Forging Time Series with Language: A Large Language Model Approach to Synthetic Data Generation
Authors: Cécile Rousseau
Tobia Boschi
Giandomenico Cornacchia
Dhaval Salwala
Alessandra Pascale
Juan Bernabe Moreno
Venue: NeurIPS 2025 poster ()
Keywords: Time Series
Synthetic Data Generation
LLMs
Primary area: deep_learning
TL;DR: Time Series Generation using Large Language Models and compact embeddings

Abstract: SDForger is a flexible and efficient framework for generating high-quality multivariate time series using LLMs.
Leveraging a compact data representation, SDForger provides synthetic time series generation from a few samples and low-computation fine-tuning of any autoregressive LLM. Specifically, the framework transforms univariate and multivariate signals into tabular embeddings, which are then encoded into text and used to fine-tune the LLM.
At inference, new textual embeddings are sampled and decoded into synthetic time series that retain the original data's statistical properties and temporal dynamics. Across a diverse range of datasets, SDForger outperforms existing generative models in many scenarios, both in similarity-based evaluations and downstream forecasting tasks. By enabling textual conditioning in the generation process, SDForger paves the way for multimodal modeling and the streamlined integration of time series with textual information. The model is open-sourced at https://github.com/IBM/fms-dgt/tree/main/fms_dgt/public/databuilders/time_series.

Forging Time Series with Language: A Large Language Model Approach to Synthetic Data Generation
Cécile Rousseau
Tobia Boschi
IBM Research Europe rousseau. wwcile@ie..co com
IBM Research Europe tobia. boschi carcchi@i.... com
Giandomenico Cornacchia IBM Research Europe Gi andomenico. Cornacchial 0imm. com
Dhaval Salwala
IBM Research Europe
dhaval vinodbhai weteeehaisswwllllll... salwwll@iibm.mmmmmmmm com
Alessandra Pascale
Juan Bernabe Moreno
IBM Research Europe apascale@ie imm. com
IBM Research Europe juan www.bbeenbbbbae merraabemoreeo@imm
Abstract
SDForger is flexible and efficient framework for generating high-quality multivari- ate time series using LLMs. Leveraging a compact data representation, SDForger provides synthetic time series generation from a few samples and low-computation fine-tuning of any autoregressive LLM. Specifically, the framework transforms univariate and multivariate signals into tabular embeddings, which are then encoded text and used fine-tune the LLM. At inference, new textual embeddings are sampled and decoded into synthetic time series that retain the original data's 's statisti- cal properties and temporal dynamics. Across a diverse range of datasets, SDForger outperforms existing generative models in many scenarios, both in similarity based evaluations and downstream forecasting tasks. By enabling textual conditioning in the generation process, SDForger paves the way for multimodal modeling and the streamlined integration of time series with textual information. The model open-sourced at https::/ gi thub. com/ /tto///////nntgttteee/////aaaaaa http:///tteeeeee//ssseeseeeeeeee ffggg/gg/////////////gg public/databuilaie setrraariiiddeeeetttneeeeeeessss
Introduction
In the era of foundation models, integrating time-series analysis with language models (LLMs) has emerged as a key research priority, spurring work on specialized models for forecasting, anomaly detection and root cause analysis (Liang al. 2024). These efforts aim harness the representational power of LLMs to tackle complex temporal dependencies. Despite these advancements, foundation models for time series still struggle with concept drift, high variability, and face performance degradation over long horizons. In addition, the scarcity of large and diverse time-series datasets often limits model generalization, especially in domains where data collection is expensive or operationally constrained, such as climate science, finance, plasma physics (Kit et al.) 2024).
In this context, synthetic data generation has emerged as a complementary research direction to improve scalability and model performance, particularly in low-quality or data-scarce settings. In particular, synthetic data can be leveraged fine-tune machine learning models domain-specific distributions, reducing the need to train models from scratch and improving sample efficiency. Indeed,
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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several generative models for time series have been proposed, including VAE- architectures (De sai et al. 2021 Lee et al.) (023). GANs (Pei et al., | Kidger al. 202I). and diffusion-based approaches (Zhou et al. 2023). While these methods have shown promise, they typically lack pre- training, require task speeifie retraining, and often struggle with long-term dependencies, multivariate coupling, and distributional shifts (Ang et al., 2023).
Recent studies have instead explored the use of LLMs for synthetic tabular data generation (Padhi et al. 102T Borisov et al. 2022), demonstrating that language models trained on text-encoded data can capture statistical relationships and feature dependencies effectively. However, extending these methods to time series is non- con-trivial: long temporal windows increase inference and training costs, while temporal and multivariate correlations require more structured modeling.
These limitations highlight the need for novel methodologies that adapt LLMs for time-series genera- tion while addressing temporal, structural, and computational challenges. We introduce SDForger (Synthetic Data Forger), a novel framework for generating high-quality univariate and multivari- ate time series, even in data-scarce settings. SDForger leverages foundation models with minimal fine-tuning by operating over compact tabular embeddings derived from functional decompositions.
Key features and ad advantages of SDForger:
Compact basis representation SDForger uses FastICA or PCA to embed time series into low-dimensional tabular data. These capture key temporal and inter-variable structures while decoupling the embedding from sequence length, enabling efficient processing of long signals. Text-to-sequence generation via LLMs The embedding tables are converted into structured textual prompts and used to fine-tune a language model. A guided inference approach is then used to generate structured embeddings, ensuring that the synthetic data retains the original dataset's statistical properties and feature relationships.
Flexible, lightweight architecture The framework leverages autoregressive LLMs, including lightweight models, and requires only a small number of training instances. Its modular de- sign enables easy adaptation to different generation tasks and architectures, while its compact embedding space ensures fast inference, even for long time-series windows.
Multivariate and multimodal readiness SDForger can model complex multivariate dynamics and supports future extensions to textual conditioning, enabling generation guided by both time-series structure and external language-based context.
By combining structured embeddings with LLM--bssed generation, SDForger establishes a new paradigm for scalable, interpretable, and high-quality synthetic time-series generation.
Our simulations demonstrate that SDForger not only generates statistically realistic time series but also improves downstream model performance, often matching or exceeding results obtained from real data alone. This is particularly valuable in practical scenarios where access to high-qualing data is limited or where distribution shifts make original training data less effective. Compared to state-of-the-arr generative models, SDForger achieves competitive or superior performance across a wide range of similarity metrics and utility-based evaluations. Notably, our experiments show that even lightweight, pretrained L.MS (e.g., GPT-2) are sufficient to produce high-quality synthetic data with minimal fine-tuning, highlighting the accessibility, efficiency, and flexibility of our approach.
In the remainder of this paper, we first review related work (Section 2). then detail the SDForger framework (Section 3) describe our evaluation setup (Section 44. present extensive experimental results (Section 55) highlight the flexibility of language models (Section 6), and conclude with key takeaways and future directions (Section
2 Related work
Time-series generation Recent advances in time-series generation have introduced variety of deep generative models, including based approaches like TimeGAN (Smith and Smith 2020
state-space models, and vector-quantized architectures such as TimeVQVAE (Lee et al.] 2023). While
these methods generate realistic sequences, they often struggle with multivariate dependencies, and require training from scratch for each dataset. More recent framework integrate mandomly-weightee combinations of time series to improve their pretraining pipeline, e.g. Chronos (Ansari et al. 2024) adapting the Mixup (Zhou et al. 2023) methodology for time series. To address evaluation challenges, TSGBench (Ang et al. 2023) proposes unified benchmark of similarity, fidelity, and utility metrics.

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Foundation models and LLMs for time series Recent advances have introduced foundation
models specifically designed for time-series tasks, offering unified frameworks for forecasting.
classification, and anomaly detection (Liang et al.] 2024). Examples include TFT (Lim et al.
202T). TimeGPT (Garza and Mergenthaler-Canseenn
(023), and Chronos (Ansari et al. 2024). while
lightweight models like TTMs (Ekambaram et al. (024) focus on efficient multivariate forecasting.
Parallel efforts have explored adapting LLMs to time-series data by encoding numerical sequences as
text (Gruver et al. 2024 Zhou et al. 2023 Jin et al. 2023), enabling zero-shot inference and transfer learning. Notably, LLMTime (Gruver et al., 2024) and GPT4TS (Zhou et al. (023) retain most the LLM architecture while fine-tuning only shallow layers, and Time-LLM (Jin et al., 2023) employs reprogramming to adapt to temporal tasks. Despite these innovations, most existing approaches
either require task-specific pretraining struggle model complex structures and may benefit from synthetic data for improving generalization and robustness.
Specialized architectures for time-series generation Several architectures have been specifically designed to capture temporal and multivariate dependencies in time series. Variational autoencoders such as Time VAE (Desai al., (02T) and Time (Lee et al., 2023) use recurrent or vector- quantized structures to model sequential dynamics. GAN- base- approaches. including RTSGAN (Pei) jet al. 2021), SDEGAN (Kidger et al. 202T), and COSCI-GAN (Seyfi et al. 2022), employ recurrent or component-wi wise disentangled generators to capture complex temporal patterns adversarially. Diffusion- based models, like LS4 (Zhou et al., 2023), generate sequences through learned reverse- time processes. These specialized architectures complement general-purpose time-series generation methods and provide valuable baselines for evaluating synthetic data. However, these architectures trained from scratch and cannot leverage existing pre-trained language or foundation models, limiting their scalability and adaptability across domains.
3 Methodology
In this section, we present our methodology, illustrated in Figure I SDForger is divided into three macro-steps: (i) Preprocessing and embedding transform the time series into tabular data (i.e., steps 1 to 3 highlighted in purple); (ii) Fine-tuning and Generation fine-tune a pre-trained L.M and generate new embedding instances (i.e., step 4 highlighted in green); (iii) Decoding reconstruct the original time-series space from the generated embeddings (i.e., steps and 6 highlighted in light blue).
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Figure 1: SDForger pipeline. Overview of the SDForger generation process. The example illustrates setting with I = 3 input segments, C' = 2 channels, kı l2 = 3 components, and î = 2 generated samples. The model performs periodicity- segmentation, extracts embeddings, and embed them into text. An LLM is then fine-tuned generate embedding sequences, which are finally decoded reconstruct synthetic time series.
Notation Hereinafter, we introduce some basic notation. Let = (X X, E RCLL represent collection of I instances of multivariate time series, where each instance has length L and consists
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of C' channels. The task of synthetic time-series generation can now be formally defined as producing instances of multivariate time series {X; X; E RCxL conditioned the given context X. Throughout the paper, we denote by x; E R$ the i-th instance of channel and by X E R the matrix collecting all instances associated with channel c.
Periodicity-awant segmentation In cases where only single time series instance X₁ E RCLL available, we apply a segmentation strategy to artificially create multiple instances. The segmen- tation procedure facilitates the estimation of the time-series distribution. Specifically, we extract periodicity- aware windows of fixed length L < L1. aligning cuts with natural cycles and minimizing overlap enhance independence and diversity. This pre- processccggg (described in Appendix A. transforms the data from a single sequence X1 into set X = {Xi)== where X; E R Rxx. preparing the data for the generation task.
3.1 From time series to tabular data
To enable tabular generation and analysis, SDForger transforms time series into structured tabular data using basis decomposition techniques. Each row represents time series embedding obtained by projecting the signal onto a set of learned basis functions. Specifically, we adopt two decompo- sition methods: Functional Principal Components (FPC) (Ramsay and Silverman 2005 and Fast
Independent Component Analysis (FastICA) (Hyvarinen) 1999):
FPC identifies principal modes of variation by performing eigen-decomposition of the covariance operator. It captures directions of maximal variance, preserving correlation across components, showing effectiveness in modeling multivariate longitudinal data (Boschi et al. (2024).
FastICA extracts statistically independent components by maximizing non- Non--Gassianitt. It decomposes contrast function, uncovering independent latent factors that may not align with the directions of maximal variance.
Formally, for each channel c, we assume the instances (Xf...., X7) are realizations of continuous functions defined over T = j0, L.J. We approximate each X as a linear combination of k basis functions (bf..... .6,, b,,)) where the choice of basis depends on the decomposition method (non-
Gaussianity- bbased for FastCA,, covariance-based for FPC), The embedding coefficients are:
e = (XF,
(1)
We define the embedding matrix for channel F E !x. By concatenating the embeddings across all channels, we obtain the final embedding table: E = (E .....,
E (E'....., R with K -E ke-
Throughout this paper, we refer to the columns of E as embedding features. We denote the i-th row of E as E,, corresponding to the embedding vector of instance X;, and the value in its k-th column as exx- More details on the choice of li, are given in Appendix A.2 and Appendix Table D.I
Notably, both methods offer the advantage that their computational cost depends on the number of instances 7 and the number of components k., but not the instance length T.. This decoupling allows our algorithm to handle very long time windows without a corresponding increase in computational complexity, ensuring great flexibility and scalability.
3.2
Generation of tabular data
Our data generation block consists three key stages: encoding tabular data into text, fine-tuning an L.M,, and generating synthetic embeddings.
3.2.1 From embeddings table to text
LLMs are designed to process textual information. Therefore, applying an L.M to tabular data requires converting each row into textual format that serve prompt during the fine-tuning stage. Inspired by Donahue et al. 2020), we introduce a Textual Encoder responsible for converting tabular instances E, into structured text representations using a Fill-In-The-Midde template.
Definition 1 (Textual encoder) Let PFT =(P.T Jimi denote the set of fine-tuning prompts, where;

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PFT "Imput:
O 1==1 (value_T(k)) is [blank],) [sep]
Target: 1== (EiT(k) [answer])"
Here, the operator O denotes the concatenation and x is random permutation of K elements.
Random Feature Order Permatation. Encoding tabular data into text can introduce unintended positional biases, as LLMs inherently process tokens in sequence. To enforce order independence (Borisov et al. 2022), we apply random permutation π to the encoded feature- each instance. This shuffling ensures that the model does not infer any spurious relationships based on the ordering of features within the textual representation. For K 2, an admissible finetuning prompt for E, is: "Input: value_2 2 is [blank], value_ I és [blank] [sep] Target: 622 [onswer] 6 [answer]"
pairs within
3.2.2 Large language model finetuning and inference
Fine-tuning By training an LLM on structured text representations of the embedding tables, we enable to learn meaningful patterns present in the data. Since the optimal number of fine-tuning epochs depends on the number of instances, the embedding dimension, and the LLM architecture, we implement an early stopping criterion prevent overfitting.
Inference After fine-tuning, inference is performed by prompting the LLM with structured textual templates that mirror the training format, allowing it to autonomously generate new embedding rows.
Definition 2 (Textual inference) Given the embedding table E R we define the set of infer- ence prompts each generation step as PINF 9 9=1 where:
G
PINF "Input: OK (valu_T(()) is [blank], ) [sep] Target:"
We use a multinomial distribution sampling strategy to reduce repetition and generate more creative and diverse outputs. The model draws from its learned token probability distribution at each step, guided by the temperature parameter, which controls sampling variability. As a result, all values internally generated by the LLM in fully conditional and self-contained manner, highlighting the model capacity to internalize statistical and structural patterns from compact embeddings and synthesize coherent time series without external noise injection or sampling routines.
At each inference step, we generate a batch of synthetic instances, repeating the process until the desired number of sequences is obtained or stopping criterion is met. We denote the set of all generated text instances as: 9 = = Ga }. Ideally, the fine-tuned LLM should generate text instances in the following format: Gg = = PINF O [answer] where is the random permutation used in PINK and (āgm()) ) are the K numerical values inferred, which form the generated embedding table.
Retrieve embedding from text Given generated text instance G, G, reconstruct the corresponding tabular data by mapping the inferred embedding values ( } to their respective features. Each textual entry split into feature-value pairs using " "[answer] as a delimiter. Missing or unrecognized features are assigned the placeholder "NaN". For specific channel c, the output of an inference step s is the reconstructed embedding matrix: He.- RRG where each row corresponds to a generated instance G, and each column represents an inferred embedding feature associated with channel c. To track all generated embeddings up to step we define: Eo.5.
In-generation filtering and stopping criterion At each inference step s, we apply an online filtering procedure that validates generated embeddings without requiring reconstruction into the time-series domain, ensuring efficient real-time evaluation. Specifically, the reconstructed embedding matrices (El....... ..... FC.O) are filtered based on three criteria: 1) Instances with missing values are discarded, as they prevent accurate reconstruction, 2) Duplicated instances are discarded to maintain diversity the generated dataset; 3) Significantly diverging instances are discarded. This combined filtering procedure not only enforces diversity and validity among the generated instances but also provides a diagnostic signal: a substantial fraction of samples is rejected, may indicate that the fine-tuned LLM requires further training or more representative data. Representative examples of
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discarded instances and details on the divergence detection procedure are provided in Appendix A.3 while Appendix re2 the rejection rates observed in representative generation scenario, illustrating the balance between filtering rigor and sample diversity.
In generation mode, SDForger employs dynamic stopping criterion that continues generating batches of G' text instances as long as sufficient diversity is preserved among the generated samples (Appendix A..4). However, for consistent comparison with baseline methods across all simulation scenarios, we fix the number of generated instances / across all algorithms. If we denote by S the final inference step, then the output of the generation process is the complete embedding table /xx where, for each channel E Ee.s.
É E R
3.3 Decoding: from tabular embeddings to time series
Given E. the time-series representation of generated embeddings can be efficiently recovered due to the reversible nature of the embedding technique used. For the channel c, given the generated coefficients EG and the corresponding basis system (bg,- ( bg the reconstructed time series are computed as follows Kokoszka and Reimherr 2017 : 55- = Σド= bg
This formulation ensures that each generated embedding is decoded back to the original space, resulting in I synthetic instances of multivariate time series X, E RCxI.
4 Evaluation methodology
Evaluation metries
Evaluating synthetic time-series data requires balancing realism, usability, and efficiency. A strong generative model should replicate key properties of real data while supporting downstream tasks such as forecasting. We adopt comprehensive evaluation framework comprising two categories: similarity metrics and utility metrics.
Similarity metrics, inspired by Ang et al. (2023), assess how closely the generated data matches the real data in terms of distribution, structure, and behavior. They fall into two subtypes: (i) Feature-based metrics which include Marginal Distribution Difference (MDD), Auto-Cone Coto-Coorelation Difference (ACD), Skewness Difference (SD), and Kurtosis Difference (KD), assess how well synthetic data retains key statistical properties of real data; (ii) Distance-based metrics include Euclidean Distance (ED), Dynamic Time Warping (DTW), and SHAP-RE (SHR), a shapelet-based reconstruction error. They quantify the similarity between synthetic and real data in raw feature space or temporal alignment. Formal definitions are provided Appendix Utility metrics assess the effectiveness of synthetic data in downstream tasks. Specifically, we fine-tune Tiny Time Mixers (TTM) (Ekambaram al., 2024). recent foundation model for multivariate time series, under four settings: (1) zero-shot (no line-tuning) (2) real data only, (3) synthetic data only, and (4) real data augmented with synthetic data. This setup quantifies the impact of synthetic data on model transferability, data efficiency, and robustness.
Evaluation protocols We consider three distinet evaluation settings assess the generative capa- bilities of SDForger across different structural assumptions:
Multisample generation aims to produce new instances by combining patterns from multiple existing time series. This setting reflects scenarios such as generating experimental samples, weather profiles, or patient trajectories from heterogeneous observations. It emphasizes diversity and generalization in data-rich contexts.
Univariate generation focuses on learning from single time series to generate plausible alternative versions. This is useful for simulating counterfactual histories, seasonal variations, or stress-test scenarios in domains like finance, weather, and demand forecasting.
Multivariate generation evaluates the ability to jointly generate multiple interdependent chan- nels. It reflects real-world settings, such energy systems, traffic flows, sensor networks, where channel interactions and cross-correlations are crucial for realism and downstream utility.
In the multisample case, multiple instances are available by design. In contrast, for univariate and multivariate settings, only one instance is provided; therefore, we first apply the period-aware segmentation procedure described in Section to extract multiple windows from each channel.

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Parameter settings We summarize here the hyperparameters for SDForger. We fix the embedding dimension = for the multisample and univariate setting. The LLM used for generation is GPT-2 fine-tuned with Adam (Diederik) 2014) optimization, a learning rate of 8 x 10 batch size 32, and maximum of 200 epochs. Early stopping criteria is applied based on the best validation loss computed every 5 steps, patience set to 5, randomly choosing 20% of the data as validation set.
Baselines We evaluated SDForger's performance against several baseline models for synthetic time series generation, covering different approaches. Variational autoencoders: Time VAE (Desai et al. 2021), which models temporal dependencies with a recurrent VAE architecture, and Time TimeVQVAL VQVAE (Lee et al. 2023), which incorporates vector quantization for better capturing discrete temporal pat- terns; generative adversarial networks: RTSGAN (Pei et al. 2021), which uses recurrent components for adversarial training. and SDEGAN (Kidger al.. 2021 which models time series solutions to stochastic differential equations; and a diffusion--ert based model: LS4 (Zhou et al.] (023), which
generates sequences via a learned reverse-time diffusion process. Hyperparameters for all baseline
competitors follow those reported in their original papers, except for SdeGAN, for which we fix the number of training iterations 1000 to balance convergence and computational cost.
Datasets We evaluated SDForger models using 12 publicly available datasets from various domains, including energy. transport, industry. weather, and finance, with sampling frequencies ranging from 2 minutes to monthly. The datasets, sourced from the Monash Time Series Forecasting Repository and other public domains, include both stationary and ota-stationary time series, reflecting diverse temporal dynamics. Detailed information is provided in Appendix
5 Results
Following, we discuss results on Similarity-based (Section 5.1). Utility-based metries (Section 5.2 and condensed ablation study (Section 5.3). Complete ablations are provided in Appendix D
5.1
Similarity-based metries results
The similarity-based results aggregated for the multisample and univariate settings are reported in Table I with detailed per-dataset scores provided in Appendix Tables D.10 D.I1 D.12 D.13 and
D.14
Overall performance. Different generative models exhibit complementary strengths: for instance, TimeVAF performs well on distribution-based metrics, while Time excels on distance- based measures such Euclidean Distance and DTTW. In contrast, SDForger achieves consistently strong and balanced performance across both metric categories, maintaining high scores without overfitting to either statistical or structural similarity (Table []. This balanced behaviour further confirmed by the normalized average scores per metric group and the average rank values. Such consistency indicates that SDForger not only preserves key statistical features but also captures the underlying temporal and distributional structure of the data, demonstrating strong generalization and robustness across heterogeneous temporal domains. By decoupling representation learning from generation, SDForger captures long-range dependencies while maintaining statistical realism, ultimately producing temporally coherent and domain-consisten synthetic samples.
Robustness to evaluation protocols Comparing multisample and univariate settings, we observe that model rankings and relative performances remain largely consistent, suggesting that SDForger is robust to variations in the evaluation protocol. This stability is an important advantage in practice, where test-time conditions may vary.
ICA vs. FPC The ICA embedding strategy consistently leads, particularly on distance-based metrics. The superior performance of the ICA-based variant likely comes from the nature of the components it produces. Unlike FPC, which orders components by explained variance and often concentrates most information in the first few components, ICA explicitly seeks statistically independent components. This tends to produce a more balanced and disentangled basis decomposition, where each component carries distinet information that have similar importance for data reconstruction. For LLM-bbased generation pipeline, this disentanglement appears advantageous because the model can learn a joint
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Table I: Aggregated performance comparison in the multisample and univariate settings, Metrics include raw similarity scores and normalized averages (in [0 1D for each metric group, plus the average rank. Lower values are better. Bold indicates the best performance per column, and underlined indicates the second-best.
Feuture based
Distance-bune bused
Norm. Avg.
MDD
ACD
KD
ED
DTW
SHI
Feat.
Dist.
Rank
SED-ICA,
0.244
1180
0.809
2.384
16.009
12.375
6.570
0.224
0.074
3.143
SDF-FFCs
0.255
2.166
1.323
4.299
17.749
11.921
16.537
0.562
0.100
4,714
MULTISAMPL
TimeVAE
0.227
0.259
0.907
1,697
18.041
11.625
14.021
0.000
0.094
2.143
Time VQVAE
0.371
5,466
1.327
3,889
13,661
10.167
2,030
0.873
0,000
3,714
REGGAN
0.279
2.857
5.256
0.276
31,806
160
0.789
6.143
SDF-ICAg
0.306
1.582
15.
12.455
4.856
2.429
SDD-PPCCS
UNIVARIATE
TimeVAE
0.288
2.013
0.611
1.245
20.778
12:125
18.534
0.066
0.158
2:714
VQVAV
0.433
4,330
0.740
2,052
15.438
11.250
2.217
0.707
0.000
3,571
REGGAN
0.363
2,389
0.776
1.325
18.951
12,926
5.464
0.384
0.081
4,000
SdeGAN
0.267
3,659
0.813
1.542
42.017
38.541
65.557
0.390
0.979
5.143
1.44
6.143
Table 2: Utility evaluation via fine-tuned forecasting models. TTM forecasting performance on downstream tasks using different training sources: zero-shot, original data, generated data, and a combination of original and generated data. Results reported for multivariate datasets: bikesharing (target: count, control: temperature, humidity), eithl (target: HUFL, control: MUFL, OT), traffic (target: junctioni, control: junction2, junction3). Metrics include RMSE, MASE, WQL, and average rank (lower is better). Bold highlights the best result within each row group; underlined the second best; unnd-undell the overall best.
bikestaring
ethhl
trafiic
RMSE
MASE
WQL
RMSE
MASE
WQL
RMSE
MASE
WOL
Avg. Rank
0-bot
0.728
2.150
0.287
0.678
2.132
0.255
0.708
L.555
0.255
1.78
Osiginal Data (OD)
0.495
0.822
0.178
0.658
1,820
0.232
0.702
1.995
0.283
1.22
SDF-ICA
0.514
0.809
0.194
0.626
1.820
0.224
0.655
1.849
0.262
2,00
SDE-FPC
0.527
0.926
0.200
0.650
1.887
0.222
0.662
1.837
0.262
3.22
GENERATEO
Tim
0.566
0.983
0.211
0.690
2,268
0.769
0.738
2,078
0.296
5333
TEneVOVAE
0.188
0.626
1.814
0.283
2.7
ReGAN
0.710
2.271
0.225
SdeGAN
0.572
0.995
0.688
2.262
1.715
0.243
LS4
0.839
1.468
0.318
0.612
1.977
0.236
0.917
2.595
0.369
5.89
3.22
ORIGINAL GEN
SDF-FPC- OD
0.493
0.829
0.179
0.666
1.754
0.231
0,743
2.087
0.297
4.78
TimeVAF on
0.492
0.814
0.176
0.654
1.252
0.228
0.721
2,039
0.200
2.89
TimeVQVAE OD
0.495
0.904
0.174
0.678
1.887
0.242
0.724
2.043
0.291
4.56
RIGGAN OD
0.498
0.819
0.177
0.637
1.872
0.231
0.607
1.647
0.234
3.44
SdeGAN OD
0.495
0.181
0.620
0.224
0.605
3.33
distribution over set of factors that all have the same "power". Thus, the results suggest that the LLM indeed better equipped to model the joint distribution when presented with independent factors rather than hierarchy of variance-ordered components.
5.2 Utility-based metrics results
Table presents the utility evaluation, where we assess the practical value of synthetic data by fine-tuning TTM on different multivariate training sources. For LS4, we modified the architecture to support multivariate generation. Furthermore, we adjust the embedding dimension SDForger according the complexity of each dataset, setting k=3 for bikesharing, k=7 for etthl, and k=5
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for traffic. To determine these values, we conducted a small ablation study to identify the optimal embedding dimension for each dataset (see Table D.7).
SDForger demonstrates strong performance across datasets, as evidenced by its top average rank, with notable results bikesharing and etth1. In bikesharing, synthetic data from SDForger alone yields competitive scores, and combining it with real data leads to the best overall performance across metrics, On etth1, SDForger-generatee data surpasses original data in RMSE and WQL, suggesting captures critical temporal and statistical structure. The hybrid setting (original + generated) maintains this advantage and further improves MASE. Performance on traffic more nuanced. Here, fine- tuning on real data is less effective, and GAN-based methods outperform others. Nevertheless, SDForger remains competitive, especially when using synthetic data alone. This suggests that the test distribution may deviate significantly from the training set, making traditional fine-tuning less useful. Indeed, high-quality synthetic data can act as a valuable supplement or even an alternative.
In no scenario does synthetic data degrade downstream performance, underscoring the reliability and utility of SDForger-generate samples across varied forecasting contexts.
5.3 Ablation
Effect of embedding dimension & Appendix Table D.6 presents an ablation study on the number of components & used in SDForger's embedding space. A compact embedding with k=3 offers strong performance across both multisample and univariate settings, indicating that a small number of components is often sufficient capture core temporal and structural patterns. However, the optimal value of k may vary across datasets, with more intricate dynamics potentially requiring higher-dimenee dimeessoiiiiii representations. In practice, users may also opt to select based on desired percentage of explained variance, adapting the representation to specific application needs.
Domain-level insights Appendix Tables D.3 and D.4 summarize the average normalized similarity scores per dataset. SDForger models achieve strong performance across a wide range of domains. Structured datasets such as Energy, Appliances, and Weather exhibit particularly high scores. In contrast, domains such as Tourism. Traffic, and Finance present greater challenges, likely due to their increased irregularity and noise. Nonetheless, SDForger maintains competitive results even in more complex settings, underscoring the flexibility of the proposed architecture.
Generation efficiency Appendix Table D.5 reports the average time to generate univariate sequences for three targets from the Bikesharing dataset, across two window lengths. SDForger substantially faster than all competitors, often by one two orders of magnitude. VAm is the closest com- petitor but remains over 4x slower. Notably, unlike GAN- time is independent of sequence length and scales with the number of embedding components (k). A minor exception occurs at 1 = 3, where the reduced latent expressivity increases LLM fine-tuning time. Overall, SDForger achieves state-of-the-ar efficiency without compromising quality.
competitors, SDForger's generation
LLM comparison GPT-2 (124M) achieves performance on par with, and sometimes better than larger and more recent models such as granite-3. O (2B) and p.i-3.5 (3.8B) (Appendix Table D.9p. This shows that SDForger's s pipeline is effective even leveraging lightweight models. While runtime cost grows with model size, SDForger remains efficient compared to basclines (Appendix Table D.8).
Filtering Procedure. Appendix Table D.2 reports rejection statistics for a representative generation scenario. We observe that the overall discard rate remains consistently low (< 2%) across settings, indicating that most generated embeddings fall within a plausible norm range. The proportion of missing values increases with larger embedding dimensions, reflecting a higher likelihood of incomplete generations in longer textual outputs. Notably, the &2 norms of accepted samples closely match those of the original embeddings, while discarded ones exhibit markedly higher values, confirming that the filtering procedure effectively removes divergent or anomalous generations.
Shaping time series with language
SDForger is designed to naturally incorporate textual information, making it well-suited for state- of-the-art time-series generation that embraces additional multi-modal inputs. To explore this, we conduct an experiment using the bikesharing dataset. Coming from the intuition that these variables stem from a common physical process and may share latent components, we embed their three

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channels (temperature, count, and humidity) into shared ICA basis. We incorporate the channel information in the textual encoder: "Condition: data temp [sep] Input: value_1 [blank] [sep] Target: 6q [answer]...
This conditioning strategy enables SDForger generate channel-specific sequences with high fidelity. For instance, using longitudinal k-nearest neighbor classifier KamossCarreenn et al. 2024 trained on real data, we achieve an accuracy 0.81 in identifying the generated curves (see Figure These results highlight SDForger's strong generative capacity and its ability to integrate and respond to textual cues, positioning
flexible and powerful baseline for multimodal time-series synthesis.
12t0
connt
humidity
Tempersture
(ree
200
600
400
200
03-
-300
Figure 2: Text-Conditioned Generation with SDForger. Visualization of 10 original (grey) and synthetic sam- ples per channel from bikesharing data. Synthetic data is generated using conditional prompts: "Condition. data cnt (blue)", "Condition: data hum (pink)", and "Condition: data is temp (orange)".
Conclusions
We introduced SDForger, a flexible and efficient framework for generating synthetic multivariate time series using large language models. By combining compact functional embeddings with textual conditioning, SDForger enables high-quality generation even data-scarce settings. Extensive evaluations across multiple datasets and tasks demonstrate that SDForger consistently achieves strong similarity scores and enhances downstream forecasting performance- matching or surpassing results obtained from real data and outperforming sate-of-the-ar baselines.
Ablation studies confirm the robustness of the framework across embedding strategies, dimensionality choices, and LLM architectures. SDForger is also highly efficient, with significantly lower generation times compared to its competitors. Moreover, by leveraging LLMs, SDForger enables seamless integration with textual prompts, paving the way for multimodal time-series generation, where natural language can guide not only content but also structure, semantics, or temporal context.
We believe SDForger can be further improved. Its modular design is intentionally built to support flexible experimentation, making easy to explore enhancements tailor components to specific needs. We see several promising directions:
Embedding Strategies While our current approach relies on linear methods like FastICA and FPC, future work could explore more expressive, nonlinear embeddings (c.g.. AE) or multivariate- aware methods like Multivariate FPCA or Multivariate Singular Spectrum Analysis to better capture temporal and inter-channel dependencies.
Caaameter-Efficieee Fine- Muni-Tunngg We currently use full fine-tuning for the LLM. However, using too many components relative the number of instances can lead unstable fine-tuning and reduced generation quality. Incorporating PEFT techniques such LoRA or adapters could improve scalability, efficiency, and facilitate domain adaptation.
Extension to encoder-only models Our current implementation supports only autoregressive LLMs; future work would extend the framework to encoder-only models and different generation paradigms such masked token prediction.
Extended Utility Evaluation While we focus on forecasting, SDForger could evaluated and optimized for broader downstream tasks such classification anomaly detection. Context and Covariate Integration By design, SDForger supports integration of external covariates (e.g., categorical textual data). Expanding this functionality could enable richer conditional generation, and multimodal transfer learning (see Section(6).
In summary, SDForger offers flexible foundation, and we see meaningful opportunities to improve it both architecturally and in terms of task generalization.
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Appendix
A Implementation details
A.1 Data preprocessing: segmentation
In many scenarios, each channel consists of single historical time series, i.e., To 1. However, to estimate embeddings that effectively capture the temporal distribution, multiple instances per channel are necessary. Therefore, when fo 1, we segment each channel into multiple overlapping windows. Specifically, for each channel c, we construct Le windows of fixed length Le, where Le < Lo. Without loss of generality, for simplicity in notation, assume Le and Ie are identical across all channels and denote them as L and I, respectively.
To ensure robust learning of the embedding distribution, must be sufficiently large. Our experiments indicate that even = 15 (i.e., 15 instances) suffices for this purpose. Once and are fixed, we segment the time series while minimizing the overlap between consecutive windows. The overlap step is determined by the dominant periodicity of the channel, ensuring that window transitions align with intrinsic temporal cycles.
The set of extracted windows W is formally defined as:
W {X L]
8, 28,
L}}
where the step size computed as: max(1, L ((ا+)) J) and then adjusted be the nearest multiple of P to maintain consistency in periodic structure.
To determine the dominant periodicity we employ the Autocorrelation Function (ACF), which quantifies the similarity between the time series and its lagged versions at different time shifts. This method is robust to noise and remains effective even when periodicity is not strictly stationary.
The estimation of P follows these steps:
1. Compute the ACF and identify significant peaks, excluding lag O.
2. Rank the detected peaks by their autocorrelation values.
3. Select the highest-ranked period P such that P << I./2.
Figure A.1: Periodicity-aware segmentation.
By leveraging this periodicity-awes aware segmentation strategy, we ensure that the extracted windows align with the natural cycles of the time series. Moreover, this approach minimizes window overlap, maximizing their independence and diversity and facilitating more effective embedding computations for downstream generative tasks.
This pre-processing transforms the data from a single sequence X2 into set X (X;) where each X; E C preparing the data for the generation task.
A.2 Choice of the number of components
The choice of & determines how well the basis representation approximates the original time-series channel Our frameword allows the user to either select the smallest h. that explains predefined percentage the total variance of the original time series or manually specify k..
There exists inherent trade-off in selecting lic A higher k, captures more of the total variability but can hinder the L.LM's 's ability to model the underlying distribution during the generation phase. Moreover, if ke is too large, the generated samples may become overly similar to the original data,
13

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limiting diversity and the introduction of novel patterns. Conversely, choosing ke too small risks omitting essential structures and temporal characteristics, degrading the reconstruction quality.
important to note that the nature of the components differs between FPC and FastICA. FPC forms parsimonious basis system, where a few components typically suffice capture most of the variability, with components ordered by the amount of variance they explain-eart components being systematically more informative. In contrast, FastICA components unordered: each component contributes independently, without hierarchical importance structure. As result, FastICA generally requires more components achieve similar reconstruction quality compared FPC. However, this property also makes FastICA embeddings more robust during generation, as information is distributed more evenly across components, reducing the risk that few badly generated components disproportionately affect the synthesized curves.
To provide a quantitative intuition, Appendix Table D. reports the proportion of variance retained across embedding dimensions for both decomposition methods. This analysis highlights how the variance explained increases with k; and how FPC typically achieves higher cumulative variance with fewer components, while FastICA distributes information more evenly across dimensions.
In practice, we recommend keeping the total number of components K reasonably small, particularly when the number of training instances is limited. Empirically, with a training set 30 instances, setting K 25 often results in unstable fine-tuning and increased rate of discarded samples due to low-quality generation. This limitation stems from the LLM's reduced ability to model high-dimensional embeddings under data-scarce conditions effectively.
A.3 In-generation filtering
Missing values and duplicated instances. To illustrate the filtering logic, report three concrete examples of generated prompts with embedding dimension K = 4. Following the inference template:
DINF "Input: O value_=x( (k) is [blank], ) [sep] Target:",
the model produces the following textual generations:
Prompt 1 (valid)
Input: value_2 is [blank], value_4 is [blank], value 1 is [blank], value_3 is [blank] [sep] Target: 0.125 [answer] -8.084 [answer] 0.217 [answer] 0. 041 [answer]
Prompt 2 (duplicated)
Input: value_4 is [blank], value_1 is [blank], value 2 is [blank], value_3 is [blank] [sep] Target: 084 [answer] 0. 217 [answer] 0.125 [answer] 0.041 [answer]
Prompt 3 (missing value) Input: value_1 is [blank], value_3 is [blank], value_2 2 is [blank], value_4 is [blank] [sep] Target: 0. 182 [answer] 0.095 [answer] -0.012 [answer]
In this example, the filtering stage identifies Prompt 2 as a duplicate of Prompt I and discards it, while Prompt is removed because does not contain all the targets' coefficients. Only Prompt I is retained for reconstruction. This simple yet effective procedure ensures that the generated embedding tables remain diverse and valid before decoding into the time-series domain.
Diverging instances To ensure the quality of synthetic data, we discard generated instances whose embedding coefficients significantly deviate from the distribution of the original data. Specifically, we compute the squared f--mrmm of each embedding vector and compare it the norms of the original embeddings. This criterion efficiently filters out extreme outliers the latent space, without requiring reconstruction into the time-series domain.
Formally, for each channel c, let h.. E Eo.s-1 be the matrix containing both original embeddings and all previously accepted generated embeddings up to inference step 1. with fe.0 E.. Denote by Aecoodd and Ne,new the sets of squared Euclidean norms of the rows of -

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and the newly generated matrix E respectively. For each newly generated row i, we compute its norm and accept only if:
21 - IQR < N. I 93 3- -QQ..
where @i and d3 are the first and third quartiles of Arooodd and IQR = 91- An instance is retained only if this condition is satisfied across all channels
This norm-based strategy is particularly well-motivated when using FPCs, due to the orthonormality of the basis. Let X be a time series in channel and by the corresponding FPC basis. Then the T.²-norm of X can be approximated by the Euclidean norm of its FPC coefficients:
ke (e
| (x 1
Σ
(X,
by
R
where eij are the FPC embedding coefficients. This justifies the norm-based filtering as a direct proxy for detecting time-series samples with unusually high low energy.
While filtering based on coefficient norms does not guarantee full statistical fidelity to the original time-series distribution, it serves reconstruction. Combined with additional checks for missing values and duplicates, this step helps preserve both the diversity and relevance of the generated data. A high rejection rate may indicate insufficient LLM fine-tuning or poor generalization, suggesting the need for more representative training data additional training steps.
effective mechanism to remove extreme outliers without
A.4 Stopping criterion
The stopping criterion monitors the diversity of the generated norms across all channels to determine when the generation process should stop. When using FPC, these norms correspond to the LL of the generated curves. When using FastCCA, they correspond to the norms of the embedding coefficient vectors; although not directly related to the curve norms, they still provide useful proxy for identifying over-sampling and loss of variability.
At inference step s, for each channel let u denote the number of unique values in Neooodd (the set of accepted norms up step 8), rounded to the fourth decimal place. Let be the total number of valid instances generated so far. We define the diversity score for channel e as:
D = u /
The diversity score provides quantitative measure how much variability remains in the generated norms. We track D at each inference step, and the stopping condition is triggered when:
max D < Astop or I Ímax-
In other words, generation stops either when the maximum diversity score across channels falls below predefined threshold Asoo, indicating reduced novelty, when the total number of generated instances exceeds a maximum cap Jmaxx
Monitoring the diversity score enables us to assess whether the model continues to introduce new variability the generated data, serving as an online signal for generation quality.
we denote by the final inference step, then the output of the generation process is the complete
embedding table É e ixx where, for each channel E = E..S
B Evaluation metrics
All the metrics presented below are adopted from Ang et al. (2023). except for Shapelet-based Reconstruction, which follows the definition in Zheng et al. (2016).
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B.1 Beature-based evaluation
Marginal Distribution Difference MDD computes empirical histogram for each dimension and time step in the generated series, using the bin centers and widths from the original series. then calculates the average absolute difference between this histogram and that of the original series across bins, assessing how closely the distributions of the original and generated series align.
AutoCorrelation Difference ACD computes the autocorrelation of both the original and generated time series, then determines their difference. By contrasting the autocorrelations, we could evaluate how well dependencies are maintained in the generated time series.
Skewness Difference SD is vital for the marginal distribution of a time series, quantifying its distribution asymmetry. Given the mean (standard deviation) of the train time series T as 1º""" (a!") and the generated time series Tgen as pgen (agen), we evaluate the fidelity of Tyen by computing the skewness difference between them as:
B (T g
ET )
SD
0 gen3
a tr
Kurtosis Difference Like skewness, KD assesses the tail behavior distribution, revealing extreme deviations from the mean. Using the previous notations, the kurtosis difference between T and Tyen is calculated as:
E [ [1gem)1]
E [
KD
9on4
B.2 Distance-based evaluation
Euclidean Distance For each original series S*" (.,, 21) and its generated gee (v1 .... y1).
VDD=Eiii Ei 2. We take the mean of ED for series and all samples. Given that the input time series has been preprocessed to fit within the range of [0, 1], ED deterministically assesses the similarity between ggen and s provides a value-wist comparison between the time series.
ED =
Dynamic Time Warping Given that ED overlooks alignment, include DTW capture the optimal alignment between series regardless of their pace timing. The alignment facilitated by DTW offers insights into the predictive quality of the generated series.
Shapelet-based Reconstructions Shapelet based RE calculated by generated time series using shapelets extracted using shift invariant dictionary learning (SIDL) algorithm (Zheng et al. 2016). Shapelets represent local discriminative patterns present in the time-series data. We learn shift invariant patterns/shapelets on the original time-series dataset and then use the learnt dictionary to reconstruct unseen generated time series. The reconstruction error is calculated between the generated time series and their reconstruction using SIDL.
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C Datasets & protocol settings
Table C.I: Overview the benchmark datasets. For each dataset, report application domain, sampling frequency, number time series, length statistics, and the type of evaluation (univariate, multivariate, multi- sample) it supports.
Datasct
Domaln
Freq.
Number
Evalnation type
Ms
uv
MY
Electriciry
energy
Applianues
energy
Rikedharing
N
Carben
Plant
8
ETTHI
1I1
N
ECL
320
Y
Exchange Rate
finance
ID
8
N
NNS
finance
1D
111
Y
Tourism
general
IM
365
Y
N
Traffle
transpott
1H
3
N
Traffic Monash
transport
I11
861
Y
Solar Weather
zature
11
633
Y
Rain Weather
ralure
386
Y
Temperature
cature
C.1
Dataset overview
Energy
Australian Electricity (Godahewa et al. 2021 contains electricity demand data from states in Australia.
Appliance contains house temperature and humidity conditions monitored with a wireless periods.
coptianseeConnainns
sensor network, and energy data logegd with m-bus energy meters averaged for 10 minutes
ETTH contains oil temperatures and other covariates of electrical transformers from two stations in China, measured at 15 minutes granularity but hourly aggregated.
ECI. contains electricity consumption of 370 points.
Mobility and Transport
Bikesharing contains the hourly and daily count of rental bikes between the years 2011 and 2012 in the Capital bike share system with the corresponding weather and seasonal information.
Traffic contains observations of the number of vehicles each hour in four different junctions Traffic Monash (Godahewa et al. 202I) contains hourly road occupancy readings from sensors in the San Francisco Bay area.
Tourism (Godahewa et al. 2021) dataset from, used for the Kaggle Tourism Forecasting competi-
tion. This dataset is non-stationary.
Nature
Carbon Capture Plant (Jablonka et al. 2023 records the emission profiles of "2-amino-2-methyl
1-propanol" (AMP) and "piperazine" (Pz) collected at every 2 minutes interval.
Weather (Godahewa et al.) (021) contains daily time series of four weather variables (rain,
mintemp, maxtemp and solar radiation) measured at weather stations in Australia.
Finance

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Exchange Rate (Godahewa et al. 2021) contains daily exchange rates for currencies of eight countries (Australia, British, Canada, Switzerland, China, Japan, New Zealand and Singapore) between 1990 and 2016. This dataset is non-stationary.
NN5 (Daily, Weekly) (Godahewa et al. 202T) contains cash withdrawal data from ATMs. This dataset combines stationary and non-stationary time series.
C.2 Protocols
Multisample setting For MS data preparation, we sampled = 30 instances, each of length T, 250, resulting in total training sequence of 15,000 timestamps. Standard scaling per timestamp applied. For evaluation, we generate 100 synthetic instances.
Univariate setting For UV data preparation, we used training sequence of length Ly 2, 000, segmented into / 30 instances of length I, 250 using our periodicity-awarc segmentation strategy (ef Appendix A. Same standard scaling was applied. For evaluation, we generate 100 synthetic instances.
Multivariate setting For fine-tuning TTM in the MV setting, we used consecutive sequences of length Lo 5000, 2500, and 2500 for training, validation, and testing, respectively. Each set was segmented into / = 30, 15, and 15 instances of length = 1120 using our period-aware segmentation strategy (Appendix A.Ip. Periodicity
estimated from the training set. Standard scaling per timestamp, computed on the training set, was applied consistently across all splits. For evaluation, we generated 30 instances, matching the size of the training set.
D Additional results
Table D.1: Variance retained across embedding dimensions. For each dataset, we report the proportion of total variance retained for embedding dimensions & 3, k 5, and decompositions.
under both FastICA and FPC
Dataset
FICA
FPC
k=3
k=5
Appliances
0.333
0.457
0.539
0.324
0.459
0.555
Australian Electricity
0.702
0353
0.912
0.787
0.895
0.938
Bikesharing
0.492
0.662
0.744
0.599
0.734
0.796
Carhon Capture Plaor
0.773
0.955
0.951
0.843
0.933
0.965
ETTH
0.536
0.686
0.775
0.635
0.754
0.823
ECL
0.809
0.911
0.971
0.991
0.997
0.999
Exchange Rase
0.776
0.907
0.942
0.957
0.982
0.989
0.479
0.590
0.719
0.376
0.564
Traffic Monash
Weather
0.449
0.605
0.725
Solar Weather
0.450
0.616
0.718
0.574
0.713
0,833
Temperitrre Mux Weather
0,493
0.602
0.685
0.864
0.883
0.915
Temperatere Mit Weather
01390
0.517
0.611
0.777
0.824
0.858
Table Filtering statistics for generated embeddings. Rejection statistics on the count variable from bikesharing dataset, averaged across 5 seeds. Each row reports the proportion of generated samples containing missing values, the fraction of samples discarded by the filtering stage, and the average f2 norms of the original, accepted, and discarded embedding vectors.
NaNS
Discard's
Norms Original (Arg)
Norms Accepted
Discarded
3.87
1.94
1.714
SDF-ICAs
SDF-ICA;
58.82
0.00
2,602
2.521
0.000
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Table D.3: Per-dataset similarity results in the multisample setting. Average normalized similarity scores
(feature-based and distance-based) for each dataset and model.
Feature-Baree
Distance-Based
ed
mn5
tourisms
traffic
weather
col
mas
tourssm
traffic
weather
SDF-ICAs
0:402
0.195
0.268
0.330
0.204
0.018
0.129
0.032
0.086
0.137
SDF-FPC3
0.576
0.323
0.504
0.293
0.296
0.054
0.183
0.073
0.009
0.136
TimeVA
0.164
0.109
0.211
0.143
0.174
0.063
0.139
0.074
0.343
0.125
TIVAVQVAE
0.754
0.380
0.818
0.477
0.498
0.03
0.068
0,009
0.853
0.099
RsGAN
0.049
0.174
0.315
0,110
0,539
0.290
0.849
0.400
0.639
0.707
Table D.4: Per-dataset similarity results in the univariate setting. Average normalized similarity scores (feature-hased and distance-hasedd haseed for each dataset and model.
Peature-Based
Distance-Burs
appl.
austc:
bike
curbon
ctth1
exch.
traffic
appl.
austr:
bike
carbon
etth1
exch.
traffic
SDF-ICAg
SDD-PFCC
0,509
0.122
0.169
0.345
0.107
0.287
0.213
0.085
0.101
0.072
0.078
0.076
0,143
0.044
TimeVA VAE
0.370
0.123
0.184
0.176
0.234
0.113
0.236
0.119
0.079
0.155
0.100
0.140
0.091
0.178
TimeV/VAE
0,531
0.439
0.371
0.572
0.354
0,578
0.312
0.045
0.031
0.037
0.005
0.631
0.031
0.035
REGAN
0,567
0.300
0.273
0.226
0,244
0.217
0.312
0.056
0.098
0,084
0,085
0.072
0.157
0.033
SAKGAN
0.634
0.466
0.765
Table D.5: Average generation time: baselines Average time (in seconds) required generate synthetic aikesharing dataset across three targets: count, temperature, and humi diiidityy
univariate time series We report results for two input sequence lengths: 250 and 500. All models were evaluated under the same computational constraints (-mem 20G -cores 1+1 -gpu v100) using single NVIDIA V100 GPU.
Length
SDF-ICAs
SDF-ICAg
SDF-ICAy
SDF-FPC3
SDF-FPC
SDF-PPCy
TimeVQVAB
RuGAN
250
28.8
33.1
138.1
4574.2
2804.4
Table D.6: Ablation study: embedding dimension. Aggregated similarity baased performance across all datasets in the multisample and univariate setting.
Feature-basod
Distanc--hased
Norm. Avg.
MDD
ACD
DTW
Dist.
SDI-FPC3
2.166
MULITSAMPLE
SDD-FPCC
3,191
11.727
SDD-FPCC FPCy
0.261
3.534
1.500
3.560
17.710
11,652
28.068
0.787
SDF-ICAg
0.344
1.180
0.869
2.384
16.669
12:373
6.870
0.050
0.333
SDF ICAs
0.261
0.782
1.378
2.699
16.743
12:228
2.251
0.371
0.307
SDF-ICAy
0.365
0.589
964
2.963
16,000
12.031
14.195
0.576
0.362
SDF-FPC3
0.308
1.480
0.801
1.690
19.540
12. 12,809
5.452
0.736
0.469
UNIVARIATE
SDF-PPCs
0.206
1.887
0.773
1.581
20.534
12.513
8.920
0.335
0.753
SDF-FPC,
0.309
2.399
0.774
1.954
20.470
12,079
10.982
0.947
0.654
SDF-ICAg
03066
18.802
4.856
SDF-ICAs
0.306
SDF-ICAy
0.306
0.597
0.736
1,458
19,989
12:381
8.102
0.175
0.543
19

---

Table D.7: Ablation study: embedding dimension. TTM forecasting performance downstream tasks using different training sources: generated data, and combination of original and generated data. Results are reported for 3 multivariate datasets: bikesharing (target: count, control: temperature, humidity). eith! (target: HUPL, control: MUFL, OT), and traffic (target: junction1, control: junction2, junction3). Metrics include RMSE, MASE, WQL, and average rank (lower is better). Bold highlights the best result within each row group; bold-underlined the overall best.
bikedhring
etth
traflic
RMSE
WQL
WQL
WQL
2.150
0.555
1,555
0.255
Original Data (OD)
0.822
0.658
0.232
1.995
SDF-FPC3
0.926
0.246
2,029
SDF-FFC,
0.988
0.693
0252
1,837
SDF-FPCy
0.15
0.650
2.265
SDF ICAg
0.514
0.899
0.194
0.647
1,829
0.233
0.730
2,068
0.294
SDF-ICAG
0.537
0.909
0.194
0.637
1.934
0.233
0.655
1.849
0.262
SDF-ICAy
0.517
0.898
0.193
0.626
1,820
0.334
0.790
2,189
0.312
SDF-FFC + OD
0.493
0.829
0.179
0.658
1,780
0.229
0.786
2.077
0.296
SDF-FPC; + OD
0.487
0.807
0.114
0.659
1,757
0.230
0,743
2,087
0.297
SDF-FFC, OD
0.492
0.821
0.177
0.666
1,754
0.231
0,706
1,993
0.283
0.228
2,074
SDF ICA, +
0.804
0.649
0.200
2.110
SDF-ICAy +
0.490
0.800
0.642
0.226
2.025
Table D.8: Average Generation Time Across L.LM Backhones. Average time (in seconds) required to generate synthetic univariate time series the bikesharing dataset across three targets: count, temperature, and humidity. We report results for two input sequence lengths (250 and 500) and compare three LLM backbones: GPT-2, granite-3. 3. 0-2b-base, and Phi-3. 1.-53..5mmm 5-mi5---iii--- S--miii-instuune instruct. All models were evaluated under the same computational constraints (-mem 100G cooes 1+1 -guu a100) using single NVIDIA A100 GPU. For fine-tuning, we use a batch size of 16 for granite and for phi.
Length
ICAg gpt2
ICAs granie
ICAg phi
ICAs + sp12
ICAs granie
ICAs phi
ICA, gp12
ICAr granite
ICAr phi
250
2277
112.8
132.6
18.3
118.5
113.9
19.0
119.9
126.1
500
16.2
93.6
98.5
17.3
99.9
103.7
18.9
125.0
110.7
Table D.9: Ablation study: LLM backbone. Aggregated similarity- performance across all datasets for different LLMs used in SDF models. We compare GPT-2 with two larger and more recent alternatives: granite-3, ---b-- -a..----baaaaa.. (2B parameters) and Phi-3.5 5--5----ni--- miint-instructie (3.8B parameters). For fine- aeentunnng. we use a batch size 16 for granite te and 8 for phi.
Festure-Sused
Distanco-based
Norm, Aug.
MDD
ACD
SD
DTW
SHR
Feat.
Dist.
SDE-FFC's
0.255
2.166
17.749
11,921
MULITISMPLLE
SDF-FRC' Grunite
0.211
1.817
16.429
11.565
SDD-FFC; + Phi-3
0.257
1,215
1.154
3.723
16.734
11.872
12.367
0.613
0.397
SDF-ICA3 + GPT-2
0.344
1.180
0.869
2.384
16,669
12.375
6,870
0.101
0.361
SDF ADF-ICA Granite
0.241
1069
0.961
2.524
16.953
12.744
6.160
0.101
0.509
SDF-ICAg Phi-1
0.347
0.907
1002
3,570
16.069
11 847
6.409
0.382
0.069
SDF-FPCCs + GPT-2
0.308
1.480
0.801
1,600
19. 340
12,809
5.452
0.947
0.804
UNIVARIATE
SDE-BC's Granite
0.305
1.268
0.673
1.185
19.026
12.556
5.457
0.297
0.505
SDF-FPC; Phi-3
0.310
1.368
0.671
1.305
19.561
12.767
5.196
0.574
0.777
SDF-ICA3 GPT-2
0.306
1.3%6
1,382
18.002
12.435
4.856
SDE-ICA, Granite
4.712
SDF-ICAs + Phi-3
0.307
1.398
0.541
1.199
19.081
12:471
5.856
0.337
0.577
20

---

Table D.10: Multisample evaluation: similarity metrics reported per dataset.
SDPPrgee Models
VAE Models
GAN Models
Others
ICAs
FPCs
TAmeVAE
TQVVVVVE
RTSGAN
SDEGAN
LS4
0.156
2,47
0.040
0.114
KD
7,342
6.895
1,001
8,673
10.011
ED
[0.14]
12.585
22.887
9.978
13461
25.951
43.715
DTW
0.715
10.955
12.025
7,97
12,456
25,431
20 143
SHAPP-E
0.424
4.027
2.21
4.125
7,01
108 287
0.245
0.37
0.366
0.259
NNS
KD
1.43
4,2.9
0.151
1.0
0.348
0.512
BD
19.308
20,576
20.514
15,019
16.07
43.33
38 88.
DTW
12857
12.617
11:223
10.914
634
36.712
24.115
SHAPPRE
9,482
40,975
20.903
2407
8.244
83.918
207.119
MDD
0.189
0:24
0.222
0.131
0.208
0.214
KD
4,477
8.307
4,251
2.677
8,852
9.616
10
ED
11,216
14,039
13,895
10.516
15,405
25 399
39 897
DTW
10:201
1.8
12,409
N.192
14.741
25.006
15
0.547
1,28
L.785
2.135
2,833
6.005
100
MDD
0.251
0.223
0.355
1.354
1405
Traffic
KD
3.177
1,937
1,503
2,612
3.113
4 4.727
BD
16,532
19,429
20.748
14.169
15.562
35.521
56 S00
DTW
10.917
10.5
343
10.050
V.164
31 89
37 078
6,568
9.188
14.948
1.995
3.101
51.49
205.07
MDD
0.282
0.300
0.256
0.296
Weather
0,005
KD
0.419
1.561
0.591
2.188
0.554
0.527
0,976
(Mastemp)
BD
25.
21.061
19,665
15.113
19.77
431055
46 180
DTW
20.530
15:354
13.238
11.219
15884
41.331
34.55
SHAPPRE
6.638
24.499
9.079
2,098
39911
34,196
152.274
MDD
0.271
0.27
0,41
0.303
0.566
Weather
0.340
0.145
KD
1,065
1,789
0.757
1,935
0.965
0.313
1.14
(Mintemp)
HD
17.199
18.535
17.375
15.177
15.575
44,094
46 366
DTW
13.148
11.255
10.48
10,875
10337
41.51
32.155
SHAAP-E
6.217
14.015
15,605
1.056
55,846
208 240
MEN
0.233
0.175
0.291
199
0.309
Weather (Rain)
KD
37238
7.94
7,447
9.639
HD
14461
16.009
13631
15,031
31 41412
50 946
DTW
10.33
11,493
11.35
10,715
10,00
28,891
33.017
SHAAP RE
10955
0,555
25.464
1.883
7.902
57.118
224 024
MDD
0.314
0.29
0.659
0.312
0.997
ACD
Weather
0.013
0.029
0.544
0.453
(Solar)
ED
18.80
20.201
000061
15.69
17.677
549
33, 34.466
DTW
10.61
11.322
9,932
11,507
11.25
36.321
17:363
SHAP RE
25.218
22.177
1.892
8.633
117. 305
60.63
httpp//Awnggguuiercccv//iieeeegp base
21

---

Table D.11: Univariate evaluation: similarity metries reported for Energy datasets.
SDForger Models
VAE Models
GAN Models
Others
ICAs
FPCs
TimeVAE
TimeVVVAE
RTSGAN
SDEGAN
3,028
Appliances
KD
3,219
3.816
2.881
2.586
2,559
4.196
5,574
ED
[9,693
19:13
20. 30.159
15.916
17.102
29 562
47.81
D3W
11,597
11.73
10.03
12.322
11.30
27.191
16.544
5,888
9.073
1,952
0.112
0.323
Australian Elee
0.423
0,452
1.296
2.12
0,325
0.765
(T00000))
ED
10.017
23.655 663
19.659
15.657
22.511
42
38.081
DTW
10:65
6655
10.899
10.583
14,942
942
26. 104
3:11
2.441
4,007
34,777
0:635
0/42
0.273
0.200
Australian Flee
0.032
KD
1.8
6677
0.503
1.99
0.264
0 889
(100001)
ED
18.308
19. 769
19.51
15.717
20.145
44103
37. 37.357
DTW
12.842
10.312
00.688
13.
201
25,000
2,211
2.91
6.051
3.291
26,963
30,768
0.313
0.297
Australion Elle
0.73
0.229
KD
0.179
0.69
0.539
2.111
2,386
0.380
8.804
(1000002)
ED
20,624
21.174
19.537
15,889
19.896
45.31
37.751
W3W
13.17
13,104
10.626
10.748
14,550
44.425
26 56.
2.683
3.04
4.904
2.58
1.572
23.29
28.057
MDD
0.789
Australian Elec
0.309
0.365
0.004
KD
0.057
3.465
0.226
1,595
0.524
0.127
1,343
(T0X003)
ED
17.406
19.377
20.146
15.975
18.751
40003
4014
DTW
T182]
14,156
11 466
11,025
11.5
37,719
28. 28.914
1888
4.92
1522
3,095
17.34
26,566
6.726
Australian Elee
0,199
0.665
1.679
2. 199
0.591
0.527
0,706
(T00000))
ED
19.85
198864
20.51
15,88
19.327
44.238
41,623
DTW
11.8
12.582
10.921
10.933
12972
40.349
13
SHAP-RE
4.11
4.68
11.67
4.131
39,504
54. 245
0.32
0.475
0.381
0.291
0.306
1,376
ETTHI
0.151
0,245
0.845
2
0,809
0.276
(HUFL)
ED
(9,32]
20.103
21 804
16,021
17.32
316
25, 175
FTW
9,475
9,579
10.69
11.35
10.616
9.745
13.299
28. 806
7,584
129 161
48.028
0.265
0.272
ETTHI
KD
0.892
0.097
0.651
1,089
0.936
0.645
0.134
1.855
(OD)
ED
20.45]
18. 18,292
22. 22.676
15,583
20.403
51.747
42.246
DIW
12.535
13.195
12.614
10.499
11,718
49.511
65,674
3.368
3.446
15.306
2.174
3,513
52871
52.156
22

---

Table D.12: Univariate evaluation: similarity metrics reported for Transport datasets.
SDForger Models
VAB Models
GAN Models
Others
ICAs
FPCc
Time VAE
TimeVQVAE
RTSGAN
SDEGAN
0.332
Bikesharing
0.042
0.25
0.035
KD
0.577
0.258
0.125
1:447
0.091
0.218
0.387
(Coun)
ED
21.389
19.006
21.313
16.172
19. 19,805
48.217
21.848
10.3 00.305
10.076
10:163
12.
11.74
10.347
13.77
2,012
247 88
64 166
1.04
Bikesharing
0.509
0.617
XD
0.521
1206
0.671
1811
0.511
0.404
1.13
(Humidity)
ED
19.761
18,098
25.8
16.097
18,475
44.841
$1.221
DTW
10,699
10347
13416
10 10.907
10.25
36,872
76, 846
4.63
43.651
2.154
88.5 84.
MDD
13339
Bikesharing
KD
T3T
0.31
0.536
1.776
1.225
0.409
1.354
(Temperature)
BD
17,172
20.38
19.349
15,702
20.391
49,379
39 39,062
DTW
T2107
12.47
11074
10.569
15.251
46.37
76.093
2,807
4.126
7:314
2.189
6.538
42.472
30,348
MDD
Traffic
KD
3.793
0.18
2131
0.769
1807
0.225
0.317
0462
0.266
1,168
(Junction 1)
BD
18.191
18.465
25 63.555
15.782
16.15]
45.
36,005
DTW
10.776
10.597
15911
10.895
16.
18A8S
5.198
5:21
31.453
2.124
82.871
58,632
MDD
03915
Traffic
039
0.295
1,212
0.615
1.135
1991
0,273
1.155
(Junction 2)
ED
17.937
18.965
21 622
16.007
17.114
44,67
41,478
DTW
10.246
10425
10.307
10 905
11.11
18, 389
19.57
5.346
6.777
30016
1.157
3.426
135 4017
93.919
MDD
0.336
0.276
Traffie
1.056
1.086
0.681
0.263
0,336
0,776
1,263
2.822
(Junction 3)
BD
17.961
18.412
22,054
FIJ1EN
19.829
36,533
$3.251
DTW
11.358
11.147
10,92
11.807
10,877
32.535
25.618
SHAPPRE
6.848
7.446
46.015
2.022
12,456
118.245
178.756
Table D.13: Univariate evaluation: similarity metrics reported for Nature datasets.
SDVFrger Models
VAE Medels
GAN Models
Others
ICAg
RPCs
TimeVAE
TimVVQVAE
RTSGAN
SDEGAN
0.166
1:501
5,556
CCP
SD
0,372
2.481
1.984
1.12
1,308
KD
1.644
3,443
4.150 1.155
3,31
377
5.00
164
(002)
ED
18.442
18.729
26 232
14.19
14.734
12.136
36 800
DTW
15.345
14,344
18.308
10.176
10311
71 196
544
1.123
1.684
13.719
2,456
0.312
0.55
CCP
KD
0.416
1.267
0,766
0.554
12212
0.272
0.441
01207
01671
0.23
0.011
0.346
0.253
2.743
(NIT)
ED
16.965
19.25
17.18
15.465
22.525
31.011
35,101
DTW
15225
17.18
14.883
12.381
19973
30 580
0.423
1,064
1:15
2/418
2,901
9.830
MDD
0.62
0.5T
CCP
KD
1,257
2.054
2,232
1,638
0.007
1005
2,244
4.00
1CETT
6.54
2.51
8. 1.7
(CAHIINO)
FD
15:92
16.128
15.
11.295
14.51
38.679
49.348
DTW
16.166
11:741
10.81
M.251
01213
37. 70.
40.586
1,255
3,426
2,801
144476
47.176
MDD
4.523
5.538
CCP
SD
0.512
1.69
KD
0.157
2.451
0.624
3,091
1351
4. 4.502
6.204
(C4HION2)
RD
15,098
17.378
19,159
13,879
21.6
46.137
45.823
DTW
11555
12,004
12,098
14,002
14
366
33.614
2.299
4.547
6.142
2.325
5.582
31.911
59.928
23

---

Table D.14: Univariate evaluation: similarity metries reported for Finance datasets.
SDFurger Models
VAE Models
GAN Models
Others
ICAg
FPCc
Time VAE
TQVAV
RTSGAN
SDEGAN
Exchange Rote
SD
(1407)
0.611
KD
0.33
1,173
0,058
1.77
0.51
0.034
1273
(Curreccy 1)
ED
18.913
19,909
15.335
26 26.589
27 353
35 258
DTW
15,072
15.91
16.319
11.356
26,05
1,259
2.52
2,44
17
22 608
MDD
0.166
Exchange Rote
1,233
0,389
0,803
0.424
1.083
KD
2,003
1.349
1,507
1.576
0.441
0.308
1676
(Currency 2)
ED
17,727
19.579
18,253
14.43
18.212
22.215
45.617
DTW
TX.12
16,076
14.15
14,89
14.48 4R8
31
042
0.967
1.186
1,744
2,443
2.117
5.69
28.819
MDD
V.9
Exclange Rate
0.22
0.122
0,433
1.154
KD
0.54
3,030
0.205
2.755
0.046
0.997
0.369
(Currency 3)
ED
19.578
21,042
19.51
14.765
21,905 11.9
28.394
259
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19,002
19.25
(8.33)
12.47
528
28 141
966
0,485
0.956
0.808
2.44
1.168
26.665
MDD
Exchange Kate
SD
0.647
0.252
0.136
0.349
KD
0,484
1,305
0.69
2
0.394
0.666
0.645
(Currency
ED
20,09
20.257
19.622
15.38
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33.075
42.121
DEW
16.021
16. 187
33.007
16,955
14.745
32 558
33.075
1,18
1,383
1,83
2.34
1858
25.273
Exchange Rate
SD
0.23
0.345
0.342
KD
0.534
3.95
0.85
1,701
1.127
0,152
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ED
[9.909
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14.579
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34.643
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18,409
17.954
14.799
812
18.02
38.671
30.317
0.569
1.035
7,067
Exchange Rate
SD>
0229
0.212
0.22
0.61
0.344
0.599
KD
0.743
3.389
1.974
2.616
0.379
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0.41
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19.50 565565
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20 27.
12375
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30.555
0.455
0.981
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SD
0.091
0.555
0.333
KD
1,009
2.867
0.716
2.751
0.202
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0.205
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20.061
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30 400
0.232
1,044
0.838
2.43
0.679
15.895
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Reviews:
[{"review_id": "O7NJyNmmky", "reviewer": "Reviewer_V1ut", "summary": "The paper introduces a novel framework for generating synthetic multivariate time series using large language models. The proposed pipeline includes transforming time series into a tabular-structured prompt, where each column contains time series components from FastICA or PCA. These prompts are then used to fine-tune an LLM, which generates new synthetic embeddings that retain the statistical and temporal properties of the original data. This work validates the proposed method through extensive experiments, demonstrating its robustness and applicability in data-scarce settings.", "questions": "1. Line 106: How is \"natural cycles\" determined? Are there some dataset-specific configurations?\n\n2. How about the method's efficiency? Especially, the cost of converting tabular data into text representations. It seems to lead to a very long context.\n\n3. Can the author prove experiments that a structured transformation (using tabular format) effectively generates multivariate time series data?", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Quality**: The submission is technically sound, with claims supported by experimental results across multiple domains (e.g., energy, finance, transport). The authors compare SDForger against multiple baselines (VAEs, GANs, diffusion models) using both similarity-based metrics and utility-based evaluations (forecasting). However, the results could gain more robustness by reporting the error bars and results on more datasets (e.g., long-term forecasting datasets from TSLib and probabilistic forecasting datasets from GIFT-Eval).\n\n**Clarity**: The paper is generally well-structured, but there are areas where clarity could be improved. (1) Abstract: The motivation of the work and the background it aims to solve are not clearly stated here (time series generation, forecasting, or multimodal modeling?). (2) Periodicity-aware segmentation: How is \"periodicity-aware\" reflected？ (3) LLM fine-tuning: How is the LLM  fine-tuned? Do the authors adopt some PEFT methods?\n\n**Significance**: This paper presents contributions that are likely to influence researchers working with time-series data synthetics. SDForger often can match or exceed GANs/VAEs in similarity and utility metrics. One of the biggest concerns in this work is that the improvement achieved by using this method is not obvious (Tables 1 and 2). I think the proposed method could have a large impact by extending it to other LLM architectures and demonstrating its effectiveness. \n\n\n**Originality**: I think the work is interesting because the paper provides new insights that LLMs can better understand time series via structured embeddings. While prior work (e.g., TimeGAN, TimeVAE) focused on specialized architectures (GANs, VAEs). This work bridges time-series generation and multimodal models. Technically, I think the author could conduct a comparison using non-structured transformation (e.g., w/o tabular structure or w/o PCA decomposition). This will enhance the persuasiveness of this work in terms of methodology.", "was_revised": true, "final_justification": "I acknowledge the efficiency of the proposed method and its performance in multivariate generation. While I no longer have any significant doubts, I believe that the true value of this work may be more apparent when applied to larger LLMs. Overall, I will maintain my positive evaluation.", "rebuttal": "## 1. Question on natural cycles\n\nThe term **\"periodicity-aware\"** refers to our method of aligning segmentation windows with the **dominant periodic patterns** of each time series channel. This is done in a fully data-driven way, without requiring dataset-specific configurations.\n\nSpecifically, for each channel, we compute the **Autocorrelation Function (ACF)** and identify statistically significant peaks. We select the most prominent peak corresponding to a period $P < L/2$, where $L$ is the target window length. This peak defines the **natural cycle** of the signal.\n\nWe then segment the time series into windows of length $L$, using a **step size that is a multiple of $P$**. This ensures that segment boundaries align with intrinsic periodic patterns, improving both **representativeness** and **diversity** of the resulting training instances.\n\nThis segmentation strategy enables meaningful augmentation from a single sequence, adapts dynamically to each channel's structure, and **avoids any manual tuning** or domain-specific heuristics.\n\nA detailed and mathematical description of this procedure is provided in **Appendix A.1**.\n\n\n## 2. Method's efficiency\n\nWe address efficiency in **Section 5.3**, with detailed benchmarks in **Appendix Table D.3**, where we report generation times on the **Bikesharing dataset** using different window lengths and embedding sizes.\n\nThe efficiency of SDForger is primarily influenced by two factors: the **embedding dimension $K$** and the **underlying LLM architecture**. As $K$ increases, the **length of the generated output** also increases. This affects inference time, as longer sequences take more time to produce, and it can **impact generation quality**, leading to a higher number of discarded samples and requiring more iterations to reach the desired number of valid outputs.  However, even at higher $K$, SDForger remains **highly efficient**, consistently outperforming all the baselines by a wide margin (from 4 to 100 times faster).\n\nThe choice of LLM also plays a role. Models like **Granite** require more memory and computation time, typically a **GPU** for inference, but **still remain significantly faster and more efficient** than generative baselines such as diffusion models, especially in low-data regimes.\n\nThe **data-to-text conversion step itself is negligible** in terms of overhead. For example, converting an embedding table of size **10 × 30 instances** takes **less than 0.002 seconds** on a **Mac M1 Max**. This step is efficiently handled by the `data_to_text` function in the **`SDForgorger.py`** file.\n\nOverall, SDForger offers a **favorable trade-off between expressiveness and efficiency**, benefiting from compact embeddings and fast generation, while remaining scalable across LLM sizes and embedding dimension $K$. While we acknowledge that more complex or multivariate datasets could lead to longer contexts, our current experiments suggest that the method scales well within practical margins.  \n\n## 3. Efficient generation of multivariate data\nTo evaluate whether our structured tabular transformation effectively supports the generation of multivariate time series, we analyse the preservation of inter-variable dependencies in the generated embeddings. Specifically, we compute the Frobenius distance between the correlation matrices of the real and generated embeddings. This distance is normalised to account for differences in embedding scales (k=3,5,7,10) and serves as a proxy for how well the generated data retains the structural relationships observed in the training data. \n\nTable below aggregates result over 5 seeds:\n\n|Dataset|Variables|K = 3*k|Frobenius Distance|\n|-|-|-|-|\n|bikesharing|['cnt','temp','hum']|9|0.434±0.015|\n|| |15|0.315±0.011|\n|| |21|0.291±0.011|\n|| |30|0.256±0.007|\n|||||\n|etth1|['HUFL','MUFL','OT']|9|0.378±0.012|\n|| |15|0.321±0.022|\n|| |21|0.294±0.010|\n|| |30|0.278±0.005|\n|||||\n|traffic|['Junction_1','Junction_2','Junction_3']|9|0.435±0.007|\n|| |15|0.351±0.008|\n|| |21|0.318±0.004|\n|| |30|0.281±0.009|\n\n\nAs the embedding dimension increases, the **decreasing Frobenius distance** indicates an enhanced ability of the LLM to capture and reproduce the structured multivariate relationships. This trend suggests that **larger embedding spaces** enable the model to more **effectively learn intricate cross-channel dependencies**, which are essential for faithful multivariate time series generation. \n\n## Clarification on utility-based evaluation\nOur utility-based metric stems from a key limitation in standard synthetic data evaluation: metrics like distributional similarity or distances often favor models that **closely replicate the training data**, potentially leading to overfitting and reduced generalization. This contradicts the central goal of synthetic data generation, which, in our case, is to produce data that not only resembles the real distribution but also **generalizes well to support downstream tasks**. In this paper, we use **forecasting** as the primary utility benchmark, where synthetic data is employed to fine-tune a predictive model. That said, **expanding utility-based evaluation** to include other real-world task, such as **anomaly detection** or **classification**, presents a promising avenue for future research. \n\n##  Clarification on LLM fine-tuning\n\nWe employ **standard full fine-tuning** of the LLM to adapt it to the structured time series generation task. At this stage, we **do not use PEFT methods** (e.g., LoRA or adapters), as our focus was to demonstrate that **even lightweight models (e.g., GPT-2)** can effectively learn compact tabular embeddings with minimal training data.\n\n**Notably, we achieve strong results without any specialized fine-tuning optimization**, which highlights the accessibility and robustness of the proposed framework. This suggests that SDForger is effective even under default training setups, without requiring task-specific or resource-intensive configurations.\n\nThat said, we recognize the **benefits of parameter-efficient fine-tuning**, especially for **scaling** to larger models, supporting **continual learning**, or **domain adaptation**. We consider this a promising direction for future work."}, {"review_id": "G8WwpMv6WS", "reviewer": "Reviewer_Ck4d", "summary": "This paper introduces a method for generating synthetic time series data leveraging LLMs called SDForger. SDForger converts time series data into a tabular representation through basis decomposition techniques (FastICA/FPC). These embeddings are then encoded in a text format for fine tuning of the LLM. Inference follows the inverse path and samples embeddings through text prompts from the LLM. These are then converted to the tabular format and finally back into time series by using the reverse process of the embedding technique. Additionally, the authors use a filtering heuristic on the tabular embeddings to improve quality of the synthetic time series. \n\nThe authors evaluate the synthetic time series generated by SDForger by employing similarly based metrics and compare with different generative baselines. In addition, the authors evaluate whether the synthetic data can be used to fine-tune downstream forecasting models. In their ablation study, the authors evaluate different choices of embedding dimensions, inference time, and different choices of the underlying LLM. Finally, the authors conduct a case study on one dataset to illustrate that the method could be further developed into a multi-modal synthetic data generation model.", "questions": "**Major**: \n\nHow exactly are the embedding dimensions chosen in the utility-based experiments? Do precisely does “dataset complexity” map to these specific values? How would the results change if the embedding dimension is changed for each dataset? This could be an interesting ablation. \n\nWhat part of the datasets in the utility-based evaluation are used for fine-tuning the LLM and for selecting the embedding dimension? Has the test part been excluded from training/tuning steps? If not, this could lead to data leakage and skew the results. \n\nHow do SDFormer perform without the heuristic filtering procedure? I think this could be another interesting dimension and it would be interesting to see how much the performance changes when this would be removed. Additionally, I would be curious to see how much such a filtering step changes the results for TimeVAE. I understand that the filtering is done on the tabular and might not be applicable to TimeVAE, but I think it should be possible to apply diversity/divergent filters here as well. \n\n\n**Minor**: \nWhat does “balanced performance across all metrics and domains” in the similarity-based evaluation mean specifically? Can this be quantified?", "limitations": "The main limitation of this work lies in the empirical design in the utility-bases section that only evaluates three datasets. This should be noted in the limitation section because it is hard to judge whether the results presented here would generalize because of the small number of evaluation datasets used.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The paper presents a sound and creative framework for generating synthetic time series data. This is of high significance because large scale pre-trained time series models might be bottlenecked through the availability of large datasets which stifles progress. The paper introduces an interesting method for synthetic time series dataset generation by leveraging LLMs through embedding techniques from time series to tabular to text and back. This methodology enables further research on embedding techniques and LLM fine tuning. The paper is written clearly and is easy to follow. \n\nThe weaknesses of the paper lie in the empirical evaluation of their method. I understand that synthetic data can be challenging to evaluate. The similarity based results use 12 datasets and several baseline methods. Here, it seems that TimeVAE is still a strong baseline method and that SDForger does not offer significant improvements. On the univariate setting it seems to perform well, but on the multisample setting it does not seem to improver meaningfully over baselines. Given the potential of the method for further development, I do not see this as an issue that would prevent publication, but I would kindly ask the authors to reflect that finding in their writing. Right now, the writing appears justifies SDFormers performance with “balanced performance across all metrics and domains” which I find too vague. \n\nThe utility based evaluation has the limitation that only three datasets have been considered and therefore the empirical results have low empirical power. My main concern with the utility based evaluation is that the setup is not quite clear which might impact the validity of the result. Another weakness is that the effect of the filtering heuristic is not shown. \n\nI will detail my specific questions in the Questions section below. I will consider increasing my score if my major questions are addressed.", "was_revised": true, "final_justification": "I updated my rating after author discussion see comments.", "rebuttal": "## Q1: Choice of embedding dimensions\nIn our utility-based experiments, we evaluated multiple values of the embedding dimension k across datasets. The values presented in the main paper reflect the best-performing configuration for each dataset in terms of downstream forecasting performance. Indeed, we observe a clear relationship between **dataset complexity** and the **optimal embedding dimension**. As discussed in our response to reviewer V1ut, more complex datasets (traffic and etth1), benefit from higher-dimensional embeddings, that allow **both better reconstruction** and a better learning of **inter-variables correlations**. \n\nWe present the utility evaluation results for embedding 3, 5, 7 in the ablation below: \n\n|Dataset|Model|RMSE|MASE|WQL|\n|-|-|-|-|-|\n|bikesharing|0-shot|0.728|2.150|0.287|\n|bikesharing|Original Data (OD)|0.495|0.822|0.178|\n|bikesharing|SDF-ICA-3|0.514|0.899|0.194|\n|bikesharing|SDF-ICA-5|0.537|0.909|0.194|\n|bikesharing|SDF-ICA-7|0.517|0.898|0.193|\n|bikesharing|SDF-ICA-3 + OD|0.487|**0.801**|**0.173**|\n|bikesharing|SDF-ICA-5 + OD|**0.486**|0.804|0.174|\n|bikesharing|SDF-ICA-7 + OD|0.490|0.810|0.175|\n||||||\n|etth1|0-shot|0.678|2.132|0.255|\n|etth1|Original Data (OD)|0.658|1.820|0.232|\n|etth1|SDF-ICA-3|0.647|1.829|0.233|\n|etth1|SDF-ICA-5|0.637|1.934|0.233|\n|etth1|SDF-ICA-7|**0.626**|1.820|**0.224**|\n|etth1|SDF-ICA-3 + OD|0.640|1.790|0.228|\n|etth1|SDF-ICA-5 + OD|0.649|1.780|0.230|\n|etth1|SDF-ICA-7 + OD|0.642|**1.746**|0.226|\n||||||\n|traffic|0-shot|0.708|**1.555**|**0.255**|\n|traffic|Original Data (OD)|0.702|1.995|0.283|\n|traffic|SDF-ICA-3|0.730|2.068|0.294|\n|traffic|SDF-ICA-5|**0.655**|1.849|0.262|\n|traffic|SDF-ICA-7|0.790|2.189|0.312|\n|traffic|SDF-ICA-3 + OD|0.734|2.074|0.295|\n|traffic|SDF-ICA-5 + OD|0.750|2.110|0.301|\n|traffic|SDF-ICA-7 + OD|0.718|2.025|0.288|\n\nThese results reinforce the embedding selection (realised on validation data) presented in our paper.\nFurthermore, we discuss in **Appendix A.2** a **variance-explained heuristic** that could be used to dynamically select k for a given dataset based on the percentage of variance to retain. \n\n## Q2: Data leakage?\n\nWe confirm that only the training portion of each dataset is used for both fine-tuning the LLM and selecting the embedding dimension. The test set is **strictly held out** and is never used during LLM training, embedding selection, or any intermediate tuning step. As explained, this ensures that there is no data leakage nor biased evaluation between the synthetic data generation process and the evaluation phase. Embedding dimensions  k=3,5,7 are evaluated using validation data (i.e., the 20% subset of the training set as explained in **Section 5**), and the best-performing configuration was selected. \n\n## Q3: Heuristic filtering procedure\n\nAs discussed in our responses to **Q1 and Q3 from Reviewer 2HPq**, SDForger includes an **in-generation filtering step** to discard invalid or outlier samples, specifically those with missing values (**NaN%**) or abnormally large total norms (**Discard%**), computed in the embedding space. This lightweight mechanism improves sample quality and stabilizes distributional properties with minimal overhead.\n\nIn the results reported in **Q3**, we show that:\n\n* Across different embedding dimensions, **Discard% remains consistently low (<2%)**, indicating that the LLM generates mostly on-manifold samples.\n* Rejected samples have norms several orders of magnitude higher than accepted ones (e.g., 19.1 vs. 1.7), which strongly impact higher-order statistics such as **skewness** and **kurtosis**.\n* The filtering step notably improves metrics like SD and KD without significantly affecting lower-order distances, showing its value in controlling rare but impactful outliers.\n\nTo extend this analysis, we implemented a **post-generation filtering step for TimeVAE**, where we discard generated samples **based on the norm of the reconstructed time series** (in the time domain). Specifically, we constructed SDForger-like intervals and removed curves whose norms fall outside the selected interquartile range $[Q1 - 3 \\cdot \\text{IQR}, Q3 + 3 \\cdot \\text{IQR}]$, with bounds computed from the original (real) samples.\n\nThe results below (Bikesharing, “count”, 5 seeds) show the effect of this post-hoc filtering:\n\n| Method                | MDD   | ACD   | SD    | KD    | ED     | DTW   | SHAP-RE | Discard% | Norms Original (Avg) | Norms Accepted (Avg) | Norms Discarded (Avg) |\n| --------------------- | ----- | ----- | ----- | ----- | ------ | ----- | ------- | -------- | -------------------- | -------------------- | --------------------- |\n| TimeVAE               | 0.313 | 0.209 | 1.117 | 0.279 | 20.512 | 9.383 | 20.646  | -        | -                    | -                    | -                     |\n| TimeVAE + post filter | 0.316 | 0.220 | 0.131 | 0.064 | 19.601 | 9.182 | 20.689  | 1.211    | 15.752               | 13.473               | 8.916                 |\n\nWe observe that:\n\n* **Only a small fraction of samples (\\~1.2%) are discarded**, yet this leads to **improvements in SD and KD**, indicating that **a few outliers can disproportionately affect distributional metrics**.\n* This supports the value of post-hoc validation, especially in models like TimeVAE that do not natively include such constraints.\n\nHowever, we would like to highlight that while post-hoc filtering is a useful safeguard, **embedding lightweight validation directly into the generation process, as done in SDForger, offers both practical and performance advantages**. It enables real-time quality control, avoids unnecessary decoding, and ensures robustness without additional overhead.\n\n\n## Q4: Clarification on \"balanced performances\"\n\nIn our similarity-based evaluation (Table 1), different generative models exhibit strengths in distinct types of metrics: For example, TimeVAE performs very well on **distribution**-based metrics. Conversely, TimeVQVAE excels on **distance**-based metrics (euclidian distance, dtw ...). In contrast, SDForger achieves a more balanced performance across both metric categories, meaning it consistently **performs well on both feature-based and distance-based metrics** **without heavily favouring one domain**. To quantify this, we computed the normalised average score per metric category per dataset in Table D.2. \n\nThis balanced performance indicates that SDForger not only preserves statistical features but also captures distributional similarities effectively, contributing to more robust and versatile synthetic time series generation. We will emphasize this in the updated version of the paper.\n\nWe hypothesize that for downstream tasks such as forecasting, it is crucial to use synthetic data generated by models that do not overly prioritize a single metric type but instead achieve consistently **strong performance across multiple metric categories and domains**."}, {"review_id": "eD2zXNuxE9", "reviewer": "Reviewer_2HPq", "summary": "This paper introduces SDForger, a novel framework for generating synthetic multivariate time series. The core idea is to leverage the generative power of Large Language Models (LLMs) by transforming time series data into a format that an LLM can process. The methodology involves three main stages:\n1) An embedding stage where time series instances are projected onto a low-dimensional basis (using FPC or FastICA) to create a tabular representation, decoupling the representation from sequence length.\n2) A generation stage where these tabular embeddings are converted into structured text prompts, which are used to fine-tune an autoregressive LLM (e.g., GPT-2). The fine-tuned LLM then generates new textual embeddings.\n3) A decoding stage where the generated embeddings are converted back into synthetic time series.\nThe authors conduct a comprehensive empirical evaluation across 12 datasets, comparing SDForger to several VAE, GAN, and diffusion-based models. SDForger outperforms traditional generative models, such as VAEs, GANs, and diffusion models, in most settings, both in terms of quality and generation speed. The framework is also shown to be multimodal-ready, integrating textual conditioning for greater flexibility.", "questions": "**Q1. Clarification on \"Data-Scarce\" Performance:**\n- The paper emphasizes the framework's effectiveness in \"data-scarce\" settings. However, the experiments use at least I=30 instances for fine-tuning. Could you elaborate on the framework's sensitivity to the number of training instances (I)? How does the generation quality and fine-tuning stability degrade when I is significantly smaller (e.g., I<10)? A clearer understanding of this boundary condition would be valuable for practitioners.\n\n**Q2. Choice of Embedding Method:**\n- The results consistently show that the ICA-based variant of SDForger outperforms the FPC-based one, particularly on distance-based metrics. Why might maximizing statistical independence (ICA) be more beneficial for this LLM-based generation pipeline than capturing maximal variance (FPC)? Does this imply that the LLM is better at learning the joint distribution from a set of disentangled factors rather than a hierarchy of variance-ordered components?\n\n**Q3. Generation Rejection Rates:**\n- The methodology includes an in-generation filtering step to discard invalid or outlier samples (e.g., those with missing values or diverging norms). Could you report the typical rejection rates observed during your experiments for different datasets or settings? A high rejection rate could signal that the fine-tuned LLM struggles to generate on-manifold embeddings, which would be an important practical limitation to understand.\n\n**Q4. Comparison with Specialized Architectures for Correlation Preservation:**\n- The paper compares against general-purpose time series generative models. However, work like COSCI-GAN (NeurIPS 2022) introduces an architecture specifically designed to preserve inter-channel correlations in multivariate time series from a common source, using a central discriminator. How do you position SDForger's implicit method of learning correlations (by encoding a full multivariate instance into a single text prompt) against such an explicit architectural approach? A discussion or comparison in the paper could further highlight the unique strengths of using an LLM for this task.", "limitations": "While the authors have done a good job of discussing the technical limitations of their work in the conclusion and the NeurIPS checklist, they have not adequately addressed the potential negative societal impact. In the checklist, the authors state that the work does not engage with high-risk applications. However, synthetic data generation, especially for domains like finance, can have dual-use potential.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 4, "strengths_and_weaknesses": "- Quality\n  - Strengths: The empirical evaluation is extensive and a significant strength of this paper. The authors test their method on a diverse set of 12 public datasets from various domains, which demonstrates broad applicability. The comparison against multiple modern baselines, including VAEs, GANs, and a diffusion model, is thorough. The use of a dual evaluation strategy, comprising both similarity metrics (statistical and distance-based) and a practical utility metric (downstream forecasting), provides a good assessment of the generated data.\n\n  - Weaknesses: The paper claims strong performance in \"data-scarce settings,\" but the experimental setup relies on segmenting a long time series into a minimum number of instances (e.g., I=30). This might not reflect true data scarcity, where only a few short series are available. The statistical robustness of the results could be improved. As acknowledged in the paper's checklist, the experiments do not report error bars or results from multiple runs with different random seeds. While testing on many datasets provides some evidence of robustness, it is not a substitute for assessing variance from stochastic elements like model initialization or data shuffling. The in-generation filtering process, while practical, relies on a heuristic (3 * IQR threshold) to discard outliers, which may not be optimal for all data distributions. \n\n- Clarity\n  - Strengths: The paper is well-written and logically structured. Figure 1 provides an excellent, intuitive overview of the entire SDForger pipeline, making the complex methodology much easier to understand. The step-by-step explanation of the embedding, generation, and decoding phases in Section 3 is clear and detailed.\n\n  - Weaknesses: The distinction between the three evaluation settings (multisample, univariate, multivariate) and how data is prepared for each could be introduced more explicitly in the main methodology section for better flow. Also, appendices contain important implementation details that might better serve the reader if summarized in the main text.\n\n- Significance\n  - Strengths: The paper addresses a real and growing need for synthetic time series in data-scarce environments. The framework's demonstrated efficiency is a major practical advantage, with generation times being orders of magnitude faster than many competitors (Appendix Table D.3). The most exciting aspect is the framework's extensibility to multimodal generation. The proof-of-concept in Section 6, where generation is conditioned on textual prompts, opens up a wide range of future research and applications in guided and context-aware time series synthesis. \n\n  - Weaknesses: The downstream utility improvements, while present, are sometimes modest. For the traffic dataset, GAN-based methods performed better, suggesting that SDForger may not be universally superior in all scenarios. The long-term impact will depend on how the approach scales to more complex, high-dimensional, and highly non-stationary time series data.\n\n- Originality\n  - Strengths: While prior work has used LLMs to generate tabular data, the application to time series through a functional embedding layer is a novel and creative leap. This approach cleverly reframes the sequence generation problem into a structured text generation problem, which is the native domain of LLMs. This is a fundamental departure from the dominant VAE/GAN/diffusion architectures typically used for this task.\n\n  - Weaknesses: The paper builds on established concepts (FPC/ICA, LLM fine-tuning), but their synthesis into the SDForger framework is entirely novel and applied effectively to a new problem domain.", "was_revised": true, "final_justification": "Based on authors' response to my questions and concerns, I have decided to revise my evaluation in authors' favour.", "rebuttal": "## Q1. Clarification on \"data-scarce\" performance\n\nWe thank the reviewer for raising this important point. In our paper, *data-scarce* refers to both the **limited number of time points** and the **small number of training instances** available for fine-tuning. Unlike most generative approaches requiring thousands of long multivariate sequences, SDForger is designed to operate effectively even when only a **single short time series** is available.\n\nOur **periodicity-aware segmentation** (Section 3.1) enables the extraction of multiple training instances by segmenting the signal into windows aligned with its dominant period. Crucially, the number of training instances $I$ can be adjusted by varying:\n\n* the **window length** $L$: shorter windows yield more segments, and\n* the **window stride**: increasing overlap results in denser sampling.\n\nTo assess the **sensitivity to small $I$**, we conducted additional experiments on the **“count” variable from the Bikesharing dataset**, varying both the number of instances and total time points. We fixed the embedding strategy to ICA with $k = 3$, used the same LLM and fine-tuning configuration as in the main paper, and averaged results over **5 seeds**. The table below reports:\n\n* similarity metrics (MDD, ACD, SD, KD, ED, DTW, SHAP-RE),\n* **NaN%**, indicating generations with missing values,\n* discard rate during filtering due to the norm criterion, and\n* average embedding norms (original, accepted, rejected).\n\n| Method    | Instances | Points | MDD   | ACD   | SD    | KD    | ED     | DTW   | SHAP-RE | NaN%  | Discard% | Norms Original (Avg) | Norms Accepted (Avg) | Norms Discarded (Avg) |\n| --------- | --------- | ------ | ----- | ----- | ----- | ----- | ------ | ----- | ------- | ----- | -------- | -------------------- | -------------------- | --------------------- |\n| SDF-ICA-3 | 30        | 1000   | 0.348 | 0.803 | 0.105 | 0.503 | 18.961 | 9.677 | 11.477  | 2.26  | 0.32     | 1.714                | 1.664                | 0.181                 |\n| SDF-ICA-3 | 10        | 1000   | 0.503 | 0.595 | 0.086 | 0.293 | 19.345 | 9.693 | 18.134  | 7.10  | 0.65     | 1.698                | 1.646                | 10.830                |\n| SDF-ICA-3 | 10        | 500    | 0.511 | 0.567 | 0.248 | 0.253 | 19.698 | 9.673 | 16.684  | 12.10 | 2.58     | 1.700                | 1.730                | 0.637                 |\n\n**Key takeaways**:\n\n* SDForger remains **functional even with just 10 instances** and as few as 500 time points.\n* As $I$ decreases, **quality degrades gracefully**, with moderate increases in distance metrics (e.g., MDD, SHAP-RE).\n* **NaN% and discard rates increase**, indicating greater generation instability, but the LLM still produces many valid, high-quality samples.\n* The **norms of accepted embeddings remain close** to those of the real data, confirming that the LLM continues to model the embedding space reliably.\n\nIn summary, while extreme scarcity naturally impacts stability, SDForger remains robust and practical even in low-resource settings, with graceful degradation and built-in filtering mechanisms to preserve sample quality.\n\n\n## Q2. Choice of embedding method\n\nThe superior performance of the ICA-based variant likely comes from the nature of the components it produces. Unlike FPC, which orders components by explained variance and often concentrates most information in the first few components, ICA explicitly seeks statistically independent components. This tends to produce a more balanced and disentangled basis decomposition, where each component carries distinct information that have similar importance for data reconstruction. For our LLM-based generation pipeline, this disentanglement appears advantageous because the model can learn a joint distribution over a set of factors that all have the same “power” and are more interpretable. Thus, the results suggest that the LLM is indeed better equipped to model the joint distribution when presented with independent factors rather than a hierarchy of variance-ordered components. This aligns with the broader literature in representation learning, where disentangled representations often lead to improved generative performance and interpretability. \n\n\n## Q3. Generation rejection rates\n\n#### **Observed Rejection Rates Across Embedding Dimensions**\n\nThe table below reports rejection statistics on the **\"count\" variable from the Bikesharing dataset**, averaged across 5 seeds. We vary the embedding dimension $K$ while keeping all other settings fixed:\n\n| Method    | NaN%  | Discard% | Norms Original (Avg) | Norms Accepted (Avg) | Norms Discarded (Avg) |\n| --------- | ----- | -------- | -------------------- | -------------------- | --------------------- |\n| SDF-ICA-3 | 3.87  | 1.94     | 1.708                | 1.714                | 19.066                |\n| SDF-ICA-5 | 36.29 | 1.94     | 2.202                | 2.248                | 9.514                 |\n| SDF-ICA-7 | 58.82 | 0.00     | 2.602                | 2.521                | 0.000                 |\n\nWe observe that:\n\n* **Discard% remains consistently low** (<2%) across settings, indicating that most generations fall within a plausible norm range.\n* **NaN% increases with larger embedding dimensions**, reflecting a higher likelihood of incomplete generations in longer textual outputs. However, these are detected and filtered early, preserving only valid samples.\n* Importantly, **norms of accepted samples closely match the originals**, while rejected samples exhibit extreme values, justifying their removal.\n\n#### **Impact of Filtering on Generation Quality**\n\nWe further evaluated the effect of filtering on similarity metrics for $K=3$, again using the \"count\" variable from the Bikesharing dataset and reporting average results over 5 random seeds.\n\n|Method|Filter|MDD|ACD|SD|KD|ED|DTW|SHAP-RE|NaN%|Discard%|NormsOriginal(Avg)|NormsAccepted(Avg)|NormsDiscarded(Avg)|\n| -| -| -| -| -| -| -| -| -|-| -| -| -| -| \n|SDF-ICA-3|Yes|0.356|0.826|0.100|0.616|19.449|9.907|13.393|3.87|1.94|1.708|1.714|19.066|\n|SDF-ICA-3|No|0.355|0.842|0.209|4.791|20.071|10.932|18.833|-|-|-|-|-|\n\nFiltering leads to a notable improvement in **higher-order statistics**, especially **Skewness (SD)** and **Kurtosis (KD)**, by removing rare but impactful outliers. These outliers, while small in number, disproportionately affect the quality and stability of the generated dataset. Overall, the observed **rejection rates are low**, and the **LLM generates on-manifold embeddings in the majority of cases**, even under tight data constraints. The filtering step acts as a safeguard, eliminating extreme outliers without undermining generation diversity or coverage.\n\nMore on the application of similar filtering procedures to alternative generative models (e.g., TimeVAE) is discussed in our response to **Q4 from Reviewer Ck4d.**\n\n## Q4. Comparison with specialized architectures for correlation preservation\n\nCOSCI-GAN and similar specialized architectures explicitly incorporate mechanisms, such as a central discriminator, to explicitly preserve inter-channel correlations in multivariate time series. These designs reflect a targeted approach to model dependencies within the data and have demonstrated strong performance on correlation preservation.\n\nIn contrast, SDForger implicitly learns the joint distribution of multivariate time series by encoding an entire instance, including all channels and temporal dynamics, into a single, unified textual prompt.\nThis approach offers several unique advantages:\n\n* **Flexibility and Generality**: Rather than engineering architectural components explicitly for correlation modeling, SDForger exploits the powerful contextual modeling capabilities of LLMs. LLM naturally captures complex, high-dimensional dependencies through its attention mechanisms and deep representations, without requiring hand-crafted modules.\n* **Multimodality**: By representing multivariate embeddings as text, SDForger enables the use of off-the-shelf LLMs pre-trained on large, diverse corpora, unlocking transfer learning benefits and opening up opportunities for multimodal extensions, like text-guided generation.\n* **Modularity**: SDForger’s design is inherently modular. While this work uses basis decomposition methods (e.g., FastICA) for general-purpose embedding, the framework allows for the integration of domain-specific or correlation-preserving embeddings. By coupling such embeddings with the LLM’s ability to model joint patterns in long textual sequences, future versions of SDForger could explicitly enhance inter-channel correlation preservation, combining explicit inductive biases with implicit sequence modeling.\n\nWhile explicit architectures like COSCI-GAN excel in focused correlation preservation, SDForger’s implicit approach via LLMs provides a complementary and versatile framework that can generalize across tasks and modalities. We agree that a clearer discussion of these trade-offs would strengthen the paper. \n\nAdditionally, in our response to **Q3 from Reviewer V1ut**, we empirically assess SDForger’s ability to generate consistent multivariate sequences. Results show that our method can effectively preserve channel-wise structure even in low-data regimes.\n\n## Limitations on potential societal impact and privacy considerations\nWe appreciate the reviewer’s important observation regarding the dual-use potential of synthetic data generation in **high-risk applications**. By relying on basis decomposition and text-conditioned generative modeling, SDForger does not memorize or directly reproduce individual time series samples. We acknowledge that synthetic data models could potentially be misused in sensitive domains such as healthcare or finance. We will update the manuscript to reflect these societal and ethical considerations."}, {"review_id": "fgp8puCCgI", "reviewer": "Reviewer_Exqs", "summary": "The paper proposes SDForger, a synthetic time series generator based on LLMs. The model proceeds as follows: During training, (1) time series are encoded to tabular data, (2) tabular data are encoded to text to tune the LLM; During inference, (1) text is sampled from LLM to decode to tabular data, (2) tabular data is decoded to time series. Extensive experiments have been conducted to validate the method's performance against existing baselines.", "questions": "For the first bulletin in the weakness, I hope the author can explain if they believe SDForger can be improved, and if so, what are the possible approaches.\n\nFor the questions below, the authors should consider either adding an explanatory paragraph or conducting experiments to address them:\n- Can SDForger handle nonstationary time series data? The author should consider adding a corresponding experiment.\n- Does embedding time series into tabular data \"lose\" temporal dependency information? If so, about how much information is \"lost\"? Would this cause SDForger's performance to degrade when handling strongly correlated sequences?\n- The paper highlighted SDForger's \"readiness\" in the intro, but I did not find an experiment supporting this claim. The author should consider providing some actual prompts generated in the experiment process that can highlight this.\n- How do alternative embedding methods, such as AE or TSNE, compare to PCA and ICA? The author should consider adding an explanatory paragraph or conducting an ablation study.\n- What is the dimensionality of time series that SDForger can handle?\n- How does SDForger handle external covariates associated with the time series data?", "limitations": "Negative societal impact: I am concerned about the privacy issue of the model deployment in practice: does SDForger ensure that its generated data does not leak sensitive information from training data?", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strength:\n- The paper seems to be clearly written and well structured.\n- The technical details seem to be rigorous.\n\nWeakness:\n- The empirical performance of the proposed method appears mixed, and the claim that SDForger achieves “consistently strong” and “balanced” performance is less convincing to me.", "was_revised": true, "final_justification": "In **SDForger readiness**, yes, I was suggesting that the author should include more prompt examples similar to that of Section 6, line 323. Due to the current space limit, I would suggest that the author consider creating a section in the appendix dedicated to illustrating example prompts.\n\nI read through the authors’ rebuttal carefully, and it addresses my concerns satisfactorily. I will revise my evaluation in the author's favor.", "rebuttal": "## Improvement of SDForger\n\nWe believe SDForger can be further improved. Its modular design is intentionally built to support **flexible experimentation**, making it easy to explore enhancements or tailor components to specific needs.\n\nWe see several promising directions: \n- **Embedding Strategies**: While our current approach relies on linear methods like FastICA and FPC, future work could explore more expressive, nonlinear embeddings (e.g., AE) or multivariate-aware methods like Multivariate FPCA or Multivariate Singular Spectrum Analysis to better capture temporal and inter-channel dependencies. \n- **Parameter-Efficient Fine-Tuning**: We currently use full fine-tuning for the LLM. Incorporating PEFT techniques such as LoRA or adapters could improve scalability, efficiency, and facilitate domain adaptation. \n- **Extended Utility Evaluation**: While we focus on forecasting, SDForger could be evaluated and optimized for broader downstream tasks such as classification or anomaly detection.\n- **Context and Covariate Integration**: By design, SDForger supports integration of external covariates (e.g., categorical or textual data). Expanding this functionality could enable richer conditional generation, and multimodal transfer learning. \n\nIn summary, SDForger offers a flexible foundation, and we see meaningful opportunities to improve it both architecturally and in terms of task generalization.\n\n## Non-stationary datasets\n\nSDForger was evaluated on both stationary and non-stationary datasets. Weather, Bikesharing, and Australian Electricity mostly contain stationary series with clear seasonal patterns.\n\nIn contrast, the **currency dataset** is fully non-stationary, reflecting the volatility of financial data. Additionally, **25% of NN5** and **99% of Tourism** series were identified as non-stationary using the **Augmented Dickey-Fuller** (ADF) test. Below are results for three example channels per dataset:\n\n|Dataset|ADF Statistic|p-value|Stationary?|\n|-|-|-|-|\n|currency_1|-1.665|0.4492|No|\n|currency_2|-2.150|0.2250|No|\n|currency_3|-1.353|0.6048|No|\n|NN5-001|-1.767|0.3971|No|\n|NN5-010|-1.958|0.3054|No|\n|NN5-110|-2.387|0.1454|No|\n|Tourism-T000000|-0.934|0.7767|No|\n|Tourism-T000001|-1.531|0.5180|No|\n|Tourism-T000002|-1.219|0.6653|No|\n\nThese experiments, coupled with the non-aggregated results in **Table D.7 and D.11**, confirm that SDForger is capable of handling both stationary and non-stationary time series effectively. However, we appreciate the suggestion and will consider adding a dedicated section in the paper to separate results on stationary and non-stationary datasets! \n\n## Temporal dependency \n\nThe embedding methods we use, FastICA and FPC, decompose each fixed-length time series segment into a linear combination of basis components. This strategy retains temporal dependencies, as the components span the entire window and reconstruction preserves their temporal structure. \nThe choice of **embedding dimension k** controls the fidelity of this representation and how much information will be “lost”: lower-dimensional embeddings retain less variance, which can lead to some loss of fine-grained temporal or cross-channel details. \n\nBelow, we report the **variance retained** by FICA embeddings across datasets:\n\n|data-target|k=3|k=5|k=7|\n|-|-|-|-|\n|appliances - Appliances|0.333|0.457|0.539|\n|bikesharing - cnt|0.633|0.725|0.774|\n|bikesharing - hum|0.424|0.598|0.682|\n|bikesharing - temp|0.418|0.662|0.775|\n|ccp - C4H11NO|0.855|0.946|0.967|\n|ccp - NH3|0.935|0.983|0.997|\n|ccp - CO2|0.697|0.883|0.943|\n|ccp - C4H10N2|0.606|0.808|0.896|\n|ecl|0.809|0.941|0.971|\n|electricity - T000000|0.785|0.922|0.958|\n|electricity - T000001|0.678|0.837|0.894|\n|electricity - T000002|0.779|0.901|0.949|\n|electricity - T000003|0.682|0.818|0.906|\n|electricity - T000004|0.592|0.785|0.855|\n|exchange_rate - currency_1|0.715|0.866|0.916|\n|exchange_rate - currency_2|0.774|0.923|0.952|\n|exchange_rate - currency_3|0.691|0.860|0.912|\n|exchange_rate - currency_4|0.759|0.902|0.943|\n|exchange_rate - currency_6|0.807|0.933|0.962|\n|exchange_rate - currency_7|0.827|0.917|0.946|\n|exchange_rate - currency_8|0.859|0.945|0.965|\n|etth1 - HUFL|0.477|0.636|0.731|\n|etth1 - OT|0.595|0.735|0.819|\n|nn5|0.336|0.479|0.590|\n|monash_traffic|0.541|0.722|0.823|\n|tourism_monthly|0.869|0.954|0.977|\n|weather_maxtemp|0.493|0.602|0.685|\n|weather_mintemp|0.390|0.517|0.611|\n|weather_rain|0.449|0.605|0.725|\n|weather_solar|0.450|0.616|0.718|\n|traffic - Vehicles_Junction_1|0.456|0.657|0.801|\n|traffic - Vehicles_Junction_2|0.379|0.567|0.699|\n|traffic - Vehicles_Junction_3|0.294|0.467|0.590|\n\nAs detailed in **Appendix A.2**, we also implement a dynamic strategy to select the number of components based on a target variance threshold, offering practical guidance to adapt \\$k\\$ to each dataset’s complexity. In practice, when dealing with strongly correlated or complex sequences, using a sufficiently high embedding dimension mitigates information loss and helps maintain SDForger’s performance. \n\nFor inter-channel dependencies, we refer to **Q3 of Reviewer V1ut**, where we assess Frobenius distance between real and generated correlation matrices. This ablation confirms that GPT-2 can effectively learn cross-channel structure from compressed multivariate embeddings.\n\n## SDForger readiness\n\nWe kindly ask the Reviewer to clarify whether the question refers to multimodal readiness. If so, this is addressed in **Section 6**, where we demonstrate **text-conditioned generation** by combining structured embeddings with free-form natural language in the prompt. This example shows that SDForger can integrate textual information during both **fine-tuning and inference** without requiring any architectural modifications. The input prompts are presented in **Section 6** (l. 323) and the generated prompts in this experiment are printed in the submitted `conditional_generation.ipynb` notebook (`cell 11`). Due to space constraints, we could not include them in the paper, but we would be happy to share excerpts in a follow-up. This experiment supports our claim of “readiness,” showcasing SDForger’s flexibility for multimodal data. That said, we agree with the Reviewer that **more robust and efficient conditioning strategies** will be important to fully unlock SDForger’s multimodal potential, and we plan to explore this direction in future work.\n\n## Alternative embedding methods\nIn our current study, we focus on classical **linear embedding** method, FastICA and FPC, due to their interpretability, computational efficiency, and well-understood properties in preserving variance, statistical independence, and temporal dependency. Alternative **nonlinear embedding** techniques like Autoencoders (AE) and t-SNE offer powerful representation capabilities and can capture more complex, nonlinear structures in the data. However, they also introduce challenges in terms of: \n- Training **stability** and **complexity**, especially in low-data regimes, \n- **Deterministic reconstruction** quality, which is critical for reliable time series synthesis\n- **Interpretability** and direct control over embedding dimensions. \n\nWhile t-SNE excels at visualization, it is not designed for reconstructive embeddings, limiting its direct applicability in our generation pipeline. That said, integrating or comparing these alternative embeddings with our LLM-based generation framework represents promising future work. We plan to explore nonlinear embeddings such as AEs in subsequent studies to assess their impact on generation fidelity and downstream task performance. \n\n## Dimensionality that can be handled\n\nSDForger is not fundamentally limited by the raw length of the time series. Long sequences are split into fixed-length windows using **periodicity-aware segmentation**, and each window is embedded and treated as a separate training instance. Longer sequences thus yield **more examples**, boosting generalization without increasing prompt size.\n\nThe main limiting factor is the **embedding dimensionality** $K$, which determines the prompt length. As $K$ increases, prompts grow longer, inference slows down, and generation becomes less stable.\nThis holds in **multivariate settings**: more variables imply higher-dimensional embeddings. The embedding size that can be handled depends on the LLM. In our tests, a small model like **GPT-2 handles up to $K = 30$** while producing valid samples.\nSince ICA and FPCA embeddings span entire windows, **window length is not a bottleneck**. The challenge is representing temporal structure with a compact embedding to ensure efficient and stable generation.\n\n## Handling of external covariates\n\nBy design, SDForger supports the integration of **external covariates**, including categorical, numerical, and textual data, into the generation process. These covariates are directly incorporated into the textual prompt, allowing the LLM to condition its generation not only on the time series embeddings but also on rich contextual information.\n\nA concrete example is a weather dataset where each time series channel (e.g., temperature, solar radiation) is associated with metadata about the station, such as geographic coordinates or station ID. These contextual features are encoded as natural language and injected into the prompt, enabling the model to generate sequences that align with both the temporal dynamics and the contextual attributes of the data.\n\nWe explore this **conditioning strategy** in **Section 6**, where we demonstrate SDForger’s ability to **generate channel-specific sequences with high fidelity**, identifying the origin of generated curves, indicating that the synthetic sequences effectively preserve contextual distinctions. Integrating richer forms of metadata (e.g. geospatial tags, or event descriptions) will unlock new applications in simulation, personalized forecasting, and beyond.\n\n## Balanced performances\nWe kindly refer to the last paragraph of Reviewer Ck4d rebuttal for a discussion on this."}]

Author rebuttal:

Meta-review: This paper studies time series generation using large language models. The submission received borderline scores (3 borderline accepts and 1 accept). Reviewers noted the clear writing and well-structured presentation, and the evaluation was significantly improved after the rebuttal.

However, concerns remain. Reviewer V1ut questioned the utilization of large language models; Reviewer Ck4d highlighted the limited evaluation datasets and weak empirical evidence; Reviewer 2HPq noted the limited technical novelty, largely combining established methods such as ICA and LLM fine-tuning; and Reviewer Exqs pointed out missing implementation details such as prompt examples.

I have carefully read the paper and the reviewer–author discussions, and I find these limitations remain valid. Considering the competitive nature of this year’s submissions, **I lean toward recommending acceptance, though I would not object if this recommendation were downgraded**.

I strongly encourage the authors to substantially revise the paper in line with the reviewers’ comments, particularly by strengthening the motivation and empirical comparisons with alternative embedding methods, providing deeper analysis on the role of large language models, and adding missing implementation details.
Decision: Accept (poster)