Early Classification of Time Series (ECTS) requires making accurate decisions as early as possible in inherently online and evolving environments. Yet, most existing methods assume stationarity and rely on separable designs, where classification and triggering are optimized independently, an assumption that fundamentally limits their adaptability under drift. In this work, we challenge this paradigm and study ECTS under non-stationary conditions. We provide the first systematic comparison between separable and end-to-end approaches across controlled drifting scenarios. Building on Reinforcement Learning, we introduce DQeND, a unified architecture that jointly learns representation, classification, and triggering decisions, while remaining directly comparable to state-of-the-art separable baselines. Across a wide range of drifts, DQeND demonstrates strong robustness across various non-stationary scenarios, consistently outperforming separable baselines. An ablation study further highlights that jointly updating representation and decision modules is critical to these gains. Overall, our results indicate that end-to-end learning can offer improved adaptation capabilities for ECTS in dynamic environments, and motivate further investigation of alternatives to separable designs.
Figures & tables
Figure 1. DQeND pipeline
Encoder
kernel sizes
{3,6,9,12}
nb. of kernels
{128,64,32,16}
embedding dim.
64
time embedding dim.
2
Decision
nb. hidden layers
1
hidden dim.
64
activation function
tanh
Table 1. DQeND hyperparameters
Figure 2. The I_loc scenario.
Figure 3. The I_noise scenario.
Figure 4. The A_loc scenario.
Figure 5. The A_class scenario.
Figure 6. Incremental drifts, deployment’s metrics, averaged over five seeds. From top to bottom: the raw cumulative cost; the hold-out AvgCost , obtained on unseen drifted data; the hold-out AvgCost original, obtained using the fixed test set from training phase. UPPERCASE approaches refers to end-to-end methods while lowercase indicates separable ones.
Figure 7. Hold-out AvgCost drift: detailed performances. The figures display decomposition of the hold-out AvgCost drift into both earliness, i.e. the average proportion of the time series used, and error rate, during the deployment phase.
Figure 8. Abrupt drifts, deployment’s metrics, averaged over five seeds. From top to bottom: the raw cumulative cost; the hold-out AvgCost , obtained on unseen drifted data; the hold-out AvgCost original, obtained using the fixed test set from training phase. UPPERCASE approaches refers to end-to-end methods while lowercase indicates separable ones.
Figure 9. Hold-out AvgCost drift: detailed performances. The figures display decomposition of the hold-out AvgCost drift into both earliness, i.e. the average proportion of the time series used, and error rate, during the deployment phase.
freeze encoder
freeze decision
( a )
( b )
( a )
( b )
I_loc
−32.42 %
−36.44 %
−36.61 %
−31.87 %
I_noise
−11.29 %
−4.04 %
−19.28 %
−6.63 %
A_loc
1.38 %
−0.34 %
−43.52 %
−45.30 %
A_class
1.32 %
2.14 %
−18.18 %
−4.39 %
Table 2. ( a ): The mean percentage difference between the cumulative cost of full updated DQeND and the partially frozen version, over five random seeds. ( b ): The mean of the median percentage difference of the hold-out AvgCost drift of the full updated DQeND and partially frozen version, over five random seeds. Negative figures indicate degraded performance compared to original DQeND.
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
I_loc
I_noise
A_loc
A_class
Alert( online / freeze )
29.02±4.08
46.14±0.3
31.06±11
32.15±1.27
Alert( online / online )
31.87±5.49
37.92±0.83
23.32±1.88
30.86±0.2
DQeND
16.18±3.40
36.2±1.04
18.86±0.55
32.98±3.88
EARLIEST
20.53±6.54
43±3.37
19.90±0.79
32.44±5.88
ELECTS
17.33±1.81
38.63±1.98
29.98±12.06
25.79±3.52
Appendix
Table 3. The mean cumulative cost and standard deviation, over five random seeds. Bold value indicates the best average performing method.
I_loc
I_noise
A_loc
A_class
Alert( online / freeze )
0.3±0.04
0.46±0.003
0.31±0.11
0.32±0.01
Alert( online / online )
0.31±0.07
0.38±0.009
0.23±0.02
0.31±0.002
DQeND
0.16±0.03
0.36±0.01
0.19±0.01
0.33±0.04
EARLIEST
0.2±0.06
0.43±0.03
0.2±0.01
0.32±0.06
ELECTS
0.17±0.02
0.39±0.02
0.3±0.12
0.26±0.04
Appendix
Table 4. The mean hold-out AvgCost drift and standard deviation, over all the deployment steps and five random seeds. Bold value indicates the best average performing method.
I_loc
I_noise
A_loc
A_class
Alert( online / freeze )
0.31±0.02
0.31±0.04
0.21±0.04
0.37±0.03
Alert( online / online )
0.33±0.06
0.33±0.02
0.18±0.02
0.37±0.003
DQeND
0.09±0.04
0.31±0.01
0.11±0.02
0.4±0.04
EARLIEST
0.27±0.07
0.36±0.01
0.11±0.07
0.51±0.01
ELECTS
0.14±0.07
0.33±0.01
0.19±0.1
0.48±0.02
Appendix
Table 5. The mean hold-out AvgCost original and standard deviation, over all the deployment steps and five random seeds. Bold value indicates the best average performing method.
Training
Deployment ( per batch )
Total ↓
Fit
Inference
Update
ELECTS
31.89
0.026
0.05
39.22
EARLIEST
119.25
0.23
0.09
138.98
Alert ( online / online )
(78.02, 46.55)
2.39
2.45
612.75
Alert ( retrain / retrain )
(78.02, 46.55)
2.71
3.59
759.86
DQeND
248.74
2.90
5.75
1124.31
Appendix
Table 6. Computation times (in s. ). The deployment are displayed on a per batch basis. The total time accounts for the all 100 deployment steps. The fit time of the Alert-based methods are decomposed over ( classifier fit time, trigger fit time).
Time series classification (TSC) is dominated by a two-stage paradigm: train a feature encoder -- either from scratch on the target dataset or via pretraining on large corpora -- and then fit a task-specific classifier on top. While effective, this decoupling optimizes representation learning independently of the classification objective, requires per-dataset training, and prevents the model from exploiting label information during inference. We introduce TimEE, a 4.5M-parameter foundation model for end-to-end TSC via in-context learning. Given a labeled support set and a query time series, TimEE directly outputs a predicted class distribution in a single forward pass with no per-dataset training required. Following the prior-data fitted network (PFN) framework, TimEE is meta-trained exclusively on synthetic TSC tasks, where each task contains time series with distinct class identities arising from structured distributional shifts in the generative process. Despite seeing no real time series during pre-training, TimEE ranks first in ROC AUC (and third on accuracy) on the UCR benchmark among all compared methods, which include both foundation models and supervised deep learning baselines. To our knowledge, TimEE is the first purely synthetic-pretrained model to reach state-of-the-art performance on the UCR benchmark. These results establish end-to-end ICL with synthetic priors as a compelling, largely unexplored direction for TSC, with scaling, prior design, and richer generation mechanisms as natural avenues for improvement. Code is publicly available at http://github.com/automl/timee.
Jaris Küken, Shi Bin Hoo, Martin Mráz +2
University of Freiburg · Zuse School ELIZA Darmstadt · Prior Labs +1
Non-stationary time series forecasting is challenged by evolving distribution shifts that static models struggle to capture. While Mixture-of-Experts (MoE) architectures offer a promising paradigm for decoupling complex drift patterns, existing approaches are limited by fixed expert pools and memoryless routing, hampering their ability to adapt to abrupt regime shifts. To address this, we propose Dynamic TMoE, a framework that unifies architectural evolution with temporal continuity during learning phase. By detecting distribution shifts via Maximum Mean Discrepancy (MMD), we dynamically instantiate heterogeneous experts and prune redundant ones to optimize capacity. Additionally, a temporal memory router leverages recurrent states and an anomaly repository to ensure stable, context-aware expert selection without requiring test-time updates. Experiments on nine benchmarks demonstrate state-of-the-art performance, reducing MSE by 10.4% and MAE by 7.8%. Code is available at https://github.com/andone-07/Dynamic-TMoE.
Jiawen Zhu, Shuhan Liu, Di Weng +1
School of Software Technology, Zhejiang University, Ningbo, China · State Key Lab of CAD&CG, Zhejiang University, Hangzhou, China
Learning robust representations for time-series signals under noise and distribution shifts remains challenging, especially in clinical applications such as electroencephalogram (EEG) and electrocardiogram (ECG) analysis. We propose Diffusion-Conditioned Representation Alignment (DCRA), a training framework that repurposes the forward diffusion process as a structured corruption scheduler for representation learning. Different from conventional augmentation and consistency-based methods that rely on independently sampled perturbations, DCRA introduces a structured corruption trajectory via the diffusion forward process, which enables continuous and controlled representation evolution across noise levels. We introduce a feature-level consistency objective that aligns representations across noise levels while preserving class-discriminative structure. This mechanism promotes structure-preserving consistency, which enables smooth and semantically coherent feature trajectories in latent space. The proposed framework is encoder-agnostic and can be integrated with state space models and Transformer architectures. The seizure detection experiments on the CHB-MIT EEG dataset show that DCRA consistently improves performance under multiple noise conditions and achieves higher sensitivity at low false-positive rates. Analysis reveals that DCRA produces more balanced and structured representations compared to baseline and diffusion-only models. These findings highlight the benefit of combining structured corruption with representation alignment for robust time-series learning.