Are Time-Indexed Foundation Models the Future of Time Series Imputation?
Authors: Etienne Le Naour
Tahar Nabil
Adrien Petralia
Ghislain Agoua
Venue: Accepted by TMLR ()

Abstract: Foundation models for time series imputation remain largely unexplored. Recently, two such models, TabPFN-TS and MoTM, have emerged. These models share a common philosophy that places them within the family of time-indexed foundation models. This paper presents the first large-scale empirical study of these models for zero-shot imputation, which enables missing value recovery without retraining across a wide range of scenarios. We conduct extensive univariate experiments across 33 out-of-domain datasets ($\approx$ 1.3M imputation windows) and evaluate their ability to integrate covariates at inference time to improve accuracy without fine-tuning. Our results demonstrate that time-indexed foundation models are a powerful and practical step toward achieving general-purpose, zero-shot imputation for real-world time series. Code is available at https://github.com/taharnbl/tsfm_imputation.

Published in Transactions on Machine Learning Research (01/2026)
Are Time-lndexed Foundation Models the Future of Time Series Imputation?
Etienne Le "aour"
ceienne.eemmoureedff
EDF R8D, Palaiseau, Prance
Tahar Nabil
tahar. fr
EDF R&D, Palaiseau, France
Adrien Petralia EDF R8D, Palaiseau, Prance
adrien Qredf.h
Ghislain Agoua
EDF R&D, Palaiscau, Prance
Reviewed OpenReview: https: htttpe://peeneeveel net/ forum? id= c7k56XpsPP
openreview.
Abstract
Foundation models for time series imputation remain largely unexplored. Recently, two such models, TabPFN-TS and MoTM, have emerged. These models share common philosophy that places them within the family of time-indexed foundation models. This paper presents the first large-scale empirical study of these models for zero-shot imputation, which enables missing value recovery without retraining across wide range of scenarios. We conduct extensive univariate experiments across 33 out-of-domain datasets (Ne 1.3. imputation windows) and evaluate their ability to integrate covariates at inference time to improve accuracy without fine-tuning. Our results demonstrate that time-indexed foundation models are powerful and practical step toward achieving general-purpose, zero-shot imputation for real-world time series. Code is available at https: httpthhh..cccmmmaammm////tttt ittrrfftmmmuttatiinnmmmmm
1 Introduction
Real-world time series from domains such as healthcare, industry, and climate science are often irregularly sampled or incomplete due to sensor failures and decentralized data collection (Schulz & Stattegger 1997 Clark & Bjornstad] 2004). Reliable imputation thus a critical first step toward downstream tasks like forecasting, classification, anomaly detection. Yet, while recent deep learning methods have advanced impulation performance (Cao el al. 2018 Du et al. 2023a Nie el al. 2024), they typically lack robustness to distribution shifts and fail to generalize to out-of-domain data.
Recently, zcro-shot forecasting models have emerged in the time series commmnity, enabling inference on unseen datasetss without retraining. This shift has given rise to time series foundation models, offering key benefits: (i) a single deployable model across diverse domains, (ii) strong performance on new datasets, often exceeding supervised baselines and (iii) emerging capabilities beyond simple memorization. While forecasting-oriented foundation models are now relatively well-studied (Auer al. 2025b Das et al. 2024 Woo et al. 2024 Ansari et al. 2024), imputation-focused counterparts remain scarce. Zero-shot imputation in out-of-domain settings is particularly challenging duc to heterogencous sampling rates, diverse missingness patterns, unaligned or irregular time series, and the polential presence of covariates whose predictive value is often underexploited.
'Equal contribution.

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A promising direction to overcome these challenges lies in continuous-timg modeling, which learns a contextual representation H (1) at each time-step thereby casting imputation as regression problem. This approach is often referred to as time-inder modelling (Woo et al, 2023). Within this paradigm, time-indexed foundation models such as TabPFN-T (Hoo et al. 2025 and MoTM (Le Naour et al. 2025) have recently been introduced, enabling zero-shot impulation through continuous-lime representations. These models offer strong out- of-domain generalization without requiring retraining, making them particularly attractive for real-world applications where training data and computational resources are limited.
In this paper, conduct the first extensive study of time-indexed foundation models for time series imputation, and summarize our key contributions as follows:
Extensive univariate evaluation. We evaluate TabPFN-TS and MoTM across 33 out-of-domain univariate datasets (covering roughly 1.3M windows to impute), benchmarking them against a wide range of baselines. TabPFN-TS yields the highest overall performance with a notable margin, whereas MoTM also surpasses all supervised and local baselines but remains behind TabPFN-TS.
Evaluating covariate integration without retraining. On three complex datasets, we show that both foundation models can seamlessly incorporate additional covariates at inference time, drastically improving imputation accuracy without any covariate-specife pretraining.
Limitations and discussion. We analyze the practical constraints of these approaches and identify scenarios where they are most effective. We also discuss potential directions toward more efficient and generalizable foundation models for time series imputation.
2 Considered imputation baselines for the benchmark
This section presents the imputation baselines considered in the benchmark, covering a spectrum of approaches from simple statistical heuristics to modern loundation models. In Section 2. we present local and supervised models, which, respectively, require dataset-specifie training or rely on handcrafted rules; and in Section 2.2 we present timo-indexed foundation models, which generalize across datasets in a zero-shot manner without retraining. Further information on the models and their implementations be found in Section
2.1 Local imputers and supervised models
Local Imputers. Within the benchmark, local imputation methods serve as fundamental baselines due to their simplicity, interpretability, and low computational cost. These approaches estimate missing values using only neighboring observations or straightforward statistical rules. Representative techniques include Linear Interpolation, which connects adjacent observations under constant-rate assumption; Last Observation Carried Forward (LDCF), which propagates the most recent available value; and the Seasonal Naive method, which repeats the last observed value a given periodicity (e.g., daily or weekly). While these methods perform adequately for small and isolated gaps, they generally fail to capture long-term dependencies, seasonal structures, nonlinear dynamics commonly observed in real-world time series.
Supervised Models for Imputation. Supervised models constitute the conventional approach for tackling complex imputation tasks, where models are trained end-to-end on specific datasets and evaluated on held-out test sets. These task-specific models such as SAITS (Du et al. 2023a BRITS (Cao et al. 2018 CSDI TTsshir et al. 2021), TimesNet (Wu et al., 2023). or TimeMixer+* (Wang et al. 2025) - are typically deep learning archilectures based on recurrent networks, atlention mechanisms, or diffusion processes. Their main advantage lies in their ability to capture intricate temporal dependencies and model complex data distributions through direct optimization on the target datasct. However, their reliance on large training datasets often limits their generalization ability in zero-shot or crtss-d scenarios, requiring retraining each new task.
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2.2 Time-Indexed Foundation Models for Imputation
The emergence of foundation models marks a paradigm shift toward series analysis. These models are characterized by their zero-shot capability: rather than being fine-tuned for the imputation task, they directly apply their pre-aequired knowledge to new data.
approaches for time
Models such as MoTM (Le Naour et al. 2025) and TabPFN-TS (Hoo et al. 2025) differ from conventional foundation models for time scries forecasting, which often roly on patch- basod attention architectures or exlended LSTM variants (e.g., xLSTM in TiReX (Auer et al. 2025b)) ). Patch- based forecasters are trained to predict ground truth values over given horizon conditioned on sequences of dense fully-observed contexts. However, such models do not handle the diverse missingness patterns of irregular time series inherent to the imputation task. On the other hand, both MoTM and TabPFN-TS adopt continuous-time modeling design that naturally generalizes to unobserved timestamps and allows, at inference time, to: (i) handle irregular or unaligned time series, (ii) operate across different sampling rates, (iii) impute arbitrarily missing regions, and (iv) integrate covariates through concatenation with contextual representations.
In essence, these two lime-indered models learn a contextual representation (1) at every timestamp 1. A regressor re(-) is then applicd to map (t) to the observed time scrics value xzt). Yet, despite their conceptual proximity, both models differ substantially in their architectural design. Below we describe both methods.
МoTM (Mixture of TimeFlow Models). MoTM (Le Naour et al. 2025 extends the continuous-time modeling paradigm by leveraging a sophisticated feature extraction mechanism inherited from the TimeFlow architecture (Le Naour et al.) 2024). Its core principle is to represent any time series through a pro-trained basis of modulated Implicit Neural Representations (INRs; see also (Li et al. 2025
(1) Representation Learning via Modulated INR Basis. Specifically, MоTM does not learn a single function for the time series but rather basis of K distinct INRs. Each INR. is a small neural network, parameterized by hypernelwork (Dupont et al., 2022), that maps continuous time coordinate L to a feature vector. These basis functions are 'modulated" in the sense that their parameters are dynamically generated for each new window, allowing them to capture a wide range of temporal patterns (e.g., trends, seasonalities, high-frequency oscillations) without being restricted to predefined frequencies like Fourier features. For any given timestamp 6, the rich contextual representation (t) is formed by concatenating the outputs of all K basis INRs evaluated at that time.
(it) In-Contezt Imputation vio Local Regression. The key mechanism of MoTM for imputation lies in its local, in-context fitting procedure. Given time scries with missing values, MoTM first considers a context window of obscrved points. It then fits a simple ridge regressor to learn the lincar mapping from the high-dimensional representations (1) of these observed points to their act values sr(). This local regressor, fitted specifically on the available context, is finally used to predict the values at any missing timestamp tmas by applying it to the corresponding representation H (tmiss).
This framework naturally extends to: Covariates inlegration with no relraining. Assuming full observation, additional contextual information available at timestamp
simply stacked to the target contextual representation (t). Ridge adaptation proceeds then in the same way as in the univariate setting, leaving the pretrained basis of INRs unchanged. Quantification of uncertainty. By replacing the ridge regressor with a quantile regressor, MoTM can generate quantile predictions to produce uncertainty quantification intervals around the imputed values.
TabPFN-TS. Hoo al. (0225) apply the continuous-time modeling philosophy by reframing the time series imputation task as standard tabular regression problem. This allows the direct application of the powerful, pre-trained TabPFN model (Hollmann et al. 2025) for zero-shot time series analysis. The model's design philosophy is conceptually inverse to that of MoTM: it pairs a simple, handcrafted feature representation with a highly expressive regression model.
(i) Handcrafted Temporal Representations. Unlike MoTM's learned representations, TabPFN-TS employs a straightforward feature engincering approach. The contextual representation (t) for each timestamp t is constructed by combining the normalized time index itself with set of pre-defined Fourier basis functions
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(i.e., sine and cosine pairs). These Fourier features are chosen to capture key scasonalities expected in the data (e.g., daily, weekly). This method results in a simple, fixed feature set that explicitly encodes temporal position and periodicity, serving as the input for the regression model (see Section A.3.2)
(ii) Imputation via In-Contert Learning with TabPFN. The core expressive power of TabPFN-TS resides in its regressor, the TabPFN model. TabPFN is a large transformer-based architecture pre-trained on hundreds of millions of synthetically generated tabular regression tasks. Its defining characteristic is in-context learning: at inference time, it ingests set of observed data points-paing of temporal features and their corresponding values, (H(tt ((toee) a single 'prompt." The model processes this entire context within its attention layers to infer the underlying functional relationship between the features and the scries values. It then applics this inferred function to predict the values x(Imiss) for the query features H (1miss) of missing timestamps, all within a single forward pass and without any gradient-based fine-tuning.
This framework also naturally supports the Integration of covariates with no retraining and Uncertainty quanlification. In particular, TabPFN inherently models uncertainly by returning distribution over outputs.
3
Experiments
We design our experimental study to assess two key aspects: (i) zero-shot generalization across out-of-domain datasets and (ii) the ability to incorporate auxiliary covariates without retraining. Thus, experiments are organized into two main parts: a large-scale univariate benchmark covering 33 datasets (Section 3.1. and a focused covariate integration study on three datasets (Section 3.2
3.1 Univariate Benchmark: Out-of-Domain Zero-Shot Imputation
In this section, we evaluate the out-of-domain (OoD) zero-shot performance of TabPFN-TS and MoTM across diverse real-world datasets. These datasets cover a wide range of sampling rates (5min, 10min, 15min, 30min, 1h) and exhibit heterogeneous temporal patterns and seasonalities. They originate from open-source collections spanning multiple domains, including climate, energy, traffic, etc. Most are drawn from LOTSA Woo et al.
2024] and GIFT-evol (Aksu et al. 2024). with strict safeguards to prevent leakage from the three pretraining datasets of MoTM. For all details on the datasets please refer to Section B.1. In total, the evaluation involves more than 1.3M incomplete windows.
Protocol and Baselines. All datasets are split. chronologically intro train, validation and test fractions with respective ratios specified in Section B.I The test split divided into four-week segments. For each window, we generate four distinet missing data scenarios, by randomly removing: either (i) 50% and (ii) 70% of the observations (Pointwise scenarios); or (iii) two and (iv) four entire days (Block scenarios). Note that only the supervised baselines (denoted as Task Specific Models) benefit from the train and validation sets. The benchmark includes all the methods described in Section 2 Implementation details, hyperparameters, and method-specinee configurations are provided in Section A
3.1.1 Quantitative univariate results
The aggregated results of our univariate benchmark are shown in Figure [ summarizing the mean normalized MAE across all 33 OoD datasets. Each bar represents the overall imputation error of a model averaged over the four missingness regimes. Models are grouped into three categories reflecting their underlying paradigm: (i) local mothods, imputing without any learned representation; (ii) task-specific models, trained in supervised manner on each dataset; and (iii) foundation models evaluated in a fully zero-shot setting. In addition, Figure 2 presents critical difference (CD) diagram (Demšar 2006) that compares models via their average ranks across datasets and missingness scenarios. See also Table t in Section
C for the full per-dataset results and Section C.4 for additional experiments on datasets with lower sampling rates (daily and weekly).
Results. As shown in Figures and three takeaways emerge from the benchmark.
(i) Time-inder foundation models lead the benchmark. TabPFN-TS achieves the lowest mean normalized MA E, followed by MoTи; both outperform all supervised and local baselines despite being evaluated fully
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TabPFN-TS
0223
SMTS
BATTS
0.47
Linear
526
Model
Seasonal
CSDI
Timesnet
0.637
Timmmixerpp
888
0.530
0.2
0.8
Agg. Normalized MAE (mean)
Foundation Models (Zero Shot)
Task Specific Models
Local Models
Figure 1: Univariate Benchmark Out-of-Domain datasets, reported results are z-normalized MAEs.
Average Rank
1
3
5
9
10
11
TabPFN-TS
Tslanet
SAITS
3.56
5.05
Timesnet
MoTM 3.52
5.00
Timemixerpp
Linear
LOCF
BRITS
528
6.67
CSDI
Seasonal naive
Figure 2: Critical difference diagram over all 33 univariate OOD zero-shot impulation tasks.
zero-shot. In terms of ranking, the CD diagram indicates that TabPFN-TS attains the best average rank and is statistically superior to all competitors (MAE' 0.293, avg. rank 1.35). While MoTM achieves the socond-lowest. aggregate MAE (MAE 0.371), it ranks third by average rank (avg. rank 3.62) and is not significantly different from SAITS under the CD comparison. These results suggest that large-scale synthetic pretrained regressor combined with explicit temporal encodings confers measurable advantage over the Ridge on top of learned continuous representations.
(ii) Task-specific models show limiled robusiness. While SAITS achieves competitive accuracy (MAE = 0.386, avg. rank = 3.56), other supervised approaches such as BRITS, CSDI, or TimesNet lag behind, sometimes performing worse than simple local heuristics (e.g., Seasonal Naive, LOCF). This mixed behavior highlights the limited generalization capacity of fully supervised models, which tend to overfit dataset-specific temporal dynamics - particularly when training data is scarce.
(iii) Local baselines remain resilient. Classical approaches leveraging temporal priors still deliver reasonable performance in heterogeneous settings, as reflected in both their MAE and ranking consistency. For instance, Linear Interpolation achieves an average MAE of 0.506, against e.g 0.664 for CSDI or 0.677 for TimesNet. However, the pronounced gap scparating them from foundation models clearly illustrates the benefits of pretraining time-indexed models, which provide both accuracy and adaptability without retraining.
Overall, the aggregated metrics and the based analysis provide clear evidence that foundation models particularly TabPFN-TS - deliver the most consistent and robust performance for zero-shot time-scries imputation across diverse domains. MoTM also achieves an honorable level of accuracy despite relying on a comparatively simple regressor, underscoring the effectiveness its pretrained fime-indexed representations. Finally, an ablation study in Appendix [ indicates that TabPFN-TS's gains are highly sensitive to the choice of time-index features: the selected handcrafted encoding (normalized time index and daily/weckts /weckly Fourier features) consistently outperforms variants that remove periodicities or replace them with random frequencies.
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3.1.2 Uncertainty quantification results
Beyond pointwise accuracy, it is important to assess how well models caplure predictive uncertainty. Both TabPFN-TS and MoTM natively support quantile estimation, allowing them to produce calibrated uncertainty bounds around each imputed value. Among the baselines, only CSDI provides comparable quantile predictions.
We report in Table 1 the average Weighted Quantile Loss (WQL) (see Section C.3 for loss definition) across eleven representative datasets (full results and more details Scction C.3.2). This metric evaluates both imputation accuracy and quantile calibration. The WQL computed over nine quantile levels, from 0.1 to 0.9, providing comprehensive measure of the models' probabilistic consistency across the predictions.
Table Weighted Quantile Loss (WQL) average scores on eleven representative univariate datasets.
TabPFN-TS
MoTM
CSDI
SAITS-Q
WQL 0.241
0.316
0.453
0.476
Results. Quantitatively, TabPFN-TS achieves the lowest overall WQL score, followed by MoTM and CSDI. SAITS-Q, variant of SAITS where one model trained independently per quantile level, obtains the highest WQL. This suggests that foundation-based models such TabPFN-TS and MoTM not only reconstruct missing values more accurately but also provide better-calibrated uncertainly estimates.
Qualitative examples in Figure 3 confirm these trends: both foundation models adjust their uncertainty bands (5-95 and 25-75 quantile ranges) to local signal variability. TabPFN-TS produces sharper, high-fidelity reconstructions that closely follow the ground truth, while MoTM yields smooth yet robust imputations with stable and well-calibrated uncertainty envelopes. Additional examples are provided in Section C.3.3
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(a) TabPFN Jena Weather!! dataset
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(b) MoTM Hog dataset
Figure 3: Qualitative quantile results in the 70% missing values scenario (Pointwise 2).

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3.2 Integration of Covariates in Zero-Shot OoD Imputation
For model to be practically deployable in real-world applications, must be capable of incorporating covariates, which often enhance predictive accuracy by providing additional contextual information. This requirement is recognized as one of the major challenges for foundation models in time series forecasting as well (Auer et al., 2025a). In this section, we investigate how TabPFN-TS and McTM integrate additional covariates in a zero-shot imputation setting. We conduct experiments on three datasets where the dependence of the time series values on covariates ranges from weak to critical. This section assumes that the covariate is fully observed; the scenario of partially observed covariates is discussed Section E.2
Datasets, Baselines, and Protocol. We evaluate the models on imputation tasks across three datasets: PV-France; aggregated photovoltaic (PV) production curves with the associated global solar irradiance covariate, Wind-France; aggregaled wind production curves with wind speed as covariate, and Load-Prance; aggregated electricity consumption curves with temperature as a covariate. Further details on the datasets and preprocessing are provided in Section B.2
The train validation Lest splits follow the same protocol as Section 3.1
We compare the following methods: TabPFN-TS and MoTM both with or without covariates, a ridge regression using only the covariate predict the target variable, and SAITS. Results are showcased in Table 2
Table Complete MAE results on datasets with covariates. The best score for each setting shown in bold, second-best is underlined.
TabPFX-TS -S
MoTN
Other baselines
TabPFX-TS Covar)
TabPFH-TS (W/o Covaz)
MoTH (M/ Covaz)
MoTN
Ridge
SAITS
Dataset
Setting
(M/o Covar)
Multivar
Pointwise I
0.045
0.109
0.054
0.102
0.115
0.390
Pointurise
0.051
0.160
0.069
0.131
0.123
0.443
PV-France
Blocks
0.052
0.175
0.086
0.191
0.104
0.496
Blocks 2
0.049
0.190
0.086
0.179
0.106
0.485
Pointwisse 1
0.101
0.098
0.128
0.186
0.318
0.359
Pointwise 8
0.138
0.153
0.161
0.244
0.322
0,408
Wind-France
Blocks
0.275
0.170
0.335
0.600
0.321
0,590
illocks
0.317
0.594
0.335
Pointwise
0.037
0.037
0.138
0.146
0.667
Load-France
Pointwiee
0.056
0.059
0.158
0.161
0.667
Blocks
0.143
0.146
0.236
0.243
0.669
0.490
Blocks 2
0.170
0.178
0.262
0.270
0.674
0.498
Integrating covariate improvement
31.54%
31.03%
Results. As shown in Table 2 incorporating covariates generally improves performance, both for TabPFN-TS and MoTM. Substantial gains are observed on datasets for which the covariate strongly informs about the target variable (global irradiance for PV power production, wind speed for wind power production). Under these scenarios and particularly in the challenging block settings, incorporating covariates allows MoTM to TabPFN-TS. This emphasizes how fundamental is
outperform the impressive univariate performances enhance pretrained univariate foundation models with additional contextual information for them to be deployable in real-world applications. On the other hand, weaker relationships, such as between national-level electricity demand and average temperature, yicld marginal to improvement. Overall, TabPFN-TS (With Covar) achieves the best results in most scenarios, confirming its strong capacity to integrate helerogeneous contextual inputs for robust zero-shot imputation.
3.2.1 Qualitative covariates results
To better visualize the impact of incorporating covariates, we present qualitative results for both TabPFN-TS and MOTM. Figure 3 and Figure show examples from the Wind-France France dataset, illustrating how the inclusion of covariate information helps each model reconstruct the four one-day missing blocks more accurately.

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3
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Figure 4: Wind-France dataset. TabPFN-TS qualitative results with and without covariates the four one-day missing blocks scenario.
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Context
MoTM (no covar)
MoTM (with covar)
Covariate
Figure Wind-France dataset. MoTM qualitative results with and without covariates in the four one-day
missing blocks scenario.
Results. As illustrated in Figures and 5 incorporating covariates visually improves the reconstructions for both TabPFN-TS and MoTи. The covariate-enhanne versions capture missing intervals more smoothly and better follow short-term temporal variations within the four one-day gaps. We observe that the interpolations of TabPFN-TS align more closely with the ground truth and preserve sharper transitions across missing regions. In contrast, if MoTM consistently benefits from covariate information, its reconstructions sometimes struggle to capture sudden changes with great accuracy. More covariate plots are showcased in Section D confirming that the most visible gains are observed on the Wind- France and PV-France datascts, while the impact remains limited for Koan-France.
4 Practical considerations
While the previous sections establish the strong zero-shot performance of foundation modcls, equally important assess their practical limitations and behavioral consistency under different conditions. This section provides complementary analyses covering two key aspects: (i) the computational efficiency of the proposed models across datasets of varying scales, and (ii) their robustness to different missingness patterns.
4.1 Computational cost
In this section, we compare the computationss ional elficiency of the proposed models across datasets of varying sizes in Figurej ( The reported times correspond solely to inference for TabPFN-TS, MoTM, and Linear, as these methods operate zero-shot manner. For the supervised bascline SAITS, we report the total time including both training and inference. The analysis spans four representative datasets ranging from small (Covid19 Energy) to large-scale (Traffic) to illustrate the scalability and practical trade-offs between

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methods. For each dataset, the reported MAE results are averaged over the four missing-data scenarios. All experiments are carried out on a single NVIDIA H100-80G GPU.
Compute Time MAE per Dataset
covid 19 energy (0.8K 80 chunks to infer)
jena weather (5K chunks to infer)
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TabPFN
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Figure 6: Compute time (log-scale) versus MAE across datasets of increasing size.
Results. As shown in Figure TabPFN-TS consistently achieves the lowest MAE but suffers from a substantially higher inference time, especially on large datasets. In contrast, MoTM offers a favorable balance between accuracy and efficiency, being up to two orders of magnitude faster while maintaining competitive performance. SAITS attains moderate error levels but requires significant computational overhead due to its supervised training phase. Finally, Linear is the fastest overall but shows markedly poorer accuracy, particularly on more complex datasets. These results highlight the trade-off between zero-shot generalization and computational cost, emphasizing MoTM as a scalable alternative to TabPFN-TS.
Practical deployment considerations. As stated above, a practical limitation of the best model, TabPFN-TS, is its inference cost (sec Section 4.1p:
NVIDIA H100 GPU, forward pass over 672-stop chunk takes approximately one second. This cost can be readily amortized in batch offline imputation low-frequency pipelines, but may be prohibitive for real-time use cases deployments operating thousands of concurrent time series. Accordingly, the clearest deployment recommendation is compute-driven: use TabPFN-TS when GPU acceleration available, and prefer MoTM in resource- coouurccconntraineed settings or when throughput across many sequences becomes the primary bottleneck. A more detailed discussion is provided in Appendix D
4.2 Breakdown by missing patterns
A detailed breakdown of results across the four missingness regimes is provided in Scction analysis highlights clear dependence of model performance on the structure of the missing values. For sparse pointwise removal (50-70% pointwise removal), Linear Interpolation remains highly competitive,
C.2 The

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occasionally matching foundation models-indicattinn that simple local contimuity assumptions suffice when gaps are isolated. However, performance rapidly degrades under structured, block-wise missingness (two and four one-day gaps), where both TabPFN-TS and MoTM maintain stable accuracy and clearly dominate all baselines. Overall, these results confirm the robustness of foundation models to temporally correlated gaps, while emphasizing that local methods remain effective only low-missingness, unstructured regimes.
5 Conclusion and Discussion
Our experiments remonstrate that TabPFN-TS achieves very strong zero-shot performance, both in univariate imputation and when integrating covariates. Nevertheless, its inference times remain significant limitation for some real-world deployment scenarios. MoTN also delivers strong zero-shot performance, outperforming all supervised baselines on the univariate benchmark. Similarly to TabPFN its ability at leveraging additional contextual information is remarkable. However, it is generally less accurate than TabPFN-TS, although it offers substantially faster inference.
These two highly flexible foundation models represent a significant step forward toward "off- the-sheh-eeff zero-shot imputation solutions applicable across wide range of domains. A promising avenue to combine performance and efficiency would be to build more powerful regressor top of the modulated INR features used by MoTM, replacing the current ridge regressor with model trained via in-context learning, potentially merging the strengths of both approaches.
Acknowledgements
We would like to thank the authors of all the time series datasets listed in Section of the PyPOTS Python toolkit (Du et al., (023b)), for cnabling this work by their strong contribution to the open-source time series research community. Finally, thank the reviewers for their thoughtful reviews that. helped improve the paper.
B as well as the authors
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A Baselines details and implementation
In this section, we present the imputers included in our experimental evaluation and detail their implementation. As introduced in Section 2 our selection spans a broad spectrum: from simple naïve baselines, through state-of thee-rrtt supervised deep-learning models, to recent dime-indexed foundation models. This diversity ensures coverage of both lightweight, assumption-free methods and advanced architectures capable of capturing long-range and cross-variable dependencies.
A.1 Local imputers
We considered three naive baselines: a simple linear interpolation, a last observation carried forward, and a seasonal repeat. Note that each imputer operates independently on each incomplete segment and does not. use any cross-variable information.
Linear. This baseline imputes a missing value at timestamp t by linearly interpolating between the closest observed neighbors surrounding the gap. Concretely, it uses the last observation before t and the first observation after t as anchors and fills the interior points on the straight line between them. a lcading gap has no past anchor, we adopt a www.oberraaiioon--rrre-aaaaaaa future anchor, we fall back to
(NOCB) fallback; if a trailing gap has no inteevaattoo-ccrrid-ffoooe (LOCF).
This baseline imputes missing value at timestamp t by copying the most recent available past value (the last observation before t). If the series begins with gap and no past value exists, we perform a single NOCB initialization by copying the first available future observation backward.
LOCF.
Seasonal Naive. This baseline imputes a missing value at timestamp t by using the observation from the previous scasonal period, i.c., the value t - S. The scasonal period pre-defined for cach dataset based on its dominant frequency (e.g., daily or weekly). If the value at (- S is also missing, the method sequentially searches for an available observation at other seasonal timestamps (e.g., L S, then - 28, etc.). If this search fails to yield value, the method falls back to simple LOCF imputation.
A.2 Supervised imputers
We considered six supervised deep-learning basclines spanning complementary neural paradigms: recurrent, Transformers, and diffusion-basser approaches. These include methods built specifically for imputation as well as recent multi-task time-series backbones (convolutional and soken-mixing mixing/Transsiinnii Transformer hybrids) that tackle imputation via balanced accuracy cosuracyyeffiiiennn /efficiency trade-off.
training. This diversity probes different inductive biases and offers a
All models implementations are taken from the PyPOTS Du et al. 2023b) Python toolbox and trained on fixed-length windows where subset of observed entries is randomly masked; each model reconstructs these masks from the remaining context (values + binary observation mask). Inputs are z-score normalized per variable, training minimizes the mean absolute error (MAF) on masked positions only, model selection uses validation MSE with early stopping, and test metrics are computed on the 4 missing points scenarios detailed in Section 3.1 For all baselines, we use the default hyporparamcter settings recommended by the original authors in their papers or public implementations. In addition, for the strongest. supervised baseline, SAITS, we perform an extensive hyperparameter study on 11 representative datascts (see Section F). These experiments show that, while careful tuning can yield modest improvements, the default hyperparameter configuration already provides competitive performance at a substantially lower computational cost than tuning each model separately every dataset. Note that we use the Adam optimizer (Kingma & Ba 2015 for all models with a batch size of 64, train for at most 50 epochs, and apply early stopping with patience of 5 epochs.
SAITS. Transformer imputer with two diagonally-mast self-attention (DMSA) blocks that jointly capture temporal and cross-fcature dependencies; a learned gating mechanism combines both blocks to predict missing values efficiently (Du et al. 2023a
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Hyperparameters. We use Mayers 2, dmodel 256, Rheaad = 4 with dę = d, 64, feed-forward size dun 128 and dropout 0.1. This setting follows the authors' recommended defaults and balances capacity with training stability.
BRITS. A bidirectional RNN imputer with learned temporal decay that processes each window forward and backward, jointly estimating hidden states and missing values while enforcing consistency between directions $Cao et al. 2018
Hyperparameters. single-stack bidirectional GRU with rnn ran_ hiddhhidddde__eee size = 64 and dropout = 0.3. This mirrors common BRITS configurations and provides a compact baseline for irregular gaps.
CSDI. A conditional dilfusson impuler that models p(Xmiss Xabs) via score-based denoising; training adds Gaussian noise to targets and conditions the denoiser (Transformer/Uue /U-Net with time embeddings) on values and masks, cnabling stochastic imputations at inference (Tashiro et al. 2021
Hyperparumeters. Translormer/Une NU-Ne backbone with Mayers = 4, Theadd = 4, Achannels 64; time, feature, and diffusion embeddings of sizes 128, 32, and 128, respectively. We use Rdiiffssion steps = 50, and a quadratic noise schedule type. These values track the public defaults for efficient training while preserving sampling quality.
TemesNet. A multi-periodic convolutional model that folds each 1D series into 2D tensors along discovered periods and applies multi-scale 2D CNN blocks to capture intra- and cross-period structure; we train it for masked-valuc reconstruction (Wu et al. 2023
Hyperparamelers.. We set Mayyers = 2, dmodel 128, den 256, Wkennels = 6, top k= 3, and dropout 0.1. This lightweight configuration keeps computation modest while retaining the multi-periodic 2D convolutional capacity.
+ A token-mixing hybrid (Transformer/ MMLP designed for multi-periodic patterns with lightweight mixing blocks and skip connections; adapted here to imputation by reconstructing randomly masked entries from the observed context (Wang et al. 2025
Hyperparameters. We use 7layers = 3, dmocel = 64, dg = 128, top k= 8, Rkeernlls = 6, Theads = 4, with channel mixing and channel independence, dropout 0.1, and downsampling (Neowwsammlingg layers = 3 and Sbownsampling_wwddee window = 2). This mirrors the authors' small/efficient setting adapted for masked reconstruction.
A lightweight convolutional model replacing self-attention with an Adaptive Spectral Block (Fourier-domain features with adaptive thresholding) and an Interactive Convolution Block for local global mixing: trained for single-pass reconstruction of masked entries (Eldele et al.) 2024
TSLANet.
Hyperparameters. Three layers (n _l_leysrs- =3) with patch size 16, embedding dimension dembedding 256, mask ratio 0.4, and dropout 0.1 matching the default hyperparameters of the official codebase.
A.3
Time- Index Foundation models
This section complements Section 2.2 by providing further implementation details for the two time-index foundation models evaluated in our experiments: MoTM and TabPFN-TS.
A.3.1 MoTM.
Implementation Details. Our implementation strictly adheres to the architecture and methodology described in the original paper (Le Naour el al. 2025). We utilize the three publicly available pre-trained TimeFlow (modulated INRs), which were respectively trained on the Electricity, Solar10T, and Sponish Temperatures datascts (further details on these datasets are available Scction B.1). For full reproducibility, both the source code and the pre-trained INR weights were obtained from the official repository: https //github. Soim//tienntnn Etwieeenre//oMMM
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A.3.2 TabPFN-TE TS.
Implementation Details. For our experiments, we utilize the official TabPFNv2 implementation from the tabpfn Python package, which includes the pre-trained TabPFNv2 model described in (Hollmann et al. 2025 We employ a consistent feature representation, (t), across all datasets, defined as:
H11)= (2, [,,sin
2xl Paay
2TL Paay
2xl P week
2xl
cos
sin
P Peeek
In this formulation, t is the normalized time index, Paay represents the number of timesteps (normalized) in 24-hour period (e.g., 24 for hourly data, 48 for 30-minute data, 96 for 15-minute data etc.), and week is set to 7 x Paay to capture weekly seasonality. For full reproducibility, the source code and pre-trained regressor are publicly available at
A.4 Excluded baselines
Our main univariate benchmark includes two foundation models, six deop supervised imputers and three local baselines. Although exlensive, this selection could be complemented by several other models. Below we motivate why other relevant foundation models (MOMENT and NuwaTS), deep supervised models and local baselines (Spline Interpolation) where not included in the main experiments. For the sake of completeness, evaluation of these excluded baselines on representative subset of the benchmark is carried out in Section A.4.1 confirming that they lack robustness to perform well on diverse datasets and settings.
MOMENT. We considered including MOMENT (Goswami et al. 2024 a large Transformer-based foundation model pro-trained on patchod time scries via a masked modcling objective. Initially, our intent was evaluate it zero-shot imputation baseline alongside TabPFN-TS and MoTM. However, its performance in our benchmark was found to be substantially lower than that of the other methods. A closer review of the original paper clarifies this result: the authors primarily advocate for fine-tuning the model on specific downstream tasks to achieve optimal performance. Moreover, their reported imputation experiments are limited to very short missing segments, a scenario that differs significantly from those addressed in our work. Given its unsuitability for zero-shot time series imputation, we excluded it from our final comparative analysis.
NuwaTS. NuwaTS is another Transeormer-based model specifically designed to address zero-shot time series imputation by repurposing pretrained language models (Cheng et al. 2024). Although the public codebase IT does not provide any off-the-shelf pretrained models, the official demonstration allows experimenting with a version pretrained on fixed segments of length 96. To integrate NuwaTS into our evaluation pipcline, wo adapted this demonstration model by splitting each considered time series into multiple 96-length segments from which NuwaTS could extract shared information. This workaround is clearly non-ideal but enables a preliminary zero-shot assessment of the model under comparable conditions. Consistently with the rest of our analysis, these experiments indicate that NuwaTS trails substantially behind
foundation models.
Other deep learning supervised imputers. The field of deep learning for supervised time series imputation a rapidly evolving area of research. Our selection of baseline models aims to provide a representative sample of this landscape, including both supervised methods that have become standard benchmarks and more recent, stale-of-the-art architectures. To ensure fair and reproducible comparisons, all selected deep learning supervised models are part of the PyPOTS library (Du et al. 2023b). This framework was essential for conducting our extensive benchmark.
Spline interpolation. Cubic Spline interpolation a simple non-linear imputation method based on piecewise polynomials of third-order. Although it produces smooth interpolations and an accurate fit, this method is known to be prone to overfitting under sparse or noisy observations.
Code available at http:///gtthhb.cc///a///a//e/eee
Demo available al
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A.4.1 Additional experiments
Setting. We conduct supplementary experiments to evaluate MOMENT (Goswami et al. 2024), NuwaTS (Cheng et al. 2024) and a Cubic Spline Interpolation. MOMENT and NuwaTS operate in a fully zero-shot setting. They are compared against TabPFN-TS, MoTM and Linear Interpolation Table shows their performance on cleven representative univariate datasets (sce Section
B and four missingness scenarios (sce Section 3.1
Table 3: Complete MAE results of additional baselines MOMENT, NuwaTS and CubicSpline 11 datasets. For each setting, the best score (lowest) is in bold and the second best is underlined.
Dataset
Setting
TabPFK-T8
NoTM
NOMENT
NuvaT8
Cubicāpline
Linear
Pointwilse
0.171
0.302
1,026
0.349
0.281
0.229
Pointwise 2
0.223
0,240
1.026
0.436
0.447
0.330
BDC2-Bear
Blacks 1
0.272
0.332
1,075
0,519
3.033
0.557
Bloccks 2
0.280
0.336
1.077
0.535
3,0000
0.861
Pointaiise
0.196
0.231
0.352
0.317
0.247
Pointwise
0.256
0.273
0.814
0.428
0.504
0.334
BDG2-Rat
Blacks 1
0.349
0.400
0.808
0.516
4.009
0.743
Blacks
0.4012
0.744
Pointwise
0.075
0,089
1,024
0.287
0.124
0.163
Pointwise 2
0.132
0.127
1,021
0.381
0.272
0 0.292
Covid19 Energy
0.202
0.949
Bllacks 2
0.201
0.212
1,033
0.474
1.107
0,928
Pointwise
0.143
0.189
0.985
0.348
0.202
0,232
GFC12 Load
Pointwiee
0.231
0.136
0.419
0,370
Blockss 1
0.353
0:382
1.033
0.486
2,622
0.820
Blocks B
0.363
0.387
1,017
0.199
2, 2,682
0.814
Pointwise
0.196
0.240
0.979
0.320
0:287
0.216
Hog
Pointwise 2
0.260
0.286
0.979
0.375
0.426
0 0,280
Blocks 1
0.396
0.458
1,029
0.491
3.043
0.505
Blocks B
0.106
0.461
1,029
0.502
2.848
0.561
Pointwiie
0.086
0.190
0.982
0.143
0.101
0.080
Jena Weather 10T
Pointwisse
0.165
Blocks 1
0.378
0.453
1,030
Nos
4.774
0.527
Blacks 2
0.384
0.459
1.024
Nan
4,246
0.544
Pointwiss
0.120
Pointwiss 2.
0.214
0,272
0.983
0.364
0.343
0.243
Weather
Blacks 1
0.366
0.463
1.078
0.475
2,898
0.552
Blacks 2.
0.370
0.464
1,055
0.489
2:605
0.555
Pointwisse
0.150
0.227
0.984
0.318
0.176
0.164
Oikolab Weather
Pointwise 2
0.228
0.278
0.981
0.391
0.316
0,218
Blacks 1
0.449
0.529
1.033
0.556
1.732
0.638
Blocks 3
0.154
0.531
1.013
0.562
1,801
0.636
Pointwise
0.062
0.091
0.981
0.209
0.120
0.191
PDB
Pointwise
0.119
0.121
0.977
0.339
01.778
0
Blocks 1
0.171
1.7
1.051
0.352
1,200
0 0.962
Blocks
1.006
Pointwrie Pointwise 2
0.150
0.196
1.015
0.133
0.401
0.329
Pedestrian Counts
0.200
0.239
1.015
0.502
0.689
0.447
Blocks Biocks 2.
0.251
3.611
1.001
0.178
0,260
1.099
0.513
5.382
1.000
Pointulse
0.257
0.298
0.968
0.360
0.359
0.259
Weather
Pointwise
0.342
0.965
0.521
0.322
Blacks 1
0.456
0.494
1.027
0.527
2.982
0.620
Blookss 2
0.455
0.488
1.018
0.528
2.998
0.618
Moan (Std)
0.252 (0.114)
0.300 (0.122)
1.002 (0.070)
0.419 (0.101)
1.613 (1.535)
0.502 (0.296)
Results. Table shows the z-normalized MAE scores across all eleven datasets and four missingness settings, enlighting why MOMENT, NuwaTS and Cubic Spline Interpolation where excluded from the main benchmark. (i) NOMENT fails to produce accurate predictions across all datascts and settings, confirming that it is not a suitable zero-shot time-series imputation model. (ii) NuwaTS outperforms NOMENT yet lags significantly behind TabPEN-TS on all datasets and settings and behind MoTM on ten out the eleven datasets. Altogether, these obscrvations strengthen the time-indexed approaches as strong alternatives to Transformer-based foundation models for time series imputation. (iit) Finally, the Cubic Spline Interpolation suffers from severe overfitting in challenging scenarios, such as high missingness rate (Pointwise 2, 70% of missing values)
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block scenarios. By contrast, the Linear Interpolation provides more robust predictions and outperforms
Cubic Splines in 39 out of 44 settings.
B Datasets details
B.1 Univariate datasets
The complete list of datasets used in our univariate experiments is shown in Table [ in total: 3 for the pretraining of MоTM and the remaining 33 for the zero-shot evaluation of both TabPFN-TS and MoTM. Each dataset is split chronologically intro train, validation and test. Unless otherwise stated, the respective ioactions are 0.7, 0.1 and 0.2. The test segments were then generated by applying four-week sliding window, where at every step random stride is drawn uniformly between 0.5 and 2 days. This procodure ensures that the inference samples are not aligned on any specific calendar information. short description of each dataset provided below. Those datasets marked with an *** were curated remove flat segments at inference to avoid biasing the evaluation towards trivial scenarios. Flat segments are caused e.g. heterogeneous sensor operating dates within datasets or by filling long missing blocks with zeros EEami
36 datasets were used
et al. 2023
Energy domain
BDG2-Bear*, BDG2-Rat* and Hog* are the energy demands of commercial buildings the US in 2016 2017. Sourcod by the BuildingsBench library (Emami et al. 2023) from the Building Data Genome (BDG2) project (Miller et al. 2020).
Borealis* and Ideal* contain the total electricity consumption of, respectively, 15 homes in Waterloo, Ontario, in 2011-2012 and 217 homes in Edinburgh, UK, between 2016-2018. Both datasets were released as part of the BuildingsBench dataset, and include a marginal amount of data preprocessing (including interpolation of missing values and outlier removal) (Emami et al. 2023
Covid19 Energy the aggregated electricity demand of an entire metropolitan area, from 2017 to 2021 Farrokhabadi et al. 2022).
GFC12 Load is sourced from the Global Energy Forecasting Competition 2012 and contains total of 20 aggregated load series (Wang et al. 2023
PDB is a Kaggle dataset containing electricity demand and outdoor temperature data in 2013-2014. We omitted the temperature and kept only the electricity demand (Wang et al. 2023).
Electricity contains the hourly-agrregated electricity consumption of 370 households in Portugal in 2011-2014 [Tiindade] 2015).
KDD Cup 2022 is dataset for the Spatial Dynamic Wind Power Forecasting Challenge hosted at KDD in 2022 (Zhou et al.] 2022). Tt contains the wind power data of 134 wind turbines from wind farm over half a year. We kept the wind power generation variable as the target variable and omitted extra covariates (wind speed and direction, temperature, etc.). The train validation / test split is 0.65 / 0.15 / 0.2.
Solar contains the syathetic power production of 137 photovoltaic power plants Alabama 2006. Datasot sourced by Lai et al. (2018) using simulations from NREL's 's Solar Power Data for Integration Studies
ETT1 and ETT2 respectively contain measurements of oil temperature of two electrical transformers in China, well as six additional covariates. We used these 7 variables in our experiments, handling them with channel independence. The datasets were collected and published by Zhou et al. 2021
the hourly energy consumption of 5561 households in the UK between 2011 and 2014. Data sourced by Godahhwa al. (2020) from https://data. london. . gov. uk/dataset/ smartmeter emarrmettr--nnrryy-uue energyy-u--rr--ee-eee catr--ussedda----e data-in- www--oonnnooousshee experiments.
London Smart Meters Small
We kept random subset of 500 samples in our
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Table 4: All datasets used in our univariate experiments and their key properties.
Release flatform
MоTM Use
Num. Series
Series Length
Num. Test
Dataset
Domain
Freq
Segments
Electricity
Zenodo
Energy
Train
III
370
35064
122623
Solar-100 10T
Zenodo
Energy
Train
10min
137
52560
9179
Spanish Temperatures
Kaggle
Climate
Train
IH
5
35000
1090
BDG2-Bas Bear
LOTSA
Energy
Test
1H
91
17544
7522
BDG2-Rat
LOTSA
Energy
Test
III
280
17544
24915
Borealis
LOTSA
Energy
Test
III
15
7447
77
1ovid19 Energy
LOTSA
Energy
Test
IH
1
31912
195
GFC12 Load
LOTSA
Energy
Test
20
39414
4960
Hog
LOTSA
Energy
Test
III
24
17544
2310
Ideal
LOTSA
Energy
Test
III
217
16167
156
PDB
LOTSA
Energy
Test
IH
1
17520
96
KDD Cup2022
LOTSA
Energy
Test 10min
134
35279
2546
ERA5 goopotential
LOTSA
Climate
Tost
1H
500
8736
19000
ERA5 humidity
LOTSA
Climate
Test
1H
500
8736
19000
ERA5 temperature
LOTSA
Climate
Test IH
500
8736
19000
ERA5 wind speed
JOTSA
Climate
Test
500
8736
19000
Oikolab Weather
LOTSA
Climate
Tost
1H
8
100057
5288
Pedestrian Counts
LOTSA
Transport
Test
1H
66
96400
7733
Traffic
LOTSA
Transport
Test
1H
861
17544
83479
PEMS BAY
LOTSA
Transport
Test
5min
325
52128
2275
PEMS 03
LOTSA
Transport
Tost
5min
358
26208
358
SHMETRO
LOTSA
Transport
Test
15min
576
8809
576
ETT1-15T
G-Fa--vval
Energy
Test
15min
7
69680
1050
ETT1-1H
GIF -eval
Energy
Test
1H
7
17420
1092
ETT2-155
GIF Tevall
Energy
Test 15min
7
69680
1050
ETT2-1H
GIF Teval
Energy
Test
IH
7
17420
1092
Solar-1H
GIF Teval
Energy
Test
1H
137
8760
8768
Jena Weather 10T
GIF T eval
Climate
Test 10min
21
52704
1428
Jena Weather 1H
GIF eeval
Climate
Test
1H
21
8784
1344
Loop Seattle 5T
GIF -vaa
Transport
Test 5min
323
105120
21964
Loop Seattle 1H
GIF'T-oo
Transport
Test
1H
323
8760
20672
MDense
GIF -vva
Transport
Test 1H
30
17520
4710
Enedis LDM Small
Zenodo
Energy
Test
30min
500
17424
20500
London Smart Meters Small
Chronos
Energy
Test
30min
500
22000
25779
Spanish Energy Weather
Kaggle
Energy
Test
1H
9
35064
1962
Informer
Climate
Test
1H
11
35064
2398
Enedis LDM Small dataset of 10k one-year individual electricity consumptions generated by a latent diffusion model at 30-min sampling rate and representative of thermo-sensitive French households (Nabil
ct al.
2025 We kept random subset of 500 samples in our experiments.
Spanish Energy is Kaggle dataset containing the electricity (i) consumption and (ii) production for Spain from 2015 to 2018. We used the total load demand as well as electricity generation of eight energy sources (biomass, fossil gas, fossil hard coal, solar, onshore wind and three technologics of hydropower). We kept these nine variables in our experiments, handling them with channel independence. Data were obtained from https //www. kaa.geee..cn//aaaaaattcccctaaaio
consumption-e wwweeeeeieeeeeiiiieeeeee and-weather
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Climate domain
Spanish Temperatures contains the hourly temperature measurements for the five largest citics in Spain, from 2015 to 2018. Data were obtained from httpps://ww. www.k..agge...
http:::/wsa...gggle...caaaatttts ccnm//attaastts/ncccollaass//// energy-consumpiicc wew.ppptooooeeeetiiooooo---ee oo wttprrooo--piiee--a--eeeeeeeeeee and-weather
generation
ERA5 is part of the ClimateLearn library, which provides historical worldwide time series of various climate (atmosphere and land-surface) variables, including geopotential, humidity, temperature, and wind speed [guyen et al. 2023). The dataset extracted by LOTSA is based on a 64 x 128 grid structure (Woo et al,, 2024). In our experiments, we used data for year 2000 and kept a random subset of 500 samples out of the 8192 available grid points.
Oikolab Weather contains hourly measurements of eight meteorological variables from a weather station located near Monash Universily, Australia (Godahewa et al., 2021 All eight. channels are kept in our experiments, treating them univariate samples (channel independence).
Jena Weather contains 21 metcorological indicators, such as air temperature, humidity, etc. collected in 2020 at a 10-minute sampling rate from a weather station in Germany. Sourced by Wu et al. (2021) from https://www. bgc-jena. mpg...p......................... de/wetter/ All 21 variables are kept in our experiments, treating them as univariate samples (channel independence).
Weather contains hourly measurements of 11 meteorological variables (including temperatures, wind speed and direction, humidity, altimeter) in the US, during the period 2010-2013. We used the 11 variables in our experiments, handling them with channel independence. Sourced by Zhou et al. 2021 from https data/
//www noaa.
Transport domain
Pedestrian Counts* contains hourly pedestrian counts captured from 66 sensors in Melbourne city starting from May 2009 and up to 2020. It is part of the Monash Time Series Forecasting Library (Godahewa et al. 2021 and is sourced from the City of Melbourne)
Traffic is collection of 48 months (2015-2016) road occupancy data from the California Department of Transportation (Lai et al. 2018). The road occupancy rates (between 0 and 1) are measured by different sensors on San Francisco Bay area freeways.
Loop Seattle contains one-year traffic state data from 323 sensor stations in the Greater Seattle Area, in 2015. Data were collected from inductive loop detectors deployed on four connected freeways (Cui et al. 2019
PEMS03 is a highway traffic dataset collected by Song et al. 2020) from the California Department of Transportation Performance Measurement. System (Pe.SS) PEMS03 contains 358 sensors with measurements from January to November 2018. We used four weeks of data for validation, four weeks for testing and the first 35 days for training.
PEMS BAY contains six months of measurements of traffic speed from 325 sensors in the Bay Area, California, in 2017 (Li et al. 2018). The train validation / test split is 0.65 0.155 (28 days) 0.195.
SHMETRO contains the passengers inflow and outflow measurements of 288 subway stations in Shanghai for three months in 2016 (Liu et al. 2020). We kept four weeks of data for validation, four weeks for testing and the first 35 days for training.
M Dense contains measurements of traffic intensity (number of cars per hour) from 30 sensors located in the city of Madrid, Spain, in 2018-2019. The dataset sourced by the LibCity library through the open data portal of the Municipality of Madrid (de Modrano & Aznarte 2020 Jiang et al.) 2023
B.2 Datasets with covariates
Table shows the key properties of the three datasets used for the evaluation of imputation with additional covariates. Each dataset is split chronologically intro train, validation and test. splits with respective fractions
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0.7, 0.1 and 0.2. Four-week segments are generated in the same manner as in Section B.1 for the univariate experiments.
Table 5: All datasets with covariates used in experiments and their key properties.
Release Platform
Target Series
Series Length
Num. Test
Dataset
Freq
Covariate
Segments
RTE
PV-France
1H
8760
38
Meteo France
RTB
Wind-France
IH
1
8760
38
Meteo France
RTE
Load-France
30min
17520 41
Enedis
PV-France contains the aggregated photovoltaic (PV) power production (target variable) and the average solar irradiance (covariate) in the southern French region Occilanie 2021. This dataset was obtained by aggregating two sources of data. (1) The target PV power production is provided by France's Transmission System Operator (RTE) and ex- tracted through their data portal https://www. www.wrree-ranceee. www.eeeccoee...eeeeeeeeeeeeee www/en/eco2miz././c////oo// wttpa////doooooddndddeeeee (ii) The global solar irradiance is obtained from the French weather institute Meteo France https://metes Lata.gour, ft/f///aaee
We aggre-
gated the in-silu observations at the department level into a region-level irradiance.
Wind-France contains the aggregated wind power production (target variable) and the wind speed (covariate) in the northern French region Hauts-de-Frui France in 2021. Similarly to PV-France, this datasct obtained respectively via RTE's data portal for the wind power production and via Meteo France for the wind speed.
Load-France contains the total French electricity demand (target variable) and the average temperature (covariate) in 2022. Similarly to PV-France and Wind-France, the total electric- ity demand is obtained from RTE's dała portal, The national temperature is provided by Enedis, the French distribution grid operator, from https://data. enedis. fr/ ftrexppore/ddtaseet aageeuudorayommmeenn///aaee wtwpa//emmmnn/nfommttiooo//////o
Univariate benchmark: extensive results
C.1 Full results
Table 0 reports the complete univariate imputation benchmark across all datasets and missingness settings. These detailed results complement the main text by providing per-dataset performance for every method, allowing finer comparison of their robustness and consistency across different missingness patterns and time series domain. For more details about the datasets please refer to Section B.1 All experiments were carried out on single NVIDIA A100-40G H100-80G GPUs.
Table 6: Complete univariate benchmark results for all datasets and missingness settings. Best in bold, second-best underlined. Settings Pointwise and Pointwise 2: respectively 50% and 70% of observations removed at random. Settings Blocks and Blocks 2: respectively two and four entire days removed at random.
Foundation models
Task Specific Models
Local Models
Dataset
Setting
TabPFX -TS
MoTM
SAITS
BRITS
CSDI
Time
Times
TS1a
Linear
Seasonal Nsive
LOCF
nizerpp
net
pet
Pointuiee 1 0.171
0.202
0.241
0.309
0.234
0.827
0.829
0.833
0.229
0.532
0.391
BDG2-Bear
Pointwise 2
0.223
0.200
0.309
0.432
0.284
0.825
0.830
0.833
0.330
0.587
0.545
Blocks
0.831
Blocks 2
0.280
0.336
0.405
0.471
0.395
0.829
0.819
0.832
0.861
0.473
0.904
Continued next
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Table 6 Continued from previous page
Foundation models
Task Specifie Models
Local Models
Dataset
Setting
TabPFx -TS
MoTN
SATTS
BRITS
CSDI
Time mixerpp
Times net
T31a
Linear
Seasonal Naive
LOCF
pet
Pointwise
0.196
0.231
0.266
0.279
0.251
0.812
0.818
0.247
0.587
0.380
Pointuisee 2
0.256
0.273
0.339
0.338
0.314
0.813
0.814
0.818
0.334
0.646
0.507
BDG2-Rat
Blocke 1
0.349
0.400
0.195
0.503
0.194
0,813
0.808
0,816
0.743
0.536
0.811
Blocks 2
0.355
0.402
0.497
0.508
0.498
0.813
0.808
0.816
0.744
0.536
0,814
Posntwiee
0.117
0.519
0.403
0.407
0.687
0.598
0.535
0.596
0.412
0.617
0.543
Pointwise 2
0.488
0.583
0.468
0.442
0.672
0.594
0.545
0.597
0.505
0.674
0.601
Borealls
Blocke 1
0.536
0.646
0,518
0.508
0.685
0.627
0.541
0,612
0.633
0.602
0.718
Blocks 2
0.522
0.629
0.519
0.504
0.658
0.612
0.537
0.602
0.658
0.612
0,638
Posntwiee 1
0.075
0.099
0.399
0,307
1.113
0,105
0.414
0.852
0.163
0.438
0.387
Covid19 Energy
Pointwise 2
0.132
0.127
0.417
0.436
1.118
0.486
0.417
0.854
0.292
0.483
0.370
Blocks 1
0.222
0.432
0.629
1.117
0.604
0,440
0.858
0.949
0.399
0.975
Blocks 2
0.201
0.232
0.436
0.638
1.114
0.599
0.461
0.842
0.928
0.392
0.939
Pointwise 1
0.143
0.189
0,188
0.263
0.174
0.789
0.776
0.803
0.232
0.603
0.448
GFC12 Load
Pointwise 2
0.237
0.231
0.280
0.457
0.248
0.789
0.787
0.804
0.370
0.670
0.600
Blocks 1
0.353
0.382
0.417
0.524
0.428
0.793
0.788
0.797
0.546
0.868
Blocks 2
0.363
0.387
0.425
0.541
0.436
0.799
0.796
0.803
0.814
0.546
0.871
Pointwise 1
0.196
0.240
0.245
0.244
0.279
0.585
0.785
0.802
0.216
0.701
0.322
Hog
Pointwisse 2
0.260
0.286
0.320
0.326
0.350
0.593
0.795
0.801
0.280
0.759
0.418
Blocke 1
0.396
0.458
0.518
0.562
0.569
0.651
0.766
0.799
0.535
0.640
0.668
Blocke 2
0.106
0.464
0,528
0,568
0,580
0.655
0.766
0.795
0.564
0.619
0.673
Pointwiise 1
0.501
0.570
0.443
0.464
0.603
0.531
0.702
0.691
0.526
0.678
0.620
Ideal
Pointwise 2
0.571
0.644
0.173
0.507
0.638
0.572
0.706
0,692
0.592
0.701
0,683
Blocks 1
0.558
0.667
0.498
0.543
0.655
0.5:3
0.706
0.696
0.730
0.650
0.724
Blocke 2
0.561
0.658
0.485
0.522
0.6-18
0.197
0.688
0.676
0.699
0.657
0.744
Pointuiise 1
0.062
0.094
0.337
0.408
1.122
0.449
0.395
0.864
0.191
0.375
0.435
PDB
Pointwise 2
0.119
0.121
0.373
0.556
1.128
0.550
0.599
0,858
0.338
0.413
0.631
Blocks 1
0.171
0.197
0.353
0.637
1.108
0.726
0.265
0.832
0.982
0.331
1.004
Blocks 2
0.177
0.201
0.356
0.653
1.113
0.740
0.291
0.847
1.006
0.336
1.010
Pointwise 1
0.099
0.237
0.115
0.764
0.171
0.761
0.758
0.775
0,092
0.955
0.139
KDD Cup2022
Pointwise 2
0.255
0.161
0.768
0.217
0.767
0.766
0.776
0.115
0.176
Blocks 1
0.571
0.636
0.628
0.763
0.914
0.763
0.764
0.769
0.467
0.939
0.654
Blocke 2
0.500
0.634
0.624
0.758
0.912
0.758
0.761
0.765
0.464
0.927
0. 0.660
Pointwise 1
0.091
0.168
0.149
0.161
0.163
0.251
0.813
0.815
0.104
0.728
0.224
ERA5 geo.
Pointwise 2
0.146
0.208
0.219
0.275
0.253
0.427
0.814
0.815
0.791
Blocks 1
0.333
0.452
0.525
0.905
0.680
0.709
0.806
0.808
0.473
0.681
0.627
Blocke 2
0.336
0.449
0.524
0.908
0.680
0.710
0.807
0.809
0.475
0.681
0.629
Pointwise 1
0.129
0.212
0.169
0.177
0.216
0.413
0.788
1.670
0.131
0.664
0.240
ERA5 humidity
Pointursse 2
0.200
0.254
0.233
0.270
0.315
0.544
0.792
1.320
0.191
0.748
0.314
Blocke 1
0.336
0.431
0.115
0.501
0.608
0,558
0.787
2.059
0.372
0.603
0.500
Blocks 2
0.417
0.503
0.608
0.784
1.989
0.373
0.606
0.506
Pointwise 1
0.094
0.168
0.158
0.157
0.177
0.181
0.817
1.084
0.112
0.700
0.237
ERA5 temp.
Pointuusse 2
0.150
0.208
0.231
0.250
0.261
0.603
0.815
0.947
0.174
0.765
0.340
Blocke 1
0.327
0.438
0.520
0.534
0.677
0.725
0.810
1.292
0.504
0.651
0.647
Blocks 2
0.331
0.436
0.521
0.539
0.681
0.808
1.258
0.503
0.653
0.647
Pointwise 1
0.124
0.225
0.176
0.182
0.195
0.797
0.790
3. 3.795
0.127
0.945
0.252
ERA5 wind
Pošntwise 2
0.201
0.281
0,248
0.298
0.285
0.793
0.795
2.637
0,187
0.991
0.3-16
Blocks 1
0.461
0.604
0.552
0.706
0.722
0.802
0.800
5.137
0.465
0.902
0.685
Blcke 2
0.464
0.604
0.553
0.713
0.720
0.799
0.797
4.954
0.467
0.910
0.687
Pointwise 1
0.150
0.227
0.207
0.207
0.226
0.802
0.824
0.827
0.164
0.811
0.313
Oikolab Weather
Pointwise 2
0.228
0.278
0.294
0.327
0.321
0.505
0.826
0.828
0.248
0.857
0.436
Blocks 1
0.449
0.529
0.581
0.669
0.739
0,820
0.815
0.823
0.635
0.766
0.786
Block 2
0.454
0.534
0.584
0.674
0.735
0.821
0.818
0.826
0.636
0.770
0.787
Pointwise 1
0.150
0.196
0.240
0.268
0.176
0.804
0.812
0.347
0.326
Pedestrian Counts
Pointuise 2
0.200
0.239
0.289
0.387
0.213
0.793
0.806
0.812
0.447
0.383
0.684
Blocke 1
0.172
0.254
0.243
0.619
0.210
0.797
0.795
0.810
1.001
0.307
1.002
Blocks 2
0.178
0.260
0.252
0.632
0.214
0.797
0.797
0.811
1.000
0.310
0.997
Pointuiise 1
0.172
0.237
0.174
0.208
0.208
0.735
0.735
0.744
0.288
0.380
0.498
Traffic
Pointwise 2
0.216
0.285
0.225
0.242
0.242
0.738
0.738
0.714
0.121
0.416
0.670
Blocks 1
0.204
0.235
0.252
0.252
0.731
0.744
0.340
0.985
Blocks 2
0.210
0.307
0.242
0.256
0.256
0.732
0.732
0.744
0.986
0.341
0.985
Pointuisse 1
0.123
0.297
0.530
0.299
1.413
0.642
0.314
0.675
0.168
0.254
0.275
SHMETRO
Pointwise 2
0.143
0.325
0.537
0.376
1.493
0.641
0.450
0.673
0.219
0.280
0.363
Blocke 1
0.190
0.407
0.538
0.632
1.283
0.612
0.277
0.671
0.963
0.217
0.970
Blocks 2
0.197
0.409
0.546
0.632
1.441
0.642
0.289
0.670
0.917
0.220
0.910
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Table 6 Continued from previous page
Foundation models
Task Specific Models
Local Models
Dataset
Setting
TabPFX -TS
MoTN
SATTS
BRITS
CSDI
Time mixerpp
Times
T31a
Linear
Seasonal Naive
LOCF
net
pet
Pointwise
0.133
0.189
0.353
0.360
1.300
0.439
0.883
0.148
0.349
0.183
PEMS08
Pointuisee 2
0.148
0.197
0.351
0.496
1.440
0.862
0.605
0.881
0.136
0.377
0.206
Blocke 1
0.233
0.333
0.376
0.862
1.150
0.867
0.323
0,879
1.098
0.330
1.109
Blocks 2
0.229
0.332
0.367
0.855
1.176
0.861
0.312
0.872
1.083
0.315
1.097
Posntwise 1
0.127
0.306
0.188
0.195
0.863
0.558
0.595
0.612
0.121
0.458
0.170
Pointwise 2
0.146
0.322
0.197
0.203
0,851
0.558
0.615
0.642
0.145
0.490
0.207
PEMS BAY
Blocke 1
0.324
0.513
0.423
0.135
0.865
0.555
0.638
0,641
0.775
0.422
0,800
Blocks 2
0.329
0.521
0.423
0.436
0.875
0.560
0,639
0.643
0.776
0.427
0,795
Posntwiee 1
0.180
0.288
0.227
0,260
0.267
0.535
0.500
0.793
0.183
0,610
0.256
Pointwise 2
0.208
0.311
0.262
0.357
0.322
0.585
0.619
0.793
0.213
0.618
0.316
ETTI-15T
Blocks 1
0.445
0.504
0.662
0.760
0.688
0.783
0.626
0.791
0.821
0.584
0.890
Blocks 2
0.452
0.513
0.660
0.759
0.698
0.780
0.648
0.790
0.814
0.581
0.883
Pointwise 1
0.230
0.279
0.314
0.309
0.380
0.787
0.596
0.797
0.279
0.588
0.446
ETTI-1H
Pointwise 2
0.306
0.326
0.404
0.399
0.482
0.784
0.692
0.797
0.381
0.630
0.582
Blocks 1
0.412
0.465
0.577
0.683
0.793
0.610
0.796
0.820
0.562
0.882
Blocks 2
0.419
0.473
0.583
0.617
0.690
0.793
0.617
0.796
0.828
0.557
0.891
Pointwise 1
0.281
0.321
0.333
0.341
0.450
0.778
0.758
0.801
0.293
0.698
0.426
ETT2-1H
Pointwisse 2
0.350
0.371
0.395
0.420
0.514
0.780
0.761
0.801
0.365
0.750
0.525
Blocke 1
0.480
0.526
0.568
0.635
0.697
0.790
0.781
0.798
0.686
0.674
0.784
Blocke 2
0.190
0.527
0,575
0,612
0.692
0.788
0.783
0.797
0.689
0.663
0.785
Pointuuise 1
0.215
0.332
0.312
0.276
0.308
0.768
0.717
0.801
0.216
0.716
0.280
ETT2-15T
Pointwise 2
0.247
0.356
0.339
0.351
0.368
0.768
0.781
0,801
0.249
0.761
0.334
Blocks 1
0.543
0.554
0.592
0.756
0.713
0.792
0.777
0.799
0.675
0,688
0.765
Blocke 2
0.547
0.553
0.594
0.759
0.718
0.797
0.783
0.805
0.697
0.691
0.785
Pointuiise 1
0.132
0.131
0.141
0.297
0.140
0.304
0.632
0.828
0.216
0.260
0.407
Solar-1H
Pointwise 2
0.176
0.168
0,213
0.415
0.187
0.310
0.685
0,828
0.365
0.277
0.589
Blocks 1
0.219
0.228
0.237
0.317
0.264
0.299
0.534
0.829
0.930
0.239
0.921
Blocks 2
0.219
0.229
0.236
0.357
0.265
0.208
0.550
0.830
0.932
0.239
0.924
Pointwise 1
0.086
0.190
0.177
0.132
0.174
0.724
0.339
0.748
0,080
0.635
0. 121
Jena Weather 10T
Pointwise 2
0.207
0.196
0.188
0.201
0.725
0.490
0.748
0.096
0.688
0.157
Blocks 1
0.378
0.453
0.557
0.681
0.685
0.739
0.699
0.746
0.527
0.591
0.640
Blocke 2
0.384
0.459
0.561
0.681
0.712
0.73G
0.700
0.743
0.544
0.598
0. 0.644
Pointwise 1
0.156
0.224
0.346
0.223
0.323
0.738
0.675
0.754
0.170
0.638
0.293
Jena Weather 1H
Pointwise 2
0.214
0.272
0.394
0.316
0.418
0.725
0.754
0.700
Blocks 1
0.366
0.463
0.532
0.583
0.674
0.736
0.703
0.744
0.552
0.608
0.662
Blocke 2
0.370
0.464
0.532
0.591
0.679
0.744
0.711
0.750
0.555
0.606
0.653
Pointwise 1
0.233
0.371
0.326
0.345
0.309
0.661
0.708
0.721
0.246
0.644
0.300
Loop Seattle 5T
Pointwise 2
0.261
0.387
0.345
0.368
0.334
0.661
0.708
0.721
0.266
0.672
0.331
Blocke 1
0.169
0.590
0.596
0.605
0.573
0.662
0.709
0.722
0.8-12
0.611
0.895
Blocks 2
0.474
0.597
0.600
0.675
0.374
0.710
0.722
0.8412
0.612
0.898
Pointwise 1
0.279
0.337
0.321
0.402
0.325
0.505
0.715
0.721
0.379
0.576
0.530
Loop Seattle IH
Pointuuise 2
0.350
0.394
0.376
0.502
0.373
0.524
0.713
0.721
0.486
0.615
0.653
Blocke 1
0.345
0.417
0.367
0.511
0.394
0.505
0.715
0.720
0.845
0.532
0.884
Blocks 2
0.354
0.425
0.376
0.523
0.400
0.511
0.717
0.721
0.533
0.890
Pointwise 1
0.209
0.233
0.274
0.422
0.276
0.851
0.456
0.855
0.341
0.447
0.552
Dense
Pošntwise 2
0.252
0.276
0.315
0.604
0.316
0.851
0.634
0.855
0.473
0.181
0.722
Blocks 1
0.225
0.284
0,288
0.415
0.302
0,849
0,433
0.856
1.039
0.405
1.060
Bloke 2
0.228
0.288
0.291
0.433
0.305
0.847
0.455
0.854
1.041
0.407
1.061
Pointwise 1
0.340
0.480
0.299
0.317
0.356
0.499
0.584
0.603
0.340
0.373
0.439
Enedis LDM Small
Pointuisse 2
0.440
0.534
0.338
0.358
0.415
0.499
0.589
0.594
0.419
0.396
0.524
Blocks 1
0.358
0.748
0.337
0.358
0.451
0.496
0.581
0,637
0.647
0.351
0.719
Blocks 2
0.366
0.515
0.341
0.362
0.456
0.498
0.581
0.633
0.707
0.345
0.722
Pointwise
0.439
0.573
0.432
0.837
0.596
0.650
0.965
0.480
0.666
0.373
London Small
Pointwise 2
0.490
0.632
0.465
0.483
0.843
0.596
0.651
0.760
0.534
0.679
0.638
Blocke 1
0.521
0.622
0.537
0.571
0.822
0.596
0.650
1.631
0.794
0.656
0.836
Blocks 2
0.528
0.628
0.512
0.576
0.825
0.595
0.650
1.570
0.798
0.656
0,836
Pointuiise 1
0.131
0.200
0.200
0.235
1.716
0.782
0.812
0.802
0614
0.680
0.298
Spanish Energy
Pointwise 2
0.207
0.246
0,290
0.316
1.905
0.783
0.810
0.802
0.253
0.735
0.413
Blocks 1
0.400
0.472
0.339
0.633
1.367
0.788
0,801
0.614
0.612
0.719
Blocks 2
0.399
0.469
0.559
0.637
1.384
0.784
0.788
0,800
0.609
0.635
0.715
Pointuisse 1
0.257
0.298
0.290
0.360
3.369
0.801
0.804
0.804
0.259
0.739
0.373
Weather
Pointwise 2
0.311
0.342
0.364
0.458
3.928
0.792
0.803
0.804
0.322
0.803
0.472
Blocke 1
0.456
0.491
0.592
0.689
1.680
0.797
0,800
0.620
0.686
0.736
Blocks 2
0.455
0.488
0.590
0.691
1.909
0.806
0.799
0.801
0.618
0.682
0.735
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Table 6 Continued from presious page
Foundation models
Task Specific Models
Local Models
Dataset
Setting
TabPFX
MoTK
SATTS
BRITS
CSDI
Time
Times
TS1a
Linear
Seasonal Naive
LOCF
mizerpp
(Std)
0.664
0.677
0.506
0.581
(0.138) (0.153)
(0.141)
(0.182)
(0.653)
(0.144)
(0.150) (0.644)
(0.287)
(0.180) (0.252)
C.2 Performance breakdown by missingness pattern
Figure 7 provides a detailed breakdown of the univariate benchmark results presented in the main paper, focusing on the four distinct missingness settings introduced in Section 3.1 Specifically, we report aggregated z-normalized MAE scores for (a) 50% and (b) 70% pointwise missingness, as well as for (c) two-day and (d) four-day block missingness. These complementary analyses aim to highlight the robustness and consistency of model performance across different temporal corruption patterns.
108PPN75
K1F2
0.255
Linar
NoTN
399
McTM
333
BRTS
6333
BRTS
352
Nodel
OSDI
Soasonal natre
0442
Seasonal
Timmmcerpp
limemarrso
4.671
Timesnet
Taanet
Isianat
Normalized MIE
Normllize MME (mean))
Foundation Models (Zero Shor)
Local Models
Task Specific Models
Foundation Models iZero Shot)
Local Models
Task Speatic Models
(a) 50 % pointwise missing values
(b) 70 % pointwise missing values
MaTN
McTM
020
Semon nélve
Seasonal 1m
Model
Timeene
Timesnet
Timemioopp
C321
LOC>
LDCK
0.2
0.6
1.
Aga: Nor malized MAE (mmai))
App. Normalzed (mean)
Foundation Models (Zero Shat)
Task Specific Modills
Local Models
Foundation Models iZaro Shot)
Task Specific Madels
Local Models
(c) Two days missing (missing blocks)
(d) Four days missing (missing blocks)
Figure 7: Normalized MAEs results for each distinct setting of missingness patterns.
The per-sctting breakdown shows a consistent advantage of TabPFN-TS across all four settings. However, the relative ranking of other methods varies with the missingness pattern: in the first pointwise setting (50%) Linear is actually stronger than MoTM and remains roughly tied with MоTM at 70% pointwise, indicating that simple local interpolation can excel when gaps are sparsc. By contrast, in block-missing scenarios (two and four days) MoTM substantially outperforms Linear, showing superior robustness structured, long gaps. SAITS the best supervised baseline but is generally behind the foundation models;
Results.
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its relative position is closer to MоTM in some settings (e.g. pointwise). Overall, these results emphasize (i) the stability of TabPFN-TS across patterns, (ii) that local methods can be competitive for sparse pointwise missingness, and (iii) that foundation/zeroo-tin models better handle large or by-block gaps.
C.3 Quantile predictions
In addition to pointwise imputations, we evaluate the probabilistic capabilities of the time-indexed foundation models by assessing the quality of their predicted quantiles. This analysis complements the deterministic metrics by measuring how well models represent uncertainty around missing points. Accurate quantile ostimation is particularly important for timo-scrics imputation under distributional shifts irregular sampling, as it reflects the model's ability to produce calibrated and reliable uncertainty quantification.
C.3.1 Implementation details
Weighted Quantile Loss (WQL) definition. We evaluate probabilistic imputations using the Weighted Quantile Loss (WQL), introdde by Koenker & Hallock (2001) and adopted in probabilistic forecasting benchmarks such as Gneiting et al. (2007); Gasthaus et al. (2019). Given predicted a-quantile q of an observation z, the quantile loss is defined as:
aa(x - 4), if q (1-a) aa) x),, otherwise.
QL,
(1)
To aggregate this quantity across all series and time steps, compute weighted average normalized by the absolute scale of targets:
2 ( xi.t)
WOL,
(2)
Σe, [ra
We then average over finile set of quantile levels {ar...., ox
WQL K
WQT
(3)
Quantiles are evaluated at (0.1,0.2,... 0.9} (K 9). Being weighted average of quantile losses across levels, WQL approximates the Continuous Ranked Probability Score (CRPS), standard metric for probabilistic accuracy.
CSDI and SAITS for quantile evaluation. For CSDI (a stochastic diffusion imputer), estimate quantiles post hoc by Monte Carlo sampling at test time. Conditioned on the observed context and the evaluation mask, draw S imputations {x(()) is from the model's posterior and compute empirical quantiles
per index (i,t): g = Quantile, ((a())) 1s J==1) We use S 50 across all datasets. For SAITS, we train one independent model per quantile level a (0.1..... 0.9).......... Fach model uses the standard pinball (quantile) loss computed only on the evaluation mask, with the same masking patterns as in the pointwise setting, At inference, obtain the full set of quantiles by stacking the predictions from the K independently trained models. Both models are evaluated on identical imputation splits and masking ratios; WQL is computed only masked targets and normalized by the absolute scale as described in Eq.
C.3.2 Quantitative results
Setting. We evaluate the models for uncertainty quantification on 11 univariate datasets, namely: BDG2- Bear & Rot, Covid19 Energy, GFC12 Load, Hog, Jena Weather 10T, Jena Weather 1H, Oikolab Weather, PDB, Pedestrian Counts and Weather, described Section B All models are trained with the same masking ratios and evaluated on the same imputation splits to ensure comparability.
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Table 7: Complete WQL results on 11 datasets. For each setting, the best score (lowest) is in bold and the second best is underlined.
Dataset
Setting
TabPFX-TS
NoTX
CSS1
SAITS-adapted
Pointwise
0.165
0:208
0.183
0.291
Pointurise
0.208
0.256
0.223
0.373
BDG2-Bear
Blocks
0.253
0.354
0.336
0.493
Blocks 2
0.257
0.355
0.338
0.493
Pointwise
0.191
0.239
0.194
0.321
Pointuiion
0.203
0.256
0.242
0.412
BDG2-Rat
Blocks
0.338
0.436
0.387
0.617
Blocks
0.331
0. 0.431
0.352
0.612
Pointusisn
0.071
0.097
0.758
0.353
Covid19 Energy
Pointwise
0.121
0. 0:130
0.757
0.118
Blocks
0.187
0.236
0.767
0,522
Blocks
0.187
0.216
0.759
0.521
Pointuise
0.148
0,258
Pointuise 2
0.212
0.219
0.233
0.371
GFC12 Load
Blocks
0.349
0.427
0.383
0.528
Blocks
0.423
0.381
0.523
Pointuiie
0.196
0.249
0,230
0.322
Hog
Pointasise
0.254
0.311
0.280
0.410
Blocks
0.395
0.513
0.505
0. 0.698
Blocks
0.507
0.685
Pointunise
0.113
0.225
0.141
0.418
Jena Weather 10T
Pointusise 2
0.134
0.235
0.164
0.445
Blocks
0.397
0.508
0.706
0,791
Blocks
0.394
0.500
0.712
0.781
Pointuise
0.181
0.254
0.246
0.354
Pointwise 2
0.234
0.313
0.317
0.437
Jena Weather 1H
Blocks
0.381
0.548
0.619
0.697
Blocks
0.382
0.528
0.605
0.683
Pointuise
0.145
0.225
0.157
0.248
Olkolab Weather
Pointwise 2
0.212
0.291
0.234
0.358
Blocks
0.584
0.578
0.761
Blocks
0.420
0.372
0.388
0.748
Pointuisse
0.057
0,084
0.766
0.272
Pointwise 9
0.111
0.118
0.764
0.347
PDB
Blocks
0.774
Blocks
0.171
0.205
0.773
0.406
Pointuise
0.147
0.201
0.171
0.228
Pedestrian Counts
Pointwise 2
0.189
0.253
0,221
0.300
Blocks
0.170
0.200
0.199
0.277
Blocks 2
0.173
0.264
0.203
0.279
Pointuise
0.252
0.301
0.263
0.378
Paintwisn
0.356
0.322
0.456
Weather
Blocks
0.448
0.528
0.601
0.734
Blocks
0.431
0.510
0.582
0.716
Mean (Std)
0.250 (0.112)
0.334 (0.
0.431 (0.244)
0.485 (0.178)
Results. Table 7 reports the WQL scores across all cleven datasots and four missingness settings. TabPFN-TS achieves the lowest WQL across most datasets, showing its ability to produce both accurate and well-calibrated uncertainty estimates. MоTM follows with higher WQL but consistent. behavior across datasets and settings. CSDI ranks third overall, with performances illustrating its limited generalization abilities: (i) consistently with its training procedure, good scores are obtained in the pointwise settings; (ii) except small-size training sets, such Covid19 Energy or PDB; (iii) CSDI generally suffers from significantly higher losses the unseen Block settings. Finally, the SAITS variant adapted for quantile prediction yields the highest WQL in most settings, highlighting the shortcomings of this straightforward per-quantile adaptation compared with models expressly designed for probabilistic imputation.
C.3.3 Qualitative results
In Figure and Figure we present qualitative examples of quantile- based imputations for both TabPFN-TS and MoTM segments where 70% of the values removed in a pointwise manner.
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For each plot, display the median prediction together with the inter-quantile ranges [5, 95] and [25, 75], which highlight different levels of predictive uncertainty.
The visualizations Figure and Figure D confirm that both TabPFN-TS and MoTM provide effective quantile-based imputations, successfully reconstructing the signal while providing meaningful uncertainty estimates. TabPFN-TS particularly excels at generating high-fidelity reconstructions that closely follow the ground truth, capturing fine-grained temporal dctails and high-froquency oscillations. Its strength lics in its highly adaptive uncertainly quantificatio;; the volatile Borealis dataset, the quantile ranges adeptly widen to reflect increased predictive uncertainty around sharp peaks, demonstrating sophisticated understanding of local signal dynamics. MoTM, for its part, also delivers strong performance by producing robust, albeit smoother, imputations that effectively capture the main trends and cyclical patterns in datasets like Hog and Era5. Its more regular uncertainty bands provide a consistent and reliable confidence envelope around the reconstructed signal. summary, while both models prove highly competent for this task, they exhibit different strengths: TabPFN-TS lavors detailed, high-fidelity reconstruction, whereas MoTM prioritizes capturing the underlying trend with stable uncertainty.
Results.
2
MMM man
1
0
-1
-2
0.0
0.2
0.4
0.6
0.8
1.0
Ground Truth
Context
TabPFN IQR 5-95
TabPFN IQR 25-75
TabPFN Quantile 0.50
(a)
Jena Weather dataset
5-
-5
0.0
0.2
0.4
0.6
0.8
1.0
TapPFN
TabPFN
TabPFN Quantile
(b) Borealis dataset
Figure 8: TabPFN-TS qualitative quantile results in the 70% missing values scenario (Pointwise 2).
C.4 Experiments on lower sampling rates datasets
The experiments presented in Section 3.1 focus on datasets with relatively high temporal resolutions (5min, 10min, 15min, 30min, 1h). In this section, we investigate whether time-index foundation models can generalize significantly lower sampling rates, such as daily or woekly obscrvations. This setup evaluates their robustness long-term dependencies and coarser temporal granularity, which are common in macroeconomic, energy, demographic data.
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2
1-
0-
1-
-2
0.0
0.2
0.4
0.6
0.8
1.0
Ground Truth
Context
McTM IQR 5 95
MoTM IQR 25 75
MoTM Quantile 0,50
Hog dataset
0.0
0.2
0.4
0.6
0.8
1.0
Ground Truth
Context
MoTM IQR 5-95
MoTM IQR
McTM Quantile 0.50
(b) ERA5 geopotential dalaset
Figure MoTM qualitative quantile results in the 70% missing values scenario (Pointwise 2).
Datasets. We consider four publicly available low- low-frequency datasets: Births Daily, M4 Daily, Births Weekly, and M4 Weekly, with statistics summarized in Table They are part of the Monash Time Series Forecast archive (Godahewa et al. 2021), and were downloaded from the GIFT-eval repository (Aksu scatiiossssssssltityyy and periodicity
et al., 2024). Each dataset exhibits distinct temporal weaker at weekly scales, while daily data contain more regular cycles and higher variance. For each dataset, we apply the same four missingness regimes as in the main benchmark (two pointwise and two block- based scenarios), allowing a consistent comparison across frequencies.
typically
Table 8: All datasets at lower sampling rates used in experiments and their key properties.
Release Platform
Num. Series
Series Length
Num. Test
Dataset
Domain
Freq
Segments
Births Daily
-eval eval
Demo.
1D
3652
104
Births Weekly
GIFT -eval
Demo.
IW
1043
7
M4 Daily
GIF -vvl
Econ./Demo.
1D
2112
2954
80256
M4 Weekly
CIFT -eval
Econ./Demo
IW
172
947
860
Births Daily contains the daily number of births in the US between 1969 and 1988, as extracted from the R
package mosaic (Pruim et al. 2020 Births Weekly aggregates these statistics at weekly frequency.
The M4 Forccasting Competition dataset contains a total of 100k time series, with six different froquencies and from diverse domains such as demography, macrocconomic, etc. (Makridakis et al., 2018 2020 We used the subsets of, respectively, daily (M4 Daily) and weekly (M4 Weekly) time series.
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Baselines and settings. We evaluate representative subset of imputation methods present in the main benchmark: local heuristics (Linear, Seasonal Naive), supervised models SAITS, CSDI, BRITS, and the two foundation models TabPFN-TS and MoTM. As before, TabPFN-TS and MoTM operate in fully zero-shot setting, while SAITS retrained for each datasct. All metrics are aggregated using the z-normalized Mcan Absolute Error (MAE), and results are reported per datasel and missingness patlern Table
Table 9: Complete MAE results on datasets with low sampling rates (daily or weekly). Best results are in bold, second-best. are underlined.
Dataset
Setting
TabFFN-TS
NolM
56113
BRIT3
CBD1
Linear
Seasonnal1 Naive
0.286
Births Daily
Pointarise 2
0.310
0.109
0.814
0.154
1,085
0.941
0.318
Blocks Blocks 2
0.272
0.361
0.783
0.447
1,064
0.588
0.201
Pointwise
0.182
0.248
0.223
0.159
0.507
M4 Daily
Pointuiie
0.246
0.304
0.234
0.268
0.273
0.195
0.006
Blocks 1
0.442
0.531
0.150
0.576
0.638
0.381
0.517
Blocks 2
0.454
0.534
0.591
0.614
0.385
0.539
Pointation
0.293
0.337
0.896
0.748
11,999
0.332
0.452
Births Woekly
Blocks 1
Potntwiie
0.301
0.020
0.358
1,036
0.544
4,008
0.723
0.385
0.481
Blocks
Pointariee 1
0.160
0.226
0.191
0.310
0.307
0.176
0,761
Poindarie
M4 Weekly
Bloks 1
0.244
0.326
0.430
0.635
0.435
0.318
0.643
Blocks 2
0.256
0.345
0.444
0.643
0.459
0.340
0.650
Mean (Std)
0.285 (0.089) 0.351 (0.097)
0.525 (0.316)
0.531 (0.204)
2,790 (4.723)
0.512 (0.120)
0.524 (0.170)
As shown in Table g our foundation models demonstrate robust performance on low-frequency data. TabPFN-TS achieves the best average score (0.285), followed by MoTM (0.351), confirming their ability gencralize coarser temporal structures without retraining. Other baselines, including specializod models like SAITS and BRITS, are significantly outperformed and show clear advantage over simpler methods, while CSDI struggles notably. Overall, these results highlight the superior generalization of our zero-shot models in low-frequency regimes compared to both classic basclines and other deep learning architectures.
Results.
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D TabPFN-TS for imputation: additional analysis
D.1 TabPFN-TS sensitivity to feature design
As shown Figure and Table TabPFN-TS delivers remarkably strong zero-shol imputation performance, both in the purely univariate setting and when auxiliary covariates are provided. However, one limitation of the current formulation that the time-index features fed to the model manually designed (Cai et al., 2025). This raises important question: to what exlent does TabPFN-TS rely lhese specific fealures, and how sensitive is its performance to alternative time encodings? This section investigates this question by systematically varying the feature set and quantifying its impact on imputation quality.
Setting. We evaluate five alternative feature configurations across 11 representative datasets and the four missingness scenarios used throughout the benchmark. Each configuration corresponds to different encoding of the time index:
TabPFN1: the original feature set used in the paper, combining the raw grid grid-normalized time index with daily and weekly sinusoidal encodings:
Htt = tt sin
Pany
2xt
cos
2xt Paay
sin
2xr Pweak
cos
2nr Paeek
TabPFN2: daily-only sinusoidal encodings:
(t)
(sin
2st Praxy
cos
Paaxy
2st
TabPFN3: raw grid-normalizer time index only:
=(()= (1)
TabPFN4: purely random periodic features using random periods Prand, and Prand,:
H())
(sin
Pronndy (T
2nr
)
cos
2nrt Poondy
sin
2xr Prandz
cos
2st Prandz
TabPFN5: the original features augmented with the random features used TabPFN4:
(1) (t, sin( Pany
cos(
2xL Play
sin
cos(
sin Frandy
), cos( 2nd
sin(
2xt cos( Prundy Prandyy
Pwock
wook
Peundy
Each variant probes a distinct aspect of the temporal encoding: (i) removing weekly structure and time index (TabPFN2) tests whether multi-frequency seasonality and the relative time index information essential: (ii) removing the raw time index (TabPFN2, TabPFN4) evaluates whether relative positional information is necessary; (iii) retaining only the grid index (TabPFN3) probes how much the model can extrapolate without any periodic cues; (iv) replacing meaningful periodicities with random ones (TabPFN4) lests the robustness of learned priors to feature misspecification; (v) adding spurious features (TabPFN5) assesses whether irrelevant periodicitics degrade performance by confusing the modcl's inductive bias. Together, these experiments provide systematic view of how much TabPFN-TS depends on feature engineering versus its own learned prior.
Setting. These variants are evaluated on eleven univariate datasets, namely: BDG2-Bos Rat, Covid19 Energy, GFC12 Load, Hog, Jena Weather 10T, Jena Weather 1H, Oikolab Weather, PDB, Pedestrian Counts and Weather, with details given in Section Table 10 reports the complete MAE results across all eleven datasets and four missingness scenarios.
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Table 10: Complete MAE results of five TabPFN-TS temporal encoding variants on 11 datasets. For each setting, the best score (lowest) is in bold and the second best is underlined.
Dataset
Setting
TabPFM:
TatPF02
TabPFN3
TabPF34
TabPFNG
Pointuise
0.502
Pointwise 2
0.223
0.552
0.317
0.971
0.220
BDC2-Bear
0.498
0.763
0.241
Blocks 8
0,280
0.492
0.779
0.809
0,296
Pointwise
0.196
0.921
0.261
0.539
0.198
Puintwise
0.007
BDG2-Rat
Blocks I
0.349
01528
0.680
0.872
0.366
0.600
Pointuise
0.075
0.397
0.171
0.989
0.075
Covid19 Energy
Pointwise 2
0.132
0.454
0.284
1.004
0.1.4
Blocks
0.363
0.774
1.203
Blocks 2
0.201
0.365
0.781
0.936
0.201
Puintuise
0.143
0.537
0,280
0.933
0.141
GFC12 Load
Pointuise
0.237
0.615
0.386
0.969
0.257
Dlocks 1
0.353
0.521
0,703
0.884
0.354
Blocks
0.363
0.519
0.719
0.364
Pointwise
0.196
0.633
0.230
0.879
0.196
Hog
Pointwise
0.716
0,287
0.9224
0.261
Blocks 1
0.396
0.626
0.532
0.863
0,397
Blocks 2
0.406
0.618
0.546
0.878
0.406
Paintwise
0.086
0.629
0.132
0.710
0.0N6
Pointwise 2
0.101
0.636
0.135
0.769
0.101
Jena Weather 10T
0.521
0.379
Blocks 8
0.384
0.647
0.535
0.660
0.384
Pointuise
0.156
0.566
0.210
0.848
0.156
Puintwise
0.628
0,2800
Jena Weather
Blocks 1
0.366
01544
0.517
0.791
0.367
Blocks
0.525
Poñutwise
0.150
0.684
0.204
0.526
0.176
Oikolab Weather
Pointuise
0.228
0.705
0.263
0.967
0.228
Blocks Blocks 2
0.681
0.000
0.454
0.683
0.611
0.909
0.154
0.207
PDB
Pointwise 2
0.119
0.387
0.324
1.033
0.119
Blocks 1
0.171
0.319
0.831
0.895
0.171
Blocks
0.177
0,331
0.855
0.947
0.177
Pointuise
0.150
0.337
0.363
0.937
0.158
Pedestrian Counts
Blocks 1
0.172
0.327
0.863
0.820
0.174
Blocks 2
0.178
0.327
0.880
0.846
0.181
Pointwise
0.257
0.655
0.273
0.915
0,258
Weather
Pointwése 8
0.311
0.739
0.325
0.952
0.316
Blocks
0.680
Blocks B
0.455
0.656
0L084
0.889
0.455
Mean (Std)
0.252 (0.114)
0.554 (0.171)
D:415 (0.241)
0.901 (0.102)
0. 0,260 (0.116)
Results. Table 10 shows clear and consistent trend: the original feature set (TabPFN1) remains the strongest across virtually all datasets and settings. (i) Daily-only features (TabPFN2) perform substantially worse, highlighting the importance of capturing both daily and weekly periodicities. (ii) Using only the raw index (TabPFN3) yields reasonable but clearly inferior performance, especially in block-missing scenarios where periodic cues are most helpful. (iii) Random features degrade performance drastically (TabPFN4), confirming that TabPFN-TS not invariant arbitrary feature choice. (iv) Finally, augmenting correct features with random ones (TabPFN5) results in little to no degradation, indicating that the model is generally robust to irrelevant. noisy features and does not easily overfit to spurious temporal structure.
Overall, these results underline the importance of well-designed time features and suggest. that part of TabPFN-TS's effectiveness stems from the alignment between its meta-training distribution and the provided temporal encodings.
Future work. An important direction for future research is the automatic construction or selection of temporal features. Our experiments highlight that TabPFN-TS is highly sensitive to the structure of the
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time encodings it receives. Instead of relying on manually crafted sinusoidal components, could learn feature representations jointly with the model, or derive them through separate meta-learning (like MoTM) or feature-search mechanism. Such an approach would be particularly valuable when dealing with highly heterogencous datascts, spanning very different temporal gramulaitics (minutes, hours, days, months) and periodic ures. Automatically discovering the most relevant periodicities and positional encodings would likely make TabPFN-TS more robust, more general, and less dependent on domain-specific feature engineering.
D.2 Extended discussion on TabPFN-TS computational bottlenecks
A practical limitation of TabPFN-TS lies in its inference cost (see Section On an NVIDIA H100 GPU, a single forward pass over a chunk of 672 time steps requires approximately one second. Depending on the computational resources available and the frequency at which predictions must be updated, this can be either acceptable or prohibitive. For example, batch offline imputation low-frequency forecasting pipelines easily amortize this cost, whereas real-time applications systems operating on thousands of concurrent time series may find the latency challenging. Reducing inference time tine-through model distillation, sparse attention, chunk parallelization, or specialized kernels thus represents a key avenue to make TabPFN-TS more broadly deployable in production environments.
In this regard, the recently introduced TabPFN 2.5 (Grinsztajn et al. 2025 appears to be promising solution, as it substantially accelerates in-context regression and could therefore mitigate the current inference bottlenecks of TabPFN-TS.
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E Experiments with covariates: extensive qualitative results
E.1
Qualitative results
To better visualize the impact of incorporating covariates, present qualitative results for both TabPFN-TS and MоTH Figure [0 and Figure [] show examples from three datasets (PV-France, Wind-Franee and Load-France) illustrating how the inclusion of covariate information helps cach model reconstruct the four one-day missing blocks more accurately.
3
2
1
0
-1
0.0
0.2
0.4
0.6
0.8
1.0
Ground Truth
Context
TabPFN covar)
TabPFN (with covar)
Covariate
(a) Wind-France
3
2
1
0.0
0.2
0.4
0.6
0.8
1.0
Ground Truth
Context
TabPFN covar)
TabPFN (with covar)
Covariate
(b) PV-France
-2
0.0
0.2
0.4
0.6
0.8
1.0
Ground
Context
TabPFN (no covar)
TabPFN (with covar)
Covariate
(c) Load- Prance
Figure TabPFN-TS qualitative results with and without covariates the four one-day missing blocks scenario (Blocks 2).
Results. As illustrated in Figure 10 and 11 incorporating covariates visually improves the reconstructions for both TabPFN-TS and MoTM. The covariate-enhanced versions capture missing intervals more smoothly and
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3
2
1
0-
-1-
0.0
0.2
0.4
0.6
0.8
1.0 Covariate
Ground Truth
Context
MoTM (no covar)
MoTM (with covar)
(a) Wind- Fronce
4
3
2
0.2
0.4
1.0 Covariate
Ground Truth
Context
MoTM (no covar)
MoTM (with covar)
(b) PV-France
2
1
MMAN
-1
-2
0.0
0.2
0.4
0.6
0.8
1.0
Ground Truth
Context
MoTM covar)
MoTM (with covar)
Covariate
(c) Load- Prance
Figure 11: MoTM qualitative results with and without covariates in the four one-day missing blocks scenario
(Blocks 2).
better follow short-term temporal variations within the four one-day gaps. We observe that the interpolations of TabPFN-TS align more closcly with the ground truth and preserve sharper transitions across missing regions. In contrast, if MoTM consistently benefits from covariate information, its reconstructions sometimes struggle to capture sudden changes with great accuracy. Overall, the qualitative plots confirm that the most visible gains are observed on the Wind- France and PV-France datasets, while the impact remains limited for One might note that quantile predictions can also be generated in this covariate setting, in similar fashion to the univariate examples presented in Figure
Coarse granularity interpolation. We extend our qualitative analysis to practical scenario of interest, namely interpolating sparse yet. regular observations, e.g. at multi-hourly time-step, to finer time
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3
2-
1-
1-
0.0
0.2
0.4
0.6
0.8
1.0
Ground Truth
Covariate
TabPFN-TS(no covar)
TabpFN-TS(with covar)
Context
(a) Wind- Frad-Prance
3
2
1
0-
6
0.2
0.4
1.0
Ground Truth
Covariate
TabPFN-TS(no covar)
TabPFN-TS(with covar)
Context
(b) PV-France
Figure 12: TabPFN-TS qualitative results with and without covariates in coarse granularity scenarios: context observed at a six-hourly sampling rate, imputation on a dense hourly grid.
resolution, e.g. an hourly time-step. Figure 12 illustrates the behaviour of TabPFN-TS when interpolating the and PV-France datasets from six- six-hourly to hourly sampling rate. On PV-France, we note that TabPFN-TS maintains shape consistency, although certain artifacts can be obscrved (typically non-zero values at night). These can be corrected by incorporating covariate information. On Wind-Prance, the model produces smooth univariate interpolations (blue line). Interestingly, adding the covariate detrimental this case: the in-context learning- based adaptation procedure of TabPFN on a sparse hour grid mislead into spurious correlations by the stronger stochasticity of the covariate.
E.2 Discussion: integration of incomplete covariate data
The integration mechanism used in Section 3.2 simply concatenates the covariate value c(t) to the representation (t) before feeding it to the regression head ro(t). This assumes that the covariate is fully observed and temporally aligned with the target series for every timestamp t. When this assumption fails (for example, if the covariate contains missing values, is recorded asynchronously, or is sampled at a different frequency) naively integrating it into the model is not straightforward.
Below, we discuss practical strategies handle such situations. These solutions are closer to implementation tricks than to principled methodological contributions, but they be useful in practice.
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Partially observed but aligned covariates. When the covariate is sampled the same time grid the target series but contains missing values, a straightforward approach is to first impute the covariate and then apply the standard integration procedure. This imputation can be performed using simple linear interpolation or more sophisticated approaches such as TabPFN-TS (or MoTM for faster imputation).
A limitation of this strategy is that the imputation of the covariate does not leverage the target series, which may lead suboptimal reconstructions. More advanced approaches could jointly model both the target and the covariate - for example using implicit neural representations to obtain functional embeddings independent of the original sampling grid but such ideas remain open research directions.
Fully observed but misaligned covariates (asynchronous sensors or differing sampling rates). If the covariate is complete but not recorded on the same timestamps as the target series, simple resampling methods such as linear interpolation can be used to align it with the target grid. More flexible approaches, such as qucrying TabPFN-TS or MoTM at arbitrary timestamps, can also be applied since these models operate in a continuous-tinee manner rather than imputing values through mask-based reconstruction (Tashiro el al. 2021 Du al. 2023a). This makes them naturally suitable for harmonizing covariates recorded at heterogeneous froquencies.
F Comparison with oyperparamettersoottiiized SAITS
The experiments reported in the main paper rely the hyperparameters recommended by each supervised baseline in their respective publications. While this ensures fair and reproducible benchmark, it is also informative to compare TabPFN-TS and MoTM against a version of SAITS whose hyperparameters have been actively tuned. This comparison is particularly relevant given that hyperparamcter optimization constitutes one of the main disadvanlages of supervised approaches, contrast with zero-shot methods.
Setting. We perform an explicit hyperparameter grid search for SAITS, varying its two main hyperparameters highlighted as important in the original paper, namely the inner model dimension (dmodet) and the number of Transformer block layers (Mayers)). The search is carried out on eleven representative datasets used throughout the benchmark-BDie
BDG2- Rat, Covid19 Energy, GFC12 Load, Hog, Jena Weather 10T, Jena Weather 1H, Oikolab Weather, PDB, Pedestrian Counts, and Weather: For the hyperparamcter search, the train/validatee validation ttett lest split follows a 0.7/0.1/0.2 ratio along the temporal axis, consistent with all other univariate experiments in the paper. For each dataset, we retain the hyperparameter configuration that yields the lowest validation MAE, averaged over the four validation- scenarios, and subsequently report the corresponding test MAE for each scenario. In addition, Figure 13 reports how the test MAE and training time vary with dmodel and Mayers for SAITS.
Table 11: Best SAITS hyperparameter configuration per dataset based on validation MAE (averaged over the four validation-mask sccnarios).
Dataset
dmodel
Players
Avg. Val. MAE
BDG2-Bear
128
0.276
BDG2-Rat
128
0.328
Covid19 Energy
128
0.213
GFC12 Load
128
0,289
Hog
128
0.416
Jena Weather 10T
256
0.367
Jena Weather 1H
128
4
0.390
Oikolab Weather
128
0.430
PDB
256
0.249
Pedestrian Counts
256
0.165
Weather
256
0.412
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Table 12: Comparison of test MAE between the two zero-shot approaches, TabPFN-TS and MoTM, and the tumed SAITS bascline (best configuration selected per dataset via validation MAE). For each setting, the best (lowest) MAE is shown bold, and the second best is underlined.
Dataset
Setting
TabPFN-TS
MoTN
SAITS
SAITS
Pointwise
0.171
0.202
0.191
Pointwise
0.223
0.240
0.253
0.309
BDG2 BDGr-Beear
Blocks
0.272
0.332
0.327
0.399
Blocks
0.280
0.336
0.325
0,405
Pointwise
0.196
0.231
0.199
0.266
Pointwise
0.256
0.273
0.270
0.339
BDG2-Rat
Blocks
0.349
0.400
0.421
0.495
Blocks
0.355
0.402
0.420
0.497
Pointwose
0.075
0.099
0.344
0.399
Pointwise
0.132
0.127
0.380
0.417
Covid19 Energy
Blocks
0.202
0.222
0.372
0.432
Blocks
0.201
0.232
0.367
0.436
Pointwise
0.143
0.189
0.189
0.188
Pointwise
0.237
0.231
0.277
0.280
GFC12 Load
Blocks
0.353
0.382
0.399
0.417
Blocks
0.363
0.387
0.406
0.425
Pointwise
0.196
0.240
0.226
0.245
Pointwise
0.260
0.286
0.292
0.320
Hog
Blocks
0.396
0.458
0.514
0,518
Blocks
0.406
0.464
0.516
0.528
Pointwose
0.086
0.190
0.241
0.177
Pointwise
0.101
0.207
0.293
Jena Weather 10T
Blocks
0.378
0.453
0.502
0.557
Blocks
0.384
0.459
0.504
0.561
Pointwise
0.156
0.224
0.241
0.346
Pointwise
0.214
0.272
0.293
Jena Weather 1H
Blocks
0.366
0.463
0.502
0.532
Blocks
0.370
0.464
0.504
0,532
Pointwise
0.150
0.227
0.188
0.207
Pointwrse
0.228
0.278
0.293
0.294
Oikolab Weather
Blocks
0.449
0.529
0.598
0.581
Blocks
0.454
0.534
0.602
0.584
Pointwise
0.062
0.094
0.201
0.337
Pointwrse
0.119
0.121
0.271
0.373
PDB
Blocks
0.171
0.197
0.317
Blocks
0.177
0.201
0.314
0.373
Pointwise
0.150
0.196
0.128
0,240
Pointwrse
0.200
0.239
0.183
0.289
Pedestrian Counts
Blocks
0.172
0.254
0.173
Blocks
0.178
0.260
0.6
0.252
Pointwris
0.257
0.298
0.281
0.290
Pointwise
0.311
0.342
0.348
0.364
Weather
Blocks
0.456
0.494
0.556
0.592
Blocks 0.455
0.488
0.553
0.590
Mean (Std)
0.252 (0.114)
0.300 (0.122) 0.340 (0.159) 0.379 10.)
Results. Table 12 reports the detailed test MAE for each datasct and masking scenario. SAITS correspond to the best. configurtaion and SAITS correspond to the default. hyperparameters baseline provided by the authors (see Section 2.Ip. Table II report the best configuration for each datasets according the lowest average MAE obtained on the validation set. Overall, hyperparameter tuning yields only modest. gains for SAITS: the tuned configuration slightly improves over the bascline, but still outperformed, on average across the 11 datasets, by the two zero-shot approaches TabPFN-TS and MoTM by average of 26%
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dmodel 128
256
512
2600
0.8
2000
MAE
0.5
1600
0.4-
$00
0.3
2
Playerrs
Blayerr
(+) Mean Average Error
Training time
Figure 13:
Hyperparameter ablation for SAITS. (a) Average test MAE across the 11 datasets as function of the number of layers, with one curve per dmodel- (b) Average training time across the 11 datasets function of the number of layers, again with one curve per dmodel-
and 12% respectively. In addition, Figure 13 8) shows that, for dmoddl E {128, 256} and Maaera E {2, 4J, the average test MAE remains essentially unchanged, indicating limited benefits from increasing depth within this range. By contrast, Figure 13 highlights that increasing either dmadel or nlagers leads to a substantial increase training time. These findings corroborate the default configuration proposed by the authors of SAITS Duu et al. 2023a), namely dmodel 256 and Bayers
38


Reviews:
[{"review_id": "iEpxYLiCaQ", "reviewer": "Reviewer_A38v", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper presents an analysis of two models, TabPFN-TS and MOTM, for time-series imputation. The authors evaluate these models on 33 out-of-distribution (OOD) datasets with 4 different settings. The paper is empirical and provides multiple scenarios with TabPFN-TS and MOTM and the comparison with existing supervised baselines.\n\n\n\nStrengths:\n\n- The biggest strength of the paper is that it is thoroughly evaluated on multiple experimental setups as well as several baselines. \nIf the question is between using TabPFN and MOTM for time series imputation then the work provides the answer for that\n\nWeakness:\n\n- The authors refer to time-indexed models, but I was not able to find a clear definition or reference for this specific term. I recommend defining it early in the paper, as its usage without explanation may be confusing to readers who are unfamiliar with it.\n\n- While the paper reports some interesting comparative results between the two models, it would benefit from a deeper inspection of why these performance differences arise. Additionally, providing more actionable guidance for practitioners, such as scenarios where one model is preferable, failure modes,would substantially improve the paper’s practical impact.\n- Although the two models evaluated are established, using only two methods may be insufficient for a purely empirical study. The authors could consider incorporating additional recent models such as TabICL and explore if it can they handle tabular/time-series structures in a manner similar to TabPFN to strengthen the empirical comparison.\n- The writing is confusing especially in result interpretation section, some examples:\n1. “The CD diagram further confirms that these two models are statistically superior compared to all others, except MoTM compared to SAITS.”: Then the statement should be TabPFN is superitor and MoTM is not. \n2. “Local baselines remain resilient. Classical approaches leveraging temporal priors still deliver reasonable performance…”\n It would be helpful to specify what is meant by reasonable performance, perhaps by grounding the statement in concrete metrics or observations.\n3. “TabPFN-TS consistently achieves the lowest MAE but at the cost of substantially higher inference time…”\n This wording suggests a trade-off between performance and inference time. If such a trade-off is intended or empirically supported, it should be articulated more explicitly; otherwise, the relationship should be clarified.\n\n\n\nRelevant works not mentioned and cited:\n1. Explore the Time Series Forecasting Potential of TabPFN Leveraging the Intrinsic Periodicity of Data - FMSD @ ICML 2025\n2. ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation, KDD 2024\n3. ImputeINR: Time Series Imputation via Implicit Neural Representations for Disease Diagnosis with Missing Data, IJCAI 2025", "claims_and_evidence_yn": "Yes", "claims_explanation": "The major claim of the paper in conclusion is TabPFN-TS is better than any of the existing approaches for time series imputation, and the work empirically shows that.", "audience_yn": "Yes", "audience_explanation": "This work can be interesting for the Time series imputation community.", "requested_changes": "* Please make the sentences in the result interpretation backed by data, as pointed out in weakness\n* Can you present an investigation on why TabPFN is so good at this particular task?\n* Add other foundation models as well, as mentioned in the weakness and maybe also explore if other tabular foundation models can be directly used for time series imputation such as tabpfn.\n* Provide more insights like limitations and bottlenecks\n* Rewrite the titles of subsections, make them more specific; titles like Main results, are not very helpful for the reader.", "broader_impact_concerns": "NA", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "JuFcUYBfA7", "reviewer": "Reviewer_nTQe", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "**Summary** - The paper presents an empirical study of time-indexed foundation models for zero-shot time-series imputation. The work compares two time-indexed foundation models with supervised and local imputation models. The evaluation is performed under four different settings - point-wise masking (50% and 70%) and block-wise masking (two or four entire days masking) across 33 univariate out-of-distribution datasets.\n\n**Strengths**\n1. The paper conducts extensive evaluation on 33 OOD datasets\n2. Several qualitative results are included and analysed.\n3. Discusses the computational cost along with the empirical performance\n\n**Weaknesses**\n1. There are other Time-series Foundation Models like MOMENT, Frozen Pretrained Transformer (FPT), NuwaTS, that claim time-series imputation ability. Given the primary focus of the work is on time-series foundation models, it is important to include all the relevant foundation models for a broader evaluation benchmark. While the paper acknowledges the limitations of MOMENT for the current evaluation, it would be good to report the results. It would be informative for the community interested in TSFMs for imputation.\n2. Related works section is too long. The paper spends a significant amount of text detailing the internals of the time-indexed foundation models - MoTM and TabPFN-TS (Section 2.2 and Appendix A.3 repeats much of the architectural description)\n3. The tables do not report standard deviation, which makes it difficult to determine if the reported gains are statistically significant (for e.g. in Table 2, the numbers are very close, std would help clarify significance of the gain)\n4. On a high-level, the work simply evaluates imputation models on different datasets and reports the results. It does not really provide any insights based on the results", "claims_and_evidence_yn": "Yes", "claims_explanation": "Most of the claims are well-supported by the experiments. TabPFN-TS and MoTM consistently achieve lowest MAE and best average ranks across benchmark datasets, and across all four missingness settings. However, the following claims are slightly less convincing and require more evidence,\n(a) integration of covariates lead to significant results - without multiple trial runs, it is difficult to assess the significance of the gains\n(b) the evaluation is extensive - not all relevant foundation models are included in the comparison", "audience_yn": "Yes", "audience_explanation": "The paper explores the rapidly emerging Time series Foundation Models, for time series imputation, which is an active field of research, with high interest across multiple domains (healthcare, climate, industry).", "requested_changes": "1. Consider other Foundation Models into the evaluation framework - MOMENT, Frozen Pretrained Transformer (FPT), NuwaTS. It would be helpful to report the results of MOMENT, with and without fine-tuning (Critical)\n2. Results reported should be based on multiple trials, and should include the standard deviation (Critical)\n3. Provide more reasoning behind the observed results, for e.g. (a) why do we see CSDI or TimesNet performing poorly on the OOD Datasets (and also in terms of the average rank), or why BRITS or even the local baselines have a better rank than CSDI/TimesNet - is it because of the size of training dataset, or does it require more hyper-parameter tuning. (Strengthening)\n4. Given linear interpolation shows competitive performance on pointwise setting, it would be useful to add a simple non-linear interpolator like Spline into the evaluation benchmark as well. (Strengthening)\n5. Related works section can be made more concise, as the Appendix covers the architectures of the foundation models in detail. This will improve the readability of the paper. (Strengthening)\n6. Currently, the covariates considered are fully observed. However, in real-world multivariate setting, multiple variables often have concurrent missing values. It would be useful to add a discussion or empirical results by carrying out experiments to show the effect of partially observed covariates (Strengthening)", "broader_impact_concerns": "No major concerns on the ethical or societal implications of the work.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "LredAWSczB", "reviewer": "Reviewer_ixDg", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper conducts a study of time-indexed time series foundation models as zero-shot imputers that do not require training, by comparing them to a variety of models that do require training. The main thesis of the paper is that that modern foundation models are good zero-shot imputers, and this thesis is corroborated by a large set of experiments. The paper does not propose a new theory, algorithm, or a learning methodology - but rather proves a position by an extensive set of empirical experiments.", "claims_and_evidence_yn": "No", "claims_explanation": "Since the paper's main thesis is corroborated mainly empirically, the evidence would be more convincing if:\n1. It was clear exactly how the non zero-shot models were trained. Pointing to a library is not enough - each combination of a model and a data-set may require a different set of training parameters, such as a learning rate, weight decay, etc.. It may be the case that some models under-perform simply because they were trained with unfit parameters. This, of course, can also be a caveat of these models - they require tuning, but this should be clearly articulated in the paper. For example, a result with thorough tuning and another one without, at least for **one** of the models, for which the computational cost is not that large, would be more convincing (unless everything is tuned - I don't know, it's not clear from the paper). \n2. It would be more convincing if it was easily reproducible. I do not see a pointer to an (anonymized) code repo for reproducing the results. Pointing to an external library is not enough. There are other reproducibility concerns, such as the ones above. Code would remove all doubt.", "audience_yn": "Yes", "audience_explanation": "I do see a lot of value in such a paper by directing practitioners and researchers to default \"well-working\" methods.", "requested_changes": "Please see the explanation for why the evidence is not convincing - address the tuning concern in some convincing way, or provide code.", "broader_impact_concerns": "NA", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "aZAkv6rYbl", "reviewer": "Reviewer_e9qb", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper presents a large-scale empirical evaluation of time-indexed foundation models, specifically TabPFN-TS and MoTM, for zero-shot time-series imputation. The authors benchmark these models across 33 out-of-domain datasets under several missingness regimes and show that they consistently outperform both classical local imputers and state-of-the-art supervised deep-learning baselines. The paper additionally evaluates the ability of these models to integrate covariates at inference time without retraining, and provides uncertainty-quantification results as well as computational analyses\n\nStrengths:\n- Clear problem motivation: Imputation in heterogeneous, irregular time series is an important and underexplored area compared to zero-shot forecasting.\n- Strong empirical work: The benchmark is large, diverse, and carefully designed to avoid leakage from MoTM pretraining datasets.\n- Comprehensive comparisons: Includes local, supervised, and foundation baselines, with a transparent discussion of why some were excluded.\n- Covariate integration analysis is thorough and practically relevant, especially for domains such as energy and climate.\n- Uncertainty quantification experiments are well executed and strengthen the argument for real-world applicability.\n\nWeaknesses:\n- Limited practical validation for physical or dynamical constraints: While extensive, the evaluation focuses mainly on statistical accuracy. For domains like energy, weather, or PV power, shape constraints (monotonicity, smoothness, daily cycles) matter and are not examined.\n- Interpretability of failure modes: The paper shows strong average performance, but provides little discussion of when these models behave pathologically (oversmoothing, unrealistic extrapolation, seasonal misalignment).\n- Computational cost discussion is descriptive but not actionable: The results are clear, but the paper does not thoroughly analyze why TabPFN-TS becomes slow at scale or how its context length limits affect performance. Especially for energy data, the applicability of imputation models for trading or scheduling purposes largely relies on inference time.\n- Covariate integration is tested only with fully observed covariates; some important use-cases involve sparse or noisy covariates.\n- Real-world scenarios such as reduced temporal granularity (e.g., 6-hourly forecast horizons) are not studied but highly relevant for the types of time-indexed interpolations the paper discusses. Certain practical claims (e.g., applicability to real-world industrial time-series settings) would benefit from additional qualitative analysis of shape fidelity and physical consistency..", "claims_and_evidence_yn": "Yes", "claims_explanation": "The empirical evidence supports the main claims convincingly. The superiority of TabPFN-TS and MoTM over both supervised and local models is consistently demonstrated across datasets, missingness patterns, and covariate settings. Method descriptions are sufficiently detailed to understand why zero-shot generalization is expected.", "audience_yn": "Yes", "audience_explanation": "Time-series foundation models are gaining increasing attention, yet the literature is heavily skewed toward forecasting rather than imputation. A systematic evaluation of zero-shot imputation is timely and valuable for researchers working on foundation models, representation learning, and applied ML in domains such as manufacturing, energy, and sensor networks. The covariate-integration results, in particular, highlight a capability that is widely demanded in practice and rarely addressed in zero-shot settings.", "requested_changes": "- Physical/shape consistency analysis for energy and climate datasets. For instance, solar power or irradiance curves exhibit known smoothness and monotonic patterns driven by diurnal cycles. It would be useful to evaluate whether the imputations produced by foundation models adhere to physically sensible shapes or occasionally produce unrealistic artifacts. This is particularly relevant for the PV-France case.\n- Discussion of reduced-granularity interpolation use cases. Many operational datasets (e.g., ECMWF IFS/AIFS) provide high granularity in the near term but only 3–6-hourly values for longer horizons. Could the proposed models interpolate such coarse weather forecasts into hourly profiles? Even a short exploratory discussion would improve practical relevance.\n- Failure-mode characterization. Given the scale of the benchmark, qualitative cases of poor or unstable reconstructions would help users understand when the models should not be deployed.\n- Clarify limitations of covariate integration. The experiments assume fully observed covariates. A short discussion of situations where covariates are missing, partially observed, or noisy would be valuable.\n- More actionable discussion on computational bottlenecks. TabPFN-TS is extremely slow for large contexts; explaining the drivers and possible mitigation strategies would be useful.", "broader_impact_concerns": "No concern.", "additional_comments": "- For the PV-France dataset, are block-missing imputations also visually coherent from a physical standpoint (e.g., smooth bell-shaped curves, monotonic morning ramps unless cloud-driven deviations)?\n- Do the authors have insight into how sensitive these models are to the choice of Fourier frequencies in TabPFN-TS, especially for datasets with irregular seasonality (e.g., traffic or weather anomalies)?", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)