Multi-mode tensor time series (TTS) can be found in many domains, such as search engines and environmental monitoring systems. Learning representations of a TTS benefits various applications, but it is also challenging since the complexities inherent in the tensor hinder the realization of rich representations. In this paper, we propose a novel representation learning method designed specifically for TTS, namely MoST. Specifically, MoST uses a tensor slicing approach to reduce the complexity of the TTS structure and learns representations that can be disentangled into individual non-temporal modes. Each representation captures mode-specific features, which are the relationship between variables within the same mode, and mode-invariant features, which are in common in representations of different modes. We employ a contrastive learning framework to learn parameters; the loss function comprises two parts intended to learn representation in a mode-specific way and mode-invariant way, effectively exploiting disentangled representations as augmentations. Extensive experiments on real-world datasets show that MoST consistently outperforms the state-of-the-art methods in terms of classification and forecasting accuracy. Code is available at https://github.com/KoheiObata/MoST.
Figures & tables
Figure 1: Illustrations of a tensor time series and three slices along different modes. (a) A tensor time series with three modes: location, query, and time. (b) Location and query dependencies of a temporal slice. (c), (d) Location and query slices have their own intra-mode dependencies, but temporal dependencies are common.
Figure 2: (a) MoST slices the TTS along each non-temporal mode and independently feeds a slice into the slice feature encoder to learn a representation of the slice. Then, the aggregator is applied to summarize mode information. (b) The parameter of the model is learned via contrastive loss, which is composed of mode loss and instance loss. Mode loss utilizes the representations from different sliced tensors, while instance loss utilizes the representations generated by random cropping as contrastive augmentations.
Dataset
MoST
CoST
TS2Vec
TS-TCC
ATD
Daily
0.726
0.164
0.688
0.478
0.249
Realdisp
0.766
0.126
0.663
0.190
0.151
Table 1: Classification results with Acc. Best results are in bold , and second best results are underlined (higher is better). The average of five runs is reported.
Methods
Self-supervised representation learning
End-to-end forecasting
Tensor forecasting
MoST
CoST
TS2Vec
Informer
LaST
NET 3
SSMF
Tf
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
US#1
2 week
0.752
0.590
0.900
0.668
1.153
0.806
1.364
0.818
1.003
0.694
1.501
0.915
1.380
0.824
8 week
0.811
0.609
1.002
0.685
1.133
0.751
1.125
0.735
1.060
0.731
2.143
1.058
1.353
0.815
32 week
0.949
0.661
1.132
0.714
1.355
0.822
1.242
0.770
1.449
0.839
1.599
0.866
1.355
0.811
US#2
2 week
0.653
0.566
0.676
0.575
0.725
0.600
0.855
0.655
0.709
0.588
0.805
0.630
1.385
0.862
Table 2: Forecasting performance (lower is better). The average of five runs is reported.
Forecasting
Classification
Avg. MSE
Avg. MAE
Avg. Acc
MoST
0.636
0.553
0.746
(a)
w/o Mode-2 dependency (M1D)
0.811 (-27.5%)
0.630 (-13.9%)
0.714 (-4.4%)
w/o Mode-1 dependency (M2D)
0.650 (-2.2%)
0.560 (-1.1%)
0.599 (-19.8%)
Random
0.656 (-3.2%)
0.556 (-2.3%)
0.626 (-16.2%)
Channel-independence (CI)
0.651 (-2.3%)
0.559 (-1.0%)
0.667 (-10.6%)
Table 3: Performance of forecasting and classification for the different (a) tensor slicing and MI approaches, (b) architectures, and (c) loss functions.
Figure 3: t-SNE visualizations of the learned representations. The colors represent the three distinct intra-mode dependencies for (top) mode-1 and (bottom) mode-2. For MoST , representations of mode-1 V(d1) and mode-2 V(d2) are shown.
Time series representation learning develops compact, transferable features that capture temporal patterns for forecasting, classification, retrieval, and anomaly detection.
Time series classification (TSC) performance depends not only on architectural design but also on the diversity of input representations. In this work, we propose a scalable multi-scale convolutional framework that systematically integrates structured multi-representation inputs for univariate time series. We introduce two architectures: MRMS-Net, a hierarchical multi-scale convolutional network optimized for robustness and calibration, and LMRMS-Net, a lightweight variant designed for efficiency-aware deployment. In addition, we adapt LiteMV -- originally developed for multivariate inputs -- to operate on multi-representation univariate signals, enabling cross-representation interaction. We evaluate all models across 142 benchmark datasets under a unified experimental protocol. Critical Difference (CD) analysis confirms statistically significant performance differences among the top models. Results show that LiteMV achieves the highest mean accuracy, MRMS-Net provides superior probabilistic calibration (lowest NLL), and LMRMS-Net offers the best efficiency-accuracy tradeoff. Pareto analysis further demonstrates that multi-representation multi-scale modeling yields a flexible design space that can be tuned for accuracy-oriented, calibration-oriented, or resource-constrained settings. These findings establish scalable multi-representation multi-scale learning as a principled and practical direction for modern TSC. Reference implementation of MRMS-Net and LMRMS-Net is available at: https://github.com/alagoz/mrmsnet-tsc
Celal Alagöz, Mehmet Kurnaz, Farhan Aadil
Computer Engineering, Sivas Bilim ve Teknoloji Üniversitesi, Sivas, Türkiye
Supervised learning demands large quantities of labeled data, a bottleneck that is expensive and reliant on domain-specific expertise. Self-supervised learning, particularly contrastive learning, has emerged as a compelling alternative, enabling rich representation learning directly from unlabeled data. Yet its success hinges critically on the design of positive and negative sample pairs. Existing approaches for time series rely on hand-crafted augmentations and masking heuristics that embed strong domain assumptions, often limiting generalization across diverse temporal patterns and potentially introducing spurious correlations. In this work, we challenge this paradigm by demonstrating that explicitly encoding temporal shift invariance through a simple, deterministic view construction is sufficient to learn strong representations for time series classification. By exploiting temporal structure, our method, Shift Invariant Feature Training (ShiFT), achieves state-of-the-art performance on six diverse real-world time series benchmark datasets, as well as the UCR and UEA archives, while reducing training time. Beyond empirical performance, we present a systematic analysis of contrastive learning dynamics in time series settings, examining the effects of batch size and the number of negatives on downstream performance. Our findings provide practical insights for designing efficient contrastive learning frameworks for time series representation learning. The source code is publicly available at https://github.com/sfi-norwai/ShiFT.
Abdul-Kazeem Shamba, Kerstin Bach, Gavin Taylor
Norwegian University of Science and Technology, Norway · United States Naval Academy, USA
Time Series Language Models (TSLMs) enable language-based understanding and reasoning over temporal data, yet a fundamental question remains: what information should their time-series representations preserve, and what variation should they factor out? Existing TSLMs typically expose the language model to a single representation, imposing a fixed inductive bias across downstream tasks. We instead introduce complementary representations as a design principle for time-series reasoning. Our model combines two visual views: line plots preserve absolute measurements and the observed coordinate frame, while normalized delay embeddings factor out positive amplitude rescaling and offsets while exposing temporal structure. Dedicated visual encoders integrate both views into a shared language model through visual tokens and multi-level feature fusion. Evaluation-time interventions verify that the two views exhibit distinct invariance profiles, while single-view ablations show that their combination is particularly beneficial beyond basic perception, with the large gains in prediction and reasoning. Built on Qwen3-VL-8B, our dual-view model improves overall TSRBench accuracy from 44.5% with line plots alone to 53.2%, substantially exceeding the strongest evaluated dedicated TSLM baseline at 36.7%. It further achieves 89.9% accuracy on TSExam and 86.8% numerical accuracy on multivariate ChatTS alignment. Together, these results demonstrate that complementary representations provide an effective design principle for general-purpose TSLMs, enabling models to exploit temporal structure without sacrificing access to the original measurement frame.