token (e.g., "no information available"), as validated in our text-random-drop ablations. When temporal alignment is uncertain, small lead-lag shifts mainly affect phase rather than frequency, so 'aTSS can still leverage the preserved periodic structure. For larger misalignments, standard preprocessing alignment methods may be applied, with TT- Wassereert serving diagnostic guide how strongly to rely on the text modality.
B.3 ETHICAL IMPACT STATEMENT
Our work solely focused on the technical challenge multimodal time series and does involve any elements that could pose ethical risks.
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C ALGORITHMS
C.I PSEUDO CODE
Algorithm 1: Texts Time Series for Forecasting Task
Input: Time series with concurrent texts embeddings
D (X {x1, X2.... XN E {e1,e2 (., }} in the input training dataset;
prediction length H.
Output: TaTS model parameters θ ( forecass: MLP).
1 Prepare training samples of sequence length L and prediction length // as:
[X +11,+ E + Y XU
Initialize time series model F(; Oroeccas): projector MI.P(:; (MIP) for dimensionality reduction.
2 while not converged do for each training sample (X E Y do
Map ((a) 0 Z 7 [
MLP(E [j: MLPP)
Compute = X (i); (z) Jdim=i as shown in Eq. (6).
Forecast: X (4) F(U; (rorccast) N
Optimize: arg ming= (0onson: (MLLP) Liorecast X (1), (1) as shown Eq. (8)
7
8 return TaTS model parameters θ =f {froreastt 0MLP}
Algorithm 2: Texts as Time Series for Imputation Task
Input: Time series with concurrent text embeddings
D == {X- {x,, X XN E {ei, . eT}} in the input training dataset;
binary mask M E [0, 1]TXX
Output: TaTS model parameters θ {9 (MLP).
1 Prepare training samples with observed entries:
X ( X1, +11 E
E L. M M,
Initialize time series imputation model (-; 0iipuue): projector MLP(:; (MLP) for dimensionality reduction.
2 while not converged do
3 for each training sample (X (
O do 7 [ MLP(E(() []: (MLP))
E())
Map E+) to Z Z
Construct the augmented input: U (x(() )
@ M (Z) Jdim=1
Impute missing values: X Imputed(()
(UU 0Impute)
Optimize: arg ming (8mmue Asar) Limpute (X X (mppttd(
8 return TaTS model parameters = {Oumpuee OMLP)
C.2 INCREMENTAL COMPLEXITY INTRODUCED BY THE TEXT MODALITY
As analyzed in Section 5.2, incorporating textual information introduces some additional computa- tional overhead. This overhead arises from two components: (1) the cost of encoding the text tokens, and (2) the cost of training the forecasting model on the augmented input. We have empirically evaluated the latter in Section 5.2: here, provide theoretical analysis of the former.
Let the language encoder process each token in time (froken)) and let each timestamp have an associated text description with an average length of / tokens. If the time series contains T timestamps, then the total time complexity for embedding all paired texts is:
O 1 T).
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This follows because each of the T timestamps requires encoding, average, 1 tokens, and each token requires (fookea) time to process. In practice, from our experiments reported in Table 13, this cost is modest for lightweight text encoders (c.g., small Transformers MLP--based tokenizers), and the embedding step is performed only once per dataset rather than per training iteration. As a result, the added modality introduces only manageable overhead relative the overall cost of training modern time-series forecasting models.
Table 13: Wall-clock costs (seconds) to embed texts for Time-MMD (Liu et al., 2024a) datasets.
Monthly Sampled
Weekly Sampled Health
Daily Sampled Environient
Agriculture
Climate
Ecanomy
Security
Social Good
Traffic
Energy
BERT
0.12
0.21
0.23
0.23
1.7
0.21
0.26
0.46
0.29
GPT-2 LLaMA-2-7B
0.18
0.25
0,31
0.28
2.5
0.30
0.28
0.55
0.35
0.28
0.29
0.37
0.32
0.42
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Agrcuuture
Time Seriec: Climate
Timee Seriess: Scoroayy
7.0
4.0
220
200
1000000
100
100
2.5
-0000
2.0
120
1.5
230000
320
200
300
400
300
100
200
3003
400
502
2,30
Tinesturry
(a) Agriculture
(b) Climate
Economy
Series:
Time Ser les, Eirs romment
252
2000 4000
5000 B000
600
1000
1000
(d) Energy
(c) Environment
Health
Time Sories; Security
Time Seriies: Sociallood
2.00
300000
12-
275007
1.25
10-
1.00
150008
0.5
120468
50
300
120
200
252
302
200
200
4000
800
1000CE
Eiecstomp
Timeertinc
(g) Security
(h) Social Good
ii) Traffic
Figure Visualization of the numerical data in each multimodal time series dataset.
D EXPERIMENT DETAILS
D.1 DATASET STATISTICS AND DETAILS
Table 14, Table 15 and Table 16 provide summaries of the statistics for the publicly available real- world datasets, Additionally, we visualize the numerical data for each Time-MMD multimodal time series dataset in Figure 9. For further details, please refer to the original work that introduced these datasets and benchmarks (Liu et al., 2024a).
Table 14:
Overview of the numerical data in the Time-MMD datasets (Liu al., 2024a). "Prediction Length" refers to the number of future time points to be forecasted, with each dataset including four distinct prediction settings. refers the number variables (or variates) each dataset.
Dataset Name/Demain
Prediction Length
Dimension
Frequency
Number Samples
Timespan
Agriculture
12
Monthly
Present
Climate
G. 8, 10, 12
5
Monthly
496
1983
Present
Economy
8, 10, 12
3
Monthly
423
1989
Present
Energy
{12, 24. 36, 48)
9
Weekly
1479
Present
Environment
(48, 192, 336)
Duily
11102
1982
2023
Health
{12, 24, 36, 48)
11
Weekly
1389
1997
Present
Security
(6, 10, 12)
Monthly
297
1999
Present
Social Good
6. 12
Monthly
Present
Traffic
6. 10, 12)
Monthly
531
1980
Present
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Table 15: Overview the numerical data the FNSPID (Financial News and Stock Price Integration Dataset) datasets (Dong et al., 2024). "Prediction Length" refers to the number of future time points be forecasted, with each dataset including four distinct prediction settings. refers the number of variables (or variates) in each dataset.
Company/Stock Name
Prediction Length
Dimension
Frequency
Number of Sumples
Timespun
Delta Airlines (DAL)
[6. 8, 10, 12)
Bi-daily
1358
- 2020
IBM (IBM)
6, 10, 12
Bi-daily
493
2016 2020
JPMorgun Chase (JPM)
8. 10, 12)
Bi-daily
2018 2020
NVIDIA (NVDA)
8. 10, 12)
Bi-daily
1203
2011-2020
Pfizer (PFE)
8. 10, 12)
Bi-daily
812
2016-2020
Tesla (TSLA)
8, 10, 12)
Bi-daily
294
2019 2020
Table 16: Overview of the numerical data the FNF (From News to Forecast) datasets (Wang et al., 2024b). "Prediction Length" refers to the number of future time points to be forecasted, with each dataset including four distinct prediction settings. refers to the number of variables (or variates) in each dataset.
Dataset Name/Domain
Prediction Length
Dimension
Frequency
Number Samples
Timespan
Bitcoin Price
(6. 8, 10, 12) (6. 8, 10, 12]
1
Daily
1237
2021
Web Traffic
1
Daily Daily
728
2015 2016
Electricity Demand
(6. 8, 10, 12]
1
1097
2019 2021
D.2 HYPERPARAMETERS
We use Adam optimizer (Kingma & Ba, 2015) when training the neural networks. The default choices of hyperparameters in code are provided in Table 17. For LLM-based text encoders, initialize them using the default configurations provided by Hugging Face!. Consistent with existing works (Wu et al., 2023a; Liu al., 2024c), we apply instance normalization to standardize the time series data within each dataset.
D.3 METRICS
Throughout this paper, we use the following metrics to evaluate performance:
MSE (Mean Squared Error): Measures the average squared difference between the predicted and actual values. It penalizes larger errors more heavily, making it sensitive to outliers.
22
MSE
tus
(30)
where y and ÿJ denote the ground truth and predicted values, respectively, and n is the number of data points.
MAE (Mean Absolute Error): Represents the average absolute difference between the predicted and actual values, providing more interpretable measure of average error magnitude.
1
MAE
ys
(31)
RMSE (Root Mean Squared Error): The square root of MSE, which provides an error measure in the same units as the original data. It is more sensitive large deviations than MAE.
1
RMSE
(ui 0.)
(32)
i=1
anttss:///igiiigggfae.oo//
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Table 17: Default hyperparameters for the TaTS framework
Hyperparameter
Description
Value or Choices
batch_size
The batch size for training
32
criterion
The criterion for calculating loss
Mean Square Error (MSE)
learning-rate
The learning rate for the optimizer
{0.0001. 0.00005, 0.00001)
seq len
Input sequence length
24
label len
Start token length for prediction
12
prior_weight
Weight for prior combination
{0. 0.1, 0.2, 0.3, 0.5)
train_epochs
Number of training epochs Early stopping patience
50
patience
text_emb
Dimension of text embeddings
{6, 12, 24)
learning.rate's
Learning rate for MLP layers Pooling type for embeddings
{0.005, 0.01, 0.02, 0.05}
p type
"avg"
init method
Initialization method for combined weights
"normal"
dropout
dropout
0.1
usc_norm
whether to use normalize
True
MAPE (Mean Absolute Percentage Error): Expresses errors as percentage of the actual values, offering scale-independent metric that facilitates comparisons across datasets.
yb
U1
MAPE
x 100.
(33)
n
MSPE (Mean Squared Percentage Error): Similar to MAPE but squares the percentage error, penaliz- ing larger percentage deviations more heavily.
y1
y4
MSPE
(34)
72
y1
These metrics collectively provide comprehensive evaluation of model performance, capturing both absolute and relative errors as well as their sensitivity to outliers. For all metrics, lower values indicate better performance.
D.4 IMPLEMENTATION DETAILS
D.4.1 CODE AND REPRODUCIBILITY
The code for the experiments included in the supplementary material, accompanied by comprehen- sive README file. We provide detailed commands, scripts, and instructions to facilitate running the code. Additionally, the datasets used in the experiments are provided in the supplementary material CSV files.
D.4.2 HARDWARE AND ENVIRONMENT
We conducted all experiments on an Ubuntu 22.04 machine equipped with an Intel(R) Xeon(R) Gold 6240R CPU @ 2.40GHz, 1.5TB of RAM, and 32GB NVIDIA V100 GPU. The CUDA version used was 12.4. All algorithms were implemented in Python (version 3. 1111.. To run our code, users must install several commonly used libraries, including pandas, scikit-learn, patool, tqdm, sktime, matplotlib, transformers, and others. Detailed installation instructions can be found in the README file within the code directory. We have optimized that the CPU memory usage remains below 16 GB, while the GPU memory usage is under 20 GB. Additionally, the execution time for single experiment is less than 10 minutes
code to ensure efficiency. Our tests confirmed
machine.
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D.4.3 DATA SPLITTING AND LEAKAGE PREVENTION
To ensure forecasting without access contemporaneous future information, we adopt chronolog- ical data-splitinng protocol for all datasets. Timestamps are divided into 80% training, 10% validation, and 10% test windows without shuffling. For a forecast at timestamp T, the model receives only time-series values and textual inputs with timestamps I T - 1, while all inputs with timestamps 2 T are masked during prediction.
Timestamp Alignment of Texts. All datasets provide pre-aligned text-time-series pairs by asso- ciating each text sample with the timestamp at which it originally became publicly available (e.g.. publication release time). We directly adopt these timestamps, ensuring that the textual inputs available to the model at time T correctly reflect real-time accessibility.
Auditing for Retrospective Leakage. Although we do not apply automated filtering procedures, we conduct human audits on random subsets of samples from each dataset to detect retrospective or cutcome-summarizae
leakage (e.g.. texts describing events that occur after the associated timestamp). Across all datasets, we did not observe such leakage. Combined with causal masking, this protocol prevents the models from accessing contemporaneous or future information from either modality.
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E FULL EXPERIMENT RESULTS
E.
WHY SHOULD WE LEVERAGE CTR?
Table I8:
Performance on time series forecasting task. Leveraging periodicity with single-dimension feature can significantly reduce the prediction error.
Economy
Social Good
Traffic
Method
MSE())
MAE())
MSE())
MAE(J)
MSE())
MAE(J)
Uniformly Random (+)
5,673
2.356
2.059
1.230
1.207
0.995
Uniformly Random (+)
11.535
2.879
8,860
2.404
3.794
1.618
Normally Random
9.284
2.878
2.926
1.374
3.163
1.511
Exponentially Random
4.521
1.960
3.724
1.564
1.141
0.911
Using 1D Text only
1.995
1.404
1.315
0.853
0.714
0.797
Parallel text provides complementary information and expert knowledge that can significantly enhance the understanding of time series data. To demonstrate the benefits of utilizing periodicity in the text modality, we present an illustrative example in the univariate forecasting task, where the goal is to use X {x1} E RTxx to predict the next H values, X H. We first concatenate the text embeddings to form E = [e : E Rd XT' then replace x with only the first dimension of the text embeddings to leverage very partial text periodicity, x :]] IR In other words, we rely solely on a single evolving dimension of the paired text features to forecast future time series values.
As shown in Table 18, leveraging just the periodicity of a single text feature significantly outperforms random time series forecasting. The random baselines mean that the forecasts purely random according to several different distributions. These random baselines use the training data as well, for example, normally random computes the mean and standard deviation of a normal distribution to forecast the time series. These results highlight that even partial periodicity from the text modality contributes valuable insights for improving forecasting accuracy.
E.2 FULL FORECASTING PERFORMANCE COMPARISON VISUALIZATION
To provide comprehensive comparison of different frameworks for modeling time series with paired texts, we visualize the forecasting performance using radar plots in Figure E.2. Each subfigure corresponds dataset, with each axis representing different time series model. The axes inverted, where values closer to the center indicate worse performance, and larger areas signify better results. The results demonstrate that TaTS consistently outperforms both baselines across all datasets while maintaining compatibility with various time series models.
E.3 FULL FORECASTING RESULTS
Due to space limitations, we provide the full results of the time series forecasting task on paired time series and text in the appendix. We conduct extensive experiments across 9 datasets using existing time series models, evaluating various prediction lengths as detailed in Table 14. The complete results presented from Table 19 to Table 27. Overall, TaTS consistently achieves the best performance across all datasets, time series models, and prediction lengths. The averaged results across all prediction lengths summarized in the main text (Table 2). For better readability, also visualize the performance of different frameworks using radar plots, as detailed in Appendix E.2 and Figure 10.
32

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Published as a conference paper at ICLR 2026
Nean Square Enor! 11] an Agr apriculture Dataset
Moan Square Error (4 Climate Dataset
Mean Square Eraor (1) Ecenomyy Dataset
Goootomer
Grosdormer
Croscfomer
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CLineze
Dunea:
PechTTTT
RED
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Werrffomer
sfommer
RUM
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Iovettmee
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Covetommer
Dinear
NOTTTT
AUZI
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Mean Square Eiror Social Good Untsset
Newn Square traffic Ustaset
Grosfomer
Gros/ormer
Crosslemmrr
Biinwer
PANGTST
RechTST
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REDremeer
FEDeommer
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Figure 10: Comparison of different frameworks for modeling time series with paired texts. Our TaTS achieves the best performance across all datasets and is compatible with various existing time series models.
33

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Published as a conference paper at ICLR 2026
Table 19: Full forecasting results for the Agriculture, Climate, and Economy datasets using iTrans- former, PatchTST, and Crossformer as time series models. Compared to numerical-only unimodal modeling and MM-TSFLib, our TaTS framework seamlessly enhances existing time series models to effectively handle time series with concurrent texts. Avg: the average results across all prediction lengths.
Models
iTransforac (20214)
PachTST (20223)
Crosfommet (2023)
Metheol
MSB
MAR
RMSE
MAPE
MSP6
MSF
MAR
RMSE
MAPS
MSPE
MSF
MAR
RMSR
MAPE:
MSPF
01:274
0.000
0.014
0.197
0.269
0.090
0.014
0.222
0.331
0:412
0.315
0.300
0.017
0.234
0,317
0.104
3.018
0.304
0.406
0.496
Uni modal
0.273
0.372
0.119
0.024
0.262
0.357
0.112
0.357
0.435
0.550
0.301
0.128
0.025
0,294
0.396
0.582
0.251
0,340
0.009
0.120
0.247
0.335
0.020
0.323
0.406
0.505
0,044
0,000
0.189
0.261
0:065
0.015
0.011
0,183
0.251
0.082
0.012
0.145
0.259
0.351
0,005
0:000
Agricultuee
0:001
0.212
0.296
0.063
0.015
0.093
0.212
0.296
0.091
0.015
0.171
0.278
0.354
0.112
0,02
MM-TSFF.b
0,150
0.248
0.346
0.105
0.019
0.176
0.251
0.344
0.108
0.030
0.352
0.344
0.428
0.396
0.02
0.158
0.207
0.375
0.112
0.002
0.168
0,788
0.991
0.119
0.074
0.
0.372
0.47)
0.144
0.086
Avg
0,312
0.230
0,320
0,099
0,018
0.114
0.235
0.323
0.100
0.018
0.215
0.313
0.396
0.124
0.027
0.067
0.184
0.256
0.063
0.012
0.066
0.171
0.247
0.076
0.011
0.348
0.264
0.352
0.105
0.000
0,094
0.210
0.297
0.091
0,015
D.196
0.217
0.300
0.094
0.016
0.197
0.296
0.374
0.119
0.025
TaIS (ours)
10
0,122
0.251
0.34]
0,109
0.000
0.126
0.360
0.349
0.113
0.021
0.215
0.315
0.397
0.124
0.025
12
0.153
0.271
0,374
0.112
0.022
0.166
0.292
0.594
0.123
0.025
0.289
0.371
0.465
0.145
0.035
Avg
00,009
(1:220
0.317
0.099
0.017
0.114
0.235
0.333
0.101
0.018
0:212
0.312
0.393
0.134
0.027
1.127
0.843
1,62
2.549
50,662
1.250
0.915
1.122
3.168
105 890
1.189
0.852
1.966
5.005
148.540
1:191
0.876
1.88
1:306
134 900
1,208
0.678
1.099
2.778
64. 64.950
1.104
0.879
1081
2
123 23.96
Uni-medd
10
1,215
01885
1.100
1.169
193.766
1,218
0.894
1.103
2.746
55.811
1.127
0.830
1007
3.346
19% 108
12
1,199
0.870
1.091
2.752
65.016
1.197
0.891
1.092
3.177
115.67
1.305
0.837
1104
3.322
194 844
Avg
1.385
0.871
1,083
2,920
93.685
1.230
0.895
1.104
2.967
85.572
1.124
0.837
1.055
3,051
165.195
1.011
0.767
1,013
2.396
18 169
1.003
0,800
1.001
2.650
57, 57,009
0.995
0.758
0.995
51.33
Climate
1,009
0.800
3.598
0.700
2.580
47
27-258
0.773
1.077
107 865
MM-TSFL.b
1,040
0.17
3.547
55.014
0.81%
1.016
2.291
28.004
0.999
0.779
0.997
05
1,057
0.828
2.504
$7.976
0.822
1.032
2.965
95.248
0.097
0.777
0.994
43.068
Aeg
1:046
0.810
1.019
2.584
57,821
1.030
0.805
1.014
56.027
1.002
0.772
0.99%
74
0.797
1,007
2.563
0.782
33.843
0.924
0.747
0.963
L,025
0.797
1.013
2.291
39.756
0.503
0.997
2.574
57.629
0,923
0.757
0.961
51
TaIS (ours)
0.808
1.014
2.647
77.647
0.796
1.007
2,057
76-257
0,963
0.764
0.979
1,003
0.812
1.013
2,007
59,107
0.810
42.571
0,943
0.754
0.967
40
Aeg
2.553
57.602
57.560
D.967
0.104
0.119
0.805
0.104
0.008
Uni-modal
0.104
0.130
0.854
0.109
0.135
0.912
0.922
0,014
0.096
0.119
0.004
0.105
0.131
0.828
0.864
0,011
0.081
0.103
0.028
0.054
0.118
0.209
0.420
0.450
Econome
0.085
0.105
0.029
0:001
0.099
0.125
0.114
0.424
0.456
MM TSEL.b
0,012
0.090)
0.110
0.01
0:001
0.091
0.115
0.277
0.463
0.522
0,012
0.090)
0.110
0.001
0,089
0.99
0.526
0.540
0,080
0.04
Avg
0:011
0.086
0.107
0.080
0.001
0.014
0.095
0.130
0.033
0,000
0.250
0.458
0.492
0.156
0.029
0:008
0.077
0,090
0.007
0:001
0.00
0,500
0.097
0.021
0.001
0.180
0.312
0.367
0,105
0,015
0:008
0.077
0,090
0.007
0:001
0006
0.075
0.091
0.027
0001
0212
0.426
0.454
0.145
0.024
TaTS (ours)
0:005
0.079
0,093
0:007
0:001
0.06
0.079
0.092
0022
0001
1200
0.510
0.594
0.174
0004
12
0:008
0.676
0.29]
0.006
0:001
0.009
0.300
0.086
0.024
0.001
0222
0.428
0.466
0.143
0.255
AAg
0:008
0.077
0,09]
0.027
0:001
0.006
0.079
0.094
0.028
0.001
0:319
0.419
0.458
0,042
0:025
34

---

Published as a conference paper at ICLR 2026
Table 20: Full forecasting results for the Energy, Environment, and Health datasets using iTransformer, PSt and Crossformer as time series models. Compared to numerical-only unimodal modeling and MM- our TaTS framework seamlessly enhances existing time series models to effectively handle time series with concurrent texts. Avg: the average results across all prediction lengths.
PachIST (2023)
Croedlencer (2023)
(2024c)
Method
MAE
RMSE
MAPE
MIPPE
MSE
MAPE
MSPE
MAE
RMSE
MAPE
MSPE
12
0.112
0.225
0.315
0.940
10.877
0.105
0.229
0.301
1.129
40.016
0.138
0.262
0.318
1.121
31.808
24
0.222
0.352
0-458
1.626
15.711
0.341
0.3611
0:456
1.507
41.679
0:281
0.399
0.682
1.619
46.00%
Uni-errdal
96
0.306
(1:00)
0.511
1,767
$8.611
0.964
0.408
0.512
1.982
60.250
0:331
0.643
0.541
3,206
679
46
0.435
0.500
0.617
2.454
05:350
0.427
0.502
0.610
2.405
91:255
0:422
0,501
0.676
4,534
547.533
Asg
(0.269
0.375
0.468
1.697
50.112
0.209
0.376
0,470
1.704
58.307
0.293
0,406
0.497
2,652
163.756
12
0.107
0.2.88
0.500
0.905
17:267
0.115
0.242
0.311
1.357
30.719
0.125
0.251
0,326
1.141
30,53
Energy
24
0.225
0.354
0.443
1.692
0.236
0.161
1.505
0:265
0.599
0.472
1.875
69
MM-TSRL
36
0.313
0.434
0.530
0.311
0.518
0.454
0.55%
7.956
48
0.423
0.507
0.615
0.426
0.610
2.404
05.480
0.534
0.617
4.716
415.667
Ang
0.266
0.378
0.469
57,013
0.212
0.473
1.785
$6.455
0.407
0.498
2.672
179.559
1.004
18277
TVTS (muns)
0.512
144
0.500
2.427
0.619
Aug
(0,265
0.376
0.466
0.258
1.681
51,056
0.485
48
0.415
0.473
0.604
2.218
214.067
0.492
0,500
0,584
2:315
25s
0.495
0,509
0.551
2,275
235.000
96
0.439
01491
0..00
2.318
250.5
(3541
0.538
0,693
2.990
256.244
0.562
0.585
0.712
1.580
130830
Uniemndal
192
0.454
01506
0.661
2.460
259.1 311
(.581
0.556
0.741
2.727
156.251
0.567
0.607
0.719
1.699
90.254
396
0.455
0.525
0.671
2.446
276.345
0.993
0.553
0.763
2.39%
434.75 764
0.582
0.621
0.761
1.656
50,409
Ang
[0:44]
0.494
0.641
2.366
250,064
0.552
0.537
0,710
2.583
318.934
0.551
0.581
0.716
1.967
134.326
48
0.413
0.410
0.600
2.157
211 190
0.441
0,489
0,221
1.554
159.971
0.421
0.472
0.604
1.982
161 UN8
Environment
96
0.420
01478
0616
2.253
213.365
[1461
0.495
0.64%
2000
179 555
0.425
0.685
0.677
1.839
125 131
MM-TSRLib ah
192
0.423
(1482
0.666
2.930
A35
(1462
0.508
0.064
2:20%
214.665
0.427
0.405
0.678
1.810
1S5
336
0.429
01483
0.51
2.306
236.965
0.472
0.513
0.683
2:210
220.009
0.434
0.500
0.656
1.867
128
| Aug
[0.42]
0.478
0.626
2.202
222.016
0.459
0.501
0.653
2.307
193.04P
0.427
0,488
0.629
1,879
135.721
48
0.268
0.310
0.450
1,140
21.157
0.211
0.371
0,483
1-115
0:224
0.373
0.635
1.152
20.91
96
0.900
04483
0.279
0.326
0.498
1.176
868
0.901
0.905
1.137
484
TVTS (mun))
23-115
0.222
0.366
0.508
1:315
0.415
0.533
1.019
14.19)
0.261
0.369
0.506
23.437
0.360
0.366
0.516
1.222
25.051
0.431
0.541
1.031
12.754
Avg
0,267
0.369
0.496
21.916
0.233
1.182
21.932
0
0,513
1.087
16.590
0.807
Uni-mndal
0.852
1.819
1.17%
751
0.923
1.313
159.590
1.842
3.392
0.841
1.208
165914
AAgg
0.817
1.175
1.652
3.491
204,832
12
0.987
(1696
0.928
5,354
190.313
1.029
0,710
0,945
3,400
(83.96)
1,017
0.954
0.915
2.786
171.177
Health
24
1,388
(1787
1113
3.457
160.317
1.588
0.760
1.05%
3:307
120.00
1.31%
0.747
1.072
2.917
161 566
MM-TSRLib
96
1.672
(1877
12166
3,74
176
1.460
0.831
11122
3.492
168 807
1.357
0.775
1.113
3,210
492.422
48
1.737
0.900
1.270
3,531
155.300
1.612
0.878
1,231
3.317
827
1.399
0.788
1.146
2.821
149 248
| Aeg
1.446
0.316
1.132
3.499
173.185
1.347
0.797
1,095
3.354
152.159
1.273
0.744
1.066
2.936
168.600
12
0.919
(1649
0.892
2764
118.30
(1900
0.600
0.912
2.721
151. 988
0:974
0.661
0.911
2.838
16% 149
24
1,251
(1712
1053
2.744
112,000
1.968
0.764
1,080
1.164
153.917
1:284
0.241
1.082
3.106
170871
TWTS (nurs)
36
1,489
(178)
1.147
2.855
112.555
1.997
0.780
1.123
2.68%
01.114
1.305
0.741
1.083
2.805
152.713
46
1,581
01834
1.215
2,000
107 107.903
1:456
0.508
1.165
2.623
88.216
1.369
0.770
1.136
2.770
144.765
Aug
1,315
0.744
1,071
2885
117.754
1,253
0.753
1,002
2.837
122.314
1.225
0,728
1.048
2,879
157.874
35

---

Published as a conference paper at ICLR 2026
Table 21: Full forecasting results for the Security, Social Good, and Traffic datasets using iTTrans- former, PatchTST, and Crossformer as time series models. Compared to numerical-only unimodal modeling and MM-TSFLib, our TaTS framework seamlessly enhances existing time series models to effectively handle time series with concurrent texts. Avg: the average results across all prediction lengths.
Models
Teansformer
(30110))
PachTST
(3U71)
Choeforec
Method
MSPE
MSB
RMSE
MSPE
MSE
RMSU:
MAPE
MSPE
113.573
5.095
10.657
5,008
1020.16 167
108.295
5.119
10:430
4.255
$49.239
124.972
6,077
11.179
2.435
113.513
115.878
5.745
10:761
5.973
1035.0 996
113:354
5.534
10.655
1.6R1
434.801
126.511
6.237
11:248
1.909
57. 67.55
Uui modal
10
116-950
5.615
10.514
3.105
352.477
114,200
5.484
10:715
2.523
185 106
127.701
6.345
11,300
1.675
T11642
117.396
10.835
262 602
114.55
5.387
10.689
1.951
112.032
128.686
6.449
11:344
1.484
35.312
Avg
115,370
1.264
482.5 301
105:240
10.452
4.346
500.000 006
125.515
5.55%
11:114
2,771
175 1400
Security
116:158
5,544
10.778
5.742
985 253
113.248
5.445
10,842
3.257
122.655
124.714
6.100
11.168
2.169
126.554
MM-TSFI Jb
10
117.340
6/1
10.853
1,000
170 100
114.109
5.403
10
3.500
619
137-701
6.346
$1.500
1.67%
64
12
116.594
5.548
10.503
2.560
243.369
114.764
5,398
10.713
2.136
165.771
125.985
6.227
11.369
1,310
42 42.745
Avn:
| 116.341
10.796
507.244
112.840
5.309
3,065
311.450
125.729
6.183
11.213
2.032
120,007
106
250.430
122.687
5,915
11.085
2.831
112.560
10,00
345.131
100
10.451
3,082
312.409
124.302
6.067
11.145
2.655
TVTS (oun))
10
113.789
5.227
10.567
2.485
204.306
111.110
5.090
10.541
2.433
205.106
126.203
6.258
11.234
1.725
50.657
13
114,754
5,318
10.713
2,057
140.148
112.699
5.257
10
2.185
171.999
127.261
0.352
11.281
1.433
96.94
Avg
112,054
5.151
10.564
2,851
252.621
109:655
5,019
10,473
2.752
243.001
125.164
6.145
11.187
2.100
116.668
1:047
0.749
1.320
Uni modil
112.00
0.749
75.225
0.916
0.465
0.728
0.709
6.748
0.866
0.559
0.766
1.642
Avg
1,212
01:83
0.700
1.651
105.170
1.007
0.495
0.776
1,500
71.161
0.865
01:67
0.711
1.157
1.051
01451
0.253
1.195
60. 20.
1.055
0.483
0.741
1,333
07.404
0.755
013511
0.004
0.753
5.436
Social
59:283
1:111
0.507
34.723
0.314
0.357
0.615
0.575
5.614
TSFL
65:938
0.520
0.799
1.504
54,594
0.366
0
0.726
1.127
10.642
0.917
Ang
0.500
64.503
0.515
0.797
1.441
50,500
0.837
0.649
0.767
7.145
0142
0.395
0.675
1.221
09.723
01935
0.436
0.723
1.153
15,095
0.711
0.307
0.631
0.749
6,772
0.957
0.433
0.713
1,400
S0.480
0.000
0.66
0.713
1.279
22.919
0.748
0.453
0.646
0.063
7.567
TVTS (ouns)
10
01996
01.03
0.200
1.558
$1,40
01986
0.461
0.776
1.348
43.373
0.800
0.373
0.:5
0.754
5.777
0.514
61.554
1.069
0.501
0.770
1.549
60.142
0.357
0.415
0.663
0.527
7.195
Aug
|
0.465
0.733
36.007
0.815
6.063
0.205
0.228
0.303
0.316
0.905
0.152
0.282
0.377
0.765
0.513
0.227
0.394
0.472
0.340
0.368
0.209
0.236
0.399
0.234
0.523
11167
0.225
0.348
0.255
0.450
0.216
0.382
0.255
0.324
0,333
Unismadal
10
0.211
01.433
0.508
0.220
0.521
0.17%
0.342
0.362
0.200
0.964
0.200
0.365
0.44
0.313
0.327
12
0:231
01246
0.392
0.241
01533
0.226
0.250
0.343
0.300
0.500
0.212
0.305
0.250
0,337
0.3W
Avg
0.215
0,370
0.188
0.243
0.370
0.278
0.502
0.314
0.376
0.455
0.329
0.362
0.165
0.229
0.353
0.248
0.591
0.154
0.335
0.46
0.307
Traffie
0.897
01:855
0.415
(1200
0.901
0.16%
0.315
0.346
0.359
0.53%
0.183
0.511
0.416
01305
0.367
XBM TSFF
10
0.190
0.335
0.423
0.285
0.283
0.174
0.235
0.357
0,252
0.402
0.154
0.331
0.416
0.303
0,363
12
0.232
01.35
0:450
0.331
0440
0221
0.259
0.378
0.761
0.524
0.200
0.540
0-411
0.329
0.427
Avg
[
0.199
01:47
0.:34
0.901
0.30
0.178
0.290
0.399
0.754
0.422
0.183
0.534
0.430
0.313
0.353
0.273
0.162
0.354
0.55
0.389
0.365
TYTS (ouno)
01:225
0.221
01304
01667
0.214
0.340
0351
0.368
0.163
0.285
0.378
0.277
0.366
01212
0.341
0.504
0.300
0.386
0360
0.468
0.184
0.201
0.985
0.595
0.478
Avg
0.187
0.217
0.359
0.227
01361
0.122
0.209
0.341
0.355
0.306
0.168
0.286
0.563
0.281
0.394
36

---

Published as a conference paper at ICLR 2026
Table 22: Full forecasting results for the Agriculture, Climate, and Economy datasets using DLinear, FEDformme, and FiLM as time series models. Compared to numerical-only unimodal modeling and MM-TSFLib, our TaTS framework seamlessly enhances existing time series models to effectively handle time series with concurrent texts. Avg: the average results across all prediction lengths.
Models
DLinee
(3023)
FED (201226)
FIMM (2022c)
Methed
MSB
MAB
RMSB
MAPE
MSPS
MSF
MAB
RMSE
MAPS
MSPE
MSF
MAB
RMSB
MAPE
MSPP
0.135
0.028
0.230
0.801
0.110
0.207
0.200
0.340
0.423
0.145
0.031
0.281
0.355
0.127
0.315
0.230
0.315
Uni-modal
6.218
0.355
0.448
0.150
0.034
0.313
0.392
0.351
0.255
0.353
0.407
0.514
0.165
0.041
0.313
0.415
0.134
0.200
0.333
0.433
Avg
0.138
0.286
0.314
0.219
Agricultree
MM-TSFL.b
0.034
0.275
0.354
0.024
0.258
0.350
0,166
0.311
0.392
0.136
0.028
0.082
0.222
0.246
0,102
0.016
0.067
0.206
0.289
0.09]
0,015
0,192
0.343
0.425
0,146
0.002
0.111
0.256
0.310
0.115
0.030
0.110
0.223
0.312
01.94
0,016
TaTS (oum)
0:215
0.358
0-451
0.152
0.005
0.147
0.288
0.377
0.126
0.025
0.145
01244
0.345
0.100
0.019
0.287
0,392
0.008
0.339
0.418
0.328
0.429
0,214
0:351
0:441
0,149
0.033
0.131
0,276
0.353
0.120
0.023
0.135
0.251
0.344
0,105
0,000
1.158
0.866
1,076
3.462
204.312
1.206
0.909
1,098
4.551
394,050
1,275
0.912
1.129
4,553
410.091
1,391
0.874
1,091
3,400
190.454
1.175
0,597
1.084
3,680
176.964
1.155
0.862
1.076
3.282
162.026
Uni-medil
1,225
0.883
1.107
1.502
185
1.199
0.893
1.095
3,215
134.917
1.160
0.857
1.077
2.182
462217
1,185
0.863
1,080
2.856
100
1.190
0.875
1.091
2,883
99.606
1.487
1.012
1.219
3,593
164.75
Arg
1,190
0.872
1,091
3,277
176.715
1.192
0,593
1,092
3,582
201.417
1,270
0.911
1.125
3.545
196.302
1,006
01822
1,096
2.597
154 862
1.012
0.795
1.006
2.092
59 88.
1.165
0.869
1.779
3.198
236.35
Climase
1.108
0.844
1,88
1.117
160 555
1.003
0.787
1.001
2.265
54, $4.993
1.17%
0.867
1083
5.590
101
MM-TSFL Jb
1.128
08844
1,000
1.335
167. 366
10111
0.810
1.004
2.133
24.004
1.184
0.843
10665
1.545
11 11.99
1,112
0.838
1,054
2.515
116.263
1.019
0.705
1.007
2.521
40.335
1:345
01904
1.116
3.64)
243.644
Avg
1:104
01837
1,000
3,400
149.767
1.011
0.797
1.004
2,301
90.851
1.179
0.871
1086
3.346
170 336
0:505
0.749
0.951
2,005
36,745
0.833
0.748
0.945
1,806
13:94%
0,912
0.758
0955
2.595
82.597
0:926
0.756
0.902
2.055
37,680
0.57
0.771
0L968
1.890
16:022
0.17
0.751
0.557
1,529
26.990
Ta75 (ouns)
10
0:941
0.764
0.971
1.989
34.295
0934
0.751
0.960
1.756
14.296
0,47
0.759
0.722
1.197
10.95
0:950
0.266
0,973
1.958
30.964
0.952
0.770
0.974
1.921
21.544
1,005
0.821
1.003
2.086
68.310
Aeg
0:011
0.750
0.964
1.992
14.044
0.936
0.760
0.963
1.844
16.737
0.945
0.772
0.973
2.305
47:214
0:056
0.189
0:196
0.065
0:006
0.02
0.16%
0.20%
0.058
0.00
0.021
0.115
0.145
0:086
0.191
0:237
0.066
0:006
0.162
0.197
0.056
0.06
0.08
0.165
0/003
Unismodal
0:047
0.173
0.316
0.000
0:006
9.36
0.153
0.158
0.03
0000
0.06
0.134
0.162
0.075
0.216
0.372
0.074
0.009
0.183
0.235
0.063
0.00
0.027
0.133
0.163
Avg
0.192
0,240
0.066
0.007
0.042
0.165
0.203
0.058
00005
0.025
0.129
0.160
Economy
0.194
0.065
0:007
0.170
0.206
0.001
0.177
TSEL.b
0.195
0.008
0,160
0.200
0.160
0.180
0.221
0.062
0,005
0.129
0.157
0.009
0.140
0.170
Aeg
0.153
0.158
0.100
0,021
0.141
0.040
0.002
0.093
0,111
0.050
0.095
0,020
0.115
0.142
0.040
0:022
0,099
0.120
0.04
0.079
0.095
TaTT (ouns)
0,019
0.112
0.157
0.00
0:002
0,106
0.126
0.33
0.079
0.095
0.157
0.044
0:005
0017
0,107
0.129
0.39
0.000
0.095
0.117
0.144
0.041
0:002
0.015
0,101
0.121
0.035
0
0,009
0.080
0.095
37

---

Published as a conference paper at ICLR 2026
Table 23: Full forecasting results for the Energy, Environment, and Health datasets using DLinear, FEDformer, and FiLM as time series models. Compared to numerical-only unimodal modeling and MM-TSFLib, our TaTS framework seamlessly enhances existing time series models to effectively handle time series with concurrent texts. Avg: the average results across all prediction lengths.
Models
DI inccer
(2025)
FEDGomar (2022l)
RILM (2022))
Method
MSB
MAE
RMSE
MAPE
MSPE
MSE
MAE
RMSE
MAPE
MSPE
MIE
MADI
RMSE
MAPE
MSPE
12
0.136
0.335
0.947
10:373
0.212
0.281
0.118
0.334
1.205
25.502
24
0.261
1.453
33.690
0.303
0.385
47.676
0.221
1,414
29,039
Uni modal
36
0,535
1,780
0.373
0,475
0.335
1.852
60,003
48
0.431
2,294
83.856
0.514
0,043
540,071
$9,205
Aug
[02201
(1 1.900
0.483
1,619
46.022
0.340
0.351
0.445
2.194
132
0.278
0.385
0.475
1.722
$0.945
12
0.135
01282
0.312
0.950
10.755
0155
0.227
0.289
1.033
152200
0.119
0.247
0.515
1,202
24.419
Energy
24
(12266
(1 1.9
0.461
1.47%
32.906
0.171
0.90 0.900
0.788
1.425
47.927
0.226
0.349
0.676
1.415
25.417
MM-TSFI.MM 1b
56
0.340
(1:442
0.533
1.90%
56.952
0:353
0.576
0.473
2.120
134.465
0,332
0.431
0.531
1.839
59.454
48
0U428
01:006
0.601
2.787
83.443
0.450
0.511
0.611
2.775
146.406
0.440
0.514
0.625
2,416
80.584
Avg
0.229
0.395
0.482
1,617
45.936
0.238
0.354
0.441
1351
53.465
0.279
0.385
0.476
1.718
50,493
0.112
(.250)
0.310
0.954
0.210
0:275
12,571
0.118
0.245
0.514
1.203
174
0.236
1.359
29.647
0.305
0.387
44,042
0.22
1,410
TaTS (ours)
36
0,340
1.505
57.123
0.372
0.412
142
0.11
0.514
1.773
55.535
0.425
0.597
2.385
84.710
0.531
0.61
0.434
0.688
2,399
V3,002
Aug
012885
1.601
45.6
48
0:478
1.791
119:315
0.543
0.671
0.494
2.323
241.400 494
0.562
1.539
65.455
0.524
0.657
237
2.639
314,062
Uni modal
192
0.592
0.748
1.938
132.178
0.555
0,702
297.619
0.612
0.759
3,001
654
536
0.600
0.618
0.768
1.988
43.
0.551
0.575
0.725
23538
S20-421
0.621
0.566
0.779
2.969
440.319
Avg
[0.558
0.591
0.722
1,501
113.600
0.503
0.549
0.689
2.399
240.927
0.577
0.543
0.722
2.755
364.507
48
0.414
01.814
0.998
1.885
0.413
0,465
0.399
1.857
138
0.669
0.084
0.622
2,046
177. 39.
Envinammnt
96
(1421))
(1.600
0615
1945
113.990
0.413
0.479
DA11
1 1998
198881
0.476
0.491
0.622
1:987
173911
MM-TSFF.JM ib
192.
(1439
(1:21
0.600
1.559
02,050
0.421
0.489
0.85
2.205
107
315
0.477
0.486
0.644
2.135
218-11
336
0.444
0.526
0.664
1,080
95 059
0.445
0.507
0.065
1850
125
600
0.490
0.497
0.696
2,233
243.544
Aug
[.470
0.500
0.61
1.942
110
0.421
0.485
0.624
1.90
147
461
(1478
0.490
0.671
2,100
203.47
48
0.272
1.085
17.000
0.369
0.484
0.269
0
1.034
13731
0.371
0.495
0.279
1,180
TWTS (ours)
192
0,506
1.007
11,494
0.379
0.500
0.271
1,201
336
0,313
0.557
0.996
10.400
0.383
0.524
1.157
18.379
0.307
0.514
1,310
Ava
002298
0.428
1,050
0.375
0.501
21.237
1,179
21.615
12
1,995
2.599
252.012
0.756
0.975
371.454
1.900
6.208
105-818
24
1,778
018355
1.170
1.542
112.139
1.491
0.933
1.166
414 765
1.966
0.913
4.194
322,873
Unismedal
16
1,269
(8.800
1.241
1.718
763.854
1.66
0.980
1.353
5.10
436 708
3,079
1.013
1.352
4.405
546.
48
1.818
08.899
1.289
2.964
976.996
1,300
0.969
1.285
4.775
302 270
3,054
1.026
1.579
4.356
305.151
Avg
1,737
0.848
1.206
2.761
276.733
1.486
0.509
1.172
4.711
406 304
1.982
1.005
1.324
4,813
537.301
12
1.805
1.061
2,055
04.554
0.975
0.885
0.300
5:311
215:283
1,405
0.915
1.141
4.781
421.324
Health
244
1.544
(17822
1.114
1667
68 256
1.173
0.804
1.023
5.588
212.521
1.700
0.915
1.257
4.258
251 997
MM TSFL.b
36
1,600
0.824
1.185
2.264
56.729
1.344
0.525
1.121
3.768
222.549
1.769
0.944
1.267
3.785
205.906
48
1.617
0.830
1.222
2.365
37.198
1.416
0.552
1.163
3.913
243 333
1.793
0.960
1.256
3.626
178,720
Aug
1.541
018000
1.145
2.216
150
1.253
0.793
1,073
3,642
939
1.675
0.949
1.218
4.114
254.486
1,273
0.742
2.702
150.075
0.671
0:925
3.211
3.570
236.057
1.421
3.231
155
0.523
1,080
731
1.414
3.160
130.456
"WI (oum))
7,990
1.164
Avg
1.412
1.108
2,931
187.367
0.791
1,000
252
1,421
3.307
155.245
38

---

Published as a conference paper at ICLR 2026
Table 24: Full forecasting results for the Security, Social Good, and Traffic datasets using DLinear, FEDformer, and FiLM as time series models. Compared to numerical-oni unimodal modeling and MM-TSFLib, our TaTS framework seamlessly enhances existing time series models effectively handle time series with concurrent texts. Avg: the average results across all prediction lengths.
Models
Diiicar
(20123)
FEDNemaz (20022))
FILM (2022))
MAPE
MAB
MAPE
6
107 1966
4.531
10.545
3,889
17A 6:51
112. 106
6.331
TIESAK
4.456
571 AM4)
130
5,597
10.731
5,009
5/71 194
100.700
4.649
10,375
2.992
295.719
113.897
5.250
10.672
3,223
355.929
112.097
5.034
10.588
3,225
336.503
Uniemedal
10
10.458
2:649
316 566
119
9.467
10,809
4.001
10.50
7.110
7011
112.343
4.904
10,599
1,950
149.507
114.452
5.135
10.698
2.697
329.415
122.711
6.425
11:077
3.554
Avx
4.713
2.728
5.156
10,699
3.235
368.373
115.551
5.467
10,748
3,500
106.821
4,545
10.301
3,788
396 715
100.654
4,500
10.451
4.252
$41.658
105 800
4.755
10.286
4,286
525 309
Security
107.445
4.670
10,365
3,101
319.555
114.833
5.235
10.716
3.110
330.374
106.045
4.638
10,394
2.727
249.534
MM-TSSP1bb
10
(10-713
6.756
10.627
2.613
251 13%
115:361
5.296
10.736
2.965
353-253
111.50
111-99
4.565
10.554
1.9%1
137 838
12
109.348
4.876
10.481
2.573
237.123
115.001
5.211
10.724
2.558
291.461
111.541
5.354
10.561
3,023
363.599
Arg
108.052
4.713
10.394
2.060
206 129
113.737
5.107
10.654
3.123
349.177
4.307
10:449
2.997
404
4.004
451
10.367
3,050
107
3.300
371.90
10.376
3,150
310,200
TaT7S
10
108.5115
4.728
10.417
2.632
500055
105
4.885
10.359
3.139
375,000
109
10.453
1.554
193 365
12
109.717
4.836
10.475
2336
234152
106.506
4.837
10.477
2.356
531.710
106.375
4,570
10.410
3.540
367.339
Arg
107.928
4.676
10.589
2.957
300 369
107.375
4.718
10.562
3-450
419.054
107.850
4.5%
10.365
3.015
575
1001
0.671
0819
1.90%
19:200
0.811
0.356
0.649
11800
28.096
1.123
0.004
0.878
2,493
1.137
0.701
1.90
19:288
0.99
0.411
0.736
1061
17:001
1.116
0.542
2:275
Uni moddll
10
1.733
21-257
0.47%
0.754
1.409
1.154
0.501
0.882
1.521
42
76-675
140.38
Avg
1.151
0.712
0915
1.677
20/044
0.979
0.476
0.751
1:375
43,857
1.761
0.654
0.941
7,163
115 116
B19466
0.58
0350
1.581
21,957
0.816
0.395
0,667
1.182
31.545
1.000
0.525
0.834
2.309
199 1I1
Social Good
L005
0.675
0.904
1.596
200006
0.910
0.438
0.717
1,010
15:845
1.120
0.584
0.569
2.154
$5.150
MM TSFLibb
10
1.128
0.709
0.924
1.713
22.953
1902
0.456
0.757
1.355
53.857
1.128
0.539
0.839
2:235
120,885
1.164
0.734
0.40
1.655
20:360
1091
0.560
0.838
1.532
71:467
1.634
0.332
1.111
3/305
Avg
1.601
21.312
1.311
7.412
0,859
0.16
0,240
1.555
29.554
0.246
0.355
0,620
0.95
23.007
0.588
0.854
1.621
115
0.965
0.592
0.82
1.582
20.073
0.550
0.466
0.301
1.231
34,945
1,001
0.550
0.806
1,500
25. 399999
TaTS (ou1s)
10
1.118
0.703
0117
1.711
23.312
01914
0.355
0.730
1.138
25, 25.181
1.00
0.383
0,57
1.407
17 T6.661
13
1.055
0.676
01805
1.657
24.340
0.883
0.455
0.718
1:315
51.284
1.354
0.792
1.005
1,900
27 141
Avg
1,006
01623
0839
1.501
26.567
0.888
0.430
0.690
1.164
34.420
1.104
0.036
0.876
1,500
25 929
0.355
0.332
Uni-modal
10
0.356
0.323
0.995
0.315
1,000
0.240
0.719
Avg
0,230
0.359
0.967
0.366
0.591
0.205
0.254
0.294
0.253
0.478
0.215
0.314
0.431
0,399
0.605
0.204
0.332
0.439
0.321
0.465
0.180
0.245
0.372
0.258
0.408
0.197
0.284
0.419
0.359
0.664
Tramfe
0,202
0:415
0.500
0.178
0.33
0.355
0448
0.139
0.151
0.540
TSFLib
10
0.525
0.520
0.154
0.234
0.364
0.250
0.328
0.312
12
0.529
0.351
0.238
0.247
0.363
0.292
0.500
0.340
0.254
0,403
0.315
0671
0.530
0.525
0.238
0.265
0.300
0.419
0.325
0.184
0.312
0.412
0.301
0.435
0.159
0.258
0.329
0.228
0.355
0.157
0.328
0.351
0.254
0.426
K
01185
1.903
11300
0.93%
0.400
01199
11209
0.333
0.710
0.167
0.760
0.170
0.766
01:00
TaTS (ours)
10
0.184
0.207
0.403
0.309
0.524
0.160
0.206
0.323
0.220
0.700
0.109
0.299
0.580
0.262
0.358
0.199
0.281
0.41%
0.480
0.315
0.934
0.968
0.369
0.51
0.311
0.156
0.181
0.194
0.62
Avg
0.212
0.348
0.270
39

---

Published as a conference paper at ICLR 2026
Table 25: Full forecasting results for the Agriculture, Climate, and Economy datasets using Auto- former, Informer, and Transformer as time series models. Compared to numerical-only unimodal modeling and MM-TSFL our TaTS framework seamlessly enhances existing time series models to effectively handle time series with concurrent texts. Avg: the average results across all prediction lengths.
Model
Autofeener (2021)
Infammer (2021)
Transfomer
Metlad
MSE
MAPE
MSPE
MSE
RMSE
MAPE
MSPE
MSE
MAPE
MSPE
0.109
0.255
0.329
0.116
0.022
0.451
0.557
0.626
0.240
0.671
0.229
0.326
0.420
0,125
0.032
0.135
0.278
0.366
0.126
0.025
0.569
0,635
0.702
0.270
0.087
0.328
0,432
0.502
0,177
0.045
Uti-moddal
10
0.373
0.311
0,413
0.138
0.651
0.618
0.633
0.724
0.263
0.088
0.358
0.422
0.510
0.166
0.045
12
0,213
0.345
0.457
0.149
0.056
0.756
0.498
0.769
0.284
0.301
0.500
0.555
0.633
0.224
0.064
Avg
10,158
0:247
0.391
0,132
0.029
0.559
0
0.710
0.264
0.087
0.354
0.434
0.516
0,175
0.16
0,005
0:221
0.305
0.100
0.018
0.218
0.352
0.422
0.145
0.002
0.197
0.319
0.392
0,125
0.029
Agricaluree
0.145
0.278
0,392
0,122
0.25
0.306
0.429
0.896
0.179
0.046
0.205
0.303
0.381
0,121
0027
MM-TSFFLib
10
0.176
0:311
0.415
0.137
0051
0
0.196
0.460
0.160
0,040
0.215
0.312
0.411
0,135
0050
12
0:217
0 0.344
0.453
0.144
0.044
0.478
0.479
0.579
0.190
0.054
0.378
0.453
0.531
0.179
0048
Avg
[0:158
0.2668
0.587
0.126
0.027
0.313
0,414
0.494
0.169
0,042
0.249
0.352
0.429
0,142
0054
00,776
01.215
0.269
0.892
0.014
0.162
0.265
0.342
0.107
0,022
0.150
0.548
0.387
0.166
0034
0.301
0.234
0.315
0.105
0.019
0.213
0.311
0.392
0.124
0,028
0.192
0.258
0.374
0.120
0025
T:TS (ours)
10
0.338
0.299
0.571
0.134
0.026
0.256
0.388
0.465
0.154
0,038
0.209
0.296
0.384
0.114
0.066
12
0.185
01:24
0.425
0.141
0.000
0.349
0.426
0.506
0.167
0.044
02113
0.310
0.401
0,121
0025
Avx
00:25
0.266
0.345
0.118
0.022
0.255
0.348
0.426
0.135
0.033
0.191
0.313
0.387
0.130
0.025
1.116
0.861
1,066
4,456
519
1.084
0,829
1.041
1.617
15,451
1.052
0.817
1.016
1.656
13.521
1.117
0.356
1,577
3
177.957
1.887
0.529
1.043
2.464
66.852
1.135
0.856
1.065
1,868
21.657
Uni modal
10
1,370
0.386
1,811
3.059
106-07
1.117
0.549
1,056
2.071
49.757
1.103
0.844
1,09
2,355
81.651
1.125
0.855
1,099
3,364
125.779
1.150
0,859
1.071
2.557
96.752
1.100
0.841
1.008
1.663
24.078
Avx
[.151
0.863
1,063
3,552
252.307
1.110
0.541
1.053
2.177
56,698
1.092
0.839
1.044
1,585
33.457
[X021
0.317
1,010
2.871
81.044
1.019
1.000
2.844
134.
0.98
0.771
0.981
2,000
21.677
Climate
1,089
0.819
1.018
3.018
99.283
0.970
0.772
0.985
2.110
43.151
0.911
0.783
0.995
21.312
MM TSFLBb
10
1,074
0.838
1,055
2.783
92.522
1.006
0.796
1.000
2311
67.011
1.026
0.750
1,000
2.755
87.785
1,078
0.836
1,088
2.731
75.154
1.009
0.791
0.959
2.499
36.993
1.011
0.769
1,000
1,855
23.637
Aug
1.053
0.827
1.005
2.851
1.001
0.792
0.919
2.465
$3.026
0.99
0.783
0.995
2.164
40.330
0:580
(.744
0:918
2.233
37.058
0.881
0.9%
2.117
57.260
0.89)
0.738
0.926
1.970
0:997
0.7668
0.068
2.166
0.909
0,953
39.665
0.11
0.955
73.564
T:TS (ours)
1,027
0.817
1.011
2.260
31.511
0.973
0.771
0,963
2,020
27.051
0.976
0.985
2.179
31.999
1.075
2.317
35.133
0.958
1.727
15.480
0.300
0.757
0.960
1,871
23.016
Aug
[0:900
01.89
2.234
0.930
0.962
32.364
0.920
0.957
2.136
41.055
0.083
0.077
0010
0.877
0.806
0.9%0
0.308
0.102
0.276
0.517
0.150
0031
0:069
0.073
0005
1,606
1,260
0.425
0.187
0.766
0.707
0.316
0078
Uni-mnda
0:070
0.072
0006
1,409
0.395
0.362
0.601
0.750
0.768
0,69
0.062
0.345
0.064
0.007
1.407
0.396
0.363
0.781
0.879
0,293
0.911
Aug
[0.07]
0.207
0.071
0.005
1.325
1,110
1.138
0.381
0.153
0.584
0.345
0.243
0,677
0.000
0.006
0.293
0.167
0.110
0.322
0012
Easomyy
0:045
0,000
0.005
0.545
0.220
0,081
0.157
0.389
0,122
0018
MM-TSFFLbb
0.075
0.009
0:227
0.073
0.005
0.518
0.060
0.347
Avg
0.067
0.007
0.632
0:211
0,049
0213
0,142
0.040
0.161
0.29
0003
0,041
0,00
0.166
0.396
0.125
0,018
0.399
0.191
TVTS (ones)
0,01
0.00
0.009
0,046
0.92
0.266
0010
0000
0.501
0.16
0.964
0017
10.004
0.142
0.003
0.174
0.079
0.262
0.000
40

---

Published as a conference paper at ICLR 2026
Table 26: Full forecasting results for the Energy, Environment, and Health datasets using Autoformer, Informer, and Transformer as time series models. Compared numerical-one unimodal modeling and MM-TSFLib, our TaTS framework seamlessly enhances existing time series models to effectively handle time series with concurrent texts. Avg: the average results across all prediction lengths.
Informee (2021)
Trandfoncez (2017)
(2021)
Method
MAE
RMSE
MAPE
M1PP
MSE
MAPE
MSPE
MAE
RMSE
MAPE
MSPE
12
0.161
0.282
0.362
1.403
24.895
0.166
0.289
0,375
1.491
35.911
0.124
0.247
0.520
1,021
3,905
24
0.279
01416
0.500
2.652
158.951
0.248
0.180
0:475
2,915
185.00
0.291
0,405
0.994
1,951
101 556
Uni-errdal
96
0.366
(1464
0.564
2.964
91.988
0.968
0.493
0.585
4.022
156. 146
0:320
0.41%
0.542
1064
478 700
46
0.471
0.550
0.664
3.106
149.3
0.457
0.580
0.640
5.615
599.886
0:445
0.537
0.642
3,804
255.953
Asg
(0.319
0.428
0.525
2.381
106.797
0.309
0.425
0.515
3.511
291.918
0.297
0,405
0,500
2,690
206.256
12
0.166
0.297
0.309
1,220
79.017
0.166
0.291
0.372
1.067
36.440 049
0.121
0.270
0,314
1.278
11.691
Energy
24
0.275
0.407
61:316
0.342
0.363
0.456
31000
0,402
0.491
2.297
115.390 390
MM-TSRL
36
0.454
065
0.342
0.467
0.565
9:221
0.419
0,510
272.91
48
0.477
0.545
0.663
192:317
0.456
5,490
600.775
0.908
0.641
5,501
748.943
Ang
0.,320
0.428
0.525
130.092
0.301
3.340
286.562
0.405
0.499
287.249
0.360
0.145
1:118
TVTS (muns)
0.555
0,515
209
178.191
178.630
0.537
Aug
0.430
0.517
2.857
0.395
0.482
172.953
48
0,505
0.564
0.6.0
1.95
141
0.414
0,481
0,502
2,190
216.476
0.412
0.683
0,600
2,190
214 565
96
0.594
0.605
0.943
2015
135.60
0.467
0.500
0.664
2.484
250858
0.45%
0,511
0.619
2,006
510210
Uniemndal
192
0.667
0.601
0.762
2.169
205.175
(.469
0.519
0.664
2.585
105.217
0.492
0.535
0.677
2:711
404 754
396
0.690
0.643
0.833
2.634
807
0.467
0.520
0,693
2.726
355.026
0.479
0.517
0.688
2.604
589 196
Ang
0..599
0.598
0.749
2.159
197.295
0.459
0.512
0.645
2.476
291,894
0,460
0,511
0.651
2.545
337.171
48
0.642
0.892
0.626
2008
164350
0.419
0,473
0,004
1.997
163.772
0.420
0.471
0,506
2,077
105
Environment
96
0.456
0.508
0.665
1930
154
0.476
0.477
0.15
2.074
177.217
0.426
0.685
0.65
2. 3.500
252.99
MM-TSRLib ih
192
0.461
01505
0666
1995
111
0:435
0.481
0.34
2-40
256-710
0.41%
0.479
0.670
2,556
252.440
336
0.447
0.506
0.666
1.94
172.423
0:427
0.489
0.651
2:083
225
580
0.435
0.457
0.657
2.551
252.514
| Aug
[0.452
0.502
0.650
1992
168.275
0.424
0,480
0.625
2.391
204.770
0.425
0
0.627
2,529
237.790
48
0.274
0.314
0.486
1.159
21,043
0.202
0.483
1.103
18.922
0:265
0.378
0.681
1,004
17.1N1
96
0.286
0.387
0.500
1181
21.118
0.367
0.507
1700
15.666
0.901
0.486
1.088
15
TVTS (mun))
0.382
0.578
0.207
909
0.908
0,512
1,000
0.288
0.403
0.534
20.057
0.256
0.419
0.089
846
0.420
0.534
1.006
15:226
Avg
0,285
0.357
0.514
21.729
0.255
0,405
1.054
15.576
0.397
0.506
1.173
Uni-mndal
390.55
3.541
1.054
1.410
3.445
125.16
Aeg
1.039
1.339
536.286
3,695
427.566
1,091
12
1,331
0.854
1.112
4.437
500
(.997
0.673
0,928
31004
221. 350
0.951
0.686
0.930
3,309
196.15
Health
24
1.454
01858
1158
3681
181
1.300
0.740
1.045
3.372
257
287.237
1.115
0.762
1.071
2.835
197 738
MM-TSRLib
96
1,574
01.06
1.266
4.051
234
1.252
0.760
1,092
3.111
211.531
1.226
0.763
1.070
2.906
197 944
48
1.616
0.911
1.255
3.554
201
1.371
0.765
1.157
3.145
542
1,330
0.750
1.109
2:569
125.761
| Aeg
1.494
0.957
1.175
4.011
280.514
1.215
0.740
1.051
3.163
231,615|
1.215
0.748
1.042
2.954
1500036
12
1,320
(1863
1:105
300 (W)
(1949
0.668
0.910
3,007
191 885
0.909
0.655
0.862
3,251
202 565
24
1.467
(1885
1150
1,465
159.690
1.150
0.736
1,000
1.907
153 660
1.187
0.7%
1.000
3.145
692
TVTS (nurs)
36
1.368
(1825
1.120
3,60
230.000
1.301
0.770
1.110
1.540
270. 559
1.175
0.73
1.048
3,006
193.525
46
1,483
0.871
1.150
4108
279.227
1.354
0.533
1.143
3.002
372. 000
1.297
0.762
1.113
3,074
185.199
Aug
1,409
0.861
1.141
33811
242.784
1.183
0.752
1,045
3.775
346.756
1.342
0,718
1.013
3.141
216.000
41

---

Published as a conference paper at ICLR 2026
Table 27: Full forecasting results for the Security, Social Good, and Traffic datasets using Autoformer, Informer, and Transformer as time series models. Compared to numerical-oni -nly unimodal modeling and MM-TSFLib, our TSTS framework seamlessly enhances existing time series models to effectively handle time series with concurrent texts. Avg: the average results across all prediction lengths.
Models
Autifomaz
(2021)
Informer (2021)
Transformer
(2017)
MAB
115.564
5:268
10,749
2.617
155 106
131. 168
6.676
11 11.540
1.591
19:155
12% 9T5
6,703
11 11.766
2.547
120. 160
113.355
4.967
10.647
2.888
298.0 107
134.283
6.804
11.992
1.236
6,780
132.005
6.641
11.328
1,209
14.174
Uniemodal
10
114.417
6.904
10,095
6.611
14833
36.413
178,80
6.443
11.350
1.590
117,301
5,253
10.854
2,092
336
125.201
6.430
11.323
1.408
26,498
136.753
7,039
11,694
1.168
Avx
115.277
10.736
2.545
240.734
1.429
131.351
6.382
42.995
108.941
4.861
10.43
3.054
246 058
127.316
6.197
11 11.279
2.326
99.099
137.275
6,233
11.262
3.592
135.753
Security
8
113,600
5,031
10.663
2.799
265 958
125.914
6,402
11.354
1.660
40.615
126.589
6.227
11.251
2,310
$4.511
MM-TSSP1bb
10
112.565
5,185
10.909
1.8555
1201011
176.775
0.334
11 143545
1.532
19 T64
137
0.760
11:315
1.530
12.213
12
110,609
4,002
10.521
2.177
199
450
130.907
0.626
11:441
1.443
33.523
132.003
6.685
11.491
1,217
11.891
Arg
111,445
4.073
10.556
2.465
207 884
125.95
6.415
11:356
1.340
53.001
138.471
6.378
11.334
1.835
4.255
2.365
5,000
2.065
4.750
455
590
2.350
11.130
2.505
TaT7S
10
110.061
4,891
10.491
3,655
503
754
0,248
11:215
2.251
134083
115.006
0.262
11.210
1.251
12
109.361
4.847
10.458
3,000
457
450
127.103
6.359
11.234
1.365
86.102
125.07
6.200
11.234
1.599
90 02.
Avg
108.400
4.787
10.415
3.65
501
126.661
6.276
11:255
2.192
116.488
134.581
6.134
11.152
2.40L
190. 197
0.684
0.95
1.900
69
0.733
0.455
0.668
0.312
11.761
0.437
0.684
1:214
1.216
0.664
0996
1996
89:017
0.81
0.449
0.206
0.933
11.089
0.877
0.460
0:119
1.520
Uni moddl
0.705
0
0.755
0.905
0.541
1:725
Avg
1,276
0.700
1.000
2.054
74.607
0.570
0.904
0.717
0.934
9.207
0.910
0.484
0.754
1.400
414
1.200
0.664
01956
1.390
66.4
0.772
0.314
0,066
0.756
0.784
0.422
0.633
0.938
Social Good
1.175
0.589
0.891
1.955
64.15
0.829
0
0,673
0.746
6,869
0.545
0.426
0.699
1,256
19.305
MM TSFLib
10
1.258
0.689
1,002
1.756
44.172
0.876
0.466
0.724
0.355
6.248
0,913
0.486
0.731
1-252
25 176
1,292
0.730
1.02
2.045
76.
0.819
0.541
0.365
0.588
7.772
0.883
0.510
0.364
1.001
15.64
Avg
1,279
1.007
67.50M
0.457
0.804
1.007
19:255
1.857
0.564
1.451
0.724
0.448
0,600
0.75
7.156
0.740
0.375
0.616
0.710
3.84
6
1184
0.686
0.054
1.76
20.567
0.788
0.453
0
0.500
8,039
0.515
0,393
0,52
0.825
11 11.467
TaTS (ours)
10
1.27%
0.714
01986
1.57%
21.250
03338
0.058
01691
0.300
8-887
0.842
0.485
0.700
1.002
11.719
13
1.261
0.069
01979
1.544
21.337
01890
0.455
0.668
0.785
4.917
0.643
0.434
0.600
0.777
5.975
Avg
1.195
0.665
0.949
1.513
24003
0.410
0.259
0,686
0.330
7.150
0.807
0.419
0.649
0,542
8.246
0.316
0.30
Uni-modal
10
0.300
0.206
0.353
0.296
0.255
0.300
0.358
0.326
01397
0.323
Avg
0,212
0.295
0.424
0.319
0.528
0.202
0.355
0.438
0.311
0,352
0.209
0.346
0,442
0.304
0.336
0.195
0.248
0.390
0.247
0.360
0.166
0.297
0.367
0.255
0
0.164
0.291
0.384
0.271
0.340
Tramfe
01724
0.777
0.68
0.95
0.195
0.385
0.512
0.173
0.105
0.174
0.118
TSFLib
10
0.224
0.55
0.305
0.52
0.237
0.283
12
0.241
0.202
0.420
0.543
0.183
0.290
0.392
0.292
0.414
0.181
0.281
0,3M2
0.287
0.369
0.212
0.222
0.254
0.299
0.256
0.295
0,279
0.161
0.225
0.356
0.255
0.440
0.159
0.252
0.315
0.266
0.337
0.199
0.274
0.373
0.269
0.364
K
0.167
0.211
0.355
1.25%
0416
01161
01749
0.37%
0.270
0.540
0.156
0.768
0.167
0.366
01386
TaTS (ours)
10
0.163
0.214
0.309
0.200
0447
0.157
0.276
0.368
0.274
0,390
0.157
0.270
0.367
0.267
0.363
0.217
0.547
0.779
0.24%
0.534
0.181
0.739
0.367
0.189
0.439
0.181
0.183
0.991
0.391
0.435
Avg
0.264
0.314
0.274
42

---

Published as a conference paper at ICLR 2026
Table 28: Full forecasting results for various datasets using different time series modeling methods. Our TaTS framework seamlessly enhances existing time series models to effectively handle time series with concurrent texts. Avg: the average results across all prediction lengths.
Metbods
TallS tours
(ours)
TaiTS (oun)
N-BRAIT
N-RVI
(2022))
(2015)
Chafline (2005)
CIPIMMI
(2117.4)
Darsses
MSE:
MAE
MSBI
MAE
MSL:
MAB
MISB:
MAN
MISE:
MARE
MSB:
MAE
MSSI
MAN:
MSI:
MAB
0,067
0.184
0.065
0.171
0.087
0.205
2,435
1.210
2.274
1.134
3.557
1,770
0.502
0.441
0.197
0,292
01994
0.210
0.891
0.217
0.130
0.223
3.671
1.445
1.575
0.816
5,078
1.919
0,510
0,339
0.352
0.426
Agricaltane
0.126
0.146
0.349
3.078
1.416
1.441
0.910
4.464
0.505
0.445
0.358
0.413
0.153
0.100
0.150
0.328
3.583
1.750
2.319
1.217
3.173
0.517
0.452
0.464
Ang
|
0.114
0.235
0.251
3.367
1.488
1.850
4.168
0.508
0.447
0.393
1,000
0.399
0.926
782
0.912
0.258
1121
0.894
1.314
0.581
1.332
0.875
1.507
1.007
1000
0.844
1,025
0.797
0.595
0.963
0.917
0.251
1.070
0.844
0.981
0.791
1,066
0.804
1.524
1.012
1.177
0.893
Clinate
10
1,053
0.818
1,022
0.755
0.917
0.250
1
0.850
1.152
0.377
1,043
0.857
1.575
1.127
1.100
0.6
12
1,033
0.812
1.022
0.810
1.005
0.821
1.085
0.856
1.166
0.864
1.167
0.926
1.664
1.031
1.150
0.895
Ang
1,088
0.804
1.004
0.788
0.45
0.232
1.000
0.361
1.303
0.858
1.098
0.366
1.568
1.019
1.132
0.87
010119
01011
0.77
0.792
0.334
0.432
5.340
2.315
0.143
0.156
Ecenomy
0.079
0.009
0.079
0.995
0.849
0.486
5.436
0,052
0.165
0.096
0.088
0.006
0.009
0.080
0.000
0.081
1.458
1.166
0.380
0.465
5.556
2,353
0.059
0.18
0.016
0.101
Aax
| 0.008
0,077
0.009
0.079
0.009
0.090
1,010
0,920
0.444
0.584
5.546
2.349
0.049
0.166
0.014
0,096
13
0.106
0.234
0.106
0.234
0.118
0.265
0.166
0.371
0.005
0.336
0.185
0.318
0.126
0.255
0.117
0.244
24
0:220
0:355
0.316
0.316
0.222
0.347
0.200
0.013
0602
0282
0.50
0.258
11305
02212
0.367
Energy
96
0:300
0:411
0.305
0.43
0:311
0:414
0.51
0:000
0:000
9-118
0:322
0.99
0.001
11685
0.128
0.44
TMD (3024))
0:421
0.502
0.416
0.501
0.434
0.510
0,460
0.552
0:301:10
0,400
0.634
0.54
0.473
0.595
0.421
0.497
0.265
0.376
0.256
0.301
0.379
0.329
0.424
0.373
0,463
0.450
0.512
0.305
0.417
0.37%
-65
0.268
0.370
0.221
0.537
0.260
0.373
0.445
0.504
0.040
0.333
0.505
0.691
0.583
0.594
0.312
0.390
96
0.267
0.370
0.279
0.376
0.279
0.377
0.540
0,502
0:421
0522
0.38
0.666
0.575
0.591
0.345
0.488
Environment
192
0:272
0.366
0.272
0.365
0:271
0.307
0.523
6350
0635
1360
0381
0.577
11596
0.358
0.40
356
0.261
0.369
0.269
0.366
0.267
0.366
0.563
0.614
0:500
0.628
0.400
0.400
0.585
0.999
0.377
0.453
Aug
| 0:267
0.365
0.275
0.571
0.272
0.371
0.518
0,573
0.521
0.583
0.254
0.713
0.540
112944
0.348
0,422
0.649
0.990
12111
0.704
1.572
0.838
1.223
0366
2.484
1,077
1.482
0,802
11157
0.704
1.60
1.05h
Heal'
1.307
1,407
1.534
0.080
0.08
1,557
0.850
1.732
0.938
1,456
1.502
0.875
1.550
0,951
03111
1,813
0142
0.957
Aog
1,315
0.744
1,283
0.753
1.421
0,838
1,600
0,938
1,666
0,398
1.538
0,970
1.665
0,909
1.756
0,875
107.
4.856
106.160
4,096
105
4:511
131.917
6.366
135:416
6,00
129.815
6,001
130.751
6.854
118,425
5.100
112.560
5.204
108.803
5002
103.657
4.702
133.095
6:257
144.7
1780
125:575
6,966
134.536
6.875
118,952
5.106
Suauriy
113.899
5:320
111:110
1060
105406
-221
168
855
2.364
116.98
6782
160129
20077
13.690
5.895
119.51
5255
114.754
5,318
112.099
5,237
108.375
4,870
111
11.0094
5.974
115.307
6,477
125.002
6.676
135.513
6.925
120733
5.351
Avg
112.054
107.880
4.7%
130.06
6.618
176
6978
116
6.473
133.106
6.887
| 119:407
0.542
0.394
01923
0.636
0.90
0.308
1.752
0.654
1,400
03650
1.535
0.917
1,213
1000%
1,214
0.485
0.967
0.433
0.900
0.461
1.01
0.350
0.882
0.551
1,33
0551
1.129
0.935
1.252
0.621
1,422
0.5%0
Social Glodd
10
0,994
0.463
0.996
0.661
L065
0:533
1.116
0.627
1.112
0.54
1.208
0.996
1.276
0.667
1.264
0,572
12.
1.045
0.314
1.099
0.59
13358
0.702
1.445
03339
1:40
0946
13385
0.096
1.315
0.712
1:357
0.622
Ang]
| 0.967
0.452
0.973
0. 1.405]
1:104
0.020
1,316
0.000
1.273
0.009
1:314
0.901
1.264
0.002
1.414
0,5%
0.218
0.155
0.214
01157
0:228
0352
0:400
02205
0272
0.229
6275
0.569
11:35
0.185
0.227
0.100
01700
0.400
0220
0.35
0.074
11:32
Truffic
0.225
0.167
0.342
0.55
0.363
0.246
0.361
0.215
0.2%6
0.364
0.305
0.177
0,364
0.675
0.359
0.422
0.272
Aag
0.167
0.217
0.172
0.209
0.176
0.248
0.347
0.464
0.268
0.382
0.708
0.744
0.363
0.429
0.195
0.246
Dela:
0.064
0.161
0.059
0.
1660
0.665
0.167
0.233
0.417
0.191
0.342
0.247
0.422
0.065
0.169
0.060
0.179
Aidine
12
0.110
0.233
0.116
0.224
0.136
0.255
0.320
0.470
0:360
0.416
0.341
0.500
0.126
0.235
0.118
0.223
(DAL)
Axg
0.07
0.197
0.086
0.192
0.055
0.201
0.386
0.444
0.336
0.379
0.294
0.466
0.098
0.202
0.099
0.201
IBM
0.34
0.642
0.554
0.500
0.667
0.913
2.001
0.996
0.655
0.40
(BM)
0.758
0.886
0.387
1.370
0.907
0.619
0,364
01550
0.
0.000
0.891
0.695
1,305
0,777
1,215
0,300
1,930
0.002
11536
00639
0.525
FNSPID (2024)
JPStorgan
1.173
0.817
1,275
0.819
1.606
0.912
1.798
1,00
2,217
1,082
3.511
1.785
1.332
0.845
1.644
0.922
Choe
12
2,214
1.124
2.470
1.161
3:421
1.281
3,090
1.367
4.635
1.385
3.557
1.657
2.742
1.244
2.622
1.325
JPM)
Aug
| 1,983
0.700
1.872
0.990
[ 2.533
1.096
2.419
1.175
3.426
1.222
3.764
1.711
2.037
1.045
[
2.33
1.123
NVIDIA
0.123
0.041
0.085
0.151
0.07
0.122
0257
0.445
0.424
0.00
0.24
0.403
0441
0.500
0.008
0.67
0.885
0.13
0.043
0.14
00033
01085
0.174
0.722
0,454
0,457
0.594
0.053
11101]
0.159
Plwer
13
0,412
0.340
0.355
0.476
0.839
0225
0.36
0. 0442
0.567
0.320
0.419
0.355
0356
0.586
0.623
0,520
0:987
0,663
0.718
0.688
00854
0.601
0.561
0.557
0.402
0.354
1,505
0.451
0.456
0.263
0.389
0,490
Avg
|
0.326
0.416
0.347
0.422
0.448
0.417
0.676
0.572
0.324
0.653
0.624
0.559
0.408
0.477
[
0.399
0,499
(TSLA)
Toda
0.153
0.321
0.071
0.345
0.204
0.390
0.088
0.122
0.335
0.253
0.166
0.110
0.306
0.350
0.01
0.247
0.381
3.784
3,168
1.929
1.773
0.123
0.192
0.256
0.343
0.196
0315
0.292
|
0.281
0.156
0.244
0.188
0.350
3,476
0.156
0.300
0.308
1.760
0.916
1.552
0.85%
1.251
0.858
123.
9.415
105.788
43895
2.525
1.085
0,894
Bitcoda
Price
19
12
3000
2.147
3.521
1,312
1.313
1.006
2.621
3,185
1.99
0.964
1.229
1.128
5:39
3:491
2.458
1,000
1.287
1.304
136 955
157.34%
159.445
11.192
11.115
9.303
163.110
187.741
179247
10690
10.759
103566
161162
53.318
6,122
7.253
7.464
3,552
3.855
4.631
1.611
1.486
1.163
3,314
2.521
3.542
1.208
1.050
1.4%6
Avg
|
2,089
1.112
2.339
1.045
|
2.715
1.142
141.738
10:355
159.019
10.555
573026
6.744
3,500
1.544
2.721
1.150
INF (2004))
Trufiic
Weth
19054
15:106
18.133
0.740
17.348
15773
15.005
1.755
17.378
16:33
3.217
2.755
2.516
21.5%6
27.141
3,408
2.754
2.501
24.046
21.993
26.011
21.976
30.144
27.759
2.157
20.164
21,341
19:365
2.024
2.875
2.869
15:106
20.611
19.902
2.422
2252
2.702
Aug
17.744
2012
17.564
2.053
15.110
2,772
22.233
3,017
23.263
3,011
21.626
2,842
20.748
2.099
19,350
2527
0:060
0:375
01247
0. 194
01260
0.375
0.185
0.470
0:114
0.463
0.446
0.506
0.510
11544
0:271
0.388
Ellctnotty
Demand
0.274
0.205
0.408
0.405
0.391
0.133
0.327
0.257
0.424
0.365
0.500
0.353
0.310
0.244
0.360
0.408
0.356
0.407
0.451
0.419
0.494
0,497
0.522
0:185
0.355
0.426
0.454
0.471
0.504
0.558
0.501
0.367
0.565
0.587
0.601
0.558
0.516
0.524
0.571
0.588
0.582
0.264
0.357
0.428
0.369
0.396
Avg
0:196
01254
0.972
0.416
0.496
0.516
0,512
0.566
0.395
43

---

Published as a conference paper at ICLR 2026
E.4 FULL IMPUTATION RESULTS
Table 29: Full imputation results for the Climate, Economy, and Traffic datasets using PST DLinear and FiLM as time series models. Compared numerical-only unimodal modeling and MM-TSFLib, our TaTS framework seamlessly enhances existing time series models to effectively handle time series with concurrent texts. Promotion: the improvement of the best baseline.
Models
PuccTST
DLinear
BLM (20222)
(20125)
MAPE
RMSF
MAPE
MAPF
Uni
3,89%
0,933
1.881
0.829
2.647
Chimane
MM TSFLib
TWTS
2.156
$1.983
0,980
1.394
25.24
18.550
0.833
1.949
51,811
56.2%
13.4%
34.2%
Economy
TaTS (uurs)
0.017
0.107
0.128
0.008
0.002
0.045
0.171
0,210
0.247
0.069
0.061
0.007
0.005
0.054
0.168
0.061
0.007
Promotion
34.8%
21.9%
20.5%
22.4%
33.3%
21.1%
10.0%
12.1%
10.3%
14.3%
28.0%
17.2%
14.4%
15.3%
22.2%
Uni-mdaal
0.210
0.330
0.444
0.358
0,600
0.345
0.417
0.489
0.400
0.720
0.175
0.301
0,409
0.345
0.508
Trfffic
MM-TSFLib
T&TS cours)
0.189
0.131
0.248
033441
0.331
0.428
0.312
0.391
0.690
0.647
0.134
0.379
0.297
0.335
0.419
0.359
0.362
0.266
0.270
0.630
0.137
0.169
0.242
0.228%
0.354
0.300
0.281
01216
0.545
0.368
Promotion
20.7%
25.8%
22.7%
12.8%
-7.8%
25.1%
11.3%
16.0%
26.5%
57.1%
18.9%
16.0%
10.6%
11.15
23.6%
44

---

Published as a conference paper at ICLR 2026
E.5
FULL HYPERPARAMETER STUDY RESULTS OF LEARNING RATE
0.200
1.10
0.175
1.05
0.150
00.125
Squared
2.00
0.0175
0.100
0.95
0.0150
0.075
0.0125
0.050
6.0100
0.025
0.0075
0.000
5e-5
10-4 1.5e-d 26-4 2.5e4 36-4
505
10.4 1.50.4
2c-4 2.5c 30 Leatning Rate
0.0050
3e-3
1e-4 1.5e-1 Ze-4 2.5e-d Je-4
Learning Rate
Learning Rate
(a) Agriculture
(b) Climate
(c) Economy
1.4
Diwe
FUM
AC2313
0.14
0.274
Mean Squared Enor
1.3
0.13
0.12
0.272
1.2
1.3
0.10
Moon
0.268
1.0
0.266
0.08
5c.5
1c:4 1.5e.4
2.50
2e-4
2.5e-4
0.9
5e-5
1e-d
1.5e-d
2e-4 2.5e-d 3e-4
Learning Rate
Learning
Learnnng Rate
(d) Energy
(c) Environment
(f) Health
108.0
1.10
0.20
107.5
207.0
206.5
Squaree
106.0
205.5
0.90
0.16
105.0
0.85
0.15
104.5
104.0
5e.5
10.4 1.50
2e 2.5 36
0.80
5e5
1e-4
1.5e-4
2e-4 2.5e-4 3e-4
0.14
3e.5
1e-4 1.5e- 2e-4 2.5e-4 Je-4
Leaming Rate
Learning Rate
Learning Rate
(g) Security
(h) Social Good
(i) Traffic
Figure 11: Parameter study on the learning rate. We evaluate the impact varying the learning rate in (0.00005, 0.0001, 0.00015, 0.0002, 0.00025, 0.0003) by reporting the squared error (MSE) of our TaTS framework across datasets. The results demonstrate that TaTS maintains stable performance across different learning rate choices.
45

---

Published as a conference paper at ICLR 2026
E.6
FULL HYPERPARAMETER STUDY RESULTS OF TEXT EMBEDDING DIMENSION
0.200
1.10
0.175
1.05
Bleex
- KUM
0.150
2.00
00.125
0.0175
0.100
0.95
0.0150
0.075
0.0125
0.050
6.0100
0.025
0.0075
0.000
12
38
24
0.0050
18
24
Projection Dimension Paired texts
Projection Dimension Paired Texts
Projection Dimension of Palred Texts
(a) Agriculture
(b) Climate
(c) Economy
1.4
0.14
NutiiTT
DLinerr
FIMM
0.274
+ PatSITET
Diine
- TUN
Mcan Squared Enor
1.3
0.13
0.12
0.272
1.2
1.3
0.10
0.268
1.0
0.266
0.08
0.9
12
24
Projection Dimension of Paired Texts
Projection Dimerssio Paired lests
Projection Dimension of Paired Texts
(d) Energy
(c) Environment
(f) Health
108.0
1.10
Dumsa
0.20
107.5
107.0
206.5
Mear red
106.0
105.5
0.90
0.16
105.0
0.85
0.15
104.5
104.0
12
18
24
0.80
12
18
24
0.14
12
10
24
Projection Dimension Paired texts
Projaction Dimansion of Fairod Texts
Projection Dimonsion Paired Toxts
(g) Security
(h) Social Good
(i) Traffic
Figure 12: Parameter study on the projection dimension of paired texts. We vary the text projection dimension in {6, 12, 18, 24} and report the mean squared error (MSE) of our TaTS framework across datasets. The results indicate that TaTS maintains robust performance across different choices text projection dimensions.
46

---

Published as a conference paper at ICLR 2026
E.7 FULL ABLATION STUDY RESULTS USING DIFFERENT TEXT ENCODERS
We conduct experiments to evaluate the performance of our TaTS with multiple language encoders. Specifically, evaluation TaTS with BERT-IIOM GPT2-1.5BB and LLaMA2-7B* as the language encoders. The results, presented Figure 13, demonstrate that TaTS remains robust across different text encoders and consistently outperforms the baselines.
0.18
CEBLE
0.30
0.05
0.34
9.33
0.04
0.32
1.00
0.00
0.08
0.0
(a) Agriculture
Climate
Economy
0.50
2017
2.0
3.0
0.45
3.6
0.35
tereaeding
0.25
heer
1ach151
(d) Energy
(c) Environment
(f) Health
31.6
0.24
114
2.3
0.22
312
1.0
0.20
310
C.38
308
0.9-
304
PatchTst
bunnar
RLM
RatchTST
Duncar
RLM
0:3
PotchTS
Ouicer
RLM
Security
(h) Social Good
(i) Traffic
Figure 13: Performance comparison of different text encoders within the TaTS framework. Specif- ically, we evaluate BERT-1 10M, GPT2-1.5B, and LLaMA2-7B across multiple datasets using PatchTST (rransformer-based model), DLinear (linear-based model), and FiLM (frequency-basee model). TaTS maintains relatively stable performance across various models and datasets.
In the main experiments, the embeddings obtained by mean pooling over token embeddings. There are more advanced embedding techniques. To this end, we conducted an additional experiment using LLaMA-3.2- 3.221B to generate sentence-leve embeddings, while keeping all other settings the same. The results are shown below in Table 30.
Table 30: Mean Square Error TaTS forecasting with different text embedding methods.
Emhodding Mathod
Agriculture
Climate
Feonomy
Security
Social Good
Traffic
GPT-2 average pooling (prediction length
0.067
1.020
0.008
107. 107.113
0.942
0.174
LLaMA-3.2 3.B--BBB sentence embeldingg (prediction length 6)
0.067
1.015
0.008
106.625
0.935
0.179
GPT22 average pooling (prediction length 12)
0.153
1.033
0.008
114.754
1.045
0.213
I.L.M-3.2.11 sentence embeddings (prediction length 12)
0.152
0.088
hnttps://hugiigg ctt..co//eeaaaeeeeeeeeeee 11 1m1amm-2-2211
47

---

Published as a conference paper at ICLR 2026
E.8 FULL EFFICIENCY RESULTS: COMPUTATIONAL OVERHEAD VS. PERFORMANCE GAIN TRADE-OFFS
We conduct experiments analyze the efficiency of TaTS, with results presented in Figure 14. Each subfigure visualizes the training time per epoch and the forecasting mean squared error (MSE) for different time series models, represented as transparent colored scatter points. The average performance is computed and marked with cross markers: the green cross represents the average performance of TaTS, while the red and blue crosses indicate the average performance of the baseline models. As TaTS introduces a lightweight MLP and augments the original time series with auxiliary variables projected from paired texts, it incurs a slight computational overhead, with an average increase of 8%. Yet this trade-off results in 14% average improvement of forecasting MSE
Unkmedil
3.2
3.30
0.2
3.20
3.30
36
0.25
0.5
1.5
05
C4
15
05
67
39
1.0
0.00
02
0.
1.0
1.2
02
02
10
32
Time
(a) Agriculture
(b) Climate
(c) Economy
0.53
C.3
9.30
045
0.00
020
3.2%
Toaning Time for Each Spoch
Traniin Time for Each Epoch
Training Time Each Epoch
(d) Energy
(c) Environment
(f) Health
3.25
3331
2.00
015
100
1
"saining Time for Each Eooch
Taining Time for Each Epoch
Taalinng Time for Each Epoch
(g) Security
(h) Social Good
(i) Traffic
Figure 14: Efficiency and forecasting performance comparison of uni-modal time-series modeling, MM-TSFLib, and our TaTS framework. While TaTS incurs a slight increase in training time due to the augmentation of auxiliary variables projected from paired texts, it significantly enhances forecasting accuracy, achieving lower MSE.
48


Reviews:
[{"review_id": "nz4A2yuqSn", "reviewer": "Reviewer_vhxM", "summary": "This paper introduces TaTS, a new multimodal time series forecasting benchmark compatible with any time series forecasting model. TaTS embeds the textual descriptions of time series, projects them using an MLP, and then combines them with the original time series to create a new input for forecasting models. The motivation behind this architecture is that time series paired with text often exhibit periodic patterns that reflect the dynamics of the numerical time series. Additionally, the authors introduce TT-Wasserstein, a metric designed to evaluate the alignment between the time series and the associated text.", "questions": "1. How did you choose the competitors and why not incorporating multimodal algorithms?\n\n2. How the method can adapt if not enough textual descriptions are not available for each time stamp if there are not alignment between time series and text or at least it is not known ?\n\n3. it seems the information from the text is not complementary but redundant information with the time series as captured by the low TT-Wasserstein. In this redundant information case one would expect the text not to improve the result and expect more an improvement when the information is complementary and critical for the forecast?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. The proposed architecture is model agnostic and delivers good improvement of the base model.\n\n2. Incorporate textual information into time series if timely and interesting.", "weaknesses": "1. The paper lacks comparison with other multimodal algorithms. For example, the authors don't compare their approach with TimeMMD, which is also model-agnostic and offers similar improvements over unimodal models. There are also several other multimodal algorithms available that could serve as valuable comparisons.\n\n2. The method requires access to a textual description for each timestamp, which may be difficult to obtain in real-world applications.", "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": "sdIWVEa7Tk", "reviewer": "Reviewer_w9od", "summary": "This paper presents TaTS, a plug-in framework that treats timestamp-aligned texts as auxiliary variables for time-series models. By embedding the texts, projecting them through a small MLP, and concatenating them to numeric inputs, the approach allows standard forecasters and imputers to exploit textual signals without changing their architectures. The work is motivated by Chronological Textual Resonance (CTR), the observation that paired texts often share periodic structure with the target series, and it introduces TT-Wasserstein to quantify this alignment. Extensive experiments across varied datasets and backbones indicate consistent gains, particularly when TT-Wasserstein suggests strong alignment. The computational overhead is modest, which enhances the practical appeal of the method.", "questions": "- How are splits constructed per dataset to ensure texts at time t do not reveal contemporaneous or near-future outcomes, and are audits/filters applied for retrospective or outcome-summarising language?\n- Which FFT, windowing, and normalization settings are used for both modalities, how sensitive are results to these choices, and can confidence intervals be reported for the correlation?\n- How does TaTS compare with (a) a small gated residual that can down-weight text channels and (b) a parameter-matched cross-attention/FiLM block?\n- Has weighting or dropping text channels based on TT-Wasserstein been tested to mitigate negative transfer when alignment is weak?\n- What are the training/inference wall-clock costs for different text encoders (e.g., GPT-2, BERT, LLaMA), and what rule of thumb should practitioners use to choose an encoder?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- The paper introduces a simple, model-agnostic plug-in that treats text embeddings as auxiliary variables, simplifying integration into existing pipelines while keeping computational overhead low.\n- The work provides an interpretable alignment rationale via CTR and the TT-Wasserstein metric, which helps explain when and why text improves performance and guides practical deployment.\n- Extensive experiments with clear ablations (shuffle/drop text, encoder swaps, multiple backbones and datasets) demonstrate stable gains.", "weaknesses": "- The central mechanism is projection followed by concatenation, which may be outperformed by comparably simple baselines, such as gated residuals or lightweight cross-attention, unless comparisons are conducted under strict parameter matching.\n- The definition and estimation of TT-Wasserstein lack sufficient statistical treatment; sensitivity to windowing, normalization, and frequency resolution is not examined, and confidence intervals are absent.\n-  The data-splitting procedure is not described in adequate detail, creating uncertainty about potential information leakage from contemporaneous or retrospective texts.\n- The framework offers no automatic protection against negative transfer when CTR is weak, which could undermine robustness in noisy or weakly aligned settings.", "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": "Y5QsyzHWfc", "reviewer": "Reviewer_aWnj", "summary": "The paper introduces TaTS, a simple framework that integrates timestamped text with numerical time series by converting text embeddings into auxiliary features for standard models. It is motivated by Chronological Textual Resonance (CTR), which captures periodic alignment between textual and numeric signals, and defines TT-Wasserstein to quantify this alignment. TaTS works with existing architectures without modification, improving forecasting and imputation performance across multiple datasets while adding minimal computational cost.", "questions": "Please address the identified weaknesses and limitations noted above.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Evaluated across multiple datasets and diverse time-series backbones, supporting robustness and generalizability.\n- Clear, well-structured framework: CTR (motivation), TaTS (mechanism), and TT-Wasserstein (diagnostic) are distinctly defined and complement each other.\n- Plug-and-play simplicity: TaTS adds a small projector to turn per-timestamp texts into features and works with existing TS backbones without architecture changes.", "weaknesses": "- CTR/TT-Wasserstein focus on magnitude-only spectral alignment, favoring stable periodicities and largely ignoring phase—so they can undervalue datasets where texts are leading or lagging indicators or where alignment is time-varying/non-stationary, even if the texts are predictive.\n- Limited discussion of TS→text (inverse direction): brief related-work mention and a single zero-shot ChatTime baseline; no deeper analysis or dedicated experiments.\n- Limited native multimodal baselines: ChatTime is the only truly native multimodal method evaluated, while others are adapted uni-modal TS models; MM-TSFLib is further extended for imputation since it doesn’t support it natively.", "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": "9MCED1aleW", "reviewer": "Reviewer_1Lkf", "summary": "This paper introduces the TaTS framework, a novel approach for integrating contextual textual information with numerical time series data to significantly enhance forecasting accuracy. The authors propose a method that projects auxiliary variables from paired texts to augment the original time series representation, theoretically underpinned by the Platonic Representation Hypothesis, which posits a convergence of multimodal representations into shared spaces. The central contribution lies in the demonstrated effectiveness of this multimodal fusion: empirical results across nine diverse real-world domains consistently show that TaTS achieves an average of approximately 14% improvement in forecasting Mean Squared Error (MSE), justifying the minor incurred computational overhead of around 8% in training time.", "questions": "Please refer to Weaknesses.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Significant Empirical Improvement: The framework demonstrates a substantial and consistent performance gain (around 14% MSE reduction) across a wide array of domains (e.g., Economy, Climate, Health), indicating high robustness and generalizability.\n\n2. Sound Theoretical Grounding: The methodology is well-motivated by the Platonic Representation Hypothesis, providing a strong conceptual basis for unifying textual and numerical time series representations.\n\n3. Practical Efficiency Analysis: The paper includes a necessary trade-off analysis, clearly quantifying that the high performance benefits come with only a marginal and acceptable increase in computational overhead (around 8%).", "weaknesses": "1. Interpretability of Textual Influence: While the model is effective, the specific mechanism by which the projected auxiliary variables qualitatively impact or modulate the time series dynamics is not deeply explored. More detailed visualization or ablation studies on the how the text is woven into the temporal narrative would strengthen the paper.\n\n2. Scalability to Text Length/Complexity: The paper does not thoroughly discuss the framework's scalability or performance behavior when dealing with significantly longer or structurally complex paired texts (e.g., full documents vs. short captions).\n\n3. Sensitivity to Text Quality: A crucial missing component is an analysis of how the model performs when the paired text is noisy, weakly correlated, or intentionally irrelevant, which would better demonstrate the robustness of the feature extraction mechanism.", "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)