TSPulse: Tiny Pre-Trained Models with Disentangled Representations for Rapid Time-Series Analysis
Authors: Vijay Ekambaram
Subodh Kumar
Arindam Jati
Sumanta Mukherjee
Tomoya Sakai
Pankaj Dayama
Wesley M. Gifford
Jayant Kalagnanam
Venue: ICLR 2026 Poster (2026)
Keywords: time series foundation models
pretrained models
time series
foundation models
TSFM
Primary area: learning on time series and dynamical systems
TL;DR: Ultra-lightweight time-series pre-trained models (1M parameters) with disentangled embeddings across spaces and abstraction levels, delivering state-of-the-art performance in anomaly detection, classification, imputation, and similarity search.

Abstract: Time-series tasks often benefit from signals expressed across multiple representation spaces (e.g., time vs. frequency) and at varying abstraction levels (e.g., local patterns vs. global semantics). However, existing pre-trained time-series models entangle these heterogeneous signals into a single large embedding, limiting transferability and direct zero-shot usability. To address this, we propose TSPulse, family of ultra-light pre-trained models (1M parameters) with disentanglement properties, specialized for various time-series diagnostic tasks. TSPulse introduces a novel pre-training framework that augments masked reconstruction with explicit disentanglement across spaces and abstractions, learning three complementary embedding views (temporal, spectral, and semantic) to effectively enable zero-shot transfer. In-addition, we introduce various lightweight post-hoc fusers that selectively attend and fuse these disentangled views based on task type, enabling simple but effective task specializations. To further improve robustness and mitigate mask-induced bias prevalent in existing approaches, we propose a simple yet effective hybrid masking strategy that enhances missing diversity during pre-training. Despite its compact size, TSPulse achieves strong and consistent gains across four TS diagnostic tasks: +20\% on the TSB-AD anomaly detection leaderboard, +25\% on similarity search, +50\% on imputation, and +5–16\% on multivariate classification, outperforming models that are 10–100× larger on over 75 datasets. TSPulse delivers state-of-the-art zero-shot performance, efficient fine-tuning, and supports GPU-free deployment. Models and source code are publicly available at https://huggingface.co/ibm-granite/granite-timeseries-tspulse-r1.

Published as a conference paper at ICLR 2026
TSPULSE: TINY PRE-TRAINED MODELS WITH DISEN- TANGLED REPRESENTATIONS FOR RAPID TIME-SERIES ANALYSIS
Vijay Ekambaram, Subodh Kumar", " Arindam Jati", Sumanta Mukherjee', Tomoya Sakai', Pankaj Dayama, Wesley M. Gifford, Jayant Kalagnanam
IBM Research vi jayee28iin in. 1bm. com
ABSTRACT
Time-series tasks often benefit from signals expressed across multiple representa- tion spaces (e.g., time vs. frequency) and at varying abstraction levels (c.g.. local patterns vs. global semantics). However, existing pre-trained time-series models entangle these heterogeneous signals into single large embedding, limiting trans- ferability and direct zero-shot usability. To address this, we propose TSPulse, family of ultra-light pre-trained models (1M parameters) with disentanglement properties, specialized for various time-series diagnostic tasks. TSPulse introduces a novel pre-training framework that augments masked reconstruction with explicit disentan- glement across spaces and abstractions, learning three complementary embedding views (temporal, spectral, and semantic) effectively enable zero-shot transfer. In-addition, we introduce various lightweight post-hoc fusers that selectively attend and fuse these disentangled views based on task type, enabling simple but effective task specializations. To further improve robustness and mitigate mask-induced bias prevalent in existing approaches, we propose a simple yet effective hybrid masking strategy that enhances missing diversity during pre-training. Despite its compact size. TSPulse achieves strong and consistent gains across four TS diagnostic tasks:
+20% on the TSB-AD anomaly detection leaderboard, +25% on similarity search, +50% on imputation, and +5-16% on multivariate classification, outperforming models that are 10-100x larger over 75 datasets. TSPulse delivers state-of-the- art zero-shot performance, efficient fine-tuning, and supports GPU-free deployment. Models and source code are publicly available at https: ///////mmggaaatt//aatttteeeeeeee
INTRODUCTION
Time-series (TS) analysis encompasses a broad class of problems that aim to extract meaningful insights and semantics from observed sequences. Among these, time-series diagnostic tasks-sur anomaly detection, imputation, classification, and similarity search- operate observed data and focus on retrospective understanding, i.e., analyzing existing sequences to characterize behavior, identify irregularities, recover missing information, or compare patterns across time. These tasks central to many real-world applications in observability, manufacturing, and industrial monitoring.
Inspired by the success of large language models (LLMs), time-series pre-trained models aim to learn reusable representations from large-scale public data for effective transfer learning. While time-series pre-trained models have seen rapid progress in forecasting (Ansari al.] 2024 Das
et al. 2023 Ekambaram et al.) 2024), their development for time-series diagnostic tasks remains relatively limited. A few pre- pre-trained models- such as Moment (Goswami et al.) 2024). UniTS (Gao et al. 2024), VQShape (Wen et al.) 2024). and GPT4TS (Zhou et al.) 2023) support subsets of diagnostic tasks. However, their performance on time-series diagnostic tasks still leaves substantial
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room for improvement, while their large model sizes further hinder real-time, low-latency deploy- ment- ment-especinne especially in lightweight and CnU-only settings. Specifically, a key limitation underlying these approaches lies in how representations are learned during pre-training. Most existing diagnostic models rely on self-supervised objectives, with masked reconstruction emerging as one of the most widely adopted strategies (Goswami et al. 2024 Gao et al. 2024). While effective in capturing local & global structure, masked reconstruction alone is insufficient to model the full complexity of time-series data.
Meaningful insights in time-series often arises, when signals are examined across different represen- tation spaces(e.g. time vs spectral) and abstraction levels (e.g. local patterns vs global semantics). For example, abrupt spikes and local irregularities are most apparent in the time domain, whereas periodic patterns emerge more clearly in the frequency domain. Likewise, some structures are visible only at fine temporal resolutions, while others manifest at higher semantic levels. To be broadly useful, pre-trained embeddings must therefore capture these complementary cues across both spaces and abstraction levels. However, simply learning them jointly within single embedding often leads to entanglement, making it difficult for downstream tasks to selectively access the information they require. For broad utility- particularly in zero-shot these insights in a disentangled form, enabling temporal, spectral, and semantic signals to be accessed needed.
must explicitly expose
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To address these challenges, TSPulse proposes a novel pretraining framework enable disentan- gled masked reconstruction across multiple spaces and abstraction levels, explicitly pro- ducing three distinct types of embeddings during pre-traimin te-trraiiin: (i) detailed temporal embeddings for fine- ene-grained time analysis. (ii) detailed spec- tral embeddings for frequency-aware fidelity, and (iii) semantic embeddings for high-level task understanding. The model formulates se- mantic and full reconstruction objectives across multiple spaces, employing multi-output heads that operate distinct segments of the embed- ding to yield disentangled representations across spaces and abstraction levels (Figure []. While prior works in traditional time-series modelling have explored
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frequency fusion (Zhang ct al,, 2022: 2023) or investigated disentangle- ment in isolation (Chang et al. 2024). TSPulse advances beyond these approaches by jointly learning disentangled representations across spaces and abstraction levels within unified pre-training framework. Optimized together, this design yields substantial gains in both performance and transferability across diverse downstream tasks.
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Figure 1: TSPulse Overview. % and X represent the accuracy and size improvements TSPulse over SOTA pre-trained models across different benchmarks.
Through extensive sensitivity analyses, we demonstrate that different segments of the learned em- beddings indeed capture distinct and complementary properties that substantially enhance transfer learning. In particular, the semantic embedding exhibits strong robustness to various distortions such as time shifts, magnitude variations, and noise which is especially important for reliable semantic analysis.
Moreover, since different tasks benefit from different combinations of these disentangled views, we introduce a set of lightweight post-hoc fusers that selectively combine these views based on the task type, providing a simple yet effective mechanism to exploit their complementary strengths for effective task specialization. Specifically, we propose two post-hoc fusers: (i) Multi-Head Triangulation (MHT) for anomaly detection and (ii) TSLens for classification, each demonstrating strong effectiveness for its respective task.
In addition, TSPulse improves pre- mre-trining robustness through a simple but impactful refinement of masking strategies. Unlike existing approaches (Goswami et al. (2024) that rely on fixed masking types and span lengths, TSPulse adopts a hybrid masking scheme that randomizes both, better
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reflecting real-world missing patterns. Despite its simplicity, this increased corruption diversity reduces overfitting and consistently boosts downstream performance.
Finally, to ensure efficiency, TSPulse replaces conventional Transformer backbones Vaswani et al. 2017) with light-weigh. TSMixers (Ekambaram al., 2023), further enhanced with improved initialization strategies. This substitution, when combined with disentangled hybrid reconstruction, yields small and fast pre-trained models, while still delivering state-of-the-art representational power.
Contributions: (1) Compact& & Versatile. We introduce family of ultra-light time-series pre-trained models (1M parameters) with rapid zero-shot and fast multivariate fine-tuning support, specialized for 4 diagnostic tasks: classification, imputation, anomaly detection (AD), and semantic search. (2) Architectural Novelties. TSPulse introduces (i) disentangled masked reconstruction across multiple representation spaces and abstraction levels, yielding temporal, spectral, and semantic embeddings; (ii) simple yet effective post-hoc fusers (MHT, TSLens) built on these disentangled views for susciaecciliization;; and (iii) hybrid masking scheme mitigate pre-training bias prevalent in existing approaches. (3) Emergent Representation Properties. Through extensive sensitivity analyses, show that the learned disentangled embeddings capture complementary properties and exhibit varied level of robustness to common perturbations, including time shifts, magnitude variations, missingness. spectral perturbations, and noise. (4) Benchmark Performance. TSPulse achieves (i) robust anomaly detection with +20% gains on the TSB-AD leaderboard, ranking first in both uni- and multivariate settings; (ii) semantic search improvements of +25% via robust semantic embeddings; (iii) +50% gains in shot imputation under diverse missing patterns; and (iv) +5-16% improvements multivariate classification on UEA benchmarks.
(5) GPU-Free Deployment. Despite its compact size, TSPulse consistently matches or outperforms models that are 10-100x larger across a broad range of benchmark datasets, while providing near near-instant, CPU-only inference suitable for real-time applications.
2 TSPULSE ARCHITECTURE
Let X E SxC be a multivariate time series with length and channels. We first project and mask X in both the time and frequency domains. The backbone and decoder then process these representations, mixing information across dimensions in both spaces. To guide learning, we use multi-output heads for semantic and full reconstruction different parts of the embeddings, which encourages disentangled representation learning. These embeddings can then be directly used across downstream tasks. Figure 2 gives overview of the framework.
Masking & RevIN [Fig DI: TSPulse begins with a masking block that hides portions of the input sequence to enable self supervisdd reconstruction. Given input X Ršx divide it into N non-overlapping patches of length pl and apply masking to obtain X RSC TSPulse
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supports two masking strategies: block masking and hybrid masking. In block masking, entire patches are randomly replaced with a learnable mask token M E R xxpl, as commonly done in prior work (Goswami et al. 2024 Gao et al., 2024). While effective for robust feature learning, this approach is inadequate for real-world imputation tasks, where missing values occur irregularly at both patch and point levels. To address this, we introduce more realistic hybrid masking pre-train strategy that masks both full and partial patches within each sample using variable masking ratios, preventing overfitting fixed patterns. A key design choice in TSPulse is to define the mask token M E R 1xpl at the raw patch level, unlike prior approaches that insert mask tokens in the embedding space (Goswami et al., 2024 Vaswani et al., (017). This enables individual time-poiin time-points to masked by selecting the appropriate value from M based on their relative index within patch (Figure Ba)), allowing a single token to flexibly support both full and partial masking. After masking, a learnable RevIN block (Kim et al. 2022) is applied to normalize the input, yielding Xm m E RR5x.
FFT Extraction [Fig 2-0 As TSPulse reconstructs in both time and frequency domains, this block extracts masked FFT features for backbone processing and also prepares the corresponding ground-truth for loss computation. Instead of explicitly masking the frequency space, we feed the scaled and masked time-series X.m directly into the Fast Fourier Transform (rfft), propagating the mask and ensuring the same data is consistently hidden in both spaces, preventing leaks. The real and imaginary FFT outputs from X., are then packaged, scaled, and processed into tensor X RSx for further backbone processing. Refer to Appendix. [A.10 for more details. Simultaneously. two ground ground-truths are computed from the frequency representation. First, the unmasked scaled time-scries is transformed using the same approach described above to get X E RSxCC a clean, unaltered frequency representation of the time-series, which is used guide the model's reconstruction. In addition, we also compute the -oggmmtge spectrum of the unmasked time-series and apply softmax to obtain X E S/-S/2x normalized global frequency signature (Appendix. A. for more details). This global signature serves as an auxiliary reconstruction target, helping the model capture bigh-level semantic patterns and improving generalization to downstream tasks. The log transformation reduces the dynamic range and stabilizes training, while softmax emphasizes dominant spectral components, mapping the output to a probability- distribution.
Encoding [Fig 2 21: This block projects the input to embedding space. The masked time- domain input Xm E SRSC is transposed and then divided into N non-overlapping patches of length pl, resulting in tensor of shape CC xpl, Now, each patch is projected via linear layer from RP + R to obtain time-encoded features Timeg E RxCNNx Similarly, the masked frequency- domain input X E BxC is transposed, patched and projected to produce frequency-encoder features FFT, E CCNDD Motivated by recent advances in vision transformers (Darcet et al. 2024. where adding learnable register tokens stabilizes training and improves transfer learning, we introduce R such tokens shared across channels: Regg E xxCXRx The full input to the backbone constructed by concatenating time, frequency, and register tokens along the patch axis and layer normalized: Inputg [Timeg; FFTg; Regg] (Cx RC
TSPulse Backbone [Fig 2 O. The TSPulse backbone receives Input, E RCCxxD a unified sequence of masked patches from both time and frequency domains, along with learnable register tokens. Its goal is to transform this input into semantically rich, task-robust representations. To maintain efficiency. we use the TSMixer backbone (Ekambaram et al., (023). an MLP-Mixer based alternative to Transformers that performs strongly with reduced compute. TSMixer has stacked Mixer blocks interleaved with lightweight gated attention, enabling flexible feature mixing across three dimensions: within-patch, across-patch, and across channels. Since Inputę already integrates both time and frequency information, TSMixer effectively fuses these views, learning dual-space representations that capture temporal and spectral correlations. Gated attentions in TSMixer further prioritizes informative regions, enhancing the model's s ability to generalize across downstream tasks.
TSPulse Mini-Decoder [Fig O The backbone output (Backboneg E RC is passed through a lightweight mini-decoder, which mirrors the backbone but is only 10-20% of its size to output Decoderg cC x D, where K 2N + R. This compact decoder adapts representations during fine-tuning, enabling fast & efficient data-specific adaptation
The decoder output Decoderg, which consists of 3 segments (Time;; FFT:; Rogr] is disentangled by optimizing each segment with a distinct head objective:
Multi-Ohjective Heads [Fig 5]:
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Full Reconstruction Heads [Fig 2 O]: The first N patch embeddings (Timeg) from the decoder pass through a linear layer (Time Head) and inverse RevIN to obtain the full reconstruction of the imput series. The next N embeddings (FF) from the decoder are projected (via the FFT Head) to reconstruct the input frequency spectrum Y/, which further reshaped, passed through torch. fft. f ft,, and inverse RevIN to yield Y', an alternate reconstruction of the imput time-series from FFT-space. Losses are computed as Mean Squared Errors (MSE): Lrimel MSE(X, Y), Lúim2 MSE(X, Y'), and Lit MSE(X/, Y where the first two losses are computed only on the masked time-points. This disentangled losses enables Timeg and FFT, to capture fine-grate tieegrained temporal and spectral insights.
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The final R register embeddings (a.k.a semantic embeddings) from Decoder: are primarily trained through a signature head that predicts Y
sign? a softmax distribution over the oog-maniiude frequency spectrum (i.e. semantic signature). This objective, sign'
optimized with cross-entropy loss Lsign CE(X Y k.gn). captures global spectral semantics and forms the core of semantic reconstruction. Optionally, a lightweight next-point prediction head Y pred can also be added, trained with 4reed = MSE (X pred: Y pred), to inject temporal cues into the semantic embeddings. Xped denotes the ground-truth future points. Importantly, this auxiliary head is limited to only few points and is not designed for full-fledged forecasting; its sole purpose is to enrich the semantic representation. Together, these objectives ensure that the register tokens converted into semantic embeddings for high-level understanding.
Finally, weighted sum of all the above losses across heads is jointly minimized during pre-training.
TSPULSE WORKFIOOSS
3.1 PRE-TRAINING:
TSPulse is pre-trained on diverse 1B TS samples as detailed in Appendix A.S Inspired by the suc- cess of small, task-specialized pre-trained models in the language/vision domain (Schick & Schütze 2020; Nguyen et al. 2024 Fu et al., 2023 Ling et al., through minimal task-specific adaptations we extend this strategy to time-series. Specifically, specialize the pre-training for every task through reweighting loss objectives to prioritize heads most relevant the target task. This enables TSPulse to refine task-specific representations while maintain- ing its lightweight design, facilitating efficient transfer learning across any datasets for the specified downstream task. Refer Appendix Appendix[A.9ffom for more details. Pre-training on 1B samples takes just one day with 8xA100 100 GPUs, thus there are no practical challenges in pre- pre-training task-specific models. In addition, given the heterogeneous channel counts in pre-training datasets, TSPulse pre-trained in univariate mode (c = 1), treating each channel independently. Cross-channel modeling is deferred to Linettnnin, where lhannel-mixing is selectively activated based on the target dataset (Ekambaram ct al. 2024).
achieve strong performance
3.2 TARGET DATA FINE-TUNING:
During fine-tuning, the pre-trained model-already strong in zero-shot settings-is further adapted to the target data by updating the decoder and task-specific heads. For multivariate inputs, we enable channel mixing in the decoder to capture inter-channel correlations, which are absent in the univariate pre- vre-training setup. Our design draws inspiration from TSMixer and TTM (Ekambaram al. 2023) 2024), where channel mixer blocks are interleaved between patch and feature mixers within each TSMixer layer. A key limitation in the original design is the random initialization of these mixers, which introduces untrained parameters between already pre-trained layers. This can disrupt information flow and create sharp activation shifts, leading to unstable gradient propagation, especially during the early stages of fine-tuning. To address this, we initialize channel mixers with identity weights, which enable smooth gradient flow between pre-trained weights. These layers gradually learn inter-chamen dependencies without interfering with earlier knowledge, leading to a significantly more stable fine-tuning process, confirmed by experiments.
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Figure 3: TSPulse Downstream Differentiators.
3.3 DOWNSTREAM TASKS& & POST-HOP FUSERS:
TSPulse delivers strong zero-shot imputation benefitting from hybrid masked pre-training (Fig. 3-A), which exposes the model to diverse corruption patterns. For semantic similarity search, the register token embeddings provide invariant representations that remain resilient to time shifts, magnitude changes, and noise (Fig. 3-B). For classification and anomaly detection, TSPulse further incorporates task-specific post-hoc fusers, detailed below.
Classification via TSLens: TSPulse supports multivariate classification through lightweight fine-tuning module, TSLens (Fig. B.C), which replaces standard pooling across channels with a learned mechanism that adaptively extracts relevant features from disentangled embeddings. Unlike conventional methods, which average or max-pool all patch-level embeddings across channels followed by linear head, TSLens selectively attends to and weights features across fine- me--granedd patch embeddings and high-level register tokens.
TSLens takes the backbone output Backbone; E CC passes it through the mini decoder (initialized with pre-trained weights and channel-mixing enabled), and learns cross-channel dependencies via -entity-initiallized channel mixers as explained in Section 3.2 The resulting representation E CC D)) is projected to a lower-dimensional space H' E (X)
flattened into Ham E (C-2244)).D and passed through linear layer to produce class logits Yped _euumclasses The model is optimized with cross-entropy loss. This design allows TSPulse to dynamically focus on the most informative features across local and global representations, improving classification accuracy across diverse datasets.
Robust Anomaly Detection via Multi Triangulation:
In anomaly detection, certain anomalies manifest in the time domain (sudden spikes), others in the frequency domain (periodicity breaks), and others in predictive space (missing trends). TSPulse leverages multi-output heads-Head..jn, Head and Headgred reconstruct predict from complementary views, capturing signal continuity, spectral consistency, and temporal dynamics. This unified design enables detection of diverse anomaly types.
During inference, anomaly scores are computed from each head based on the deviations between the original and predicted signals(Fig. 3 D). Once the deviations are obtained from all heads, two approaches are possible. Approach 1 (Head is to fuse the normalized scores using statistics, such as the maximum, to generate unified score. In Approach (Headeriang.)) when small labeled validation set is available, it can be used to select the most effective head in zero-shot from the above four heads (including He-denseeble).. This allows the model to adapt to the anomaly type and structure specific to each application. Notably, TSPulse is the first pre-trained model to unify and triangulate multi-space outputs in a single lightweight framework, enabling robust anomaly detection in both zeoo-shot and fine-tuned settings.

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4 EXPERIMENTS
We evaluate TSPulse across 4 TS diagnostic tasks: classification, anomaly detection, imputation, and similarity search. Details of the pre-trained model configurations are in Appendix A.9 Pre-training datasets are listed in Table TO. and they do not overlap with any of the evaluation datasets.
4.1 ANOMALY DETECTION (AD)
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Figure 4: VUS-PR (official metric, higher is better) scores of different AD methods on the TSB-AD leaderboard; IMP(5)) ( the percentage improvement of TSPulse over baselines; A maximum of top three SOTA models have been reported in each category. Full results across all 40 models are in Appendix A.
(recent compre- hensive leaderboard for AD), which comprises 40 eval datasets, covering both univariate (TSB-AD-U) and multivariate (TSB-AD-M) anomaly detection. The benchmark includes results from 40 SOTA methods and establishes VUS-PR (Paparrizos al.) 2022) as the primary and robust evaluation metric. A small labeled official tuning-set set is provided for hyperparameter selection, consistently used across all leaderboard methods. We adopt this tuning set for multi-head triangulation to select the best- best-performing head and report scores the test set for both zero-shot (TSPulse-7S) and fine-tuned (TSPulse-FTY variants. In the zero-shot case, TSPulse is evaluated directly without training on the target data; in the fine-tuned case, is self-supervised using the official training split without access to any anomaly labels. Note that all non-pretrained neural network models are also trained using the same training split. Figure summarizes VUS-PR results. Full details in Appendix A.II
Setup: We evaluate TSPulse on the TSB-AD benchmark (Luu & Paparrizos 2024
Results: As illustrated in Figure TSPulse (ZS) outperforms all existing SOTA methods on both the uni and multi-variate AD benchmarks. Specifically, TSPulse (ZS) achieves 14% and 16% higher VUS- PR scores compared to the best-performing base- lines-SubPCA for the univariate setting and CNN for the multivariate setting, respectively. Notably, TSPulse, without any training on the target data, out- performs all models trained it, underscoring its strong transfer learning. TSPulse also outperforms all the pre-trained models by +30% by using just fraction of their model size. The fine-tuned variant, TSPulse (FT), further improves results, achieving 24% and 26% gains over SOTA on uni and multi- variate benchmarks. These results underscore the effectiveness of TSPulse for diverse AD tasks.
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4.2
CLASSIFICATION
Setup: We evaluate TSPulse results on 29 datasets from the UEA Multivariate Time Series Classifica- tion Archive (Bagnall et al. 2018). Dataset and hyperparameter details provided in Appendix A. We compare against recent pre-trained models Baaieels-VShhap VQShape (Wen et al.] (024)), Moment (Goswami et al. 2024), and UniTS (Gao et al. 2024) as well as strong data-specific baselines including T.
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Rep Fraikin et al. 2024). Ve2 Yue et al. 2022). T-Loss (Franceschi al. 2019) TS-TCC (Eldele ct al. 2021) and TNC (Tonekaboni et al. 2021).
Results Classification results finettune//trainee on the labeled data are reported in Figure 5 TSPulse achieves ofate-of-the-ar accuracy, surpassing VQShape, UniTS, and Moment by 5-16%, while being drastically smaller (1M vs. 10-340M parameters). It also outperforms contrastive and supervised baselines by 5- 3-1,,, highlighting the effectiveness of TSPulse fine-tuning with TSLens
4.3
IMPUTATION
Setup: We evaluate TSPulse on 6 LTSF benchmark datasets (Wu et al. 2021): ETTh1, ETTh2, ETTml, ETTm2, Weather, and Electricity, under mask ratios (12.5%, 25%, 37.5%, 50%) using irregular hybrid masking (a mix of block and point masks) to simulate real-worke missingness.
Results: We first evaluate TSPulse in fully Zero-Shot (ZS) setup, requiring no data- sita--peeific tuning. Among pre-trained baselines, MOMENT supports native zero-shot imputation, for UniTS (Gao et al. 2024) the pretrained model is prompt-tuned (PMT) with 10% data multi-task setup. We also compare against statistical baselines in 7S setup. As shown in Figure G TSPulse (ZS) outperforms MOMENT by over 70% and UniTS by 50% despite prompt-tuning Compared statistical interpolation methods, TSPulse shows 50%+ gains, highlighting the effectiveness of TSPulse in hybrid masking setup and robust sero generalization. More details in Appendix A.113
When Fine-Tuning (FT) is desired, TSPulse can be extended with a channel-mixing decoder to capture vaterlvariable dependencies, outperforming strong su- pervised models like TimesNet (Wu et al. 2022),
8.276
78%
Mean MSE
0.2
6.161
FedFormer (Zhou al., 2022), and Non-Station Stationary Transformers (Non-Stat.) (Liu et al. (022) by over 40%. Remarkably, TSPulse's zero-shot performance already exceeds many of the fine-tuned benchmarks, demonstrating its strong generalization and transfer- ability. We further evaluated TSPulse under the full block masking strategy in both 7S and FT settings, as illustrated in Appendix Figure 13 TSPulse continues outperform all baselines by significant margin in
0.000
0.039
45%
91%
TSeutie (03)
Uni78 (PA0))
HOMENT
Maive
Liner
Talroter IF1
Hon-dtat.
PEStormer
Zero Shopt Tuned Statistical
Figure Hybrid Masking imputation MSE results (Lower is better). IMP(%) the percentage im- provement of TSPulse over baselines.
this setting well.
4.4 TIME-SERIES SIMILARITY SEARCH
Setup: We evaluate TSPulse's similarity search using its zero-shot semantic embeddings to re- trieve time-series segments with similar patterns, even under real-world distortions like time shifts, magnitude changes, and noise. Since time-series typically indexed via high-stride sliding
0.78
windows for efficient storage, the same pattern appear in different positions, making distortion- invariant embeddings essential for similarity search. We use real and synthetic data for indexing, and gen- erate query samples by applying complex augmen- tations (time shifts, magnitude changes, and noise distortions) from indexed samples.
0.6
0.59
0.58
0.53
35%
28%
0.42
0.4
61%
0.28
0.25
0.2
160%
2916
0.18
This setup tests the embeddings' robustness in retriev- ing distorted similar patterns and simplifies evalua- tion, as the correct matches for each query are already known. Two tasks are defined: Family Match for high-level pattern retrieval and Fine-Grained Match for precise pattern matching and evaluated using PREC @k and MRR @k (Valcarce et al.) 2020). We construct synthetic dataset and real dataset based on the UCR dataset (Chen et al., 2013), and report the average across both for each task. See Appendix A.14 for full details.
222
PREC@3
MRR@3
PREC@3 MRR@3 Fine-grained match
Family
CPU [ms]
GPU [ms] Emb, dim. Size
TSPulse
0.287
0.050
240
1M
Chronos
40.71 (105X)
0.77 (163) 512
46M
Figure 7: Similarity Search results using zero-shot embeddings (Higher is better). IMP(%) the per- centage improvement of TSPulse over baselines.
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Variate
ISPulse Head
VUS-PR
Model Variant
Accuracy
Model Varlant
MSE
Headeriang
0.48
TSPulse
0.747
TSPulse
1.074
Haaduseenie
0.44
9%
w/o Short Embedding
0.689
8%
w/o Dual-Space
Headrrie
w/o Long Embedding
w/o Hybeid PT
0.354 79%
Haadrre
0.42
14%-
w/o Mask
0.691
8%
Headpred
0.30
60%
wro CM Identity Init
0.685
9%
(c) Imputation MSE
Headeriang
0.36
w/o Channel Expansion
0.734
2%
1.0
TSPulse
Chronce
Haadessemiie
w/o TSLens (Avg-Pool)
0.675
11%
Multi.
Headerre
0.31
16%
w/o TSI ens (Max- (Max-Pool)
0.645
16%
0.7
Hnadere
0.31
16%
wro Dual-space Learning
0.696
7%
0.3-
Headdpedd
0.24
50%
0%
10%
20%
50%
40%
50%
(a) Zero-shot Anomaly Detection
(b) Classification Accuracy
(d) Similarity Search
Table I: Ablation results across tasks. [VUS-PR, Accuracy, MRRJ: Higher is better; [MSE]: Lower is better.
IM)(%) indicates the percentage improvement of the bold variant over the compared variant.
Figure compares TSPulse's similarity search performance against zero-shot embeddings from MOMENT and Chronos. We use their smallest variants to closely match TSPulse's ' embedding size and enable faster indexing for fair comparison. As shown, TSPulse outperforms MOMENT by over 25% in family-level and 40% in fine-grained match accuracy, and surpasses Chronos by 100%. Notably, TSPulse's s zero-shot embeddings are 2X smaller and enable 10-100X faster CPU inference, 9-15X faster GPU inference, and come from model that is 40x smaller than the baselines. Further discussion in Appendix A.
Results:
ABLATION STUDIES
Anomaly Detection (AD) We evaluate the performance of individual TSPulse heads for anomaly detection. Table a reports average VUS-PR scores for each head used independently. The proposed multi-head triangulation outperforms all single-head variants on both TSB-AD-U and TSB-AD-M, demonstrating the strength of multi-head TSPulse. See Appendix A.1I for details.
Classification We evaluate the impact of key design components in Table [b). using representa- tive subset of 17 UEA datasets for faster analysis. Removing either the short long embedding from the disentanglement design reduces mean accuracy by 8-10%, confirming the importance of capturing both semantic and fine- fine-grained features. Disabling masking during fine-tuning leads to an 8% drop-especially on smaller hatasets-highlighhe
its role as a regularizer. Replacing TSLens with simple pooling causes an 11-16% drop, emphasizing the value of feature-attention. Randomly initializing the thameel-mixing (CM) blocks instead of using identity weights leads to a 9% drop, reflecting the need for stable gradient flow. Removing dual-space learning (i.e., recon- structing only in time domain) lowers accuracy by 7%, and omitting virtual channel expansion, critical for low-channel datasets- causes a further 2% drop. More details in Appendix [8]
Imputation Table [e)) shows that removing dual-space learning leads to an 8% drop in zero- shot accuracy. When pre-training (PT) is done with only block masking (i.e., w/o Hybrid PT). performance drops by 79% under hybrid-mask eval settings, underscoring the importance of hybrid masking in pre-training for robust, generalizable imputation, where missingness is irregular and more reflective of real-world scenarios.
Similarity Search Table d) shows that TSPulse and baselines perform similarly without distor- tion. As augmentation distortion increases, all models degrade, but TSPulse remains notably more robust time shifts, magnitude changes, and noise- highhlhihii the resilience of its embeddings in retrieving distorted yet similar patterns. Also, use of hybrid masking & semantic embedding boosts search performance by over 20% Coppendi[AA114
Efficiency Appendix A.2 shows TSPulse significantly faster, smaller and CPU-friendly.
6 SENSITIVITY ANALYSIS OF EMBEDDING DISENTANGLEMENT
To validate that TSPulse learns genuinely disentangled temporal, spectral, and semantic represen- tations, we conduct controlled experiments on synthetic signals under three perturbation settings: missing data, additive noise, and phase/time shifts. These perturbations allow to isolate how each

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Published as a conference paper at ICLR 2026
embedding type responds to missing data in the imput (masking), stochastic changes (noise), and temporal misaligmment (phase shift).
We quantify embedding stability using distortion metric that measures how much each embedding changes under controlled perturbations (formal definitions in Appendix A.3) Representative results summarised in Table Lower values indicate greater robustness.
Table 2: Representative distortion results (in %). Lower indicates less distortion. Time and FFT embeddings have dimension d = 1536, while the semantic embedding has dimension = 256.
Experiment
Time (d = 1536)
FFT (d = 1536)
Semantic (d = 256)
30% Missing Data Noise Level = 0.5
8.3%
27.4%
4.6 %
2.7%
6.8%
2.5 %
Phase / Time Shift
130%
21% %
12 %
The results exhibit clear and expected disentanglement patterns.
Temporal embeddings are highly sensitive to phase/time shifts (130% distortion), confirming preservation of fine-grained temporal alignment. This property is critical for tasks that depend on precise timing cues.
FFT embeddings demonstrate substantially lower phase sensitivity, reflecting invariance to temporal alignment while retaining spectral characteristics.
Semantic embeddings (a.k.a Register embeddings) are the most robust to missing data and noise and the least sensitive phase shifts, consistent with their role as high-level structural abstractions rather than fine-gres ame-grained signal encoders.
These complementary behaviours directly translate to downstream utility. Tasks such as anomaly detection and imputation benefit from time and FFT embeddings for high-fidelity reconstruction, while retrieval tasks primarily leverage semantic embeddings for compact summarisation. More- over, disentangled reconstruction across spaces enables triangulation-basee mechanisms that detect anomaly types missed by single-view models.
For more details, refer to Appendix A.3 We have also conducted sensitivity deep-dive analysis focused on register embeddings as explained Appendix AA.4. Together, these results confirm that TSPulse achieves effective disentanglement across both representational spaces (time vs. FFT) and abstraction levels (fine-grained vs. semantic), forming a core foundation for its strong zero-shot transfer performance.
CONCLUSION
TSPulse sets a new benchmark for ultra-compact time-series pre-trained models, achieving state- of-the-art performance in classification, imputation, anomaly detection, and similarity search-all with under IM parameters. Powered by innovations like disentangled masked reconstruction across spaces and abstractions, TSLens, hybrid masking, and multi-head triangulation, TSPulse enables robust zero-shot and fine-tuned performance. Despite its small size, it outperforms models 10-100X larger and runs efficiently on CPUs, making both powerful and deployment- outlines limitations and future directions, including opportunities to expand to additional downstream tasks, enable incremental learning and reduce supervision requirements. We believe this work will inspire more advanced research and innovation in the field of lightweight time-series modeling.
Appendix(A.11
REPRODUCIBILITY STATEMENT
Models and source code are publicly available at bttps:/hugqinggfac co/ ibm-granite http://rrrrrrneteteeeeeeeeeeeeee
Detailed model parameters are included in Appendix A.9 All pretraining datasets are publicly available and referenced in Appendix A.8. and all evaluation datasets likewise publicly accessible.
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A
APPENDIX
A.1
Use of Large Language Models (LLMs))
15
A.2
Runtime Computational Analysis of TSPulse and other Pre-trainn trained models
15
Sensitivity Analysis across different TSPulse Embeddings
15
A.4
Sensitivity analysis of TSPulse Semantic embeddings
19
A.5
Notation Details
23
A.6
Related
23
A.7
Baseline Methodologies
25
A.8
Pre-training Datasets
25
Model Details
25
10 FFT Extraction Details
26
A. 1l1 Time series Anomaly Detection
27
12 Classification
A.13 Imputation
31
A. 14 Similarity Search
35
A.15 Unified Pre- Trained Model Across Multiple Downstream Tasks
................................
40
A. Robustness Under MAR and MNAR Missingness Patterns
41
A. 17 Limitations and Future work
44
A.1 USE OF LARGE LANGUAGE MODELS (LLMs)
LLMs were used only as writing aid polish phrasing and correct grammatical errors in the manuscript.
A.2 RUNTIME COMPUTATIONAL ANALYSIS OF TSPULSE AND OTHER PRE-TRAINED MODELS
In this section we do the computational analysis of TSPulse with all the other pre- pre-trained mod- els that used for benchmarking across different tasks in this work. These models include MOMENT (Goswami et al.) 2024), UniTS (Gao et al., 2024), VQShape (Wen et al. 2024). Chronos Ansari al. 2024 TimesFM (Das et al. 2023 and Lag-Ilama (Rasul et al.) 2023
In this analysis, we demonstrate the suitability of TSPulse for rapid time-series analysis by high- lighting its computational advantages over larger pre-trained models. With only 1M parameters, TSPulse offers significant efficiency benefits in terms of per-batch CPU inference time, GPU inference time, and peak GPU memory usage. These comparisons are made against all pre- pre-trained baselines discussed above. Refer to Tor detailed results.
All computational analysis experiments were conducted on a system equipped with an NVIDIA A100 GPU (80GB), 16 CPU cores, and 256GB of RAM. For inference time and peak memory usage measurements, zero tensor input of shape (batch size 32, sequence length 512, channels 5) was used.
A.3 SENSITIVITY ANALYSIS ACROSS DIFFERENT TSPULSE EMBEDDINGS
We performed detailed control experiments on a synthetic dataset to investigate disentanglement properties in the TSPulse embedding space.
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GPU Inference
CPU Inference Time (s)
Model
Params (M)
Max. Memory (GB)
Time (ms)
TSPulse
1.06
7.16
0.06
0.39
82
89
2.23
5,42
GPT4TS/OFA
(77X)
(12.43X)
(37.16X)
(13.89X)
37.09
65.37
1.15
6.88
VQShape
(35.0X)
(9.1X)
(19.2X)
(17.6X)
2.45
236.00
0.24
1.01
Lag-Ilama
(2.3X)
(33.0X)
(4.0X)
(2.6X)
203.57
101.80
0.87
TimesFM
(192.0X)
(14.2X)
(19.0X)
(2.2X)
MOMENT
35.34
32.57
2.74
0.56
(small)
(33.3X)
(4.5X)
(45.7X)
(1.4X)
MOMENT
109.64
120.27
7.60
1.15
(base)
(103.4X)
(16.8X)
(126.7X)
(2.9X)
MOMENT
341.24
405.42
21.98
2.30
(large)
(321.9X)
(56.6X)
(366.3X)
(5.9X)
3.5
7.94
1.50
0.57
UniTS
(3.24X)
(1.11X)
(25X)
(1.4X)
CHRONOS
8.39
39.81
66.15
2.91
(tiny)
(7.9X)
(5.6X)
(1102.5X)
(7.5X)
CHRONOS
46.15
112.62
201 .62
5.86
(small)
(43.5X)
(15.7X)
(3360.3X)
(15.0X)
CHRONOS
201.37
328.37
642.38
8.97
(base)
(190.0X)
(45.9X)
(10706.3X)
(23.0X)
CHRONOS 708.96
897.86
1754.87
12.80
(large)
(668.8X)
(125.4X)
(29247.8X)
(32.8X)
Table 3: Computational Analysis of TSPulse and other pre-trained models. Per batch GPU inference time in milli-seconds(nne CPU inference time in scconds(s), Maximum memory usage in GB and Number of parameters millions(M) are reported. Lower better.
A.3.1 DATASET
The dataset consists of three distinct signals, each constructed by scaling and exponentiating a pure sine wave to obtain different periodic shapes (see Appendix Figure 10). White noise was added at specified signal-to-noise to-noise ratio (SNR) to generate the final dataset.
A.3.2 EXPERIMENTAL SETUP
We designed three controlled experiments analyse the effect of missing data, noise, and phase shift on the learned embeddings.
Missing Data. TSPulse supports user-defined masks during inference. We leverage this capability emulate missing observations. From the synthetic dataset described above, we randomly sampled 2,000 instances and extracted embeddings under different user-defined masks. The proportion of zeros in each mask corresponds the fraction of missing data.
The synthetic generator allows precise control noise levels. We created multiple groups of samples from are aligned such that the same index corresponds to the same underlying base signal across all noise conditions.
Noise.
the same base signal while varying only the noise level. Within each group, indices
Phase Time Shift. We utilise a non-linearly scaled sine wave as the base signal to explicitly control frequency and phase. A base dataset is generated by sampling the signal fixed frequency
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and waveform type. Across subsequent groups, only the phase is varied in discrete steps from 0 to while keeping all other parameters constant.
A.3.3 EXPECTED BEHAVIOOR GOOD SEMANTIC EMBEDDING
Missing Data Robustness. An embedding should exhibit minimal sensitivity to missing data. For samples masked with fixed ratio, their neighbourhood relationships should remain preserved.
Noise Robustness. Embeddings should be robust to noise, such that similarity in embedding space reflects similarity of the underlying signal rather than noise perturbations.
Phase Sensitivity. Temporal embeddings should be sensitive to phase/time shifts. In contrast, spectral (FFT) and semantic embeddings should exhibit minimal sensitivity to phase variations.
A.3.4 EVALUATION METRICS
We measure distortion as the & norm ratio of embedding changes induced by missing data, noise, phase shifts relative to the base embedding. Lower distortion indicates greater robustness.
Distortion.
We slightly refine the distortion definition to align with the expected behaviour described above.
A.3.5 NOTATION
Exr, M):
Embedding of dataset under user-defined mask M.
E(r): Embedding without mask.
r(]):: Data instance with noise level where zr(0) denotes the pure signal.
(x): Phase associated with signal x.
A.3.6 DISTORTION MEASURES
Mask-Induced Distortion.
For a given mask Mi:
[1E(:;; M) 8 Eyy; MI]l ||E(x) - Evy)ll
8m (M)
E
(1)
(#
Noise-Induced Distortion.
For a given noise level ry:
[[((()))I| {((()))]
(. =
(2)
Phase-Induced Distortion.
For phase difference Φ:
[8(x) { (p(d) (x,y)e ((z) +())= min ([(((x) (v)
(3)
A.3.7 REPRESENTATIVE RESULTS (LOWER IS BETTER)
Table Representative distortion results across missing data, noise, and phase shift experiments (in %). Lower
better.
Experiment
Time (1536)
FFT (1536)
Register (256)
30% Missing Data
8.3%
27.4%
4.6%
Noise Level r7 = 0.5
2.7%
6.8%
2.5%
Phase Time Shift
1300%
21 21%
12%
Table 4 summarises the key findings across the three controlled perturbation settings.
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Time embeddings (dimension 1536) exhibit very high distortion under phase/time shifts (130%), indicating strong temporal sensitivity. This confirms that temporal information preserved critical property for tasks that rely on timing cues, which are typically lost in purely spectral representations.
FFT embeddings (dimension 1536) show substantially lower distortion under phase shifts (21%), reflecting their ability to capture frequency characteristics while being relatively invariant to temporal alignment.
Compact semantic (register) embeddings (dimension 256) demonstrate the lowest distortion under phase shifts (12%). well the strongest robustness missing data and noise. This behaviour aligns with their intended role of encoding high-level structural abstractions. Additional sensitivity analyses and PCA visualisations are provided in Appendix A.4
Each embedding type therefore provides complementary strengths. Some datasets rely primarily on raw temporal dynamies, others on frequency characteristics, and some on high-level semantic summaries. TSLens attends jointly to all three embeddings, allowing the model to automatically emphasise the most informative view for given dataset.
Anomaly detection and imputation benefit primarily from time and FFT embeddings, which preserve fine-grained reconstruction details. Disentangled reconstruction across spaces enables triangulation, improving detection of anomaly types that may be missed by single-view models. In contrast, retrieval tasks benefit mainly from semantic embeddings, which provide compact summary-level representations.
By explicitly exposing disentangled embeddings, TSPulse enables flexible and effective transfer across diverse zero-shot tasks. The framework introduces disentanglement across both representa- tional spaces (time vs. FFT) and abstraction levels fine-grained vs. semantic), leading to double-digit performance gains across multiple benchmarks.
A.3.8 DETAILED RESULTS FOR EACH EXPERIMENT
All distortion values are reported in %. Lower is better.
Table 5: Distortion under varying levels of missing data (in %).
Embedding
11%
19%
30%
36%
70%
Time
3,8%
5.6%
8.3%
9.4%
23.1%
FFT
11.8%
18.9%
27.4%
32.6%
61.8%
Register 1.6%
2.8%
4.6%
5.7%
11.8%
As shown in Table 5 semantic embeddings consistently exhibit the lowest distortion across all masking levels, demonstrating strong robustness to missing observations. FFT embeddings are most affected, indicating higher sensitivity to partial signal removal.
Table Distortion under varying noise levels 7 (in %).
Embedding
0.1
0.25
1)
0.5
1)
0.75
Time
1%
1.4%
2.7%
4.3%
FFT
2.4%
4%
6.8%
11.7%
Register 0.8%
1.3%
2.5%
4.3%
Table further confirms that semantic embeddings maintain the strongest robustness additive noise, while FFT embeddings are more sensitive to spectral perturbations.
Finally, Table highhights the clear separation between representational roles: time embeddings highly phase-sensitive while FFT and semantic embeddings remain comparatively invariant. This confirms that disentanglement across representational spaces has been successfully achieved.
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Table 7: Distortion under varying phase shifts & (in %).
Embedding Φ
2nT
7T
Time
169%
163%
76%
FFT
24%
23%
19.6%
Register 13.6%
13.7%
10.5%
A.4 SENSITIVITY ANALYSIS OF TSPULSE SEMANTIC EMBEDDINGS
In this section, we study the behavior of the short register embeddings-i.e. zero-shot semantic embeddings- by TSPulse. These embeddings are designed to capture compact, meaningful representations of time-series patterns and are primarily used for retrieval and semantic similarity tasks. We perform detailed sensitivity analysis to understand how these embeddings respond when various properties of the input data are altered, including magnitude changes, added noise, missing values, time-shifts (i.e., phase variations), and changes frequency and patterns.
Ideally, we want the embeddings to remain invariant to factors such as noise, magnitude scaling, missing values, and temporal misalignments, while being highly responsive to core semantic char- acteristics like frequency patterns (e.g.. periodicity, seasonality) and distinctive shape structures in the data. Such behavior ensures robust semantic retrieval-retrieviing similar patterns despite distortions-whil preserving the ability to distinguish fundamentally different signal classes.
Sensitivity to magnitude scaling To assess whether the register embeddings capture only semanti- cally meaningful variations, we analyze their sensitivity to magnitdee/mpplttde scaling and compare it against their responses to frequency shifts. Frequency shift directly influences the structural se- mantics of time-series signals- such as periodicity-wheree irrelevant. This contrast allows us to quantify and appreciate the embedding's 's robustness to irrelevant perturbations. We generate a synthetic dataset using sinusoidal signals with three distinct frequencies, and we apply a linear amplitude scaling factor sampled uniformly from the range [1, 25]. We then extract register embeddings for each scaled variant and analyze their variation in the embedding space.
magnitude scale changes are often
Our results in Figure Sa show that while register embeddings vary noticeably across different frequencies, they remain very stable under magnitude scaling. For this analysis, extract the TSPulse register embedding for each data point, along with its associated scaling factor and frequency label. PCA projections reveal that the intra-cluster variation caused by amplitude scaling is small compared to the inter-cluster separation induced by frequency differences. This indicates that the embeddings largely invariant to amplitude, essential property for semantic retrieval tasks, where magnitude often varies due to normalization, sensor artifacts, or contextual shifts. By maintaining sensitivity to core signal properties such as frequency while suppressing irrelevant variations like scale, the model yields robust and meaningful representations suitable for retrieval.
Sensitivity noise We evaluate the impact of additive noise on the register embeddings by analyzing how noise-induced variations compare to those caused by changes in frequency. Synthetic sine wave signals are generated with distinct frequency groups, and Gaussian noise is added to simulate varying signal-to-noise ratios. Embeddings extracted for each noisy signal, and their spatial variation is analyzed using intra-group and inter-group distances. Intra-group variation reflects sensitivity to noise, while inter-group separation captures the embedding's 's response frequency changes. As shown in Figures 8bb, the impact of noise on the embeddings is minimal compared to the clear separation observed across different frequencies. This highlights the robustness of TSPulse embeddings to noise-as an essential property for maintaining semantic consistency in real-world applications where signal degradation to noise is common.
Sensitivity to time shifts (phase variations) To assess the sensitivity of register embeddings to phase (i.e. time-shift) variations, we conduct a control experiment using synthetic signals the form sin(frr + c) + e, where f {3, 3.2. 3.5) represents the frequency, denotes the phase shift (i.e., time-shift), and e is Gaussian noise. We change the phase c continuously from - - to æ to simulate temporal misalignments commonly seen in real-world indexed data.
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c. (sin(frxx + E)
sin(frix) + C.N(O, 1)
0.10
1.25
f=2
1.00
f=
1.0
0.75
(Regisserr
PCy(Registerg)
0.50
0.5
0.25
0.00
0.0
-0.50
5=5
Fw 5.4
-0.5
f= 5,4
0.002
0.00
-2
4
(Re(Riiste
(C,(Registerg)
(a) Sensitivity to Magnitude Scaling: PCA of regis- ter embeddings with three distinct frequency groups, colored by amplitude scale factor (c). The embeddings remain compact across scale variations.
(b) Sensitivity Noise: PCA register embeddings for noisy sine waves with three distinct frequency groups, colored by noise factor (c). Embedding vari- ation due noise is small compared to frequeney- induced separation.
Figure 8: Scatter plots of the first two PCA components of 7SPulse register embeddings under (a) amplitude scaling and (b) additive Gaussian noise. Each setup contains three distinct frequency-baset groups (f (5, 5.2,5.4)) 5.4)). The colour the scatter plot indicates the value of the variable indicated by the corresponding equation.
sin(fnx +
+
x + sin(3nx) +
f=322
2
(Regiittt)))
-1
PC, (
1.5
3.5
3.0.0
1.0
--
D.5
-2
-2
4
-2
2
PC₁ (Registers)
PCy(Registera)
(a) Sensitivity to Phase Shifts: PCA projections of (b) Sensitivity Trends: PCA projections of the register embeddings of phase shifted instances register embeddings of data with varying trend. with three distinct frequencies.
Figure 9: Data patterns in register embedding space. The colour in the seatter plot indicates the value of the variable indicated by the corresponding equation. The control experiment reveals, register embeddings are strongly sensitive to data trend and frequency and relatively less sensitive to phase (time shift).
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This setup emulates practical scenarios in semantic time-series search, where the same underlying pattern may be indexed at different time offsets in a database. In such cases, time shift invariant embeddings enable robust retrieval, ensuring semantically similar signals matched even with minor time shifts. Conversely, sensitivity to frequency is desirable, as frequency often encodes core data characteristics such seasonality periodic structure. Thus, heing able to distinguish small frequency differences allows the model to separate fundamentally different patterns more effectively.
PCA on register embeddings shows variations in frequency lead to significantly larger shifts in the embedding space compared to phase changes. The first two PCA components reveal tight, well-separated clusters corresponding to each frequency, while phase shifts produce only minor within-cluster variation (Figure Pa). This confirms that the embeddings are relatively less sensitive to phase shifts while remaining distinctly responsive frequency variations an ideal characteristic for robust semantic search.
Sensitivity to data trend Here, we investigate how the register embedding models data trends. To carry out the control experiment with synthetic data with functional form xx sin(3 + By varying the variable c, we generate different monotonic trend patterns in the data. We continuously varied the data trend parameter (c) from 0 to 2.5. Where 0 means no data trend, while 2.0 represents a quadratic pattern in the input data. The PCA analysis of the register embeddings shows that it distinctly models the monotonic data trend.
Sensitivity to shape space In these experiments, analyse the sensitivity of the embedding space to changes in the function shape, compared to frequency and phase change. For these experiment we use three distinct data generating functions, of the form F (z) sin(x), F22 = 2 (sin(1) + (1) and F3 = * + (in())) + (Figure 10). Fach of these functions is periodic and trigonometric. We generate dataset using these three generating functions. For each generating function, sample data with three distinct frequency groups f = {5, 5.2, 5.4]. for each frequency we generate synthetic data by randomly sampling phase between (- T). We carry out PCA analysis the register embedding of this dataset (Figure [T]. The analysis reveals the frequency groups form distinct clusters. Frequency clusters from same generating function are closer compared clusters from different generating function.
sin(fix)
(sin(/mx)
2-(Sin/frx)
100
200
500
100
200
400
500
100
400
500
Figure 10: Data generated from the three synthetic data generator functions with varying frequencies.
Sensitivity to missing values To assess the robustness of register embeddings to missing data, we generate synthetic signals using the function sin (cxæ), where the frequency parameter is uniformly sampled from the range [1, 15). Missing values are simulated by applying block masks of fixed patch length (pl = 8) to the input sequence, and we vary the mask ratio to control the extent of missingness.
We extract register embeddings under different masking levels and project them using PCA. As shown in Figure 12, the embedding space remains highly stable and preserves the underlying frequency- based structure even when up to 35% of the input data missingness. Distortion in the embedding manifold is observed only at very high mask ratios, where a majority of the signal is occluded. These results demonstrate that TSPulse embeddings very robust to moderate levels of missing data- valuable property in real-world time-series applications where sensor dropouts and irregular sampling common.
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ACrr () +
1..
10.
Ax-= (In
PCylReyister))
0.5
0.0
100 sinja)
#M (sink) +1 -1
5.0
PCy(Register)
Figure 11: Sensitivity shape: Cluster analysis register embedding of the data with three distinct function class. The cluster corresponding to the respective generator function is annotated in the figure. The colour represents the frequency associated with the data point (c). The strong separation between the embeddings of the data instances from different generator functions indicates that register embedding distinguishes the data instances by their shapes.
19%
36%
70%
(CInopptoo))
16
35
in
1o (GJ(Regster))
20
IGGjRegster,]
PGWReggtter
PGg(Regleerr)
PCG[Register]
Figure 12: Sensitivity to missing values: First two principal components computed register embeddings. with varying mask ratio applied to the input data. The colour indicates the frequency the synthetic data point. The plot indicates register embedding is fairly robust missing data.
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A.5
NOTATION DETAILS
In this section, we detail the notations used in the architecture for clarity, Table has the notation summary.
Symbol
Description
Sequence length
C
Number of input channels
pl
Patch length
D
Feature dimension
M E RixA
Mask token
X RSxC
Multivariate time series input
X E RSxC
Masked time series
X E R
Masked and scaled input time series
X RoxNxpl
Transposed and patched X.. Normalized frequency domain ground truth signal
X BSXC
X e RS/2x
Normalized frequency probability
ground truth signal
X/, E RSxc
Normalized frequency masked signal
domain
X RCxNxl
Transposed patched X!
Xymd E BFxc
Next-Point Ground Truth
length F
Time; E RCXNXD
Time-encoded features
FF E RCXNXD
Frequency-encoded features
Regg é RCXRXD
Learnable register tokens Concatenated input the backbone Output embedding from the backbone Output embeddings from the decoder Time domain signal reconstruction Frequency domain signal reconstruc- tion
Input,- [Timeg: FFT;; F e (Cx(N)+))
Backbone; E RCX(2N4RjDD
Decoderg e RCX(2N48)XD
Y E R
Y, E
Y' Y RSxC
Time domain signal reconstructed from frequency embedding
Y! E RS/2xC
Predicted frequency probability
Y pao E RFxx
Predicted Next Points of length
Table 8: Notation Summary
A.6 RELATED ART
A.6.1 DATASET-SPECIHE NEURAL ARCHITECTURES
Neural Architectures for Time-Series Forecasting Tasks Over the past few years, time-series forecasting has benefited significantly from advances in neural architectures, particularly with the adaptation of models from NLP and vision temporal data. Early breakthroughs came from transformer-based designs such as Informer (Zhou et al.) 2021). Autoformer (Wu et al.) 2021). and FEDFormer (Zhou et al., 2022), which extended attention mechanisms model long-range dependencies and seasonal- trend decomposition in time-series. Despite their success, these models were soon challenged by simpler alternatives. DLinear (Zeng al., 2022) revealed that with basic principles like per-channel modeling and time-series decomposition, linear model could match or surpass many transformer-based approaches. This raised important questions about the cemplexity-performaann
tradeoff in time-series modeling. A key turning point the introduction of PatchTST (Nie et al. 2023), which demonstrated that transformers could be highly effective when embeddings retrieved at the patch level instead of the time-poni level. This patching strategy not only preserved local semantics and improved scalability, but also re-established the superiority of transformers across multiple benchmarks.
To overcome the computational burden of transformers, new lightweight models began to emerge. TSMixer (Ekambaram et al. 2023), built upon the MI.P-Mixer (Tolstikhin et al. 2021) paradigm,
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replaced attention with feedforward mixing operations, achieving competitive performance with significantly reduced memory and latency. Similarly. iTransformer (Liu et al., (024) introduced attention mechanisms over the variate (feature) dimension rather than the temporal axis, enabling better generalization across multivariate inputs. TimeMixer (Wang et al.) 2024) leveraged multi-scale mixer blocks to simultaneously capture short- and long-term dynamics, while TimesNet (Wu et al.) 2022) incorporated an inception-style architecture to disentangle intra- and inter-period patterns, enhancing its ability model complex seasonal behaviors.
These developments highlight a growing diversity in time-series modeling strategies- from heavy transformers to fast feedforward mixers-eeee offering a different balance of accuracy, interpretability. and efficiency. However, these innovations have predominantly focused on time series forecasting tasks.
Unsupervised Representation Learning for Time-Series Diagnostic Tasks Learning meaningful representations from unlabeled time-series is foundational step for many downstream diagnostic tasks, including classification, retrieval, imputation, and anomaly detection. Contrastive learning has emerged as a dominant strategy in this space. Temporal Neighborhood Coding (TNC) (Tonek- aboni et al.] 2021) introduced a local context-aware contrastive learning framework that defines neighborhoods over smoothed signals, pushing representations of nearby time segments closer while distinguishing distant ones. TS2Vec (Yue et al., 2022) extended this idea by contrasting hierarchical segments both temporally and across instances, achieving robust scale-invariant em- beddings. T-Rep (Fraikin et al. (2024) focused on interpretability by encoding temporal attributes like trends and periodicity explicitly in the representation. BTSF (Yang & Hong 2022) proposed joint time-frequency contrastive approach, fusing insights from both domains to learn rich, dis- criminative embeddings. TimeDRI. (Chang et al., 2024) proposed disentangled representation learning framework that separately captures timestamp-leve level and instance-level embeddings, yielding improved performance across five classification and six forecasting datasets. TF-C (Zhang et al. 2022) introduced a method that encourages entangled representations by aligning temporal and spectral embeddings within the representation space. TF-C was evaluated under both one-to-one and one-to-many transfer learning settings. While these methods demonstrate strong performance, they typically rely on compact architectures trained individually per dataset. Consequently, their malability-ppariculuaa in scenarios involving pretraining large corpora and evaluation across extensive test retmanns unestablished. Moreover, contrastive approaches, though effective, face inherent scalability limitations due to their reliance on contrastive sampling. The quadratic growth in pairwise comparisons not only increases computational overhead but also hinders generalization across diverse domains.
A.6.2 TIME-SERIES PRE-TRAINED MODELS
Inspired by advances in pre-trained models from language and vision domains, the time-series community has begun exploring large-scale pre-trained models capable of generalizing across datasets and tasks. These time-series pre-trained models are typically trained using self-supervised objectives such as masked reconstruction (particularly suited for TS diagnostic tasks) or forecasting on millions of sequences (more suited for TS forecasting tasks).
Transformer-Baset TS Pre-trained Models Several high-capacity models have been introduced with a focus on either task specialization or general-purpose transfer. In task-specialized models for forecasting, Chronos (Ansari et al. 2024), TimesFM (Das al. 2023). and Moirai (Woo et al. 2024) represent key milestones. Chronos adopts a T5-style encoder-decoder trained on discretized sequences for forecasting, while TimesFM uses an autoregressive decoder with fixed-length patch tokens. Moirai leverages an encoder-only design with multi-scale patches and outputs probabilistic distributions, supporting multivariate forecasting with high fidelity. task-specialized models for classification, VQShape (Wen et al.] 2024) offers state-of-the-ar results with interpretabilty as they convert time-series in to sequence of meaningful and interpretable tokens. Generalist models such as Moment (Goswami et al.) 2024), GPT4TS (Zhou et al. 2023), and UniTS (Gao et al., (024) expand support to a wider set of tasks like classification, anomaly detection, and imputation. Moment employs masked reconstruction using a T5 encoder, while GPT4TS reuses frozen GPT2 backbone with -psc-fie heads. UniTS introduces prompt and task tokens and replaces attention with inear layers (dynamic operators) for efficient inference.
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Non-Transformer TS Pre-trained Models In parallel, compact TS pre-trained models have emerged to challenge the notion that larger is always better. TinyTimeMixer (TTM) (Ekambaram et al. 2024) exemplifies this category by using TSMixer architecture trained forecasting objectives. Despite having a minimal 1-5 M parameters, it delivers competitive zero/few-shot forecasting, showcasing the potential of compact FMs. However, TTM is primarily tailored for forecasting, and there is growing interest in extending this compact modeling paradigm to a broader range of downstream diagnostic tasks-including anomaly detection, classification, and wwputation-where efficiency remains an open challenge.
In summary, while contrastive and supervised representation learning methods are typically compact and effective, they are often trained separately on each dataset and lack transferability across domains. In contrast, TS pre-trained models offer strong generalization by pre-training on large, diverse corpora-but but at the cost of significantly higher model complexity and computational demands. The ongoing challenge is to combine the generalization of pre-trained models with the compactness and efficiency of specialized architectures- an area where models like TSPulse seek to make impactful strides.
A.7 BASELINE METHIODOLOGIES
Refer to Table 9 for an overview of the methodologies used to report the baseline results. We either report the results directly from the associated papers or run their official/popular implementation to get the results.
Task Anomaly
Model
Results Derivation
Reference (Code/Paper)
Detection
All SOTA Models
Reported in
Liu & Paparrizos
2024
TSB-AD-Leaderaoed
MOMENT
Reported in
Goswami at,
2024
MOMENT
VQShupe
Official Implementatonn Official Implementation
VQShape
UniTS
Unr
Classification
T-Rep
Reported in
(Faikin et al
2024
1-Kop
TS2Vec
Reported
Yuc
152
TNC
Reported in
Yue et al
1S2
TS-TOC
Reported
TTue et
1S2Vec
T-Loss
Reported in
Prainceshh ot
2019
1-1.055
MOMENT
Offiiaal Implemeniation
MOMENT
UniTT
Oflicial Implemeniation
Statistical
Implementation
MOMEETT
Imputation
TimesNer
Officaal Implementation
Time-Neres- Library
FEDforeer
Implemeutation
Timic-Srress-Lloee
Non-Stat. Transformer
Implementation
Time-Neres Labrary
MOMENT
Ofiicial Impleemeniation
MOMENT
Search
Chronos
Official Implementation
Chronos
Table Summary of Baselines used in this work across different tasks
A.8 PRE-TRAINING DATASETS
Pre-training utilizes subset of ~ IB time points drawn from the Monash (Godahewa et al. 2021
and LibCity (Wag et al. 2021 I Woo et al. 2024) data collections. We leverage the same pre-training data as used in (Ekambaram | 2024) for training our models. For Monash, we select subset of datasets from the Monash Time Series Forecasting Repository (Godahewa et al.) 2021]. For LibCity, incorporated the data from the source locations. The complete list of datasets employed for pre-training is provided in Table TO All datasets used are selected under permissive licenses that allow both open-source and commercial use.
A.9 MODEL DETAILS
The default pre-training configuration for TSPulse is as follows: context length (S) 512, patch length (p/)= 8, stride pl. hidden feature size D =0 3xpl, dropout = 0.2, head dropout 0.2, number of backbone layers (L) = 8, number of decoder layers = 2, masking strategy = hybrid masking, training epochs 20, and gated attention activation function softmax. During pre-training, the backbone and the decoder are both operated in hhannel-indeeenden approach, i..., channel- mixing is not activated in the TSMixer modules.
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Origin
Duta Source
Temporal Granularity
wind sec
DRS
4-sec, 15-min, 30-min, Hourly
wind farms minutely dataset (no missing) + DRS
Min, 10-min, min, 30-min, Hourly
us births dataset
Daily
solar 10 minutes dataset DRS
10-min, 30-min, Hourly
australian electricity derand dataset DRS
30 min, Hourly, Daily
kaggle web traffic dataset (no missing)
Daily
nn5 daily datasct (no missing)
Daily
Monash
solar see dataset DRS
4-sec,
15-min, 30-min, Hourly
saugeenday dataset
Daily
sunspot dataset (no missing)
Daily
kdd cup 2018 dataset (no missing)
Hourly
bitcoin dataset (no missing)
Daily
london
datasct missing) DRS
30-min, Hourly, Daily
australian weather dataset
Daily
PEMS 103,04,07, [08] DRS
S-min. 10-min, 15-mnin, 30-min, Hourly
LibCity
PEMS BAY DRS
5-min, 10-min, min, 30-min, Hourly
LOS LOOP DRS
5-min, 10-min, 15-min, 30-min, Houry
Table 10: Pre-training Datasets for TSPulse.
We leverage the same pre- training data used in Ekambaram al. (202)) training our models. Entries annotated with DRS" reflect the application Diversity Resolution Sampling strategy to derive versions at different lower temporal resolutions, as proposed in [kkambarm ct al. (2024). All pre-training datascts are strictly disjoint from evaluation sets. For example, austra an electricity demand dataset and austral rariian weather dataset unrelated to the standard ECL and Weather datasets used in the evaluation tasks.
Motivated by the success of lightweight, task-specialized pre-trained models in the language do- main (Schick & Schütze 2020 Nguyen et al. (2244, Fu et al. [023) Ling al. [022] which achieve strong performance through minimal task-specific adaptations- we extend this strategy to TSPulse via head reweighting during pretraining. We offer flexibility in pretraining: either by assigning equal weight to all heads or by specializing the pretraining through reweighting loss objectives to prioritize heads most relevant to the target task. Specifically, for aask-specialized pre-training, we adjust the head usage and weighting as follows: (i) For anomaly detection, all heads are retained and assigned equal loss weights to facilitate triangulation across time, frequency, and prediction perspectives. (ii) For tasks such imputation, classification, and retrieval, we emphasize Headeime and Head,ign by assigning them higher weights, while nown-weighting or pruning the remaining heads to reduce task- irrelevant complexity. This enables TSPulse refine task-specific representations while maintaining its lightweight design, facilitating efficient transfer learning across any dataset for the specified task.
Additionally, based on our validation analysis, we observe that for classification tasks overall performance improves when using a longer patch size (pl = 16) with full patch/block masking during pre-training. This reflects an important insight: while block masking tends to hurt performance in realistic imputation settings (where masking follows irregular patterns patch point impute). it is beneficial for classification, where the objective to learn strong semantic embeddings the patch level. Block masking introduces more challenging pre- traininiing conditions, helping the model extract more meaningful patch representations.
Thus, TSPulse adopts hybrid masking for all reconstruction-orien oriented tasks (imputation, anomaly detection, retrieval) and block masking specifically for Cassification-orienter pre-training. Pre- training one model per task does not pose any practical issues with TSPulse, its pretraining is extremely fast and efficient. We can pre-train model on the full 1B samples in just one day using 8xA100 GPUs, enabling rapid training of task- auskispecal models with ease. We use 8-32 A100 GPUs for rapidly pre- pre-traine training these task-specialized models. For more details on the used evaluation datasets, hyperparameter optimization and train/valid/test split ratios, refer to the associated downstream task sections in the Appendix.
A. FFT EXTRACTION DETAILS
Since TSPulse performs masked reconstruction in both time and frequency domains, first extract masked FFT features for processing by the backbone and prepare the corresponding ground-truth targets for loss computation.
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The input time-series X RSC is scaled and masking is applied in the time domain, resulting in the scaled, masked version Xm. Importantly, we avoid explicitly masking the frequency space. Instead, directly feed the scaled, masked time-series X into the Fast Fourier Transform (FFT) via the function torch. fft. rfft (PyTorch Contributors, 2025). This operation transforms the time-domain signal into the frequency domain. By using the masked input, the transformation naturally propagates the masking into the frequency space, meaning that the same data is masked both in the time and frequency domains, making the reconstruction task more challenging. This step is critical for ensuring that information leakage does not occur between the two domains.
The FFT operation produces a complex-valued tensor of shape R(S/2)+IXC where each element contains both real and imaginary component. This represents the signal in the frequency domain, capturing both amplitude and phase information for each frequency bin. To maintain consistency in the output dimensions and to simplify further processing, we discard the last frequency bin, reducing the tensor shape to S/2xC
Next, we normalize the real and imaginary components separately for each channel by dividing them by their respective maximum absolute values. This step ensures that both components are within a comparable scale, preventing issues related to uneven amplitude distributions across channels. After normalization, the real and imaginary components are concatenated together form the masked requenccydomaal features X E R This tensor is then ready for further processing by the backbone, ensuring that it is compatible with the expected input shape and aligns with the time-domain features.
We now compute two separate ground-trute from the frequency representation of the input. These ground-trutie serve as targets for the reconstruction tasks during training.
First, we apply the same FFT transformation to the unmasked input, yielding the frequency-domain ground-truth truth representation X E S&C, This serves as the clean, unaltered frequency representation of the time-series, which will be used to guide the model's ' reconstruction.
To create the second ground-truthe truth, we compute the -oggaain spectrum of the frequency rep- resentation X', excluding the DC component (the first frequency bin, which represents the mean signal). The log-magnitude spectrum is computed as:
(VRe(XT) + Im(X/)²
log-magnitude ( = =log
where Re(X)) and Im(X/) represent the real and imaginary parts of the FFT output, respectively. The log transformation reduces the dynamic range of the frequency values, making the learning process more stable and preventing potential issues caused by extreme values in the frequency domain.
After computing the log-magnitude spectrum, apply softmax across the frequency bins for each channel. This produces X S/22xC normalized global frequency signature. The softmax operation converts the frequency magnitudes into probability-like distribution, emphasizing the dominant spectral components. This normalized frequency signature serves as an auxiliary reconstruction target, encouraging the model learn the most significant global patterns in the frequency domain.
The two ground-truth targets-X X/ (the raw frequency-domain representation) and Sign (the normal- ized global frequency signature) are used during training for the reconstruction task. The first target guides the model in recovering the original frequency representation, while the second target helps the model learn high-level semantic patterns that enhance its generalization to downstream tasks, such as classification or anomaly detection.
A.11 TIME SERIES ANOMALY DETECTION
A.11.1 BASICS
Model-based time-series anomaly detection (AD) leverages predictive models such as TSPulse to identify anomalous regions within sequence. Any significant deviation between the model's
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prediction (Y R) and the actual observed sequence (X R) is interpreted as a process deviation and quantified as an anomaly score, denoted by a. These scores reflect the degree of divergence and serve as indicators of potential anomalies, particularly when they represent out-of- distribution behavior.
The anomaly score is computed by aggregating the prediction enror defined temporal window, referred to as the aggregation window, w, using Equation 4 as shown below.
-+w-1 Σ -
ar.r+ (X. Y)
(4)
WC
Therefore, a smaller window size (w) more effective for detecting point anomalies, whereas larger window size is better suited for identifying range anomalies.
A.11.2 IMPLEMENTATION DETAILS OF MULTI-HEAD TRIANGULATION
TSPulse utilizes both time and frequency representations of time series, and produces multiple prediction outputs, each output either utilizes a specific data representation for data reconstruction or next point prediction. While the reconstruction task relies on estimating data distribution, the prediction task focuses on data evolution. Hence, errors in the reconstruction or prediction tasks can potentially indicate different types of anomalies. We leverage multiple output streams from TSPulse (Headeize: Headget. and Headprea) derive different anomaly scoring mechanisms:
1. Headeime The first AD score is generated using the time reconstruction head of TSPulse. Following the notation of Equation the score can be expressed as, time 5- Here, w < S, i.e., the aggregation window size smaller than the context length of the TSPulse, and the last w points from the TSPulse's reconstruction are utilized to calculate the aggregated error. The resulting error is assigned as the anomaly score the time point the center of the aggregation window, and this process is repeated with stride of one.
2. Headfst:
Similarly, this AD score utilizes the FFT reconstruction head of TSPulse, and can be expressed as m 333-:5-1-
3. Headgres: Following the existing pre-trained forecasting models in TSB-AD leader- board (Liu & Paparrizos) 2024) like Chronos and TimesFM, we utilize the first time point in the forecast horizon coming out of the prediction head of TSPulse to caleu- late the forecast error, and assign it to that particular time point as the anomaly score: pred (Xred, Y preed) ?/ Σド= (AXpedls.s (prddss)) 0s
4. Headensemble In this scoring mechanism, temporally align the above three scores, and generate an ensemble score for every time point by computing the maximum of the three scores.
A.11.3 TSB-AD LEADERBOARD
Datasets The TSB-AD leaderboard (Liu & Paparrizos) 2024) features a comprehensive collection of 1,070 time series drawn from 40 diverse datasets, all curated and annotated by human experts. stands one of the most recent and extensive benchmarks for anomaly detection (AD) in time series data.
The leaderboard is divided into two tracks:
TSB-AD-U: Univariate time series anomaly detection,
TSB-AD-M: Multivariate time series anomaly detection.
Each dataset contains one or more time series. To ensure fair evaluation, the data is split into distinct subsets. For detailed information on the data splits (evaluation and tuning), refer to Figure 3 in Liu & Paparrizos 2024).. Here, we provide a brief summary:
Evaluation Data: The TSB-AD-U and TSB-AD-M benchmarks contain 350 and 180 time series for evaluation, respectively. Their average anomaly ratios are 4.5% 5.5% and 5%.
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A short, anomaly-free (hence, unlabeled) historical segment from each evaluation time-series is provided for optional model training or fine-tume ane-tuning. For TSPulse (FT), we utilize a fraction (20%) of this training data as validation data to perform early stopping.
Small Training Data:
Tuning Data: A set of time-series different from the evaluation series are kept aside for tuning hyperparameter optimization (HPO). All the models can leverage this tuning data and labels for finding optimal hyperparameters. A total of 48 and 20 time-series are kept for tuning for univariate and multivariate benchmarks, respectively.
Models and Workflows The TSB-AD leaderboard supports two primary workflows for anomaly detection:
Unsupervised AD: Models are applied directly in zero-shot setting to the evaluation data to generate anomaly scores. TSPulse se (ZS) falls into this category.
Sent-SSupervisee/SerSSSSerrrrrre AD: Models are trained or fine-tuned using the small, anomaly-free training segment before being evaluated. Note that no labels are available for the training. TSPulse (FT) falls into this category.
In both workflows, models are allowed to use the tuning data (with labels) for hyperparameter optimization.
The leaderboard currently reports results for 40 models across both the univariate and multivariate benchmarks, categorized into three broad sets: statistical (mostly unsupervised), neural networks (mostly self-suuprvised),, and pre-trained/foundatio models (both unsupervised and self-supervised).
HPO for TSPulse As mentioned briefly above, the TSB-AD leaderboard (Liu & Paparrizos 2024) provides separate tuning datasets for univariate (TSB-AD-U) and multivariate (TSB-AD-M) benchmarks. All the algorithms (including zero-shot and fine-tuned/trained models) leverage the tuning dataset for hyperparameter tuning. First, we employ the tuning data to find an optimal value of the aggregation window size, w, for the two reconstruction-bart and ft. From set of three candidate values (64, 96, 128). we find the optimal value, w" 96, following zero-shot VUS-PR scores obtained in the tuning datasets. Next, we utilize the tuning data for selecting the optimal scoring mechanism for each dataset. For each setting (univariate or multivariate), perform zero-shot inference of the TSPulse the tuning data and generate the VUS-PR PR metrics for all four scoring mechanisms as stated above. Now, for each dataset, we choose the best scoring mechanism for that dataset (see Table [[aand Table [2). This is performed only once with the zero-shot workflow of TSPulse, and the selection is utilized in both zero-shot and fine-tuned workflows of TSPulse.
scoring mechanisms, atimme
A.11.4 FULL RESULTS TABLES
Table 13 shows the full version of Figure 4 containing all algorithms. VUS-PR scores for all methods except TSPulse are directly taken from Liu & Paparrizos (2024). Table 14 and Table 15 show the dataset-wiss average VUS-PR scores of TSPulse along with SOTA algorithms.
A.12 CLASSIFICATION
We evaluate TSPulse on the UEA Multivariate Time Series Classification Archive (Bagnall et al. 2018), a widely used benchmark for multivariate time-series classification tasks. Table [ the key statistics of the datasets. TSPulse is designed with a base input context length of 512. To accommodate sequences of arbitrary lengths both shorter and longer- we apply interpolation using torch. nn. functitn cnal. interpolate (PyTorch Contributors 2025) to bring them to the base context length 512. Our framework supports up to 20x interpolation, enabling the model to process sequences long as 10,000 time steps, which is sufficient for most real-world applications. Based on this context scaling capability, we benchmark TSPulse on 29 diverse UEA datasets. Importantly, none of the UEA datasets included in the TSPulse pre-training corpus.
Since the UEA archive does not provide predefined validation splits, we randomly sample 10% of the training data get tuning validation set. We use the cross-entropy loss the primary
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Dataset
Best TSPulse Output
Exathlon
Headgru
IOPS
Headcine
LTDB
Headrru
Dataset
Best TSPulse Output
MGAB
Headpred
MITDB
Headerseable
CATSv2
Headpred
MSL
Headrime
Exathlon
Headrtt
NAB
Headersemble
GHL
Headr
NEK
Headerseable
LTDB
Headcime
OPPORTUNITY
Headerseeble
MITDB
Headensemble
SED
Headpred
MSL
Headeime
SMAP
Headeime
OPPORTUNITY
Head
SMD
Headeft
SMAP
Headensemble
SVDB
Headrrt
SMD
Headensemble
Stock
Headpred
SVDB
Headret
TAO
Headpred
TAO
Headpred
TODS
Headgime
UCR
Headeime
Table Best TSPulse output head as detected
WSD
Headersemble
Tuning dataset for multivariate AD benchmark.
YAHOO
Headpzed
Table Best TSPulse output head as detected on Tuning dataset for univariate AD benchmark.
metric for performing Hyperparameter Optimization (HPO). The HPO conducted based on the performance on the validation data, tuning the following parameters: TSLens projection size D' or 2), mask ratio (0.3 or None), channel expansion factor (1 2), and head activation function (softmax or sigmoid). When mask ratio is enabled, block masking is applied during fine-tuning but disabled during evaluation improve generalization and reduce overfitting. The default decoder configuration uses the mix-channel mode, which works effectively for most realistic channel counts (up to several hundred channels). In extreme cases where the number of channels is exceptionally high (c.g., DuckDuckGrese dataset with 1000+ channels), avg-pooling for computational efficiency, as the size channel-mixer blocks scales proportionally with the number of channels. Additionally, given the very large channel count but extremely limited number of training samples in DuckDuckGeese, we employ k-fold cross-validation for this instance for improved stability. In general, the batch size and number of epochs chosen from predefined pool set based on the scale of the training samples to prevent out-of- error and enable faster fine-tuning.
disable mix-channel and revert simple
We benchmark TSPulse on classification against a broad set of baselines, including recent pre- praitrained models (MOMENT (Goswami et al.) (2024). VOShape (Wen et al.) 2024). UniTS (Gao al. 2024) and data- Sata-specific methods (T-Rep (Fraikin et al. 2024), TS2Vec Yue et al. (022), TNC (Tonekaboni al. 2021). T-Loss (Franceschi et al.) 2019). TS-TCC (Eldele al.] (021)). As detailed in the Table we either report the results directly from the paper run their official implementation. Specifically, for UniTS, we adopt the prompt-tuned (PMT) approach proposed in Gao al. (2024), applying to the available pretrained model across all 29 datasets in multi-task setting and report the resulting accuracy. The overall classification results, including comparisons against basclines, are presented in Table 17 and detailed ablation studies shown in Table 18
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Method
VUS. PR
TSPalse (FT)
0.52
TSPalse (ZS)
0.48
Suh-PCA
0.42
KShupeAD
0.40
Method
VUS-PR
POLY
0.39
TSPulse (FT)
0.39
Series2Graph
TSPulse (ZS)
0.36
MOMENT (FT)
0.39
MOMENT (2S)
0,38
Omminnnomlly
0.31
KMeansAD
0.37
PCA
0.31
USAD
0.36
I.STMAD
0.31
Sub-KNN
0.35
MatrixProfile
0.35
USAD
AutoEnncoeer
0.30
KMeansAD
0.29
CNN
0.34
CBLOF
0.27
LSTMAD
0.33
MCD
SR
0.32
OCSVM
0.26
TimesFM
Donut
0.26
Forest
0.30
RobustPCA
OmniAnomaly
0.29
FITS
0.21
Lag-Llama
0.27
OFA
0.21
Chronos
0.27
EIF
0.21
TimesNet
0.26
COPOD
AutoEncoder
0,26
IForest
0.20
TranAD
HBOS
0.19
FITS
0.26
TimesNet
Sub LOF
0,25
KNN
OFA
0.24
TmaAD
0.18
Sub-MCD
Sub-HBOS
0,23
LOF
0.
Anomaly Transformer
Sub-OCSVM
0,23
Sub-IForest
0.22
Donut
0.20
(b) TSB-AD-A
LOF
0.17
AnomalyTramee Transformrr
0.12
(a) TSB-AD-U
Table 13: Anomaly Detection Full Table. VUS-PR metric (Higher is better) averaged across all time series across all datasets for all available algorithms in the TSB-AD leaderabord.
A.13 IMPUTATION
Dataset We evaluate TSPulse and several baseline methods on six real-world datasets from the LTSF benchmark suite (Wu 2021 ETTh1, ETTh2, ETTml, ETTm2, Weather, and Electricity, We use context length = 512, stride = and the same train/valide waiin/said/test split ratio as proposed in Wu al. 2021).
We assess model performance under two masking regimes: block masking and hybrid masking, defined as follows:
Masking Strategies
This setup simulates scenarios like sensor failures maintenance intervals, where data is missing in contiguous segments. Specifically, blocks of 8 consecutive time- points (i.e. full patch) are masked and must be reconstructed by the model.
Block Masking:
To reflect more realistic settings, this scheme introduces both structured and unstructured missingness. Half of the missing points occur in full-length patches (8- point blocks), while the other half are scattered randomly across the sequence. This design captures mix of localized and irregular masking patterns.
Hybrid Masking:
To evaluate the effectiveness of TSPulse under both masking setups, benchmark it against a diverse set of baselines categorized as follows:
Baselines
Zero-Shot / Prompt-Tuned / Statistical: We include two recent pre-trained mod- 100-MOMENT (large) (Goswami et al., 2024) and UniTS (Gao et al.) 2024). MOMENT is evaluated in pure zero-shot manner, consistent with TSPulse. UniTS is prompt-tuned using
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AMPORTTON CONETNNTTY
Tuwer
SWS
SABOO
Method
TSPike (PT)
0:40
01:4
0.53
0.11
0.22
0.0
0.51
0.58
008
908
0.00
1024
0.30
11:6
0.00
0.98
100
0.68
11.8
11:1
KShagoAD
Sub- PCA
0.26
0.25
0.84
0.33
0.09
0.33
6.2
0.09
0.36
0.55
0.37
0.3
0.33
0.39
0.89
0.00
0.53
0.58
0.15
0.45
033
0,43
0.75
0.91
0.03
0.75
0.54
0.58
0.10
935
POLLY
0.35
0:51
0.54
0.1
0.5
0:11
8.5
0.44
0.00
0.4
061
6.00
0.2
0.11
8.5
0.41
0.3
Serpo
0.31
0.19
0.2
6/00
024
0.4
011
0:00
013
535
646
6:2
6.39
091
0.2
0.28
013
053
0.29
007
092
625
023
600
MOMENT
0.30
0.52
0.04
0954
0.56
0.45
KMamAD
0.33
0.04
0.41
0.06
0.49
681
0.27
0.48
0.35
0.20
0.30
0.90
0.00
065
0.18
0.44
6.00
0.79
0.0
0.65
0.58
0.10
0.5
USAD
0140
0.12
0.89
0.15
0.55
0.00
0.18
0.2
0.28
0.25
0.67
806
0.00
021
008
023
637
0.05
6.0
0.53
0.06
0.84
0.00
Sch- KNN
0.39
011
0.4
0.10
0.58
0.14
0:36
0:1
0.29
112
0:30
9:31
0.77
051
M1
6.0
0.35
0/6
027
6.10
0.11
Mantchootle
0.73
047
615
0.70
CSN
0.32
0.40
061
0.26
0.2
0.1
0.15
0.33
0.19
0.73
0.40
D086
0.06
0.34
0.55
021
0.65
0.92
100
0.54
0.05
0.24
0.55
LSSTAAD>
0.35
8:13
0.7
0.30
8.9
0.0
1.12
0.3
0.18
1033
0:38
8:06
0.5
0.49
1111
6AT
0.8
100
041
6.11
0.5
0.38
0:20
0.2
0.01
0.1
620
050
0:31
8:10
810
0.2
6.6
6.35
1.00
100
0.4
800
TiasEM
0.25
0.0
0.06
022
0.25
0.15
039
0,0
099
0.55
0,07
OmniAmeddy
0.12
0.16
0.83
0.30
0.3
6.00
0.10
0.25
0.89
085
0.60
0.07
0.06
0.15
0.36
0.09
0.62
0.6
0.44
0.08
0.14
0.19
Leg Lian
0.31
0.39
0.53
0.22
0.2
0.00
1108
031
0.15
033
0.35
006
1.07
0.2
0.36
0.0
0.09
0.50
0.9
0.61
000
0.2
068
Chroos
0.30
0.31
0.45
0.18
0.56
0.00
8.06
0.88
0.28
1124
000
D06
0.19
0.5
0.14
0.99
100
0.70
0.15
0.80
Tinz/Nai
0.10
0.39
0.00
0.08
03:
6.20
003
968
0.66
0.38
0,99
6:11
0.79
091
0.59
0.00
ThEAD
0.06
0.13
0.18
0.00
1100
0.18
0.38
0.13
0.16
094
0.45
0100
PITS
0.17
0:33
0.55
1.17
0.5
0.00
0.36
0.24
1149
007
000
0447
0.5
11
6.50
0.76
091
0.16
800
6114
011
Sab-LOF
0.31
0.04
0.25
0,11
0.34
044
0.36
0:35
0.22
0.5
0.12
0.14
0.22
640
0.04
0.18
6.11
0.76
0.02
0.53
0.29
0m
0227
OFS
0.16
0.36
0.30
0,0
0.07
0.9
6.21
0.00
0.33
045
0.11
0.76
091
0.54
0.02
Sab-IROS
0.06
009
0.45
0.08
0.00
0.12
0.25
0.50
025
0.8
0.54
0.10
0.34
0.70
091
0.64
0.16
0.11
0.66
SED-OCSVMI
0.36
0.66
0.29
0.07
0.33
0.11
0.14
0.2
0.26
0.25
0.11
9.36
0.06
0.51
008
0.3
0.99
0.73
082
0.65
0.18
0,3
0.33
Sub- iRoest
0.06
0.07
0.49
0.04
0.66
0.00
0.34
0.36
0.30
0.2
007
0.2
0.79
0,4
0.09
0.2
0.13
0,00
0.00
0.66
0.10
0.0
0.06
0.06
0.06
0:31
0,89
0:18
0.99
0:31
0.78
091
0.68
6.11
LOF
0.06
0.14
0.46
Table 14: VUS-PR score (Higher is better) averaged over all time series for each dataset for univariate anomaly detection. Note that every dataset has one or more time series, and the mean scores reported in Figure(4a) 4a in the main text and Table [3 above are averaged over all 350 "Eval" time series (similar to the TSB-AD-U lcaderboard). This table can be compared with the dataset-wise 6 Liu & Paparrizos (2024).
OPPORTUNTTY AATTT
CATS<2
CreditCard
Duphaet
Exathlon
GECCO
GHL
Genesis
LTDB
MITTIN
MSL
PSM
SMAP
SMD
SVDE
TAO
Method
TSPulse (IT)
0.00
0.35
0.91
0.02
0.14
0.21
0.07
0.32
0.36
0.47
0.93
TSPulsc (ZS)
0.05
0.00
0.35
0.89
0.17
0.01
0.01
0,36
0.07
0.20
0.07
0.14
0.30
0.35
0.38
0.13
0.95
CNN
0.08
0.02
0.21
0.68
0.03
0.02
0.10
0.33
0.14
0.35
0.16
0.22
0.19
0.35
0.41
1.00
OronAnnmmaly
0.04
0.02
0.34
0.84
0.02
0.07
0.00
0.44
0.11
0.22
0.18
0.16
0.12
0.17
0.35
0.15
0.81
PCA
0.12
0.10
0.13
0.95
0.20
0.01
0.02
0.24
0.07
0.15
0.30
0.16
0.09
0.36
0.11
0.45
1.00
LSTMAD
0.04
0.02
0.31
0.82
0.02
0.06
0.04
0.30
0.09
0,12
0.17
0.24
0.24
0.16
0.33
0.15
0.16
0.99
USAD
0.02
0.34
0.02
0.06
0.00
0.41
0.12
0,23
0.18
0.19
0.11
0.16
0.32
0.15
0.81
AutoEncoder
0.06
0.03
0.13
0.91
0.05
0.05
0.01
0.21
0.04
0.22
0.14
0.28
0.13
0.30
0.06
0.58
1.00
KMeansAD
0.12
0.02
0.30
0.37
0.06
0,03
0.89
0.41
0.06
0,44
0.06
0.21
0.38
0.36
0.20
0.16
0.86
CBLOF
0.03
0,10
0.86
0.02
0.02
0.04
0,21
0.14
0.19
0.14
0.22
0.07
1.00
MCD
0.13
0.06
0.14
0.80
0.03
0.01
0.06
0.21
0.04
0.23
0.17
0.26
0.10
0.26
0.07
0.54
1.00
OCSVM
0.08
0.02
0.06
0.83
0.04
0,04
0.08
0.20
0.04
0,22
0.12
0.19
0.12
0.28
0.06
0.44
0.81
0.02
0.17
0.05
0.18
0.12
0.30
0.15
0.18
0.19
0.11
0.75
RobosICA
0.04
0.02
0.06
0.77
0.02
0.03
0.00
0.23
0.04
0.22
0.13
0.12
0.07
0.10
0.08
0.12
1.00
FITS
0.13
0.02
0.33
0.63
0.03
0,01
0,10
0.23
0.05
0,17
0.05
0.13
0.08
0.17
0.10
0.15
0.78
OFA
0.13
0.02
0.31
0.58
0.04
0.01
0.22
0.29
0.06
0.14
0.05
0.17
0.08
0.17
0.12
0.12
0.78
EIF
0.06
0.02
0.15
0.41
0.04
0.02
0.06
0.19
0.04
0.18
0,10
0.18
0.13
0.32
0.07
0.32
0.89
COPOD
0.05
0.05
0,11
0.40
0.04
0.03
0.08
0.21
0.04
0,21
0.17
0.20
0.10
0.19
0.07
0.31
0.99
Porest
0.05
0.03
0.13
0.35
0.04
0.05
0.08
0.21
0.04
0.21
0.18
0.19
0.09
0.26
0.07
0.39
0.95
HBOS
0.05
0.04
0.15
0.32
0.04
0.04
0.08
0,21
0.04
0.23
0.17
0.17
0.09
0.25
0.07
0.30
0.85
TimesNet
0.07
0.02
0.27
0.42
0.03
0.01
0.02
0.27
0.07
0,17
0.06
0.14
0.09
0.14
0.11
0.14
0.79
KNN
0.02
0.25
0.91
0.04
0.19
0.04
0.18
0.06
0.12
0.30
0.06
0.11
0.78
TranAD
0.04
0.02
0.31
0.10
0.02
0.06
0.04
0.26
0.07
0.24
0.16
0.23
0.09
0.30
0.12
0.15
0.81
LOF
0.05
0.02
0.11
0.16
0.13
0.01
0.08
0.19
0.04
0,14
0.10
0.15
0.09
0.16
0.06
0.15
0.79
AnomalyTransformet
0.02
0.07
0.10
0.02
0.03
0.01
0.05
0.12
0.07
0.06
0.07
0.08
0.18
0.77
Table 15: VUS-PR score (Higher is better) averaged over all time series for each dataset for multivariate anomaly detection. Note that every dataset has one or more time series, and the mean scores reported in Figure in the main text and Table [3 above averaged over all 180 "Eval" time series (similar to the TSB-AD-M leaderboard). This table can be compared with the tataset-wise Table-7 of & Paparrizos (2024)
32

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Published as a conference paper at ICLR 2026
ID
Dataset
of (Train, Test Samples
Classes
[Length, Channels)
1
Articulary WordRecognition
{275, 300}
25
{144, 9]
AtrialFibrillation
[15, 15]
[640, 2]
3
BasicMotions
[40, 40]
4
[100, 6]
Cricket
1108, 72]
12
{1197,
5
Epilepsy
[137, 138
4
{206, 3]
EthanolConcentrattion
{261, 263
(1751,
7
ERing
[30, 30]
6
[65,4]
8
FingerMovements
(316, 100)
2
(50, 28)
9
HandMovvemnntireetionn
[320, 147]
4
(400, 10)
10
Handwriting
[150, 850)
26
(152,3)
11
Japanese Vowels
{270, 370]
9
[29, 12)
12
Libras
{180, 180)
15
[45,
13
LSST
(2459, 2466)
14
[36, 6)
14
MotorImagery
{278, 100)
2
(3000, 64)
15
NATOPS
[180, 180)
[51,
16
RacketSports
[151, 152]
4
[30. 6)
17
SeIfRegulattonSCCP
{268, 2931
1896, 6]
18
SelfRegulationSCCP2
{200, 180]
2
(1152, 71
19
SpokenArrabiDDigits
(6599, 2199)
10
[93, 13)
20
StandWalkJump
{12, 15]
3
(2500, 4]
21
UWaveGisturreL.brreg
(120, 320)
8
(315.3)
22
PEMS-SF
(267, 173]
7
(144, 963]
23
Phoneme
(3315, 3353)
39
{217,
24
PenDigits
(7494, 3498)
10
(8,
25
Heartbeat
{204, 205
2
{405, 61)
26
FaceDetection
(5890, 3524)
2
(62, 144)
27
CharacterTrajectorie
(1422, 1436)
20
(182,
28
DuckDecGGeese
[60, 40)
(270, 1345)
29
Insect Lingbeting
[30000, 20000)
10
{78, 200)
Table 16: Summary of the UEA Multivariate Time Series Classification Archive (Bagnall et al. 2018
10% of the dataset (across all six benchmarks) in multi-task setting, as per the original implementation.
MOMENT Setup: For block masking, missing patches are replaced with the learned mask token the embedding space, following Goswami al. (2024). In hybrid masking, adopt mixed approach-using the mask token for fully missing 8-point patches and zeros for the irregularly missing points. This Heterogeneous strategy consistently outperformed the simpler Only-zeros strategy (where all missing points are zeroed out) for MOMENT, as detailed in Table
UniTS Setup: We similarly compare Heterogeneous and Only-zeros masking strategies. likely due prompt tuning
For UniTS, the Only-zeros approach yielded better results fiilts---kklly 10% of the data, allowing the model to better adapt to uniformly zero-masked inputs than to mix of learned tokens and zeros. Full ablations shown in Table [5]
Note: TSPulse uses single learnable raw-level mask patch, enabling uniformly handle both block and hybrid masking without requiring masking strategy-spech speccffc adjustments. In addition to these pre-trained models, we evaluate four classical interpolation methods:
Naive, Linear, Nearest, and Cubic.
Fine-Tuned Supervised:
We include fully supervised baselines Tetesseet (Wu al. 2022), Non-Stationary Transformer (Non-Stat.) (Liu et al.) (2022). and FEDformer (Zhou et 2022 trained end-to-end on the complete datasets individually. These are compared against the fine-tuned variant of TSPulse (TSPulse-FT)).
Results Figure and Figure 1 summarizes TSPulse's imputation performance across all six datasets and masking ratios under hybrid and block masking setups respectively. Detailed per-dataset results averaged over four mask ratios are presented Table [9 Complete breakdowns for each dataset and ratio provided in Table 20 (hybrid masking) and Table 21 (block masking).
33

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Published as a conference paper at ICLR 2026
Dataset
se
VQShape
MOMENT
UniTS
1
T T-Rep
TS2
T.L
NC
TS-TCC
Articulary WordRecognition
0.98
0,987
0.99
0.947
0.968
0.987
0.943
0.973
0.953
AtriaFFibiilltiion
0.467
0.52
0.2
0.2
0.354
0.2
0.133
0.133
0.267
BusicMotions
1.0
0.885
1.0
0.8
1.0
0.975
1.0
0.975
1.0
CharacterTrajectoriis
0.987
0.962
0.964
0.968
0.989
0.995
0.993
0.967
0.985
Cricket
0.917
0.975
0.986
0.958
0.958
0.972
0.972
0.958
0.917
DuckDuckGcess
0.72
0.344
0.26
0.457
0.68
0.65
0.46
0.38
ERing
0,937
0.947
0.959
0.841
0.943
0.874
0.133
0.852
0,904
Epilepsy
0,971
0.755
0.993
0.949
0.97
0.964
0.971
0.957
0.957
EthanolConcentratiin
0.247
0,306
0.357
0.266
0.333
0,308
0.205
0.297
0.285
FaceDetection
0.675
0.653
0.633
0.569
0,581
0,501
0.513
0.536
0.544
FingerMovements
0.53
0.616
0.49
0.53
0.495
0,48
0.58
0.47
0.46
Danddoovemenniirretionn
0.649
0.514
0.324
0.284
0.536
0.338
0.351
0.324
0.243
Handwriting
0.215
0.266
0,308
0.149
0.414
0.515
0.451
0.249
0.498
Hcartbeat
0,702
0,632
0.722
0.61
0.725
0.683
0.741
0.746
0.75
Insect Wingbeat
0,723
NA
0.246
0.484
0.328
0.466
0,156
0.469
0,264
Japanese Vowels
0,976
0.941
0,716
0.851
0,962
0,984
0.989
0.978
0.93
LSST
0,518
0.511
0.411
0.467
0.526
0,537
0.509
0.599
0.474
Libras
0.767
0.808
0.85
0.756
0.829
0.867
0.817
0.822
Motorlmagery
0.58
0.638
0.5
0.49
0.495
0.51
0.58
0.5
0.61
NATOPS
0,878
0.804
0.828
0.75
0.804
0.928
0.917
0,911
0.822
PEMS-SF
0.855
0.85
0.896
0.855
0.8
0.682
0.676
0.699
0.734
PenDigits
0,969
0.973
0,972
0.956
0.971
0,989
0.981
0.979
0.974
PhonemeSpectra
0.156
0.087
0,233
0.173
0.232
0,233
0.222
0.207
0.252
RacketSports
0.901
0.838
0.796
0.697
0.883
0.855
0.855
0.776
0.816
SellRegulatioSCPP
0.836
0.889
0.84
0.823
0.819
0.812
0.843
0.799
0.823
SellRegulationSCP2
0.511
0,586
0.478
0.556
0.591
0.578
0.539
0.55
0,533
Spoken
0.984
0.976
0.981
0.957
0.994
0.988
0.905
0.934
0.97
StandWalkJump
0.733
0.707
0.4
0.4
0,441
0.467
0.333
0.4
0.333
UWaveGestureLibbrayy
0.881
0.879
0.909
0.85
0.885
0.906
0.875
0.759
0.753
Mean
0.733
0,701
0.675
0.634
0.699
0.699
0.652
0.665
0.664
IMP(%)
5%
9%
16%
5%
12%
10%
10%
Table 17: Classification accuracy results (Higher is better) on UEA datasets. We report both the mean accuracy and the IMP (h)-thc percentage improvement of TSPulse over cach baseline in terms of mean accuracy. On the InsectWingbeat dataset, VQShape encountered large data volume dataset. However, for averaging purposes, we substitute the best-performing baseline result in place of VQShape to maintain consistency in the overall mean accuracy comparison. For CharacterTrapie Trajectories dataset we used the official implementation of MOMENT get the results.
out-of-memory (OOM) error due the relatively large model size. Accordingly, the VQShape result is reported as NA for this
w/o Short w/o Long
w/o
w/o CM
w/o Channel w/ TSLens
w/o TSLens
w/o
Data
TSPulse
Emb
Emb
Mask
Identity Init
Expansion
Avg-Pool)
(Max Puol)
Dual-space
Articulary WordRccogniiion
0.98
0.973
0.963
0.983
0.973
0.987
0.973
0.953
0.98
AtrialFinrillaioon
0.467
0.267
0.333
0.333
0.333
0.467
0.333
0.333
0.467
BasicMotions
1.0
1.0
0.975
1.0
0.975
0.975
0.975
0.875
Cricket
0.917
0.944
0.917
0.944
0.944
0.931
0.972
0.986
0.944
FRing
0.937
0.922
0.889
0.919
0.922
0.937
0.837
0.848
0.915
Epilepsy
0.971
0.986
0.942
0.978
0.964
0.971
0.957
0.899
0.949
EthanolConcentration
0.247
0,262
0.247
0.262
0.251
0.259
0.319
0.243
0,266
FingerMovements
0.53
0.52
0.54
0.51
0.57
0.52
0.46
0.48
HandMoovementDireetion
0.649
0.486
0.486
0.351
0.527
0.649
0.473
0.351
0.473
Handwriting
0.215
0.189
0.055
0.215
0.199
0.026
0.034
0.182
0.175
Japanese Vowels
0.976
0.976
0.97
0.968
0.959
0.981
0.968
0.719
0.97
Motorlmagery
0.58
0.47
0.52
0.58
0.52
0.58
0.47
0.47
0.49
NATOPS
0.878
0.817
0.861
0.861
0.811
0.878
0.894
0.778
0.872
RacketSports
0.901
0.816
0,803
0.783
0.829
0.842
0.842
0.809
0.803
SelfRegulationSCCP
0.836
0.802
0.829
0.836
0.853
0.836
0.867
0.816
0.853
StandWallJump
0.733
0.4
0.4
0.333
0.133
0.733
0.267
0.333
UWaveGesture
0.881
0.878
0.847
0.891
0.875
0.9
0,825
0.859
0.866
Mean
0.747
0.689
0.681
0.691
0.685
0.734
0.675
0.645
0.696
IMP )
8%
10%
8%
9
2%
11%
16%
7%
Table Classification Ablation study (Higher is better). We report both the mean accuracy and IMP (%) the percentage improvement of TSPulse over each dropped component in terms of the mean accuracy.
As shown in Table 2 removing dual-space reconstruction (i.e. using only time space and ignoring FFT space) during pre-training results a consistent 8% drop in zero-shot imputation accuracy for hybrid mask set-up. Furthermore, when pre-training is done with only block
Ablation study
34

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Published as a conference paper at ICLR 2026
0.560
0.55
0.545
81%
0.316
90%
MSE
0.3
66%
0.196
0.2
0.176
46%
0.106
40%
0.098
0.107
0.052
47%
51%
340 M
M
0.0
TSPulse (ZS)
Units (PMT)
MOMENT
Naive
Linear
TSPulse (FT)
Non-Stat.
TimesNet
FEDformer
Zero.Shottroomptiuneltttttt
FineTuneed/Sperriseed
Figure 13: Block Masking imputation MSE results (lower is better). Averaged across 6 LTSF benchmark datasets (Wu al. 2021: ETTh1, ETTh2, ETTml, ETTm2, Weather, and Electricity, under 4 mask ratios (12.5%, 25%. 37.5%. 50%)
masking (i.e w/o Hybrid pre-training). model suffers a drastic 79% drop hybrid-masked settings, where missingness is irregular and more reflective of real- world scenarios. This sharp contrast underscores the critical role
during pre-training for achieving robust, generalizable imputation across diverse masking patterns.
Block Masking
Hybrid Masking
FTSUPP
ZS/PM17/tatistica
FI7SUP
TSP
UTS
TSP
Non-
TSP
UTS
TSP
Non-
Dataset
MNT
Naive
Lin.
TNT
FED
Naive
Lin.
TNT
Zs
PMT
FT
Stat.
ZS PMT
FT
Stat.
Th
0.238
01284 00.00
0.660
0.088
0.1
1.
0.163
0.269
0.437 0.675 0.346
0.346
0.060 0.
0.
ETTh2
0.095 0.239 0.1
0.228
0.140
0.058
0.1
0.114
1.124
0.070
0.254
0.302
155 0.093
0.093
0.085 0.629
ETTml
0.094 0.195 0.224
0.437
0.157
0.035
0.076
0.098
0.335
0.057 0.172 0.270 0.197 0.070
0.0553
0.059
ET
0.054 0.132 0.082
0.062
0.052
0.060
0.037
0.1 0.247 0.070 0.039
0.023
0.422
Weather
0.056 0.078 0.081
0.107
0.062
0.040
0.060
0.056
0.229
0.039
0.072 0.107 0.071 0.042
0.034
0.045
0.044
0.132
Electricity
0.097 0.126 0.252
1.371
0.797
0.060
0. 114
0.126 0.271
0.077
0.
0.293 0.808 0.378
0.049
0.4
0. 1.1 0.236
Mean
0.106 0.176 0.19
0.560
0.3
0.052
0.098
O. 107 0,545
0.074
0.170
0.2 0.276 0.329 0,161
0.039
0.076
0.08 0.314
% IMI. of
40%
46%
81
66%
56%
73%
78%
54%
TSP zs
% IMP. of TSP
47%
51%
90%
49%
51%
88%
Table 19: Imputation Result (MSE, Lower is better): Hybrid and Block masking setup averaged across all 4 mask ratios. Lowest MSE score across models is highlighted in Bold and second lowest MSE score is underlined.
Abbreviations: FT: Finetuned, PMT Prompt_Tumme SUP Supervised, 7S Zeroshot, TSP: TSPulse, MNT: MOMENT, UTS UniTS, TNT: TimesNet, Lin. Linear Interpolation, Non-Stat. Nonn-Staionnary Transformer.
FED: FEDformer. Refer to Table 20
and and Table 21 for detailed results
A. SIMILARITY SEARCH
We evaluate the zero-shot similarity search capabilities of TSPulse, using its short register embeddings (i.e. zero-shot semantic embeddings) to identify time-series segments that share similar patterns with given query, even under noise. Such similarity search is valuable in practical time-series analysis, where retrieving similar patterns from historical data is often essential for interpretability and post-diagnostics- example, understanding the context of detected anomaly performing root-cause analysis by matching query patterns to historical logs.
distortions such as time shifts, magnitude changes, and additive
This task is particularly challenging because time-series data typically long and stored short windows using high-stride sliding windows to reduce indexing memory. This leads to the same underlying pattern appearing different positions across windows making exact alignment between query and index samples unlikely. Thus, models must learn robust and distortion invariant embeddings enable effective retrieval.
35

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Published as a conference paper at ICLR 2026
Zeroshot/Prompt
Tuned/Statisical
Finetuned/Supervieed
Datasel
MR
TSPulse
UniTS
MOMENT
Naive
Linear
Nearest
Cubic
TSPulse
Non-Stationary Transformer
TimesNel
FED-
(PMT)
former
0.125
0,146
0.220
0.324
0.608
0.284
0.388
0.491
0.042
0.089
0.098
0.180
0.250
0.155
0.250
0.387
0.648
0.321
0.425
0.618
0.051
0.113
0.120
0.241
BTTh
0.375
0.168
0.287
0.468
0.696
0.365
0.471
0.791
0.065
0.135
0.127
0.298
0.500
0.183
0.319
0.568
0.749
0.414
0.525
1.011
0.081
0.156
0.169
0.358
Mean
0.163
0.269
0.437
00.655
0.346
0.452
[0.728]
0.060
0.123
0.129
0.2669
0.125
0.065
0.151
0.132
0.143
0.084
0.114
0.296
0.041
0.081
0.071
0.375
0.250
0.068
0.199
0.202
0.150
0.090
0.119
0.358
0.043
0.088
0.080
0.553
ETTh2
0.375
0.072
0.300
0.332
0.159
0.095
0.124
0,430
0.047
0.097
0.088
0.716
0.500
0,077
0.364
0.542
0.169
0.103
0.132
0.505
0.053
0.104
0.100
0.873
Mcan
0.070
0.254
0.302
0.155
0.093
0.122
|0.397|
0.046
0.093
0.085
0.629
0.125
0.049
0.123
0.156
0.154
0.056
0.091
0.173
0.018
0.040
0.048
0.109
ETTml
0.250
0.053
0.156
0.218
0.179
0.064
0.101
0.210
0.022
0.048
0.058
0.169
0.375
0.058
0.187
0,299
0.209
0.073
0.114
0.254
0.026
0,057
0.061
0.225
0.500
0.066
0.222
0,407
0.248
0.086
0.131
0.305
0.031
0.067
0.070
0.275
Mean
0.057
0.172
0.270
0.197
0.070
0.109
|0.235|
0.024
0.053
0.059
0.195
0.125
0.034
0.096
0.085
0.063
0.036
0.049
00.115
0.020
0.035
0.036
0.214
0.250
0.036
0.092
0.149
0.067
0.038
0.052
0.139
0.022
0.039
0.038
0.353
ETTm2
0.375
0.038
0.126
0,272
0.072
0.040
0.055
0.171
0.024
0.042
0.041
0.492
0.500
0.041
0.172
0.480
0.079
0.044
0.058
0.207
0.026
0.047
0.045
0.628
Mean
0.037
0.122
0.247
0.070
0.039
0.054
|0.158]
0.023
0.041
0.040
0.422
0.125
0.036
0.059
0.069
0.065
0.038
0.053
10.131
0.036
0,040
0.039
0.076
Weather
0.250
0.038
0.070
0.086
0.068
0.040
0.055
0.163
0.033
0,043
0.042
0.106
0.375
0.040
0.074
0.115
0.072
0.043
0.057
0.190
0.033
0.045
0.046
0.148
0.500
0.042
0.085
0.158
0.0780
0.046
0.060
0.228
0.035
0.050
0.048
0.198
Mcan
0.039
0.072
0,107
0.071
0.042
0.056
[0.178|
0.034
0.045
0.044
0.132
0.125
0.070
0.109
0,181
0,712
0.289
0.417
00.43||
0.043
0,100
0.120
0.213
0.250
0.074
0.3
0.235
0.773
0.344
0.468
0.573
0.047
0.102
0.123
0.229
Electricity
0.375
0.078
0.136
0.317
0.837
0.405
0.528
0.755
0.050
0.105
0.122
0.244
0,500
0.085
0.151
0.439
0.910
0.475
0.601
1 1.008
0.054
0.107
0.124
0.259
Mean
0.077
0.130
0.293
0.808
0.378
0.504
[0.693|
0.049
0.104
0.122
| 0.236
Table 20: Full Imputation Results (MSE, Lower is better): Hybrid Masking setup. Lowest MSE score indicated in Bold and second lowest MSE score is Underlined
Datasets We construct two benchmark datasets-one synthetic and one real-world, which are indexed for retrieval:
Synthetic Dataset: We begin with 8 distinct base patterns (see Table 27) and form 56 unique combinations by pairing them through addition and multiplication operations (s x 2). Each combination is then varied by a frequency parameter augmentations- 1% Gaussian noise and 1% magnitude scaling- resulting in three variants per time-series. This process yields total of 56 10 3- 1,680 indexed time-series segments.
1, ...., 10. Light -aeggg--re-aae are applied to each sample,
We use the UCR Archive (Chen et al. 2015), which consists of 128 time- series classification datasets. For each class in each dataset, we randomly sample 10 time-series segments of length 512. The datasets with fewer than 10 samples in a class are excluded. This results in total of 5,960 indexed time-series segments.
Real Dataset:
Query Generation To construct the query sets, we apply stronger augmentations to the indexed samples to simulate real-world distortions and test the robustness of the learned embeddings. Specifi- cally, each query is created by applying a combination of:
within +20% random time shift,
within +00 random scaling transformation, and
Gaussian noise with standard deviation of 10% magnitude of the scaled time-series data.
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Zeroshot/Prompt Tuned/Statistial
Finetumed/Supervieed
UniTS
Von-Staliinary Transformer
FED-
Dataset
MR
TSPulse
MOMENT Naive
Linear
Nearest
Cubic
TSPulse
TimesNel
(PMT)
former
0.125
0.209
0.239
0.302
1.035 0.530
0.645
1.100
0.055
0.115
0.138
0.264
0.250
0.225
0.269
0.355
1,092 0.633
0.760
1819
0.070
0.156
0.157
0.377
ETTh
0.375
0.246
0.299
0.430
1.131
0.729
0.875
2.978
0.098
0.192
0.201
0.469
0.500
0.272
0.331
0.518
1.165
0.816
0.987
5.101
0.129
0.234
0.263
0.554
Mean]
0.238
0.284
0.401
1.106
0.677
0.817
|2.749|
0.088
0.174
0.19
0.416
0.125|
0.081
0.150
0.105
0.201
00.177
0.147
0.640
0.050
0.093
0.089
0.556
0.250
0.088
0.195
0.121
0.218
0.132
0.163
0.997
0.055
1.9
0.104
0.948
ETTh2
0.375
0.098
0.250
0.142
0.235
0.148
0.182
1.640
0.059
0.121
0.123
1.320
0.500
0.113
0.360
0.168
0.255
0.165
0.202
2.871
0.068
0.136
0.140
1.673
|can|
0.095
0.239
0.134
0.228
0.140
0.173
|.537]
0.058
0.115
0.114
1.124
0.1125
0.068
0.137
0.133
0.279
0.088
0.140
0.373
0.023
0.047
0.060
0.181
ETTml
0.250
0.081
0.175
0.179
0.369
0.120
0.181
0.595
0.028
0.062
0.082
0,280
0.375
0,100
0.206
0.246
0,480
0.170
0.238
0.976
0.038
0.085
0.106
0.384
0.500
0.128
0.262
0.339
0.620
0.248
0.325
1.732
0.052
0.107
0.146
0.493
Mean
0.094
0.195
0.224
0.437
0.157
0.221
[0.919|
0.035
0.076
0.098
0.335
0.125
0.046
0.099
0.061
0.092
0.051
0,066
0.251
0.022
0.041
0.046
0.448
0.250
0.050
0.113
0.072
0.104
0.057
0.074
0.393
0.027
0.047
0.057
0.712
ETTm2
0.375
0.056
0.138
0.088
0.119
0.065
0.083
0.630
0.030
0.055
0.068
1.015
0.500
0.065
0.179
0.108
0.139
0.076
0.096
1.094
0.039
0.064
0.070
1.404
|Man]
0.054
0.132
0.082
0.113
0.062
0.080
[0.592
0.030
0.052
0.060
0.895
0.125
0.048
0.065
0.063
0.090
0.053
0.068
0.288
0.034
0.051
0.046
0.133
0.250
0,053
0.075
0.072
0.099
0.058
0,074
0.447
0.038
0.056
0.052
0.197
Weather
0.375
0.058
0.081
0.086
0.112
0.065
0.082
0.731
0.042
0.062
0.057
0,262
0.500
0.066
0.093
0.103
0.128
0.074
0.093
1.219
0.047
0.073
0.067
0.324
Mcan|
0.056
0.078
0.081
0.107
0.062
0.079
[0.669
0.04
0.060
0
0.229
0.115|
0.084
0.110
0.159
1.257
0.571
0,718
1.018
0.053
0.110
0.121
0.238
0.250
0.090
0.121
0.197
1,351
0.732
0.880
1.741
0.057
0.114
0.124
0.262
Electricity
0.375
0.100
0.131
0.264
1.416
0.878
1.050
2.924
0.062
0.114
0.128
0.283
0.5
0.115
0.141
0.388
1.46
1.005
1.212
5.008
0.068
0.118
0.131
0.302
[Mean|
0.097
0.126
0.252
1,371
0.797
0.965
[2.673|
0.060
0.114
0.126
0.271
Table 21: Full Imputation Results (MSE, Lower is better): Block-wise masking setup. Lowest MSE score indicated in Bold and second lowest MSE score is Underlined
Model Variant
MSE ()) IMP(%)
Irregular Hybrid Masking Eval
TSPulse
0.074
w/o Dual-Space
0.081
8% 4
w/o Hybrid Pretraining
0.354
79% $
Regular Block Masking Eval
TSPulse
0.106
w/o Dual-Space
0.115
8% $
w/o Hybrid Pretraining
0.098
7.5% 1
Table 22: Imputation-Ablation Study Summary, MSE, Lower is better. Detailed results in Table 23
This setup serves two purposes: (i) it evaluates whether embeddings are invariant to temporal misalignment and other distortions and (ii) allows for automatic ground- -otudhtruuhhh labeling since each query is derived from known indexed sample. The same augmentation strategy is applied to both the synthetic and real datasets, ensuring a consistent evaluation framework. These challenging augmentations make the retrieval task more realistic and better reflect practical use cases in time-series analysis.
Tasks We define two types of retrieval tasks evaluate semantic similarity different levels:
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Block Masking
Hybrid Masking
TSPulse w/o S
TSPulse
TSPulse
TSPulse
TSPulse
TSPulse
w/o Hybrid Pre-training w/o Dual-Space
w/o Hybrid Pre-training
ETThl
0.251
0.238
0.220
0.173
0.163
0.539
ETTh2
0.099
0.095
0.091
0.074
0.070
ETTml
0.105
0.094
0.088
0.063
0.057
0.485
ETTm2
0.056
0.054
0.053
0.039
0.037
0.163
Weather
0.058
0,056
0,055
0.041
0.039
0.155
Electricity 0.120
0.097
0.083
0.094
0.077
0.552
Mcan 0.115
0.106
0.098
0.081
0.074
0.354
Table 23: Imputation Result (MSE, Lower is better): Block and Hybrid masking setup averaged across all different mask ratios different variants TSPulse. Lowest MSE score across variants highlighted Bold second lowest MSE score is Underlined. More Detailed results in Ta
Block Masking
Hybrid Masking
TSPulse Dual space
TSPulse
TSPulse
TSPulse
ISPulse
w/o Hybrid Pre-training w/o space
TSPulse
Hyhrid Pre-training
0.125
0.227
0.209
0.189
0.158
0,146
0.498
ETTbl
0.250
0.241
0.225
0,208
0.166
0.155
0.528
0,375
0.258
0.246
0.230
0,177
0.168
0,553
0.279
0.272
0.255
Mean
0.251
0.238
0.220
0.173
0.163
0.539
0.125
0.086
0.081
0.077
0.069
0.065
0.216
0,250
0.093
0.088
0.084
0.072
0.068
0.226
ETTh2
0,375
0.102
0,098
0.094
0.075
0.072
0.235
0,500
0.115
0.113
0.107
0.080
0.077
0.247
Mean
0.099
0.095
0.091
0.074
0.070
0.231
0.125
0.078
0.068
0.065
0.055
0.049
0.449
ETTml
0,250
0.091
0 081
0.076
0.060
0.053
0.470
0,500
0.139
0.128
0.119
0,072
0.066
0,526
Meun
0.105
0 0.094
0.088
0.063
0.057
0.485
0.048
0.044
0,250
0.052
0.050
0.049
0.037
0.036
0.159
ETTm2
0.375
0.058
0.056
0.055
0.040
0.038
0,166
0,500
0.067
0.065
0.063
0.042
0.041
0,174
0.056
0.054
0.053
0.125
0.051
0.048
0.048
0.038
0.036
0,146
Weather
0.250
0.055
0.053
0.051
0.039
0.038
0.151
0,375
0.060
0.058
0.057
0.042
0.040
0.157
0.067
Mean
0.058
0.056
0.055
0.041
0.039
0.1.5
0.125
0.105
0.084
0.069
0.085
0.070
0.488
Electricity
0,250
0.113
0.090
0.076
0.090
0.074
0.539
0.375
0.124
0. 0.100
0.086
0.096
0.078
0.575
0.500
0.188
0.115
0.102
0.104
0.085
0.607
Mean
0.120
0.097
0,083
0.094
0.077
0.552
Table 24: Full Imputation Results (MSE, Lower is better): Comparison of three variants of TSPulse (a) TSPulse w/o Dual Space: TSPulse model only pre-trained with time domain input (b) TSPulse TSPulse model pre-trained with both time and frequency patches (c) TSPulse w/o Hybrid Masking TSPulse model pre-trained with block masking
Family Match:
Measures coarse- searse-grained retrieval- -i..., finding samples with the same high-level structure. For synthetic data, each of the 56 pattern combinations defines class. For real data, each dataset name is treated as a class.
Fine-Grained Match: Measures fine-grained retrieval-ice. ic.. In synthetic data, each pattern- frequency combination (56 x 10 560) is treated as class. In real data, each (dataset name, class index) pair defines a unique class, totaling 596.
Implementation & Evaluation Metrics We compute semantic similarity using Euclidean distance between embeddings from the pre-trained models. We use the Faiss library (Douze et al.) 2024 to index embeddings. Performance is evaluated using standard retrieval metrics applied to the top-3 retrieved candidates:
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MOMENT
UnITS PMT
Dalasel Mask_Ratio
Neterugenous Only Zeros Feieeogeenous Only Zerus
0.125
0.324
0.315
0.220
0.220
0.250
0.387
0.391
0.251
0.250
ETThl
0.375
0.468
0.487
0.288
0.287
0.500
0.568
0.599
0.322
0.319
Mean
0.437
0.448
0.27
0.269
0.125
0.132
0.256
0.150
0.151
0.250
0.202
0.441
0.2111
0.199
ETTh2
0.375
0.332
0.649
0,326
0.300
0.500
0.542
0,939
0.371
0.364
Mean
0.302
0.571
0.264
0.254
0.125
0.156
0.173
0.123
0.123
0,250
0.218
0.251
0.156
ETTml
0.375
0.299
0.344
0.187
0.187
0.500
0.407
0,462
0,226
0.222
Mean
0.270
0.308
0.173
0.172
0.125
0.085
0.217
0.096
0.096
0.250
0.149
0,405
0.096
0.092
ETTm2
0.375
0.272
0.605
0.136
0.126
0.500
0,48
0.895
0.186
0.172
Mcan
0.247
0,530
0.129
0.122
0.125
0.069
0.090
0.059
0.059
0.25
0.086
0.124
0.070
0.070
Weather
0.375
0.115
0.166
0.075
0.074
0.500
0.158
0,223
0.087
0.085
Mean
0.107
0.151
0.073
0.072
0.125
0.181
0.189
0.110
0.109
0,250
0.235
0.252
0.124
0.123
Electricity
0.375
0.317
0.344
0.137
0.136
0.500
0.439
0.472
0.153
0.151
Mcan
0.293
0.314
0.131
0.130
Table Full Imputation Results (MSE, Lower is better): MOMENT & UniTS PMT hybrid setup. Heterogenous : Used the learned mask token to replace the fully missing patches and zeros at other missing positions, Only_Zeros: Using zeros as input to the model at every missing position.
PREC@3: Precision at top-3.
MRR @ 3: Mean Reciprocal Rank at top-3.
AP@3: Average Precision at top-3.
NDCG@* @3: Normalized Discounted Cumulative Gain at top-3.
We evaluate the inference time of each model. Specifically, we set the batch size to 1,024 and accumulate the forward computation time of the model over the dataset. The measured computation time is divided by the size of the dataset to derive the per-sample computation time.
Results Figure 7 presents comparative evaluation of TSPulse's similarity search performance against the zero-shot embeddings produced by two recent pre-trained models: MOMENT and Chronos. To ensure a fair and resource-efficient comparison, we use their smallest available variants, aligning closely with TSPulse in embedding dimensionality and enabling comparable indexing throughput.
As shown in the figure, TSPulse consistently outperforms both baselines across retrieval tasks. For the Family Match task, which assesses the model's ability to retrieve semantically similar patterns, TSPulse achieves over 25% higher accuracy than MOMENT. In the more challenging Fine-Grained Match task, which requires precise pattern localization, TSPulse demonstrates a 40% performance gain MOMENT. TSPulse also outperforms Chronos by +100% in both settings.
In addition to accuracy gains, TSPulse also offers substantial efficiency benefits. Its embeddings 2x smaller than those of MOMENT and Chronos, leading faster search and reduced memory
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overhead. In deployment benchmarks, TSPulse enables x0-100x faster inference CPU and 9-15x faster inference on GPU, owing to its lightweight architecture and low memory footprint. Importantly, TSPulse achieves these results while being over x0 smaller in model size, making it highly suitable for real-time, resource-constrainge environments.
Tables 28 and 29 summarize the scores of PREC@3, AP@3, NDCG@3, and MRR @3. The average scores In Table 28 are plotted in Figure 7
Impact of Different Model Configuration We conducted the experiments to investigate the impact of different model configurations, as summarized in the table below. Removing Hybrid pre-training (i.e.. using only block masking) results in 23.1% drop PREC@3 performance. Furthermore, excluding the register embeddings and relying solely on the Time or FFT embeddings leads to even greater reductions of 51.3% and 68.8%, respectively. These results emphasize the importance of both hybrid pre-training and register embeddings in achieving high retrieval accuracy.
Model Variant
PREC@3
MRR @
TSPulse
0.645
0.856
w/o Hybrid PT
0.496
23.1%
0.669
21.8%
w/o register (Time emb.)
0.314
51.3%
0.439
48.7%
w/o register (FFT emb.)
0.201
68.8%
0.274
68.0%
Table 26: Impact of Different Model Configuration
Robustness Augmentation Complexity To further evaluate the robustness of pre-trained models in the similarity search task, we systematically vary the intensity of augmentations used to generate the query samples. Specifically, we introduce scaling factor s E {0, 10, 20, 30, 40, 50), which controls the strength of three types of distortions: time shifts, magnitude scaling, and additive noise. For example, when s = 10, a 10% random temporal shift, 10% scaling perturbation, and 10% additive Gaussian noise applied to each query. The noise level is capped 10% across all values of to maintain a realistic noise regime, as extreme noise rarely dominates practical time-series settings.
The motivation behind increasing lies in simulating more challenging retrieval scenarios. In time- series data, even small time shifts or scaling changes can result in significantly different signal appearances, despite underlying similarity in semantics. By gradually increasing s, we create controlled framework to stress-test the distortion invariance of learned embeddings. The setting where corresponds
sanity check: since the query is identical to indexed sample, high retrieval score is expected from any well-trained model.
Figure 14 presents the retrieval performance of TSPulse, MOMENT, and Chronos across different augmentation levels. As expected, all models perform well at s = 0, but performance declines with increasing augmentation strength. Notably, TSPulse exhibits significantly greater resilience, main- taining higher scores across all values of s. Compared to MOMENT and Chronos, the performance of TSPulse degrades more slowly, demonstrating superior robustness to distortions in temporal align- ment, signal scaling, and additive noise. These results highlight the effectiveness of TSPulse's 's hybrid masking pre-training and register-token embeddings in capturing stable, semantically meaningful representations under realistic, noisy retrieval conditions.
A.15 UNIFIED PRE- TRE-TRAINED MODEL ACROSS MULTIPLE DOWNSTREAM TASKS
While the primary design of TSPulse adopts task-specialized pre-training to maximize downstream accuracy, we additionally evaluate a unified setting in which single pre-trained checkpoint used across all downstream tasks without task-specific specialization.
A. 15.1 EXPERIMENTAL SETUP
In this setting, select the pre- rre-trained variant originally optimized for imputation and retrieval/search tasks and directly evaluate on: (i) classification, (ii) anomaly detection (AD), (iii) search retrieval, and (iv) imputation.
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Base pattern name
Base pattern equation
sin
Ft sin(b:)
modcos
It cos(b;) sin (br (b//2)
square-modeos
= sign (sin (b:)
cos((2b))
gaussian-spike
Jt. = exp(-400 (- - f //2)²)
1 mod (t, 10f) =
impulse
Ft = 'o otherwise
randwalk
+ Σ =0=00 Ev'
sincos
It = sin(b;) (1)) cos + by)
tanhmix
It (3 b,)) 0.2s.
Table 27: Eight base patterns for synthetic data. b. 2xrt, /512, f = 0, 1, 1..... 511, sign the sign function, & is drawn from the standard Gaussian distribution, i.c., E ~ (00, 1), and mod is the modulo operation.
Family match
Fine Stne-grained match
PREC@3
MRR@33
P
MRR 60
Tspate
MOMENT
Cross
T
M
C
T
M
C
Real
0.645
0.389
0.116
0.856
0.491
0.144
0.474
0.216
0.057
0.750
0.335
0.087
Synth.
0.711
0.674
0.352
0.713
0.679
0.361
0.695
0.615
0.295
0.697
0.619
0.304
Avg. 0.678
0.532
0,234
0.784
0.585
0.252
0.584
0.415
0.176
0.723
0.477
0.195
Table 28: Similarity Search. PREC@3 and MRR@3 on Synthetic and Real data. Higher is better.
Thus, all four downstream tasks share single pre-trained backbone and checkpoint. This experiment isolates the impact of task specialization and evaluates the intrinsic generalization ability of the learned representation.
A.15.2 RESULTS
Table 30 summarizes the comparative performance between: (1) task-specialized TSPulse, (2) single unified TSPulse model (one checkpoint for all tasks), and (3) the best reported baseline per task. The single unified model remains highly competitive, typically ranking within the top one or two positions across tasks. This demonstrates that TSPulse maintains strong generalization even without task specialization. Enabling task-specific loss reweighting further yields additional strong performance gains.
A.16 ROBUSTNESS UNDER MAR AND MNAR MISSINGNESS PATTERNS
In this section, we further evaluate whether TSPulse remains robust under empirically grounded missingness patterns, including Missing At Random (MAR) and Missing Not At Random (MNAR) settings Rubin (1976). Before describing these experiments, we first clarify the motivation behind the hybrid masking design.
A.16.1 MOTIVATION: PRE-TRAINING MASK BIAS
While hybrid masking may appear to be a simple combination of point and block masking, its purpose is to address critical pre-truining mask bias present in existing imputation-oriented foundation models. Many prior approaches rely exclusively on fixed-length block masking during pre- pre-traniing.
As shown in Appendix Table 19 popular pretrained models perform well under fixed-length block masking and substantially outperform linear interpolation in that setting. However, when evaluated under irregular partially missing spans where only portion of a block is missing- the expected improvement (due to shorter gaps) does not occur. Instead, performance often degrades below that of linear interpolation.
Further investigation reveals that these models impute effectively primarily when the inference time missing-span length matches the mask length used during pre-training. Since real-worke missingness
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Family match
Fine Vine-grained match
AP@3
NDCG@3
AP@3
NDCG@3
TsPalec
MOMENT
Chasse
T
M
T
M
T
M
C
Real
0.619
0.366
0.105
0.683
0.403
0.118
0.447
0.195
0.050
0.525
0.234
0.061
Synth.
0.710
0.672
0.348
0.711
0.675
0.353
0.694
0.613
0.290
0.695
0.615
0.295
Avg.
0.664
0.519
0.226
0.697
0.539
0.235
0.570
0.404
0.170
0.610
0.425
0.178
Table 29: Similarity Search. A and NDCG@3 on Synthetic and Real data. Higher is better.
0.9
1.0
TSPulse MOMENT Chronos
TSPulse
0.8
MOMENT
Chronos
0.7
PREC@3
0.6
MRR@3
0.6
0.5
0.4
0.3
0.2
0%
10%
20%
30%
40%
50%
0%
10%
20%
30%
40%
50%
Augmentation complexity
Augmentation complexity
(a) PREC@3 on Family match
(b) MRR @ on Family match
1.0
0.8
TSPulse
TSPulse
MOMENT Chronos
MOMENT
0.7
0.8-
Chronos
0.6
PREC@3
MRR@3
0.5
0.4
0.3
0.2
0.2
0%
10%
20%
30%
40%
50%
0%
10%
20%
30%
40%
50%
Augmentation complexity
Augmentation complexity
(c) PREC @3 on Fine-grained match
(d) MRR @3 on Fine-grained match
Figure 14: TSPulse Similarity Search Ablation Study
patterns are highly variable and unpredictable, this creates a systematic mismatch between pre- training assumptions and deployment conditions. We refer to this phenomenon pre-training mask bias.
TSPulse addresses this issue through hybrid masking, which exposes the model wide spectrum of variable-length missingness patterns during pre-training rather than a single fixed-length mask. Variable-length masks more closely reflect practical missingness patterns. For clarity, we refer to these as variable-lenge missingness patterns.
A.16.2 MAR AND MNAR SCENARIO DESIGN
MAR (missing at random): If the probability a point being missing is the same only within groups defined by the observed data, then the data are missing at random (MAR).
MNAR (missing not at random): If the probability of a point being missing varies for reasons that are unknown (unobserved) to us, then the data missing not random (MNAR).
42

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Published as a conference paper at ICLR 2026
Table 30: Performance comparison between task speciappee and unified TSPulse variant across downstream
tasks.
Task
Metric
Task-Specialized
Unified Model
Best Baseline
Classification
Accuracy
0.73
0.71
0.70 (VQShape)
AD (Univariate)
VUS-PR f
0.48
0,42
0.42 (Sub-PCA)
Search (Family Match)
PREC@3
0.68
0.68
0.53 (MOMENT)
Search (Fine-grained Match)
PREC
0.58
0.58
0.42 (MOMENT)
Imputation (BInck)
MSE 4
0.106
0.106
0.176 (UniTS)
Imputation (Hyhrid)
MSF /
0.074
0.074
0.161 (Linear Interpolation)
Below, we explain several real-world MAR and MNAR situations and how we simulate them. All evaluations are done on ETThl from the LTF benchmark, real multivariate hourly electricity- transformer dataset.
MAR Scenarios
- Peak--ohuur sensor overload
Sensors often fail more during peak load hours. Simulation: In each 24-point block, the middle 12 points have missing probability of 0.6, and the remaining points have 0.05.
Real world:
S2 - Cross-channel failure due to high readings Real world: High readings in channel (e.g., very high temperature) cause other sensors to fail.
Simulation: Missingness in channel increases when another channel's value lies in the top 10%.
S3 Crossneel failure due to volatility Real world: Sudden fluctuations in variable (e.g., power/voltage instability) disrupt other sensors.
Simulation: Missingness in channel increases when another channel shows high short-term variance.
MNAR Scenarios
S1 - -Sensor breakdown under extreme values
Real world: A sensor becomes unreliable measurement (e.g., temperature) crosses high thresholds.
Simulation: Missingness increases with the magnitude of channel's values.
$2 - Latent stress, combining load levels rate of change Real world: Failures happen when system experiences both high load and rapid fluctua- tions.
Simulation: A latent variable combining one channel's value and another channel's derivative determines missingness.
$3 - 33-SSstem-wiie wide stress causing multi-sensor degradation
Real world: Many sensors degrade together when the entire system's 's operational load or stress increases.
Simulation: Missingness increases with the moving-average trend of the sum of all non- temperature channels.
S4 Time-dependent degradation
Real world: Sensors degrade and drop data more frequently over time. Simulation:
Missingness probability increases gradually with time.
A.16.3 DISCUSSION
Across all MAR and MNAR settings, TSPulse consistently outperforms MOMENT. These results support the hypothesis that hybrid masking improves robustness under heterogeneous and diverse missingness conditions. By exposing the model to variable-length missing patterns during pre-training.
43

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Published as a conference paper at ICLR 2026
Table 31: Robustness evaluation under MAR and MNAR missingness (MSE). Lower is better.
Scenario
TSPulse
MOMENT
Scenario
TSPulse
MOMENT
SI
0.334
0.760
MAR
S1
0.147
0.575
MNAR
S2
0.134
0.552
S2
0.154
0,501
S3
0.141
0.498
S3
0.138
0.402
S4
0.174
0.687
TSPulse reduces pre-training mask bias and generalizes more effectively to realistic missingness
mechanisms.
A.17 LIMITATIONS AND FUTURE WORK
While TSPulse demonstrates strong performance actoss range of tasks, including similarity search, classification, anomaly detection, and imputation, there are several important areas for future de- velopment. One key direction is expanding its application more downstream use cases, such as regression and full-fledged forecasting, to further extend its versatility. Additionally, TSPulse can be adapted for more challenging few-shot learning scenarios, particularly in classification tasks with limited labeled data. This would allow the model to perform effectively even in situations where labeled data is scarce, a common challenge in many real-world applications.
Another exciting direction is the expansion of TSPulse's capabilities by infusing semantic search with anomaly detection. By leveraging powerful embeddings, future work could focus on identifying similar anomaly patterns from historical time-series data and retrieving related solutions from associated ticketing systems or knowledge bases. This would enhance its application in anomaly detection and make TSPulse a valuable tool for problem resolution across various industries, such as IT operations and healtheare. Additionally, exploring those from other data types like text and images could unlock cross-domain applications, enabling more sophisticated models for complex tasks.
fusion of TSPulse embeddings with
Finally, while TSPulse is lightweight and efficient, there is potential to enhance its ability to perform continuous learning. dynamic environments where new data is constantly being generated, is crucial to update the pre-trained model with new information while ensuring that previously learned knowledge preserved. Future work will focus on implementing incremental learning techniques, enabling TSPulse to adapt to new data without forgetting the patterns learned from prior training. This approach will make TSPulse even more robust for real-time applications, where the model can continuously improve over time, maintaining both accuracy and stability across evolving datasets.
44


Reviews:
[{"review_id": "Jx9fRWkI18", "reviewer": "Reviewer_RHFo", "summary": "The paper introduces TSPulse, a 1M parameter pre-trained model for time-series analysis, which is built upon the TSMixer architecture. The authors claim state-of-the-art (SOTA) performance across four distinct downstream tasks: classification, anomaly detection, imputation, and similarity retrieval. The model's purported advantages stem from a collection of \"innovations,\" including:\n\n1.  **Architectural:** A dual-space (time and frequency) masked reconstruction strategy and a dual-embedding disentanglement (detailed vs. semantic) mechanism.\n2.  **Task-Specific:** A `TSLens` fine-tuning module for classification, a `multi-head triangulation` (MHT) method for anomaly detection, and a `hybrid masking` strategy for imputation.\n\nDespite the impressive reported results, the paper suffers from fundamental methodological flaws, a severe lack of focus, and claims that are not substantiated by the experimental design. The work reads less like a scientific contribution and more like an engineering report for a model that has been over-tuned on a specific set of benchmarks.", "questions": "The key weaknesses outlined above raise several questions that the authors need to address:\n\n1.  The core claim of a single, general-purpose model appears to be contradicted by the task-specific pre-training (Appendix A.6). Could the authors please provide results for a **single model**, pre-trained with a **single, unified objective** (e.g., the hybrid-masking, all-head-loss model), and then evaluated on all four downstream tasks? This is essential to validate the paper's central thesis.\n2.  The current ablation study is \"destructive\" (removing parts from the whole). Could the authors provide a \"constructive\" study, starting from the TSMixer baseline and *incrementally adding* each new component (e.g., 1. TSMixer, 2. TSMixer + Dual-Space, 3. TSMixer + Dual-Space + Dual-Embedding, etc.) to clearly demonstrate the marginal performance contribution of each proposed innovation?\n3.  How much of the performance gain is simply due to pre-training the TSMixer backbone on 1B samples, versus the novel architectural components? A crucial missing baseline is a standard TSMixer (with a simple reconstruction head) pre-trained on the *same* 1B sample dataset.\n4.  The `TSLens` module is described as learning to \"focus on the most informative regions.\" How does this mechanism fundamentally differ from a standard attention-pooling layer (e.g., a single-head attention followed by a weighted sum) commonly used in classification heads?\n5.  **Proof of Disentanglement:** The paper claims the dual-embedding approach generates \"detailed\" and \"semantic\" embeddings. Beyond their use in different reconstruction heads, what qualitative or quantitative evidence is there that these embeddings are truly disentangled? For instance, do the \"semantic\" embeddings (from register tokens) show quantifiably more invariance to noise and time shifts compared to the \"detailed\" embeddings?", "limitations": "", "rating": 2, "confidence": 5, "soundness": 2, "presentation": 1, "contribution": 2, "strengths": "There are several strengths in the paper worth highlighting:\n\n1.  The goal of creating a single, compact model (even if the pre-training is specialized) that excels at four major time-series tasks is highly ambitious and addresses a clear need in the community.\n2.  The paper's strongest contribution is its relentless focus on efficiency. Achieving the reported results with a 1M parameter model is a significant engineering feat, especially the \"GPU-Free\" (CPU-capable) inference. This is a crucial and practical research direction, providing a counter-narrative to the \"bigger is better\" trend in foundation models.\n3.   While the methodology is questionable, the sheer scale of the reported performance gains (e.g., +20% on TSB-AD, +50% on imputation) is eye-catching. It demonstrates that small, well-engineered models can be *tuned* to outperform large, general-purpose ones, which is an interesting finding in itself.", "weaknesses": "### 1. Fundamentally Flawed Experimental Premise\n\nThe paper's central narrative, that **one** tiny 1M model can be pre-trained for general-purpose use and subsequently outperform massive foundation models (like MOMENT, Chronos, etc.)—is directly contradicted by the authors' own methodology, which is buried in Appendix A.6.\n\nThe authors state:\n> \"...we specialize the pre-training for every task through reweighting loss objectives...\" And more damningly:\n> \"TSPulse adopts hybrid masking for all reconstruction-oriented tasks (imputation, anomaly detection, retrieval) and block masking specifically for classification-oriented pre-training.\"\nThis is a **fatal flaw**. The authors are not evaluating a single, general-purpose pre-trained model. They are training *multiple, distinct models* where the pre-training objective and masking strategy are *already specialized for the downstream task*.\n\nThis completely invalidates the comparisons against general-purpose foundation models like MOMENT or UniTS. Of course, a model pre-trained *specifically* for imputation using hybrid masking will outperform a general-purpose model on an imputation task that uses hybrid masking. The paper is comparing apples to oranges: a bespoke, task-specific small model against a general-purpose large model. The extraordinary claims of +50% in imputation or +20% in anomaly detection are therefore not surprising, but rather an expected outcome of this flawed, self-serving experimental design.\n\n### 2. Lacking a Coherent Contribution\n\nThe primary weakness of this paper is its overwhelming complexity and lack of a central, verifiable contribution. The authors introduce no fewer than five new, named components: `Dual-space reconstruction`, `dual-embedding disentanglement`, `TSLens`, `multi-head triangulation`, and `hybrid masking`. This obscures any real scientific insight. It is impossible to determine if a single, principled idea is responsible for the alleged gains, or if the model is simply a fragile collection of ad-hoc engineering tricks, each providing a marginal boost on a specific benchmark. The paper fails to present a clear, unified thesis, instead opting for a laundry list of features that make the work difficult to interpret \n\n### 3. Insufficient and Unconvincing Ablation Studies\n\nGiven the model's complexity, the ablation study (Section 5) is the most critical piece of evidence needed to justify the design. The provided study is wholly inadequate.\n\n* The ablations only remove one component at a time from the *final, complex model*. This fails to prove that all components are necessary. A proper study would start from the TSMixer baseline and *add* each component one-by-one to show its marginal contribution.\n* The study fails to disentangle the contributions. For example, in Table 1(b), removing `TSLens` causes a 16% drop, and removing `Dual-space` causes a 7% drop. What happens if *both* are removed? Does the performance revert to the TSMixer baseline, or is there a complex, non-additive interaction?\n* What is the performance of *just* the TSMixer baseline + `TSLens`? What about TSMixer + `Dual-space`? Without this, it's impossible to know if the \"dual-embedding\" or other components are providing any real value or are simply needless complexity. The ablations feel selected to justify the components rather than to genuinely investigate them.\n\n### 4.  Many of the paper's \"novel\" contributions appear to be re-brandings of existing, standard techniques.\n\n* **Dual-Space Learning:** Using both time and frequency domains is a classic signal processing technique. The paper itself cites prior work like **FEDformer** and **BTSF** that already leverage this. Claiming this as a novel contribution for \"unifying\" them in a *lightweight* model is a weak, incremental claim.\n* **Multi-Head Triangulation (MHT):** This is just a simple ensemble. The model computes reconstruction error from three different heads (time, FFT, forecast) and picks the best one (`Headtriang.`) or combines them (`Headensemble`). This is a standard validation/ensemble technique, not a novel anomaly detection framework.\n* **TSLens:** The description (\"selectively attends to and weights features\") is functionally identical to a standard attention mechanism applied as a pooling layer for classification. Giving it a new name does not make it a new contribution.\n* **Hybrid Masking:** This is a data augmentation strategy, not a model innovation. It is an obvious heuristic to combine point and block masking.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Ca1ismfgp6", "reviewer": "Reviewer_6n4K", "summary": "TSPulse proposes a tiny pre-trained backbone for time-series diagnostics, including classification, anomaly detection, imputation, and similarity search, that is designed for low-latency CPU/GPU inference. The approach learns disentangled representations by reconstructing signals in both time and frequency domains and by separating fine-grained from semantic information, supported by a hybrid masking scheme that varies mask type and span to reflect realistic missingness. Built on a TSMixer backbone with a lightweight mini-decoder, the work integrates task-oriented adapters (e.g., TSLens for multivariate classification and multi-head triangulation for anomaly detection) to translate the embeddings into downstream gains. Empirical results across standard benchmarks indicate consistent improvements over larger baselines, while maintaining a compact footprint that facilitates deployment.", "questions": "- What default loss weights work reliably across domains, and how sensitive are downstream results to these weights during task-specialised pre-training and fine-tuning?\n- Do the disentangled embeddings support causal long-horizon forecasting if a forecasting head is added, and how do they compare with forecasting-oriented pre-trained models under strict parameter matching?\n- How does TSPulse perform against equally small plug-ins—such as a gated residual or lightweight cross-attention when total parameters and training budget are held constant?\n- Can empirical missingness models from real datasets (e.g., MAR/MNAR) be provided, and can robustness be tested under these distributions to validate the hybrid masking design?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "- The approach provides a ~1M-parameter pre-trained model with low-latency CPU/GPU inference, facilitating practical deployment.\n- The work employs a dual time–frequency objective with hybrid masking that mirrors realistic missingness and yields robust representations.\n- Task-oriented modules (e.g., TSLens, triangulation) translate the embeddings into measurable gains across multiple diagnostic tasks.", "weaknesses": "- Reliance on task-specific loss re-weighting may limit out-of-the-box generality and increase tuning burden.\n- The representation is not assessed on long-horizon causal forecasting, which constrains claims of transferability beyond diagnostics.\n- The lack of parameter-matched plug-in baselines (e.g., gated residuals, lightweight cross-attention) weakens isolation of design effects from model capacity.\n- The empirical evidence would be stronger with uncertainty estimates and per-dataset breakdowns to substantiate the reported gains.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "sDGZ9cwvfv", "reviewer": "Reviewer_9eiE", "summary": "TSPulse is a 1M-parameter pre-trained model for time-series analysis that learns disentangled temporal, spectral, and semantic representations through multi-head masked reconstruction. Using a lightweight TSMixer backbone, hybrid masking, and a small decoder, it achieves efficient and robust pre-training. During fine-tuning, identity-initialized channel mixers enable multivariate adaptation without retraining the full model. TSPulse delivers strong performance across classification, anomaly detection, imputation, and similarity tasks while maintaining high efficiency on CPUs.", "questions": "Please address the identified weaknesses and limitations noted above.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- The model uses a PEFT-style multivariate adaptation. It is pre-trained on univariate data and activates decoder-side channel mixers only during fine-tuning, initialized to identity for stability. This allows lightweight adaptation without retraining the entire model.\n- The design is highly efficient, with about 1M parameters, low latency, and small memory usage. The pre-training setup on 1B samples in one day on 8×A100 makes it practical and scalable.\n- The representation is disentangled into three segments—time, FFT, and register embeddings—and each task selectively uses the relevant parts. This improves transfer flexibility and prevents unnecessary coupling between features.", "weaknesses": "- The register-token design introduces inductive bias. Predicting spectral signatures forces phase invariance, which may hurt tasks that rely on absolute timing. The paper does not compare this approach to CLS-style aggregators or include related ablations.\n- The hybrid masking strategy lacks novelty. Mixing block and point masks is common, and the argument that it better captures “real randomness” is weak. Patching is a modeling choice, while masking should reflect a data property (i.e., real-world missingness patterns). The paper conflates these levels and provides no statistical evidence that its hybrid masking aligns with realistic data gaps.\n- The paper omits forecasting evaluation despite clear architectural similarity to imputation. In most time-series models, forecasting can be tested simply by changing the final output layer, so excluding it removes a standard and low-effort comparison point. Given that nearly all major time-series foundation models are benchmarked on forecasting, this omission significantly limits comparability and completeness.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "wVB4bvsXav", "reviewer": "Reviewer_viWQ", "summary": "This paper proposes ultra-light pre-trained models for various time series analysis tasks, including classification, imputation, anomaly detection, and semantic search. Key techniques involve dsentangled masked reconstruction for fine-grained and semantic embeddings and a hybrid masking scheme to avoid pre-training bias and boost generalization. More importantly, the proposed TSPulse outperforms models 10–100× larger on 75+ datasets.", "questions": "Please refer to the weakness", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. novel and practical problem setting for designing fast and efficient time series foundation models.\n\n2. Technical designs seem to be reasonable and solid.\n\n3. Experimental results are promising and demonstrate the efficiency of the model.\n\n4. Pretrained models, source code, and example scripts are included in the supplementary materials.", "weaknesses": "1. The presentation for the proposed method should be improved to enhance clarity. It is suggested to use 1 or 2 sentences to describe the key idea of the proposed TSPulse model.\n\n2. According to Figure 6, the imputation performance is extremely good, which needs more discussion.\n\n3. Why do we need the tasks for Similarity Search? Are there some applications?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)