arXiv CSopen access

TimEE: End-to-end Time Series Classification via In-Context Learning

T IM EE: End-to-end Time Series Classification via In-Context Learning

Jaris Küken 1,2,* Shi Bin Hoo 1,* Martin Mráz 1 Frank Hutter 3,4,1 Lennart Purucker 3,1 1 University of Freiburg, 2 Zuse School ELIZA Darmstadt, 3 Prior Labs, 4 ELLIS Institute Tübingen * Equal contribution {kuekenj,hoos}@cs.uni-freiburg.de

arXiv:2607.07500v1 [cs.LG] 8 Jul 2026

Abstract 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 T IM EE1 , 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, T IM EE 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, T IM EE 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, T IM EE 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, T IM EE 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 https://github.com/automl/timee.

1

Introduction

The dominant approach to time series classification (TSC) decomposes the problem into two stages: first, a feature encoder maps each time series to a fixed-dimensional representation; second, a task-specific classifier is trained on these representations to produce predictions. Despite the surfacelevel differences of existing methods, this two-stage design is universal. Classical methods such as MiniRocket [Dempster et al., 2021] and Hydra [Dempster et al., 2023], per-dataset deep learning methods such as TS2Vec [Yue et al., 2022], and recent foundation models such as Chronos-2 [Ansari et al., 2025], TiRex [Auer et al., 2025b], and MantisV2 [Feofanov et al., 2026] all instantiate it. We argue that this is not merely an implementation convention, but a structural bottleneck. The encoder is optimized independently of the classification objective, and a new classifier must be fitted for every new dataset. Most critically, at inference time, the encoder cannot directly access the labeled training samples and therefore cannot produce representations tailored to the dataset’s class structure. 1 T IM EE pronounced as "Timmy"

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Figure 1: We compare mean rank across all 128 UCR benchmark datasets. T IM EE achieves the lowest mean rank on ROC AUC (left), outperforming all compared methods including task-specific and foundation model baselines, while ranking third on accuracy (right). DTW-1NN is excluded from the ROC AUC comparison as it does not produce calibrated probability scores.

In-context learning (ICL) eliminates all three of these downsides simultaneously. Rather than fitting per-dataset weights, an ICL model observes the labeled training set at inference and directly outputs a predicted class distribution in a single forward pass. No weight updates are required. This paradigm has proven transformative for tabular classification: TabPFN [Hollmann et al., 2023, 2025, Grinsztajn et al., 2026] and TabICL [Qu et al., 2026, 2025] achieve state-of-the-art performance by meta-training over synthetic labeled tasks drawn from a structured prior, with no per-dataset training at test time. Extending this to TSC, however, requires solving a non-trivial data generation problem. The tabular ICL literature has largely resolved synthetic pre-training through structured Bayesian priors over causal graphs. Existing synthetic generation approaches for time series either produce unlabeled corpora [Xie et al., 2025] or assign class membership arbitrarily [Yeh et al., 2025]. Neither approach provides the structured, label-meaningful datasets that ICL meta-training requires to learn a classification prior. To address this problem, we introduce a novel synthetic data generation pipeline. We introduce T IM EE, a 4.5M-parameter model for end-to-end TSC via ICL. T IM EE is meta-trained exclusively on synthetic, labeled time series classification tasks and requires no per-dataset training at test time. Despite seeing no real time series during pre-training, T IM EE achieves the lowest mean rank on ROC AUC across all 128 UCR benchmark datasets, outperforming all compared methods, including both foundation models and supervised baselines. T IM EE lies on the Pareto front of inference speed versus predictive performance. Our contributions are: (I) a new end-to-end ICL paradigm for TSC requiring no per-dataset training; (II) a transformer architecture that jointly models temporal and cross-series structure for in-context classification; (III) a VARX-based synthetic prior that generates labeled TSC tasks grounded in the data-generating process; (IV) state-of-the-art results on the UCR benchmark with strong probabilistic calibration and competitive inference speed.

2

Background

We introduce the time series classification problem and review key concepts and related work. 2.1

Time Series Classification n

Consider a time series classification problem with labeled training data Dtrain = (xi , yi )i=1 , where xi ∈ RT ×d is a d-dimensional time series of length T and yi ∈ Y is the corresponding class label. The goal is to estimate the predictive distribution p(· | xtest , Dtrain ) for a held-out test sample xtest . 2

2.2

The Two-Stage Paradigm

The dominant approach to TSC decomposes the problem into two stages. First, a feature encoder Fθ : RT ×d → Rm maps each time series to a fixed-dimensional representation. Second, a taskspecific classifier Gϕ is trained on these representations to produce predictions ŷ = Gϕ (Fθ (x)). We describe three general classes of methods below. A detailed comparison is provided in Appendix Table 1. Classical and Time Series Features Engineering Methods define Fθ (x) without gradient-based learning, either through hand-crafted time series features or random convolutional projections. DTW1NN uses dynamic time warping distance, while Catch22 [Lubba et al., 2019] extracts a curated set of 22 time series features. Rocket [Dempster et al., 2019] and MiniRocket [Dempster et al., 2021] transforms each series using a large bank of random convolutional kernels, aggregating features via global pooling. Hydra [Dempster et al., 2023] extends this by organizes kernels into competing groups to bridge random projections and dictionary-based pattern counting. Despite requiring no representation learning, these methods remain surprisingly competitive on standard benchmarks Chen et al. [2015]. Per-Dataset Deep Learning Methods learns Fθ on each target dataset. InceptionTime [Ismail Fawaz et al., 2020] trains a convolutional encoder jointly with Gϕ . TS2Vec [Yue et al., 2022] instead learns representations via hierarchical contrastive objectives over time and instance dimensions on the unlabeled target dataset, before fitting a downstream classifier head. These methods can achieve strong per-dataset performance but require training from scratch on every new dataset with no cross-task transfer. Time Series Foundation Models amortize representation learning through large-scale pre-training. TSC-focused models, namely NuTime [Lin et al., 2024], MOMENT [Goswami et al., 2024], Mantis [Feofanov et al., 2025], and MantisV2 [Feofanov et al., 2026], pre-train encoders via contrastive or reconstruction objectives on large corpora of real and/or synthetic time series data, producing general-purpose embeddings that can be passed to lightweight downstream classifiers. As a complementary line of work, Auer et al. [2025a] studied transferring forecasting foundation models (notably Chronos-2 [Ansari et al., 2025] and TiRex [Auer et al., 2025b]) to classification using the extracted representations. In practice, however, competitive performance across all these models requires non-trivial layer selection: intermediate representations systematically outperform final-layer embeddings [Auer et al., 2025a]. Shared Structural Limitation Despite their differences, all of the above share a fundamental constraint: Fθ is optimized independently of the target classification task, and a new Gϕ must be fitted per dataset. This decoupling has also been identified as a key source of sub-optimality in Shi et al. [2023].2 Furthermore, Fθ encodes each series in isolation, without any awareness of the other labeled samples in the dataset, and therefore cannot exploit discriminative structure across classes during encoding. Most critically, at inference time, Fθ does not exploit the labeled training samples, and therefore cannot produce representations tailored to the class structure of the dataset at hand. T IM EE address these three constraints simultaneously via end-to-end in-context learning. 2.3

In-Context Learning for Supervised Prediction

In-context learning (ICL) offers an alternative to task-specific classifiers: rather than updating model weights, the model observes Dtrain at inference and approximates the conditional predictive distribution p(· | xtest , Dtrain ) in a single forward pass. This idea was first introduced in Prior-data Fitted Networks (PFN) [Müller et al., 2024]. TabPFN [Hollmann et al., 2023] extended this paradigm for tabular classification by defining a synthetic Bayesian prior over tasks, while TabPFNv2 [Hollmann et al., 2025] scaled this substantially by introducing advancement in the synthetic priors and architecture. Parallel works that adopt the same paradigm include TabICL [Qu et al., 2025] and TabICLv2 [Qu et al., 2026] which introduce different architectures and synthetic priors. For TSC, Fang et al. [2026] introduce ICL by pre-training an ICL head atop a fixed feature encoder. While this yields strong results, it remains structurally two-stage: the encoder is frozen and cannot be shaped by the classification objective. TiCT [Yeh et al., 2025] addresses the problem more directly 2 InceptionTime is an exception to this limitation, as F and G are trained jointly on the target dataset. θ ϕ

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by pre-training an end-to-end model on binary tasks, using threshold-based mixing of KernelSynth examples as synthetic prior. T IM EE extends this line of work to multi-class tasks and grounds the synthetic prior in a structured data-generating process that reflects meaningful class differences in the underlying dynamics. For a more in-depth discussion on the differences in the two approaches, we refer to Appendix A.2. 2.4

Synthetic Data Generation for Time Series Foundation Models

Due to the scarcity of high-quality labeled real-world time series data, synthetic generate has become a key enabler of zero-shot generalization in many time series foundation models. KernelSynth, originally introduced in Chronos [Ansari et al., 2024], generates diverse synthetic time series for forecasting through compositions of Gaussian process kernels. Chronos-2 further introduces using temporal causal models in order to generate synthetic univariate time series. In a separate direction, several works have proposed data mixing strategies to further diversify synthetic pre-training data. TiRex [Auer et al., 2025b] applies augmentation techniques including spike injection and convex mixing of base sequences, as well as an extended version of KernelSynth. CauKer [Xie et al., 2025] uses Structural Causal Models to produce clustering structure suitable for contrastive pre-training of time series encoders. ICL pre-training for classification imposes a strictly harder requirement: synthetic data must consist of labeled classification tasks, not merely diverse time series. No prior work generates classification tasks in which class identity reflects differences in the data-generating process itself.

3

Method

We formulate the training objective of T IM EE and detail the key components of our approach, beginning with the synthetic data generation procedure and concluding with the model architecture and pre-training setup. 3.1

Problem Formulation and Training Objective

While existing approaches solve each instance of p(· | xtest , Dtrain ) independently via fine-tuning or two-stage pipelines, T IM EE learns an amortized predictor fθ that approximates it in a single forward pass with no per-dataset weight updates. Rather than assuming a fixed dataset or label space, fθ accepts tasks of varying support size ntrain and number of classes K. Following the PFN [Müller et al., 2024] training objective, we train fθ by meta-learning over synthetic tasks drawn from a prior psynth . At each iteration, a synthetic dataset Dk = {(xi , yi )}N i=1 is sampled and partitioned into: train Dk,train = {(xj , yj )}nj=1 ,

test Dk,test = {(xl , yl )}nl=1 ,

and the model minimizes the negative log-likelihood over query positions:   X L(θ) = −ED∼psynth  log pθ (y | x, Dk,train ) .

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Synthetic Data Generation

The design of the prior psynth is central to the performance of T IM EE. While prior work (Section 2.4) has established synthetic data generation as a promising data source for pre-training time series foundation models, these approaches target either forecasting or produce classification tasks in which class identity does not reflect meaningful differences in the underlying generative process. We address this gap by pre-training T IM EE on synthetic labeled TSC datasets in which class structure arises from controlled variation in the data-generating process itself. Data-Generating Process. The foundation of our data-generating process is a temporal structural model over d endogenous variables. Let yt ∈ Rd denote a multivariate3 random variable at time t. 3 The univariate case d = 1 is also covered by this model.

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Figure 2: Class generation mechanisms in the T IM EE prior: Left – Structural Variation: samples from Class 1 (blue) are generated under the full graph, while samples from Class 2 (orange) are generated under a graph with a subset of edges dropped (×); and Right – Signal Variation: Class 1 (blue) and Class 2 (orange) share the same underlying signal pattern, and class identity is determined by the warping speed of the exogenous signal (grey nodes). We model its evolution as a Vector Autoregressive process with exogenous inputs (VARX) [Lütkepohl, 2005]: yt =

p X k=1

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s X

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where Ak ∈ Rd×d are the lag-k autoregressive coefficient matrices, encoding inter-variable temporal relationships, xt ∈ Rq is a q-dimensional exogenous input signal and Bj ∈ Rd×q maps lag-j exogenous inputs to endogenous variables. Class Identity Mechanism. Classification structure is introduced through two complementary and independently controllable mechanisms: • Structural Variation: Classes are defined by structural variation in the dependency structure encoded in Ak and Bj as shown in Figure 2 (left). Concretely, class identity is determined by which the set of edges that are present (or absent) in the dependency graph. This reflects well-established observations that many real-world classification tasks correspond to qualitatively different regimes of inter-variable interaction [Qian et al., 2025]. • Signal Variation. Classes are defined by the statistical properties of the exogenous input xt while the underlying dependency structure Ak , Bk remains fixed. In particular, we consider warping of xt as class-discriminative feature, as shown in Figure 2 (right). The same underlying signal is hereby expressed at different speeds across classes, inducing systematic distributional differences in the endogenous yt without any change to the inter-variable structure [Kamycki et al., 2019]. Augmentations. To further enhance the diversity of our synthetic pre-training corpora, we apply a set of augmentations at the individual time series level. Concretely, we consider three transformation types: (1) smoothing via a randomized Gaussian filters; (2) spike injection: by sampling spike st and augmenting the series by yt′ = yt + st [Auer et al., 2025b]; and (3) nonlinear transformations: by applying non-linearity on the time series, i.e. yt′ = g(yt ) where g is a randomly sampled nonlinearity. Additionally, we apply a mixup scheme [Ansari et al., 2024, Auer et al., 2025b], to generate convex combinations of synthetic time series across the dataset level. Full details about the augmentations are provided in Appendix C.2 and C.3. 5

3.3

Model Architecture

The architecture of T IM EE is designed to jointly reason over all time series in the context, enabling in-context comparison between support and query examples in a single forward pass. It consists of five stages: (i) Tokenization to represent each series as a sequence of patch embeddings; (ii) Label Conditioning to inject class information to the patch embeddings; (ii) Encoder Stack to build class-aware contextual representations for each series (iv) In-Context Reasoning to perform cross-sample comparison; (v) Decoder to map query representations into class probabilities. The complete pipeline is illustrated in Figure 3, with an in-depth evaluation of each component provided in Appendix B.4. Tokenization. Like many time series foundation models (mentioned in Section 2), we first normalize each series to remove the individual scale, in order to encourage the model to focus on temporal shape rather than magnitude. Like Chronos-2 [Ansari et al., 2025], we apply sinh−1 transformation to better handle the outliers. A subsequent cross-normalization step, computed using only the trainingseries statistics, further standardizes the representation across the context. Each series is then divided into non-overlapping patches of size p = 16 and projected to d = 128 dimensions via a shared linear layer. Decoder

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Encoder Stack. The goal of the encoder is to produce a compact, class-aware summary of each series that captures both its internal temporal structure and its relationship to other series in the context. To this end, K learnable CLS tokens are prepended to each series’ patch sequence, yielding representations Z ∈ RN ×(P +K)×d . The encoder then operates in two sequential phases: Lt temporal attention layers first process each series independently across its own patches using Rotary Positional Embeddings (RoPE) [Su et al., 2021], capturing within-series temporal structure; Lc cross-series attention layers then apply attention across all N series at each patch position, allowing each series to condition on the full labeled context. Queries attend to support examples but not to one another (see Appendix B.2 for details). Finally, a compression layer collapses each series into its K CLS vectors by attending only over patch positions, producing a compact series summary ri ∈ RK×d .

Predictive Dist. for each query

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Label Conditioning. A key advantage of the end-to-end paradigm is that class labels are available throughout the forward pass. We exploit this by conditioning the encoder directly on label identity. Concretely, following TabICLv2 [Qu et al., 2026], a learned class embedding is added to each training series’ patch representations, while query series receive no such signal. This allows subsequent attention layers to build class-aware contextual representations that are more discriminative and separable across classes, while preserving the label ambiguity of query patches that the model must resolve through incontext reasoning.

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Figure 3: Architecture of T IM EE.

In-Context Reasoning. Given compressed summaries of all series, the in-context reasoning layers perform the classification decision by comparing each query against the labeled support examples in the context. The N series summaries {ri } are processed by Licl = 2 transformer layers operating in a 512-dimensional space. Class embeddings are again added to training summaries to keep support representations class-aware at this stage. The same masking strategy applies (Appendix B.2), ensuring queries attend over labeled support examples without conditioning on one another. Decoder. To produce a final classification decision, query representations are passed through layer norm and a two-layer MLP to produce logits over C classes. The model is trained with cross-entropy loss over query positions (Equation 1). 6

Many-Class Extension. T IM EE is trained with at most Cmax = 10 classes, which covers the majority of UCR datasets. For datasets with C > Cmax , we adopt a one-vs-rest (OvR) decomposition strategy, reducing any C-class problem to C binary classification contexts. While more sophisticated strategies exist, we find OvR to be a simple and effective solution; we leave richer many-class handling as future work. 3.4

Pretraining and Inference

Pretraining Setup. T IM EE is pretrained on 7M synthetic TSC tasks, derived from 1.5M unique VARX-generated datasets via augmentation (Section 3.2). Each task is constructed by uniformly sampling a support-query split and cropping all series in the context to a shared length sampled uniformly from [16, 1024]. We train for 30K steps on a single NVIDIA H200 GPU with bf16 automatic mixed precision, taking approximately 40 hours. Following recent advances in optimizer design, we use Muon [Jordan et al., 2024] for matrix parameters and AdamW [Loshchilov and Hutter, 2019] for all remaining weights, which we find leads to faster and more stable convergence than AdamW alone. Details of pre-training setup are included in Appendix D.1. Inference. To optimize inference, T IM EE ensembles predictions across a small set of differently preprocessed inputs, combining two elementary transformations. We apply interpolation of short time series and first-order differencing, both individually and in composition. Final predictions are obtained by averaging predicted distributions across 4 ensemble members. We provide a more detailed description of our inference pipeline in Appendix D.2.

4

Experiments

Win Rate over ROCAUC T EE

4.1

Evaluation setup

Datasets. We evaluate T IM EE on the UCR archive [Chen et al., 2015], a standard benchmark comprising 128 univariate TSC datasets, using the data splits and loading pipeline provided by aeon [Middlehurst et al., 2024]4 . Baselines. We compare against a broad set of baselines spanning three categories (Section 2): classical and featurebased methods (DTW-1NN, Catch22, MiniRocket, Hydra), deep learning methods (InceptionTime, TSVec), and time series foundation models (NuTime, MOMENT, MantisV2, TiCT, Chronos-2, and TiRex).

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InceptionTime 51% - 57% 64% 61% 59% 79% 81% 75% 81% 91% 89% MiniRocket 40% 43% - 61% 63% 64% 83% 83% 71% 80% 93% 90% MantisV2 35% 36% 39% - 58% 60% 85% 79% 62% 82% 93% 87% Chronos-2 33% 39% 37% 42% - 46% 82% 82% 54% 84% 94% 83% TiRex 31% 41% 36% 40% 54% - 80% 80% 52% 83% 91% 85% NuTime 18% 21% 17% 15% 18% 20% - 46% 34% 56% 78% 75% Moment 13% 19% 17% 21% 18% 20% 54% - 30% 60% 73% 71% TS2Vec 23% 25% 29% 38% 46% 48% 66% 70% - 70% 82% 80% Catch22 14% 19% 20% 18% 16% 17% 44% 40% 30% - 79% 66% TICT 6% 9% 7% 7% 6% 9% 22% 27% 18% 21% - 59% Hydra 12% 11% 10% 13% 17% 15% 25% 29% 20% 34% 41% -

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Inc T ep tio EE Min nTim iR e Ma ocke t Ch ntisV ron 2 osTi 2 Nu Rex T Mo ime m TS ent 2 Ca Vec tch 22 TIC Hy T dra

We evaluate T IM EE against a broad set of state-of-the-art baselines for time series classification, assessing predictive performance, calibration, and inference efficiency.

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Figure 4: Win rate over ROC AUC across 128 UCR benchmark datasets. T IM EE ranks joint first alongside I NCEP TION T IME, outperforming all other compared methods. Notably, T IM EE outperforms all existing pre-trained foundation As discussed in Section 2.2, most foundation model base- models by a significant margin. lines require tuning—such as selecting the optimal intermediate layer representation—to achieve competitive performance; we therefore report both default and tuned results for these models. Full tuning details are provided in Appendix E. Regarding downstream classifier, for Catch22, MiniRocket, and Hydra, we use the aeon implementations with their canonical classifier pairings. For the remaining representation and foundation models, we select between Random Forest and SVM based on validation performance, with Random Forest generally preferred except for TS2Vec where SVM performs better. See Appendix E for more details. 4.2

Main Results

Figure 1 illustrates the mean rank across 128 UCR datasets. T IM EE achieves the best mean rank on ROC AUC, outperforming all baselines in class discrimination. While T IM EE ranks 3rd in Accuracy, its superior ROC AUC suggests it is the most robust choice across varying deployment thresholds and class distributions [Provost et al., 1998]. Notably, ridge-regression-based models like H YDRA and M INI ROCKET rank substantially lower on ROC AUC despite competitive accuracy, a discrepancy 7

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Figure 6: Pareto front of inference speed vs. ROC AUC on UCR datasets with at most 10 classes. T IM EE lies on the Pareto front, approaching the performance of M INI ROCKET with 15-20x faster inference.

indicative of overconfident predictions that degrade outside of a fixed 0.5 decision threshold. We present full per-dataset results in Appendix F.3 Probabilistic Calibration. To evaluate whether these scores represent well-calibrated probabilities, we report mean rank over log-loss for datasets with ≤ 10 classes5 (n = 102) in Figure 5. T IM EE achieves the top rank by a significant margin. As Log Loss is a strictly proper scoring rule, this result confirms that T IM EE provides better-calibrated probabilistic estimates. The gap in Accuracy suggests that while ridge-based methods may force correct hard-label decisions on boundary samples via their objective function, T IM EE maintains a more reliable representation of uncertainty, yielding more robust inputs for downstream decision-making. Inference Speed. T IM EE’s end-to-end ICL mechanism enables fast inference without any per-dataset training. While many other methods require a costly separate training phase, T IM EE combines the traditional fit+predict stages in a single forward pass that directly produces predictions. As a result of this, as shown in Figure 6, T IM EE lies on the Pareto front of inference speed vs. predictive performance. Note that this comparison is restricted to datasets with at most 10 classes, as OvR is required for larger class counts and this introduces additional inference overhead (see Appendix Figure 15). This remains as a limitation of T IM EE and is discussed in Section 5.

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We present ablation studies on: 1. examining how T IM EE can be extended to multivariate tasks; and 2. probing the Figure 7: Mean rank over ROC AUC on internal mechanisms that drive its in-context classification 24 UEA datasets. We compare two variants of T IM EE multivariate extensions: performance. (i) T IM EE (PV) denotes per-variate variant; (ii) T IM EE (VP) denotes variateMultivariate Extension. We consider two strategies for pooling variant. T IM EE reaches competadapting T IM EE to multivariate settings: (i) Per-variate: itive results despite being primary develpredict independently on each variate and average the reoped for univariate setting. sulting class probabilities; and (ii) Variate-pooling (details 5We restrict this to ≤ 10 classes as larger sets require OvR decomposition for T IM EE, which introduces normalization artifacts that would confound comparison against native multi-class baselines. We provide a comparison for > 10 classes in Appendix F.1

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Figure 8: Representation alignment across encoder stages. The leftmost panel shows six time series from a 2-shot binary classification task on synthetic data: class 0 (blue, sinusoidal) and class 1 (orange, sawtooth). The three heatmaps show pairwise cosine similarity of series representations at successive stages of the encoder, comparing the patch embeddings at (i) initial state; (ii) after temporal attention; (iii) after cross-series attention. in Appendix B.3): encode each variate independently and aggregate the M resulting CLS token sets via attention pooling before the ICL phase. The variate pooling variant is fine-tuned on synthetic multivariate data generated with our prior (Section 3.2). We evaluate both strategies against the baselines from Section 4 on the UEA archive. We restrict to 24 out of 30 UEA datasets6 as baselines’ prediction failure. As shown in Figure 7, the per-variate variant achieve competitive performance despite treating variates independently. Fine-tuning the variate-pooling variant, however, only yields a marginal gain. We attribute this to a limitation of our synthetic data generation: although the prior is natively extensible to multivariate inputs, the per-variate discriminative signal appears sufficient in practice, leaving little room for cross-variate aggregation to help. We discuss this further in Appendix C.1.3. How the Encoder Stack Builds Class-Discriminative Representations. To understand how the encoder progressively builds class-discriminative representations, Figure 8 traces pairwise cosine similarities across its successive stages. Initially, patch embeddings are largely undifferentiated – similarities are uniformly high across all series regardless of class membership. Temporal attention begins to differentiate series by refining within-series structure, and same-class representations grow slightly more similar to one another. Cross-series attention then sharply accentuates this emerging structure akin to a contrastive separation in representation space. Crucially, query series — which receive no class-label signal during the forward pass — nonetheless align to their correct class cluster, confirming that the encoder builds class-discriminative representations that prime the subsequent in-context reasoning stage.

5

Conclusion

We introduced T IM EE, a foundation model for time series classification that departs from the twostage paradigm by framing TSC as an in-context learning problem. The key enabler is a synthetic prior grounded in a structured data-generating process, which produces labeled classification tasks where class identity reflects meaningful differences in the underlying dynamics. To our knowledge, no prior work addresses this for TSC. Our strong empirical results on the 128 UCR datasets suggest that the gap between the two-stage paradigm and end-to-end ICL is not merely from architecture, but also from the right synthetic prior and the ability to leverage class structure at inference time. We hope this work encourages further exploration of prior design, model scale, and richer class generation mechanisms, which is likely to lead to further substantial performance improvements. Limitation 1: Many-class handling. T IM EE is pre-trained with at most 10 classes and relies on a one-vs-rest decomposition for larger label spaces, which introduces significant inference overhead and diminishes the speed advantage of ICL-based classification (Figure 15). Extending T IM EE to natively support larger class counts is an important direction for future work. Limitation 2: Multivariate classification. Extending T IM EE to multivariate inputs via variate pooling yields only marginal gains over the simpler per-variate baseline, which we attribute to a limitation of the VARX prior: class-discriminative information tends to concentrate in individual 6 SpokenArabicDigits, InsectWingbeat, PhonemeSpectra, FaceDetection, EigenWorms, and PenDigits are excluded.

9

variates, leaving little signal for cross-variate aggregation to exploit. Designing priors that better leverage inter-variate structure remains an open problem. Future Direction: Prior design and scale. T IM EE is a small model trained on a single family of synthetic priors. The strong UCR results suggest that prior quality is a primary lever for performance in this paradigm — richer class generation mechanisms and larger model scale are therefore natural and promising avenues for future work.

10

Acknowledgments and Disclosure of Funding J.K. is supported by the Konrad Zuse School of Excellence in Learning and Intelligent Systems (ELIZA) through the DAAD program Konrad Zuse Schools of Excellence in Artificial Intelligence, sponsored by the Federal Ministry of Education and Research. L.P. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under SFB 1597 (SmallData), grant number 499552394; F.H. acknowledges the financial support of the Hector Foundation. The authors gratefully acknowledge the computing time made available to them on the high-performance computer at the NHR Center of TU Dresden. This center is jointly supported by the Federal Ministry of Research, Technology and Space of Germany and the state governments participating in the NHR (www.nhr-verein.de/unsere-partner). We thank the maintainers of the UCR [Chen et al., 2015] and UEA [Bagnall et al., 2018] archives for providing and maintaining the datasets used for evaluation. We thank the developers of open-source libraries used in the development of T IM EE, including but not limited to: torch [Paszke et al., 2017], transformers [Wolf et al., 2020], scikit-learn [Pedregosa et al., 2011], numpy [Harris et al., 2020] and aeon [Middlehurst et al., 2024].

Author Contributions J.K. and S.B.H. co-led the project, code development and experiments and writing of the paper. J.K. led the synthetic data generation and contributed to the model development, training infrastructure, and evaluation. S.B.H. led the model development and contributed to the synthetic data generation, training infrastructure, and evaluation. M.M. contributed to the evaluation and writing of the paper. F.H. supervised L.P. during the project. L.P. supervised J.K., S.B.H., and M.M. during the project, contributed ideas, and technical advice.

Competing Interests L.P., and F.H. are affiliated with Prior Labs, a company focused on developing tabular foundation models. The authors declare no further competing interests.

References Abdul Fatir Ansari, Lorenzo Stella, Ali Caner Turkmen, Xiyuan Zhang, Pedro Mercado, Huibin Shen, Oleksandr Shchur, Syama Sundar Rangapuram, Sebastian Pineda Arango, Shubham Kapoor, Jasper Zschiegner, Danielle C. Maddix, Hao Wang, Michael W. Mahoney, Kari Torkkola, Andrew Gordon Wilson, Michael Bohlke-Schneider, and Bernie Wang. Chronos: Learning the Language of Time Series. Transactions on Machine Learning Research, May 2024. ISSN 2835-8856. URL https://openreview.net/forum?id=gerNCVqqtR. Abdul Fatir Ansari, Oleksandr Shchur, Jaris Küken, Andreas Auer, Boran Han, Pedro Mercado, Syama Sundar Rangapuram, Huibin Shen, Lorenzo Stella, Xiyuan Zhang, Mononito Goswami, Shubham Kapoor, Danielle C. Maddix, Pablo Guerron, Tony Hu, Junming Yin, Nick Erickson, Prateek Mutalik Desai, Hao Wang, Huzefa Rangwala, George Karypis, Yuyang Wang, and Michael Bohlke-Schneider. Chronos-2: From Univariate to Universal Forecasting, October 2025. URL http://arxiv.org/abs/2510.15821. arXiv:2510.15821 [cs]. Andreas Auer, Daniel Klotz, Sebastinan Böck, and Sepp Hochreiter. Pre-trained forecasting models: Strong zero-shot feature extractors for time series classification, 2025a. URL https://arxiv. org/abs/2510.26777. Andreas Auer, Patrick Podest, Daniel Klotz, Sebastian Böck, Günter Klambauer, and Sepp Hochreiter. Tirex: Zero-shot forecasting across long and short horizons with enhanced in-context learning, 2025b. URL https://arxiv.org/abs/2505.23719. Anthony Bagnall, Hoang Anh Dau, Jason Lines, Michael Flynn, James Large, Aaron Bostrom, Paul Southam, and Eamonn Keogh. The uea multivariate time series classification archive, 2018, 2018. URL https://arxiv.org/abs/1811.00075. 11

Yanping Chen, Eamonn Keogh, Bing Hu, Nurjahan Begum, Anthony Bagnall, Abdullah Mueen, and Gustavo Batista. The UCR Time Series Classification Archive, July 2015. Angus Dempster, François Petitjean, and Geoffrey I Webb. Rocket: exceptionally fast and accurate time series classification using random convolutional kernels. arXiv preprint arXiv:1910.13051, 2019. Angus Dempster, Daniel F Schmidt, and Geoffrey I Webb. Minirocket: A very fast (almost) deterministic transform for time series classification. In Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining, pages 248–257, 2021. Angus Dempster, Daniel F Schmidt, and Geoffrey I Webb. Hydra: competing convolutional kernels for fast and accurate time series classification: A. dempster et al. Data Mining and Knowledge Discovery, 37(5):1779–1805, 2023. Juntao Fang, Shifeng Xie, Shengbin Nie, Yuhui Ling, Yuming Liu, Zijian Li, Keli Zhang, Lujia Pan, Themis Palpanas, and Ruichu Cai. Rethinking Zero-Shot Time Series Classification: From Task-specific Classifiers to In-Context Inference, January 2026. URL http://arxiv.org/abs/ 2602.00620. arXiv:2602.00620 [cs]. Vasilii Feofanov, Songkang Wen, Marius Alonso, Romain Ilbert, Hongbo Guo, Malik Tiomoko, Lujia Pan, Jianfeng Zhang, and Ievgen Redko. Mantis: Lightweight Calibrated Foundation Model for User-Friendly Time Series Classification, February 2025. URL http://arxiv.org/abs/2502. 15637. arXiv:2502.15637 [cs]. Vasilii Feofanov, Songkang Wen, Jianfeng Zhang, Lujia Pan, and Ievgen Redko. Mantisv2: Closing the zero-shot gap in time series classification with synthetic data and test-time strategies, 2026. URL https://arxiv.org/abs/2602.17868. Mononito Goswami, Konrad Szafer, Arjun Choudhry, Yifu Cai, Shuo Li, and Artur Dubrawski. MOMENT: a family of open time-series foundation models. In Proceedings of the 41st International Conference on Machine Learning, volume 235 of ICML’24, pages 16115–16152, Vienna, Austria, July 2024. JMLR.org. Léo Grinsztajn, Klemens Flöge, Oscar Key, Felix Birkel, Philipp Jund, Brendan Roof, Benjamin Jäger, Dominik Safaric, Simone Alessi, Adrian Hayler, Mihir Manium, Rosen Yu, Felix Jablonski, Shi Bin Hoo, Anurag Garg, Jake Robertson, Magnus Bühler, Vladyslav Moroshan, Lennart Purucker, Clara Cornu, Lilly Charlotte Wehrhahn, Alessandro Bonetto, Bernhard Schölkopf, Sauraj Gambhir, Noah Hollmann, and Frank Hutter. Tabpfn-2.5: Advancing the state of the art in tabular foundation models, 2026. URL https://arxiv.org/abs/2511.08667. C. Harris, K. Millman, S. van der Walt, R. Gommers, P. Virtanen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. Smith, R. Kern, M. Picus, S. Hoyer, M. van Kerkwijk, M. Brett, A. Haldane, J. del Río, M. Wiebe, P. Peterson, P. Gérard-Marchant, K. Sheppard, T. Reddy, W. Weckesser, H. Abbasi, C. Gohlke, and T. Oliphant. Array programming with numpy. Nature, 585(7825):357–362, 2020. N. Hollmann, S. Müller, K. Eggensperger, and F. Hutter. TabPFN: A transformer that solves small tabular classification problems in a second. In The Eleventh International Conference on Learning Representations (ICLR’23). ICLR, 2023. N. Hollmann, S. Müller, L. Purucker, A. Krishnakumar, M. Körfer, Shi Bin Hoo, Robin Tibor Schirrmeister, and Frank Hutter. Accurate predictions on small data with a tabular foundation model. Nature, 637(8045):319–326, 2025. Hassan Ismail Fawaz, Benjamin Lucas, Germain Forestier, Charlotte Pelletier, Daniel F. Schmidt, Jonathan Weber, Geoffrey I. Webb, Lhassane Idoumghar, Pierre-Alain Muller, and François Petitjean. Inceptiontime: Finding alexnet for time series classification. Data Mining and Knowledge Discovery, 34(6):1936–1962, 2020. ISSN 1573-756X. doi: 10.1007/s10618-020-00710-y. URL http://dx.doi.org/10.1007/s10618-020-00710-y. Keller Jordan, Yuchen Jin, Vlado Boza, You Jiacheng, Franz Cesista, Laker Newhouse, and Jeremy Bernstein. Muon: An optimizer for hidden layers in neural networks, 2024. URL https://kellerjordan. github. io/posts/muon, 6(3):4, 2024. 12

Krzysztof Kamycki, Tomasz Kapuscinski, and Mariusz Oszust. Data augmentation with suboptimal warping for time-series classification. Sensors, 20(1):98, 2019. Chenguo Lin, Xumeng Wen, Wei Cao, Congrui Huang, Jiang Bian, Stephen Lin, and Zhirong Wu. Nutime: Numerically multi-scaled embedding for large-scale time-series pretraining, 2024. URL https://arxiv.org/abs/2310.07402. Ilya Loshchilov and Frank Hutter. Decoupled weight decay regularization, 2019. URL https: //arxiv.org/abs/1711.05101. Carl H Lubba, Sarab S Sethi, Philip Knaute, Simon R Schultz, Ben D Fulcher, and Nick S Jones. catch22: Canonical time-series characteristics, 2019. URL https://arxiv.org/abs/1901. 10200. Helmut Lütkepohl. New Introduction to Multiple Time Series Analysis. Springer, Berlin, Heidelberg, 2005. ISBN 978-3-540-40172-8 978-3-540-27752-1. doi: 10.1007/978-3-540-27752-1. URL http://link.springer.com/10.1007/978-3-540-27752-1. Matthew Middlehurst, Ali Ismail-Fawaz, Antoine Guillaume, Christopher Holder, David GuijoRubio, Guzal Bulatova, Leonidas Tsaprounis, Lukasz Mentel, Martin Walter, Patrick Schäfer, and Anthony Bagnall. aeon: a python toolkit for learning from time series. Journal of Machine Learning Research, 25(289):1–10, 2024. URL http://jmlr.org/papers/v25/23-1444.html. Samuel Müller, Noah Hollmann, Sebastian Pineda Arango, Josif Grabocka, and Frank Hutter. Transformers can do bayesian inference, 2024. URL https://arxiv.org/abs/2112.10510. A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer. Automatic differentiation in PyTorch. In A. Wiltschko, B. van Merriënboer, and P. Lamblin, editors, NeurIPS Autodiff Workshop, 2017. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay. Scikit-learn: Machine learning in Python. 12:2825–2830, 2011. Foster J. Provost, Tom Fawcett, and Ron Kohavi. The case against accuracy estimation for comparing induction algorithms. In Proceedings of the Fifteenth International Conference on Machine Learning, ICML ’98, page 445–453, San Francisco, CA, USA, 1998. Morgan Kaufmann Publishers Inc. ISBN 1558605568. Chen Qian, Xiucai Ding, and Lexin Li. Structural classification of locally stationary time series based on second-order characteristics. arXiv preprint arXiv:2507.04237, 2025. Jingang Qu, David Holzmüller, Gaël Varoquaux, and Marine Le Morvan. Tabicl: A tabular foundation model for in-context learning on large data, 2025. URL https://arxiv.org/abs/2502.05564. Jingang Qu, David Holzmüller, Gaël Varoquaux, and Marine Le Morvan. Tabiclv2: A better, faster, scalable, and open tabular foundation model, 2026. URL https://arxiv.org/abs/ 2602.11139. Hiroaki Sakoe and Seibi Chiba. Dynamic programming algorithm optimization for spoken word recognition. IEEE transactions on acoustics, speech, and signal processing, 26(1):43–49, 1978. Zhenmei Shi, Jiefeng Chen, Kunyang Li, Jayaram Raghuram, Xi Wu, Yingyu Liang, and Somesh Jha. The trade-off between universality and label efficiency of representations from contrastive learning. In The Eleventh International Conference on Learning Representations, 2023. URL https://openreview.net/forum?id=rvsbw2YthH_. Jianlin Su, Yu Lu, Shengfeng Pan, Bo Wen, and Yunfeng Liu. Roformer: Enhanced transformer with rotary position embedding, 2021. Floris Takens. Detecting strange attractors in turbulence. In Dynamical Systems and Turbulence, Warwick 1980: proceedings of a symposium held at the University of Warwick 1979/80, pages 366–381. Springer, 2006. 13

Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, Rémi Louf, Morgan Funtowicz, Joe Davison, Sam Shleifer, Patrick von Platen, Clara Ma, Yacine Jernite, Julien Plu, Canwen Xu, Teven Le Scao, Sylvain Gugger, Mariama Drame, Quentin Lhoest, and Alexander M. Rush. Transformers: State-of-the-art natural language processing. In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing: System Demonstrations, pages 38–45, Online, October 2020. Association for Computational Linguistics. URL https://aclanthology.org/2020.emnlp-demos.6/. Shifeng Xie, Vasilii Feofanov, Marius Alonso, Ambroise Odonnat, Jianfeng Zhang, Themis Palpanas, and Ievgen Redko. CauKer: classification time series foundation models can be pretrained on synthetic data only, August 2025. URL http://arxiv.org/abs/2508.02879. arXiv:2508.02879 [cs]. Chin-Chia Michael Yeh, Uday Singh Saini, Junpeng Wang, Xin Dai, Xiran Fan, Jiarui Sun, Yujie Fan, and Yan Zheng. Tict: A synthetically pre-trained foundation model for time series classification, 2025. URL https://arxiv.org/abs/2511.19694. Zhihan Yue, Yujing Wang, Juanyong Duan, Tianmeng Yang, Congrui Huang, Yunhai Tong, and Bixiong Xu. Ts2vec: Towards universal representation of time series, 2022. URL https: //arxiv.org/abs/2106.10466.

14

A

Related Work Details

A.1

Comparison to related methods for Time Series Classification

Table 1: Structural decomposition of compared methods into encoder Fθ and classifier Gϕ . New Gϕ indicates whether a task-specific classifier must be re-fitted for each new dataset. Class-aware indicates whether Fθ has access to the labeled support set at inference time. † Competitive performance requires tuning the intermediate layer used for feature extraction [Auer et al., 2025a]). Method

Encoder Fθ

New Gϕ per dataset

Class-aware at inference

1-NN Linear / SVM Ridge regression Ridge regression

— ✓ ✓

× × ×

✓

×

Softmax head (joint) Linear / SVM

✓

×

✓

×

>1M seq.

Linear / SVM

✓

×

Large real-TS corpus Large real-TS corpus CauKer synthetic

Linear SVM† Linear SVM† Linear SVM†

/

✓

×

/

✓

×

/

✓

×

Forecasting (quantile) Forecasting

Large TS corpus Large TS corpus

Linear SVM† Linear SVM†

/

✓

×

/

✓

×

ICL crossentropy (binary) ICL crossentropy

KernelSynth mixup

ICL head (bit-encoded labels) ICL head (single forward pass)

×

✓

×

✓

Fθ objective

Fθ data

Classifier Gϕ

— — —

— — —

—

—

Cross-entropy (joint) Contrastive (unsupervised)

Target dataset

Classical & Time Series Features Engineering Methods DTW-1NN Catch22 Rocket / MiniRocket Hydra

Dynamic warping distance 22 hand-crafted statistics Random conv. kernels; PPV & max pooling Competing random conv. kernels; per-group argmax counts

Per-dataset deep learning InceptionTime

Multi-scale conv. encoder

TS2Vec

Hierarchical contrastive encoder

Target dataset (unlabeled)

Foundation models — TSC-focused NuTime MOMENT Mantis MantisV2

Transformer; multi-scaled window embedding Masked autoencoder transformer ViT encoder

BYOL contrastive Masked reconstruction Contrastive

ViT encoder + test-time strategies

Contrastive

Foundation models — forecasting, repurposed Chronos-2

Transformer encoder

TiRex

Transformer encoder

End-to-end in-context learning TiCT

ResNet encoder

TimEE (ours)

Transformer encoder

A.2

VARX structured synthetic

Comparison T IM EE vs TiCT [Yeh et al., 2025]

Concurrent with this work, TiCT proposes end-to-end ICL for TSC with synthetic pre-training — the paradigm most directly related to ours. TiCT pre-trains a ResNet-based encoder on binary synthetic tasks via KernelSynth mixup, uses bit-based label encoding for arbitrary class counts, and selects context via 64-nearest-neighbor retrieval at inference. TimEE departs from TiCT in three key respects: our class generation mechanism — structural breaks in a VARX process – produces multi-class tasks where class identity reflects differences in the underlying dynamics; our transformer architecture explicitly models both temporal within-series structure and cross-series ICL; and we use the full training set as context without a retrieval step. We evaluate against substantially stronger baselines on both UCR and UEA. That TiCT and TimEE independently converge on the same paradigm strengthens the case that end-to-end ICL with synthetic pre-training is a promising direction for TSC. 15

B

Model Architecture

B.1

Model Hyperparameters

We report the model hyperparameters for T IM EE in Table 2 Table 2: Architecture hyperparameters of T IM EE. Hyperparameter Value Tokenization 16 16

Patch size Patch stride Architecture Model dimension dmodel Temporal layers, Lt Cross-series layers, Lc ICL layers, Licl Attention heads dkv dICLkv MLP hidden dimension Decoder MLP hidden dimension Dropout

128 5 5 2 4 32 64 512 512 0.1

Classification 4 10

CLS tokens Maximum classes

B.2

Attention Masking Strategy

Let S = {1, . . . , n} and Q = {n + 1, . . . , n + m} denote the indices of training and query series respectively, with N = n + m. The binary attention mask M ∈ {0, 1}N ×N , applied consistently across all cross-series attention layers, is defined as:  1 Mij = 1  0

if i ∈ S if i ∈ Q and j ∈ S ∪ {i} otherwise

(2)

where Mij = 1 indicates that series i is permitted to attend to series j, and masked positions are set to −∞ in the pre-softmax attention logits. The resulting block structure is:

S M= Q

 S Q ✓ ✓ ✓ I

(3)

Training series attend to all series; query series attend to all training series and themselves, but not to other query series. Temporal attention layers and the compression layer operate within each series independently and require no masking. B.3

Extension to Multivariate

Architecture. T IM EE is designed and trained to operate on univariate series only. To handle multivariate inputs X ∈ RN ×S×M , we encode each of the M variates independently through the 16

shared encoder, producing M sets of CLS token vectors per series. These are aggregated via slot-wise attention pooling: each of the K CLS slots has a learnable query that attends over the M variate embeddings via a softmax, allowing each slot to specialize on the most informative variates. The resulting pooled summary ri ∈ RK·d is then passed to the ICL phase. Fine-tuning Details. Queries are zero-initialized so that pooling starts as a uniform average, providing a stable initialization from the pretrained univariate checkpoint. The encoder weights are frozen and only the pooling queries, ICL block, and decoder are updated during multivariate fine-tuning. B.4

Ablation of Model Components.

We conduct the following ablation studies in the following training setup while we modify the architecture configuration by: • scaling down the model configuration to dkv = 16, nheads = 2; • fixing the sequence length at 512 with batch size 64; • training on our synthetic univariate data for 25K steps; • evaluating on the train split of 86 UCR datasets (defined by: at least 100 samples, the least frequent classes must at least have 2 examples) with stratified 3-fold cross-validation. Results reported are averaged over 3 seeds. Contribution of Temporal and Cross-Series Attention. We ablate the contribution of cross-series (vertical) attention within the encoder by varying the allocation of encoder layers between temporal (Lt ) and cross-series (Lc ) attention, keeping the total fixed at Lt + Lc = 8 with Licl = 2. Table 3: Ablation of encoder layer allocation between temporal and cross-series attention. Configuration

Lt

Lc

ROC AUC

Accuracy (%)

Temporal only

8 6 4 2 0

0 2 4 6 8

70.70 ± 0.08 71.06 ± 0.10 71.26 ± 0.09 71.20 ± 0.05 71.25 ± 0.02

78.21 ± 0.39 79.96 ± 0.29 80.32 ± 0.57 80.45 ± 0.36 79.65 ± 0.15

Base config Cross-series only

Removing cross-series attention entirely (Lc = 0) causes a clear 2pp drop, confirming that encoderlevel cross-series context provides complementary signal to the ICL phase and cannot be recovered from CLS-level comparison alone. Removing temporal attention (Lt = 0) causes a smaller but still notable drop of approximately 1pp; local patch features provide a partial substitute for temporal structure, while cross-series comparison at the patch level is harder to replicate from compressed representations. Performance is stable across all mixed configurations, indicating that the model is insensitive to the exact allocation as long as both components are present. We note that all configurations retain a single compression attention layer (Section 3.3), so the Lt = 0 condition is not strictly temporal-attention-free. Contribution of conditioning on Class Label. We ablate the two class embedding injection sites: patch-level conditioning (added to training patches before the encoder) and ICL-level conditioning (added to CLS tokens before the ICL block). Table 4: Ablation of label conditioning sites. Patch conditioning

ICL conditioning

ROC AUC

Accuracy (%)

✓ ✓ – –

✓ – ✓ –

71.26 ± 0.09 71.16 ± 0.08 71.01 ± 0.09 50.13 ± 0.43

80.32 ± 0.57 80.35 ± 0.13 78.55 ± 0.18 22.27 ± 0.37

17

Without any class conditioning, accuracy collapses to below 30%: the model has no access to label information during the forward pass and cannot associate support series with their classes. Patch-level conditioning is the dominant contributor—and in isolation sufficient: removing ICLlevel conditioning while retaining patch-level conditioning leaves accuracy essentially unchanged (80.32 → 80.35, within run-to-run variance), whereas retaining only ICL-level conditioning drops accuracy by ∼1.8pp (80.32 → 78.55), because the encoder’s cross-series attention operates on class-unaware patch representations and produces less discriminative CLS summaries. Although ICL-level conditioning provides no measurable benefit over patch-level conditioning alone, we retain it in our final model: it was included in the large-scale pretraining run, and the negligible overhead does not justify re-training without it. Together, the two sites interact non-linearly: their individual contributions do not account for the full ∼50pp collapse when both are removed, confirming that the model requires at least one explicit class signal to function.

18

C

Synthetic Data

C.1

Details on the T IM EE Prior

C.1.1

Sampling Procedure

Synthetic datasets under the structural variation mechanism are sampled from a VARX-based prior [Lütkepohl, 2005], in which class identity is determined by class-specific edge dropout applied to a shared base dependency graph. The full sampling procedure is given in Algorithm 1. Synthetic datasets under the signal variation mechanism are sampled from a VARX-based prior in which the dependency structure Ak , Bj remains fixed across all classes, and class identity is instead determined by statistical indicators of the exogenous input signal. The full sampling procedure is given in Algorithm 2. Algorithm 1 Structural Variation Prior Require: Number of classes C, Number of samples per class n, Max lag orders pmax , smax 1: Sample dimensions d ∼ U {dmin , dmax }, q ∼ U {1, qmax } 2: for c = 1, . . . , C do 3: Sample lag orders p ∼ U{1, pmax } and s ∼ U {0, smax } (c) 4: Sample sparse base coefficient matrices Ak ∈ Rd×d for k = 1, . . . , p (c) 5: Sample Bj ∈ Rd×q for j = 0, . . . , s 6: for i = 1, . . . , n do 7: Sample exogenous signal xt ∈ Rq for t = 1, . . . , T (c) (c) 8: Unroll VARX using Ak , Bj to obtain y1 , . . . , yT 9: Assign class label yi ← c 10: end for 11: end for (1:T ) 12: return {(yi , yi )}

Algorithm 2 Signal Variation Prior Require: Number of classes C, Number of samples per class n, Max lag orders pmax , smax , Signal variation range [ωmin , ωmax ] 1: Sample dimensions d ∼ U {dmin , dmax }, q ∼ U {1, qmax } 2: for c = 1, . . . , C do 3: Sample lag orders p ∼ U{1, pmax } and s ∼ U{0, smax } (c) 4: Sample sparse base coefficient matrices Ak ∈ Rd×d for k = 1, . . . , p (c) 5: Sample Bj ∈ Rd×q for j = 0, . . . , s 6: Partition [ωmin , ωmax ] into C buckets {Wc }C c=1 7: for c = 1, . . . , C do 8: for i = 1, . . . , n do 9: Sample base exogenous signal x̃t ∈ Rq for t = 1, . . . , T 10: Sample signal variation ωi ∼ U(Wc ) (i) 11: Apply signal variation ωi to base exogenous signal x̃i to obtain xt (c) (c) 12: Unroll VARX using Ak , Bj to obtain y1 , . . . , yT 13: Assign class label yi ← c 14: end for 15: end for 16: end for (1:T ) 17: return {(yi , yi )}

19

C.1.2

Relation to ARX

The VARX process described in Section 3.2 naturally subsumes the univariate setting as a special case. For d = 1, the system reduces to a scalar AutoRegressive process with Exogenous inputs (ARX):

yt =

p X

ak yt−k +

s X

b⊤ j xt−j + εt ,

εt ∼ N (0, σ 2 )

j=0

k=1

where ak ∈ R and bj ∈ Rq are the scalar and exogenous coefficient vectors respectively. All structural properties of our original VARX prior, the class-discriminative structural variations as well as the signal variations, carry over directly to this special case without modification. This ensures that the same DGP underlies both the univariate and multivariate synthetic data, and that results on univariate benchmarks such as UCR are fully consistent with the general VARX formulation. We note, however, that the limited transfer from multivariate synthetic pre-training data to real-world multivariate classification tasks remains a limitation of T IM EE and identify it as an active avenue for future research. C.1.3

Multivariate Synthetic Data

Synthetic VARX: best single-variate vs. all-variates lift (N=20)

Lift (acc - chance)

0.5

best single variate variate-pooling

0.4 0.3 0.2 0.1 0.0

0

1

2

3

4

5

6

7

8

9

10

11

Dataset index

12

13

14

15

16

17

18

19

Gap (all - best single)

LiftDataset gain from using all variates overvariation best single variate Figure 9: generated using structural mechanism. 0.06

Our 0.04VARX-based prior natively supports multivariate data generation for arbitrary d > 1, and using the extension discussed in Section 4.3 T IM EE can in principle be applied to multivariate time series 0.02 classification tasks directly. However, we observe that in synthetically generated VARX datasets, the information necessary for class discrimination is typically well-concentrated in individual variates 0.00 already. As a consequence, averaging predictions across all d variates rarely improves over the best single-variate prediction, and often even degrades performance due to the inclusion of uninformative 0.02 channels. This behavior is consistent with observations in the forecasting literature [Ansari et al., 0.04 and finds motivation in Takens’ embedding theorem [Takens, 2006], which states that under 2025] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Dataset index mild conditions, an observation function of a dynamical system suffices to reconstruct the full state space of that system. While Takens’ theorem applies strictly to deterministic smooth dynamical systems, the underlying intuition is suggestive in our setting: in the VARX process, each observed (i) yt is a linear combination of the full history of all endogenous and exogenous variables, meaning inter-variable information naturally propagates into individual channels through the autoregressive dynamics. We highlight this through an empirical study on 20 synthetic multivariate datasets generated by the T IM EE prior, shown in Figure 9. For each dataset, we compare the predictive performance of the single best univariate prediction - that is, the best performance achieved by any individual variate, against predictions obtained via variate pooling as described in Section 4.3. In nearly all datasets, variate pooling fails to improve over the single best variate prediction, and in several cases actively degrades performance. This confirms that under our VARX prior, class-discriminative information is already captured by individual variates, and aggregating across channels provides little to no benefit. 20

C.2

Augmentations

Smoothing. We apply a Gaussian filter with bandwidth σ ∼ U (σmin , σmax ), independently sampled per time series. Spike Injection. The number of spikes ns ∼ U{nmin , nmax } is sampled per series. Spike positions are drawn uniformly from {1, . . . , T }, and each spike amplitude is sampled independently as s ∼ U(smin , smax ), giving yt′ = yt + s · 1 for a randomly drawn position t. Nonlinear Transformation. A nonlinearity is sampled uniformly from {tanh, sin, ReLU, | · |} and applied pointwise as yt′ = g(yt ). C.3

Mixup

To further diversify our synthetic pre-training datasets, we follow the mixup scheme used to augment forecasting data [Ansari et al., 2025, Auer et al., 2025b]. We adapt this mechanism to the classification setting by forming convex combinations of samples drawn from within the same dataset, thereby preserving label structure while increasing intra-class diversity. Concretely, given k time series samples ỹ(1) , . . . , ỹ(k) drawn from arbitrary classes, the mixed sample is: ymix =

k X

λi ỹ(i) ,

λ ∼ Dir(α)

i=1

where ∼ U {1, Kmax } and mixing weights λ are drawn from a Dirichlet distribution. The full procedure is described in Algorithm 3. Algorithm 3 Time Series Mixup Require: Dataset D := {y(1:t) , y}, Target Length T 1: Dout ← ∅ (1:t) 2: Sample subset of time series {(yi , yi )} ⊂ D 3: Preprocessing: 4: yi (1:t) ← Normalize(yi (1:t) ) 5: yi (1:T ) ← Resize(yi (1:t) , T ) 6: Mixture Generation: (1:T ) k 7: Select k samples {yj }j=1 with labels {yj }kj=1 8: Sample weights λ ∼ Dirichlet(α) Pk (1:T ) (1:T ) 9: ymix ← j=1 (λj · yj ) + N (0, Σ) 10: Pseudo-Label Assignment: 11: Assign ymix based on λ and {yj } using threshold (1:T ) 12: Append (ymix , ymix ) to Dout 13: return Dout

C.4

▷ Interpolate or truncate

Examples of synthetic data

We present example datasets generated from our synthetic prior, for different class generation mechanisms. Figures 10, 11 present samples generated by structural variation. Figures 12 13 present datasets generated by signal level variation. Further we showcase the impact of the mixup scheme described in Section C.3 on a generated synthetic dataset, where Figure 14a shows the originally sampled dataset before applying mixup while Figure 14b shows the same dataset after applying mixup.

21

Class 1

Class 2

Class 3

Class 4

Class 5

Figure 10: Dataset generated using structural variation mechanism.

Class 1

Class 2

Class 3

Figure 11: Dataset generated using structural variation mechanism.

D

Pretraining and Inference

D.1

Pretraining Configurations

Table 5 summarizes the full set of hyperparameters used during pretraining. D.2

Inference Pipeline

At inference, we found it beneficial to apply lightweight preprocessing transformations and ensemble predictions across differently preprocessed inputs. Concretely, we consider two elementary transformations: interpolation of short time series to a target length in {128,256,512}, and first-order differencing. Each ensemble member is formed from one of the individual transformation (or compositions of multiple individuals). Final predictions are obtained by averaging the predicted distributions across all members. By default, T IM EE ensembles 4 preprocessing variants.

22

Class 1

Class 2

Figure 12: Dataset generated using signal variation mechanism.

Class 1

Class 2

Figure 13: Dataset generated using signal variation mechanism.

23

Class 1

Class 2

Class 1

(a) Dataset generated using signal variation before applying the mixup scheme.

Hyperparameter

Class 2

(b) Dataset generated using signal variation after applying the mixup scheme.

Table 5: Pretraining hyperparameters. Value

Training steps Warmup steps Learning rate LR schedule Optimizer (matrix weights) Optimizer (non-matrix weights) Batch size Mixed precision Number of classes C Support-query split Series length Hardware Training time

E

Implementation of Baselines

E.1

Statistical Methods

30,000 1,500 (5% of total) 3 × 10−4 Cosine decay with linear warmup Muon [Jordan et al., 2024] AdamW [Loshchilov and Hutter, 2019] 240 bf16 AMP Uniform ∼ U{2, 10} per task Uniform ∼ U[0.1, 0.9] per task Uniform ∼ U[16, 1024], shared across context Single NVIDIA H200 GPU ≈ 40 hours

MiniRocket [Dempster et al., 2021]: We apply MiniRocket feature extraction followed by a StandardScaler and RidgeClassifierCV, using the aeon implementation. Hydra [Dempster et al., 2023]: We use the aeon implementation with default hyperparameters. Catch22 [Lubba et al., 2019]: We extract 22 canonical time-series summary statistics via pycatch22 and classify with a RandomForestClassifier (n_estimators=300). DTW-1NN [Sakoe and Chiba, 1978]: 1-nearest-neighbour classifier with Dynamic Time Warping distance, using the aeon implementation. E.2

Deep Learning Methods

TS2Vec [Yue et al., 2022]: A contrastive self-supervised encoder trained independently per dataset with output dimension 320. We extract full-series embeddings and classify with an SVM whose regularisation parameter C is selected via 5-fold cross-validation on the training set. InceptionTime [Ismail Fawaz et al., 2020]: An ensemble of 5 InceptionTime networks trained for 1500 epochs per dataset, using the aeon implementation. 24

E.3

Foundation Models

For all foundation models we use a RandomForestClassifier from scikit-learn [Pedregosa et al., 2011] with n_estimators=300 consistent with Feofanov et al. [2026]. All remaining hyperparameters take their default values. Where a tuned variant is reported, we select the encoder layer whose embeddings yield the highest mean ROCAUC across the evaluation suite and apply it uniformly across all datasets. E.3.1

TSC Foundation Models

Mantis-V2 [Feofanov et al., 2026]: We use the official implementation. 7 As Mantis-V2 requires input sequences of length divisible by num_patches, we interpolate to next higher num patches. For the tuned version, embeddings from the 3rd layer yielded the strongest downstream performance. We also interpolate each time series to a minimum length of 512. Moment [Goswami et al., 2024]: We use the large size model for all experiments with Moment. We follow all defaults from the official implementation. 8 Using later encoder layers performs comparably; we use the 13th layer for the univariate setting and the 11th for the multivariate setting. NuTime [Lin et al., 2024]: A window-based ViT pretrained via BYOL on UCR datasets. We extract the frozen CLS-token embedding and classify with the above classifier. Input series are resampled to length 512. For the tuned variant, embeddings from the 6th layer yielded the strongest downstream performance. TiCT [Yeh et al., 2025]: A 47M-parameter ResNet pretrained for in-context time series classification. For each test sample, we retrieve its 64 nearest neighbours from the training set as context and perform a single forward pass; no separate classifier is required. E.3.2

Forecasting Models

For both forecasting models, we extract patch-level embeddings per time series, apply mean pooling over patches to obtain a fixed-size representation, and classify using the above mentioned classifier. Chronos-2 [Ansari et al., 2025]: We use the base model throughout. By default, embeddings are extracted from the final encoder layer. For the tuned variant, we take embeddings from the 5th layer, which yielded the strongest downstream performance. TiRex [Auer et al., 2025b]: We apply the same extraction and classification strategy. For the tuned variant, we likewise use the 6th layer, following the same selection procedure. E.4

Multivariate Setting

For models where we implement the multivariate adaptation ourselves, we reuse the best layer settings identified in the univariate search. Per-channel embeddings are concatenated before classification; mean pooling consistently degraded performance across models. We use a RandomForestClassifier throughout, as SVMs struggled with the extended embedding dimension produced by concatenation. TiCT classifies each channel independently and averages the per-channel softmax probabilities. DTW-1NN, MiniRocket, Hydra, and InceptionTime use their native multivariate implementations via aeon without modification. For TiRex, reusing the univariate tuned settings did not transfer to the multivariate setting and the default outperforms the tuned version.

F

Experiment Results

F.1

Inference Time vs. Performance on datasets

To evaluate the trade-off between the inference efficiency and the predictive performance, we measure the inference time of each method. For GPU baselines, we evaluate all GPU-accelerated candidates on a NVIDIA H100 GPU; for CPU baselines, we evaluate them on 32-cores AMD EPYC 9655. 7 https://github.com/vfeofanov/mantis 8 https://github.com/moment-timeseries-foundation-model/moment

25

> 10 Classes (n=25)

85

MiniRocket

Mean Raw Accuracy (%)

80 75

T EE

MantisV2

Hydra InceptionTime

TS2Vec TiRex Chronos-2

70 Catch22 Moment

65 NuTime 60 55

TICT

101 102 Mean Total Time (seconds, log scale)

100

Statistical Deep Learning

FMs Pareto Front

103

GPU CPU

Figure 15: Pareto front of inference speed vs. predictive performance on UCR datasets with more than 10 classes. OneVsRest many-class strategy of T IM EE imposes significant inference overhead. This remains as a limitation of T IM EE. F.2

Critical Difference Diagram CD = 2.18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

T EE (4.66)

(14.08) TICT

InceptionTime (5.39)

(13.46) Hydra

MiniRocket (5.44)

(11.48) Catch22 (11.11) NuTime (Default)

MantisV2 (Tuned) (6.04)

(10.95) Moment (Default)

Chronos-2 (Tuned) (6.60)

(10.82) NuTime (Tuned)

TiRex (Tuned) (6.70)

(10.66) Moment (Tuned)

TiRex (Default) (6.83)

(10.64) MantisV2 (Default)

TS2Vec (8.12)

(10.01) Chronos-2 (Default)

Pairwise ROCAUC CD Diagram

Figure 16: Critical difference diagram over ROC AUC across 128 UCR datasets (Wilcoxon–Holm post-hoc test, α = 0.05). Methods connected by a horizontal bar are not significantly different. F.3

Per-dataset results

26

Table 6: UCR univariate ROCAUC. Bold = best per dataset. Dataset ACSF1 Adiac AllGestureWiimoteX AllGestureWiimoteY AllGestureWiimoteZ ArrowHead BME Beef BeetleFly BirdChicken CBF Car Chinatown ChlorineConcentration CinCECGTorso Coffee Computers CricketX CricketY CricketZ Crop DiatomSizeReduction DistalPhalanxOutlineAgeGroup DistalPhalanxOutlineCorrect DistalPhalanxTW DodgerLoopDay DodgerLoopGame DodgerLoopWeekend ECG200 ECG5000 ECGFiveDays EOGHorizontalSignal EOGVerticalSignal Earthquakes ElectricDevices EthanolLevel FaceAll FaceFour FacesUCR FiftyWords Fish FordA FordB FreezerRegularTrain FreezerSmallTrain Fungi GestureMidAirD1 GestureMidAirD2 GestureMidAirD3 GesturePebbleZ1 GesturePebbleZ2 GunPoint GunPointAgeSpan GunPointMaleVersusFemale GunPointOldVersusYoung Ham HandOutlines Haptics Herring HouseTwenty InlineSkate InsectEPGRegularTrain InsectEPGSmallTrain InsectWingbeatSound ItalyPowerDemand LargeKitchenAppliances Lightning2 Lightning7 Mallat Meat MedicalImages MelbournePedestrian MiddlePhalanxOutlineAgeGroup MiddlePhalanxOutlineCorrect MiddlePhalanxTW MixedShapesRegularTrain MixedShapesSmallTrain MoteStrain NonInvasiveFetalECGThorax1 NonInvasiveFetalECGThorax2 OSULeaf OliveOil

DTW-1NN Catch22 MiniRocket Hydra InceptionTime TS2Vec TICT Chronos-2 TiRex Moment NuTime MantisV2 TimEE – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

0.986 0.985 0.886 0.901 0.899 0.892 0.983 0.801 0.850 0.980 0.997 0.904 0.987 0.677 0.949 1.000 0.806 0.906 0.928 0.914 0.961 0.995 0.865 0.871 0.845 0.829 0.765 0.997 0.908 0.911 0.956 0.905 0.870 0.692 0.911 0.617 0.966 0.942 0.949 0.934 0.965 0.967 0.845 1.000 0.995 0.997 0.981 0.978 0.928 0.968 0.958 0.994 0.995 1.000 0.997 0.672 0.918 0.746 0.511 0.983 0.808 0.997 0.959 0.930 0.959 0.953 0.869 0.935 0.997 0.974 0.964 0.975 0.650 0.854 0.753 0.989 0.975 0.946 0.996 0.996 0.945 0.917

0.996 0.979 0.940 0.959 0.951 0.978 1.000 0.954 1.000 0.900 1.000 0.968 0.995 0.878 0.970 1.000 0.794 0.974 0.980 0.974 0.973 0.975 0.892 0.871 0.879 0.903 0.941 0.984 0.965 0.886 1.000 0.894 0.835 0.672 0.890 0.811 0.997 1.000 0.998 0.983 0.998 0.988 0.891 1.000 0.995 1.000 0.975 0.970 0.898 0.989 0.983 1.000 1.000 1.000 1.000 0.812 0.961 0.813 0.768 0.991 0.814 1.000 1.000 0.947 0.993 0.957 0.803 0.974 0.998 1.000 0.969 0.997 0.599 0.919 0.781 0.997 0.994 0.976 0.998 0.998 0.996 0.989

0.917 0.911 0.835 0.851 0.825 0.883 1.000 0.896 0.900 0.900 0.995 0.953 0.988 0.785 0.997 1.000 0.716 0.895 0.914 0.889 0.861 0.952 0.830 0.768 0.741 0.717 0.817 0.984 0.850 0.762 1.000 0.767 0.724 0.490 0.809 0.726 0.968 0.931 0.966 0.861 0.994 0.961 0.825 0.998 0.926 1.000 0.872 0.836 0.732 0.933 0.929 1.000 1.000 1.000 1.000 0.742 0.927 0.695 0.735 0.956 0.703 1.000 1.000 0.810 0.966 0.912 0.715 0.895 0.966 0.938 0.837 0.961 0.601 0.826 0.639 0.988 0.977 0.927 0.970 0.977 0.990 0.945

0.996 0.992 0.962 0.976 0.972 0.976 1.000 0.942 1.000 1.000 1.000 0.955 0.996 0.947 0.971 1.000 0.880 0.984 0.989 0.988 0.981 0.997 0.858 0.851 0.854 0.852 0.917 0.992 0.967 0.927 1.000 0.930 0.879 0.662 0.894 0.958 0.995 0.992 0.999 0.991 1.000 0.992 0.937 1.000 0.900 1.000 0.958 0.938 0.807 0.987 0.970 1.000 1.000 1.000 1.000 0.828 0.983 0.821 0.734 0.972 0.841 1.000 1.000 0.938 0.990 0.979 0.905 0.967 0.999 0.997 0.972 0.999 0.599 0.905 0.759 0.998 0.989 0.955 0.999 0.999 0.997 0.967

27

0.989 0.981 0.949 0.946 0.954 0.937 1.000 0.889 0.990 0.800 1.000 0.909 0.989 0.919 0.950 1.000 0.744 0.976 0.971 0.973 0.980 1.000 0.881 0.787 0.866 0.862 0.980 0.991 0.957 0.936 1.000 0.903 0.862 0.544 0.916 0.695 0.994 0.972 0.995 0.958 0.992 0.983 0.875 0.998 0.956 0.008 0.920 0.880 0.740 0.949 0.965 0.998 0.999 1.000 1.000 0.770 0.948 0.792 0.641 0.957 0.781 1.000 1.000 0.949 0.985 0.951 0.937 0.976 0.989 0.998 0.974 0.998 0.649 0.901 0.768 0.989 0.978 0.933 0.998 0.998 0.973 0.903

0.777 0.922 0.876 0.874 0.854 0.895 0.848 0.858 0.880 0.990 0.992 0.836 0.977 0.711 0.862 0.995 0.744 0.894 0.905 0.917 0.942 0.969 0.856 0.825 0.818 0.850 0.916 0.991 0.882 0.884 0.921 0.805 0.787 0.637 0.840 0.597 0.966 0.940 0.931 0.905 0.944 0.958 0.807 0.971 0.851 0.988 0.958 0.946 0.827 0.962 0.957 0.985 0.999 1.000 0.996 0.718 0.929 0.733 0.654 0.989 0.738 0.983 0.899 0.866 0.934 0.853 0.789 0.909 0.871 0.805 0.943 0.972 0.633 0.842 0.741 0.986 0.948 0.956 0.984 0.988 0.925 0.696

0.989 0.994 0.912 0.922 0.934 0.936 1.000 0.928 0.970 0.970 1.000 0.934 0.996 0.851 1.000 1.000 0.828 0.960 0.966 0.958 0.977 0.999 0.904 0.878 0.874 0.879 0.942 0.997 0.927 0.942 0.996 0.909 0.871 0.673 0.918 0.686 0.988 0.982 0.976 0.973 0.988 0.977 0.872 0.999 0.973 0.996 0.981 0.983 0.959 0.989 0.990 1.000 1.000 1.000 1.000 0.783 0.953 0.807 0.740 0.982 0.804 1.000 0.988 0.953 0.993 0.972 0.824 0.972 0.998 1.000 0.962 0.998 0.645 0.939 0.783 0.995 0.989 0.981 0.996 0.997 0.991 0.991

0.990 0.992 0.922 0.944 0.935 0.964 1.000 0.992 1.000 0.940 1.000 0.940 0.995 0.874 1.000 1.000 0.808 0.953 0.967 0.957 0.980 0.991 0.899 0.866 0.875 0.905 0.921 0.992 0.934 0.953 1.000 0.915 0.907 0.719 0.902 0.852 0.997 1.000 0.989 0.965 0.994 0.991 0.924 1.000 0.983 0.997 0.978 0.984 0.951 0.989 0.992 0.999 0.998 1.000 1.000 0.825 0.947 0.797 0.720 0.991 0.843 1.000 0.998 0.959 0.993 0.932 0.815 0.971 1.000 0.994 0.972 0.998 0.649 0.921 0.763 0.998 0.994 0.979 0.998 0.998 0.995 0.982

0.976 0.989 0.902 0.924 0.917 0.945 0.991 0.924 1.000 0.980 0.996 0.911 0.995 0.832 0.900 1.000 0.733 0.954 0.960 0.956 0.972 0.997 0.881 0.877 0.878 0.808 0.880 0.988 0.946 0.936 0.967 0.886 0.831 0.635 0.893 0.638 0.972 0.964 0.958 0.972 0.989 0.962 0.846 0.968 0.861 0.999 0.972 0.982 0.917 0.981 0.981 0.997 0.992 0.999 0.995 0.792 0.945 0.776 0.659 0.975 0.712 0.980 0.972 0.946 0.990 0.900 0.861 0.955 0.998 1.000 0.963 0.987 0.627 0.921 0.790 0.983 0.962 0.971 0.997 0.997 0.964 0.973

0.972 0.988 0.907 0.883 0.911 0.912 0.960 0.942 0.950 1.000 0.999 0.932 0.982 0.789 0.947 0.995 0.832 0.946 0.959 0.950 0.970 0.993 0.877 0.842 0.858 0.819 0.848 0.985 0.905 0.911 0.914 0.865 0.778 0.709 0.900 0.631 0.949 0.989 0.958 0.953 0.997 0.962 0.842 0.999 0.995 0.974 0.947 0.955 0.873 0.961 0.971 0.994 0.997 0.998 1.000 0.825 0.939 0.775 0.656 0.956 0.742 1.000 1.000 0.900 0.950 0.891 0.778 0.956 0.992 0.996 0.955 0.996 0.666 0.867 0.738 0.992 0.986 0.991 0.991 0.994 0.960 0.958

0.977 0.994 0.945 0.947 0.956 0.940 1.000 0.915 1.000 0.990 1.000 0.941 0.989 0.831 0.959 1.000 0.794 0.977 0.978 0.981 0.979 0.986 0.906 0.869 0.885 0.863 0.886 0.991 0.928 0.916 0.984 0.937 0.857 0.613 0.912 0.614 0.963 0.993 0.982 0.971 0.991 0.981 0.881 1.000 0.987 0.997 0.974 0.979 0.938 0.990 0.993 0.998 1.000 1.000 1.000 0.733 0.952 0.806 0.766 0.992 0.821 1.000 1.000 0.942 0.982 0.925 0.847 0.966 0.997 1.000 0.968 0.998 0.645 0.931 0.779 0.996 0.990 0.987 0.996 0.997 0.996 0.991

0.983 0.992 0.947 0.960 0.954 0.975 1.000 0.997 1.000 0.960 1.000 0.956 0.995 0.803 1.000 1.000 0.722 0.981 0.988 0.986 0.984 1.000 0.886 0.876 0.891 0.923 0.972 0.991 0.957 0.952 1.000 0.929 0.891 0.730 0.897 0.878 0.999 1.000 0.995 0.985 0.996 0.987 0.901 1.000 0.991 1.000 0.980 0.982 0.938 0.979 0.970 0.996 1.000 1.000 1.000 0.780 0.966 0.817 0.526 0.988 0.802 0.998 0.992 0.959 0.994 0.867 0.898 0.979 0.999 1.000 0.972 0.997 0.642 0.928 0.762 0.999 0.997 0.973 0.999 0.999 0.990 0.982

Table 7: UCR univariate ROCAUC. Bold = best per dataset. (continued) Dataset

DTW-1NN Catch22 MiniRocket Hydra InceptionTime TS2Vec TICT Chronos-2 TiRex Moment NuTime MantisV2 TimEE

PLAID PhalangesOutlinesCorrect Phoneme PickupGestureWiimoteZ PigAirwayPressure PigArtPressure PigCVP Plane PowerCons ProximalPhalanxOutlineAgeGroup ProximalPhalanxOutlineCorrect ProximalPhalanxTW RefrigerationDevices Rock ScreenType SemgHandGenderCh2 SemgHandMovementCh2 SemgHandSubjectCh2 ShakeGestureWiimoteZ ShapeletSim ShapesAll SmallKitchenAppliances SmoothSubspace SonyAIBORobotSurface1 SonyAIBORobotSurface2 StarLightCurves Strawberry SwedishLeaf Symbols SyntheticControl ToeSegmentation1 ToeSegmentation2 Trace TwoLeadECG TwoPatterns UMD UWaveGestureLibraryAll UWaveGestureLibraryX UWaveGestureLibraryY UWaveGestureLibraryZ Wafer Wine WordSynonyms Worms WormsTwoClass Yoga

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

0.953 0.866 0.778 0.935 0.842 0.992 0.953 1.000 0.962 0.924 0.898 0.902 0.717 0.941 0.707 0.941 0.914 0.968 0.971 0.999 0.984 0.922 0.966 0.978 0.973 0.991 0.973 0.996 0.997 1.000 0.950 0.856 1.000 0.929 0.961 0.978 0.977 0.959 0.946 0.950 1.000 0.420 0.892 0.946 0.936 0.866

0.987 0.905 0.718 0.988 0.997 1.000 0.998 1.000 1.000 0.919 0.959 0.865 0.663 0.946 0.655 0.968 0.922 0.977 0.999 1.000 0.994 0.948 0.996 0.994 0.984 0.994 0.993 0.999 0.996 1.000 0.988 0.979 1.000 1.000 1.000 0.994 0.998 0.979 0.963 0.971 1.000 0.907 0.939 0.913 0.845 0.968

0.897 0.793 0.570 0.900 0.882 0.993 0.983 1.000 0.978 0.859 0.865 0.725 0.646 0.957 0.620 0.846 0.697 0.857 0.956 0.989 0.964 0.856 0.945 0.930 0.948 0.974 0.974 0.988 0.988 0.974 0.963 0.879 1.000 0.999 0.991 0.995 0.985 0.916 0.882 0.888 1.000 0.907 0.786 0.824 0.761 0.926

0.768 0.912 0.776 0.985 1.000 1.000 0.999 1.000 1.000 0.926 0.960 0.898 0.682 0.891 0.780 0.941 0.869 0.930 0.966 0.999 0.997 0.902 0.999 0.994 0.991 0.993 0.996 0.999 1.000 1.000 0.990 0.993 1.000 1.000 1.000 0.999 0.995 0.971 0.958 0.962 1.000 0.805 0.956 0.936 0.888 0.973

0.844 0.859 0.632 0.962 0.977 0.674 0.909 0.999 0.992 0.938 0.934 0.918 0.236 0.763 0.604 0.990 0.985 0.995 0.980 1.000 0.992 0.880 0.999 0.992 0.968 0.991 0.993 0.997 0.999 1.000 0.980 0.970 1.000 0.998 1.000 1.000 0.995 0.967 0.948 0.962 1.000 0.918 0.921 0.931 0.879 0.950

0.907 0.852 0.618 0.946 0.687 0.779 0.734 1.000 0.979 0.899 0.897 0.827 0.695 0.831 0.704 0.917 0.866 0.959 0.936 0.968 0.959 0.885 0.948 0.977 0.958 0.992 0.964 0.979 0.990 1.000 0.941 0.933 1.000 0.984 0.894 0.998 0.991 0.948 0.926 0.927 0.993 0.944 0.804 0.859 0.858 0.899

0.977 0.904 0.841 0.969 0.845 0.993 0.978 1.000 0.988 0.938 0.939 0.916 0.778 0.984 0.712 0.975 0.939 0.970 0.984 1.000 0.995 0.949 0.995 0.984 0.957 0.994 0.990 0.998 0.998 1.000 0.978 0.960 1.000 0.994 0.990 0.999 0.994 0.971 0.953 0.964 1.000 0.913 0.932 0.953 0.888 0.895

0.981 0.905 0.831 0.971 0.922 0.998 0.988 1.000 0.995 0.948 0.953 0.927 0.789 0.985 0.740 0.986 0.943 0.974 0.988 1.000 0.991 0.941 0.993 0.995 0.959 0.995 0.991 0.998 0.998 1.000 0.995 0.981 1.000 0.999 1.000 0.999 0.995 0.974 0.958 0.964 1.000 0.835 0.916 0.968 0.926 0.915

0.958 0.905 0.789 0.945 0.578 0.772 0.701 0.999 0.967 0.934 0.929 0.921 0.705 0.942 0.609 0.879 0.858 0.925 0.974 0.988 0.990 0.865 0.948 0.989 0.964 0.988 0.986 0.996 0.998 1.000 0.981 0.946 1.000 0.946 0.995 0.995 0.991 0.968 0.950 0.958 0.999 0.931 0.933 0.928 0.811 0.923

0.968 0.844 0.789 0.968 0.925 0.998 0.993 1.000 0.992 0.932 0.906 0.916 0.722 0.886 0.698 0.947 0.927 0.944 0.977 0.978 0.988 0.934 0.986 0.963 0.918 0.994 0.983 0.996 0.996 0.999 0.944 0.895 1.000 0.990 0.969 0.995 0.987 0.973 0.956 0.964 1.000 0.881 0.885 0.943 0.852 0.909

0.989 0.889 0.828 0.990 0.979 0.996 0.992 1.000 0.991 0.942 0.927 0.928 0.726 0.952 0.688 0.977 0.949 0.973 0.995 0.997 0.993 0.948 0.995 0.982 0.987 0.995 0.989 0.999 0.998 1.000 0.996 0.970 1.000 1.000 0.999 0.999 0.989 0.975 0.961 0.967 1.000 0.936 0.935 0.958 0.893 0.929

0.965 0.904 0.823 0.973 0.734 0.986 0.983 1.000 0.999 0.940 0.955 0.937 0.699 0.994 0.657 0.992 0.974 0.996 1.000 0.996 0.996 0.933 1.000 0.996 0.976 0.993 0.994 0.999 0.998 1.000 0.989 0.986 1.000 0.986 1.000 0.999 0.999 0.981 0.968 0.973 1.000 0.863 0.959 0.970 0.928 0.955

Average Mean rank

– nan

0.928 8.69

0.954 4.77

0.904 10.08

0.952 4.77

0.937 5.94

0.924 9.67

0.958 5.62

0.962 4.32

0.939 8.23

0.942 8.00

0.960 4.41

0.964 3.51

Table 8: UEA multivariate ROCAUC. Bold = best per dataset. Dataset

DTW-1NN Catch22 MiniRocket Hydra InceptionTime TS2Vec TiCT Chronos-2 TiRex Moment NuTime MantisV2 TimEE (VP) TimEE (PV)

ArticularyWordRecognition AtrialFibrillation BasicMotions CharacterTrajectories Cricket DuckDuckGeese ERing Epilepsy EthanolConcentration FingerMovements HandMovementDirection Handwriting Heartbeat JapaneseVowels LSST Libras MotorImagery NATOPS PEMS-SF RacketSports SelfRegulationSCP1 SelfRegulationSCP2 StandWalkJump UWaveGestureLibrary

– – – – – – – – – – – – – – – – – – – – – – – –

0.999 0.323 1.000 0.998 0.998 0.794 0.994 0.999 0.536 0.539 0.499 0.799 0.641 0.961 0.878 0.991 0.463 0.973 1.000 0.952 0.790 0.581 0.530 0.980

1.000 0.227 1.000 1.000 1.000 0.895 1.000 1.000 0.697 0.602 0.642 0.899 0.799 1.000 0.873 0.995 0.561 0.991 0.967 0.966 0.971 0.541 0.693 0.992

0.995 0.350 1.000 0.994 0.992 0.800 0.991 1.000 0.699 0.552 0.483 0.721 0.624 0.987 0.684 0.964 0.500 0.923 0.882 0.946 0.867 0.589 0.550 0.948

1.000 0.413 1.000 1.000 1.000 0.872 0.994 0.999 0.522 0.567 0.679 0.951 0.767 1.000 0.743 0.990 0.595 0.997 0.970 0.975 0.944 0.485 0.653 0.988

0.999 0.303 1.000 1.000 0.999 0.842 0.993 0.998 0.628 0.532 0.563 0.843 0.729 0.997 0.905 0.991 0.542 0.990 1.000 0.962 0.907 0.526 0.377 0.991

0.999 0.260 1.000 0.994 0.999 0.664 0.978 0.998 0.520 0.549 0.610 0.729 0.628 0.915 0.801 0.961 0.541 0.941 0.993 0.931 0.803 0.461 0.880 0.950

0.999 0.453 1.000 0.999 1.000 0.791 0.999 1.000 0.609 0.550 0.526 0.780 0.750 0.970 0.880 0.993 0.633 0.970 1.000 0.956 0.895 0.530 0.807 0.988

0.999 0.560 1.000 0.999 1.000 0.757 0.999 1.000 0.559 0.559 0.551 0.770 0.750 0.968 0.854 0.994 0.559 0.970 1.000 0.956 0.900 0.509 0.767 0.986

0.999 0.427 0.997 1.000 0.998 0.784 0.997 1.000 0.509 0.587 0.550 0.800 0.740 0.959 0.837 0.985 0.595 0.972 1.000 0.945 0.854 0.459 0.843 0.992

1.000 0.410 1.000 1.000 1.000 0.757 0.999 1.000 0.680 0.546 0.602 0.738 0.784 0.999 0.874 0.995 0.601 0.976 1.000 0.978 0.926 0.520 0.653 0.986

1.000 0.360 1.000 0.999 1.000 0.810 1.000 1.000 0.674 0.565 0.552 0.810 0.790 0.998 0.906 0.996 0.505 0.983 1.000 0.977 0.948 0.534 0.587 0.990

0.999 0.353 1.000 1.000 1.000 0.689 0.999 1.000 0.831 0.632 0.568 0.827 0.761 0.981 0.861 0.994 0.478 0.977 0.995 0.973 0.957 0.426 0.580 0.990

0.998 0.580 1.000 0.999 0.999 0.681 0.997 1.000 0.833 0.606 0.629 0.837 0.738 0.968 0.881 0.991 0.582 0.968 0.997 0.967 0.959 0.472 0.580 0.986

Average Mean rank

– nan

0.801 9.31

0.846 4.12

0.793 10.00

0.838 5.48

0.817 7.29

0.796 10.65

0.837 6.33

0.832 6.77

0.826 7.92

0.834 5.31

0.833 4.75

0.828 6.29

0.844 6.77

28

Table 9: UCR univariate accuracy. Bold = best per dataset. Best variant shown for models with multiple checkpoints. Dataset ACSF1 Adiac AllGestureWiimoteX AllGestureWiimoteY AllGestureWiimoteZ ArrowHead BME Beef BeetleFly BirdChicken CBF Car Chinatown ChlorineConcentration CinCECGTorso Coffee Computers CricketX CricketY CricketZ Crop DiatomSizeReduction DistalPhalanxOutlineAgeGroup DistalPhalanxOutlineCorrect DistalPhalanxTW DodgerLoopDay DodgerLoopGame DodgerLoopWeekend ECG200 ECG5000 ECGFiveDays EOGHorizontalSignal EOGVerticalSignal Earthquakes ElectricDevices EthanolLevel FaceAll FaceFour FacesUCR FiftyWords Fish FordA FordB FreezerRegularTrain FreezerSmallTrain Fungi GestureMidAirD1 GestureMidAirD2 GestureMidAirD3 GesturePebbleZ1 GesturePebbleZ2 GunPoint GunPointAgeSpan GunPointMaleVersusFemale GunPointOldVersusYoung Ham HandOutlines Haptics Herring HouseTwenty InlineSkate InsectEPGRegularTrain InsectEPGSmallTrain InsectWingbeatSound ItalyPowerDemand LargeKitchenAppliances Lightning2 Lightning7 Mallat Meat MedicalImages MelbournePedestrian MiddlePhalanxOutlineAgeGroup MiddlePhalanxOutlineCorrect MiddlePhalanxTW MixedShapesRegularTrain MixedShapesSmallTrain MoteStrain NonInvasiveFetalECGThorax1 NonInvasiveFetalECGThorax2 OSULeaf OliveOil PLAID PhalangesOutlinesCorrect Phoneme PickupGestureWiimoteZ PigAirwayPressure PigArtPressure PigCVP

DTW-1NN Catch22 MiniRocket Hydra InceptionTime TS2Vec TICT Chronos-2 TiRex Moment NuTime MantisV2 TimEE 0.620 0.609 0.717 0.730 0.651 0.800 0.980 0.667 0.700 0.700 0.996 0.767 0.953 0.650 0.930 1.000 0.620 0.772 0.759 0.746 0.712 0.935 0.626 0.725 0.633 0.588 0.927 0.978 0.880 0.925 0.797 0.475 0.475 0.727 0.619 0.282 0.808 0.886 0.912 0.758 0.846 0.691 0.607 0.907 0.676 0.823 0.639 0.600 0.377 0.826 0.778 0.913 0.965 0.975 0.965 0.600 0.862 0.412 0.531 0.941 0.387 0.827 0.695 0.585 0.955 0.795 0.869 0.712 0.914 0.933 0.747 0.816 0.520 0.766 0.506 0.909 0.833 0.866 0.811 0.871 0.612 0.867 0.834 0.761 0.227 0.660 0.096 0.197 0.159

0.830 0.719 0.529 0.613 0.521 0.760 0.933 0.600 0.750 0.850 0.961 0.783 0.921 0.599 0.808 1.000 0.724 0.579 0.546 0.636 0.651 0.941 0.712 0.783 0.669 0.519 0.693 0.944 0.820 0.938 0.777 0.552 0.456 0.748 0.725 0.352 0.764 0.648 0.695 0.602 0.749 0.920 0.752 0.998 0.950 0.903 0.746 0.662 0.469 0.779 0.753 0.953 0.956 0.994 0.975 0.600 0.854 0.445 0.578 0.958 0.451 0.960 0.827 0.566 0.881 0.827 0.705 0.671 0.899 0.867 0.762 0.804 0.617 0.766 0.532 0.918 0.864 0.867 0.852 0.882 0.707 0.700 0.767 0.784 0.309 0.540 0.308 0.909 0.538

0.910 0.813 0.729 0.753 0.736 0.869 1.000 0.833 0.900 0.900 0.999 0.917 0.983 0.758 0.868 1.000 0.732 0.808 0.828 0.826 0.763 0.928 0.748 0.761 0.669 0.688 0.850 0.984 0.920 0.945 1.000 0.605 0.519 0.748 0.738 0.596 0.807 0.989 0.958 0.840 0.977 0.951 0.804 1.000 0.968 1.000 0.738 0.692 0.446 0.907 0.899 0.993 0.997 1.000 1.000 0.686 0.943 0.526 0.688 0.966 0.476 1.000 1.000 0.669 0.966 0.856 0.754 0.795 0.946 0.967 0.797 0.969 0.571 0.838 0.526 0.969 0.951 0.932 0.945 0.964 0.959 0.933 0.922 0.837 0.285 0.880 0.870 0.986 0.947

0.850 0.818 0.703 0.731 0.686 0.834 1.000 0.833 0.900 0.900 0.993 0.933 0.983 0.760 0.995 1.000 0.716 0.800 0.841 0.805 0.734 0.948 0.763 0.786 0.712 0.519 0.819 0.976 0.870 0.949 1.000 0.572 0.492 0.734 0.752 0.588 0.898 0.886 0.956 0.842 0.989 0.961 0.825 0.998 0.926 1.000 0.754 0.685 0.485 0.890 0.886 1.000 1.000 1.000 1.000 0.743 0.941 0.513 0.750 0.958 0.491 1.000 1.000 0.655 0.966 0.883 0.721 0.808 0.941 0.917 0.778 0.931 0.597 0.835 0.539 0.981 0.965 0.929 0.943 0.958 0.988 0.933 0.873 0.823 0.324 0.820 0.769 0.986 0.966

0.930 0.831 0.774 0.789 0.806 0.846 1.000 0.667 0.850 0.950 0.999 0.883 0.985 0.855 0.845 1.000 0.832 0.841 0.862 0.862 0.797 0.941 0.719 0.757 0.683 0.571 0.858 0.984 0.930 0.941 1.000 0.616 0.486 0.748 0.708 0.822 0.796 0.955 0.962 0.791 0.983 0.961 0.859 0.997 0.840 0.995 0.669 0.508 0.246 0.855 0.835 1.000 0.978 0.997 1.000 0.705 0.957 0.558 0.703 0.924 0.473 1.000 1.000 0.631 0.969 0.896 0.787 0.849 0.949 0.933 0.795 0.975 0.513 0.842 0.552 0.967 0.916 0.897 0.963 0.962 0.950 0.800 0.467 0.838 0.352 0.920 0.947 1.000 0.952

29

0.890 0.754 0.726 0.721 0.709 0.829 0.987 0.667 0.850 0.800 0.999 0.683 0.959 0.825 0.775 1.000 0.660 0.797 0.756 0.815 0.750 0.967 0.727 0.732 0.676 0.662 0.921 0.984 0.910 0.935 1.000 0.506 0.506 0.748 0.731 0.454 0.777 0.886 0.929 0.765 0.920 0.927 0.798 0.984 0.885 0.962 0.485 0.392 0.200 0.692 0.722 0.980 0.965 0.997 1.000 0.676 0.916 0.523 0.594 0.908 0.424 1.000 1.000 0.617 0.964 0.861 0.869 0.822 0.887 0.933 0.812 0.964 0.649 0.825 0.584 0.920 0.855 0.860 0.937 0.940 0.843 0.900 0.540 0.772 0.310 0.740 0.644 0.971 0.861

0.400 0.481 0.570 0.583 0.493 0.766 0.687 0.600 0.850 0.900 0.942 0.617 0.930 0.601 0.643 0.964 0.688 0.603 0.579 0.610 0.656 0.869 0.719 0.732 0.683 0.532 0.858 0.944 0.790 0.927 0.861 0.403 0.390 0.755 0.629 0.340 0.739 0.784 0.684 0.587 0.754 0.898 0.723 0.896 0.807 0.796 0.646 0.577 0.338 0.767 0.759 0.940 0.972 0.997 0.987 0.667 0.886 0.451 0.656 0.899 0.384 0.900 0.795 0.494 0.867 0.717 0.754 0.712 0.501 0.617 0.758 0.805 0.578 0.784 0.545 0.919 0.797 0.899 0.769 0.813 0.727 0.400 0.667 0.784 0.183 0.700 0.139 0.332 0.250

0.850 0.831 0.586 0.639 0.601 0.829 0.987 0.733 0.850 0.900 0.999 0.767 0.980 0.714 0.926 1.000 0.744 0.708 0.721 0.751 0.736 0.899 0.763 0.812 0.698 0.558 0.866 0.952 0.860 0.935 0.941 0.533 0.401 0.741 0.749 0.420 0.742 0.716 0.783 0.670 0.874 0.918 0.791 0.972 0.925 0.935 0.754 0.654 0.554 0.890 0.873 0.993 0.987 0.991 0.997 0.705 0.914 0.526 0.688 0.950 0.433 0.996 0.884 0.653 0.958 0.888 0.721 0.699 0.909 0.933 0.729 0.945 0.604 0.863 0.552 0.942 0.909 0.926 0.867 0.892 0.901 0.933 0.844 0.836 0.399 0.800 0.351 0.812 0.745

0.890 0.788 0.604 0.684 0.590 0.829 1.000 0.900 0.950 0.900 0.998 0.833 0.974 0.749 0.992 1.000 0.752 0.697 0.754 0.726 0.747 0.869 0.755 0.793 0.683 0.623 0.843 0.952 0.860 0.940 0.980 0.561 0.470 0.748 0.713 0.672 0.881 0.852 0.849 0.701 0.920 0.958 0.838 0.994 0.919 0.930 0.746 0.708 0.500 0.890 0.905 0.980 0.975 0.994 1.000 0.762 0.900 0.526 0.625 0.966 0.442 1.000 0.968 0.675 0.964 0.813 0.738 0.726 0.959 0.917 0.763 0.953 0.604 0.859 0.539 0.964 0.943 0.922 0.918 0.931 0.938 0.933 0.838 0.841 0.389 0.820 0.399 0.923 0.851

0.820 0.772 0.590 0.647 0.587 0.823 0.967 0.733 1.000 0.900 0.967 0.783 0.980 0.709 0.605 1.000 0.668 0.687 0.667 0.713 0.711 0.866 0.734 0.786 0.691 0.442 0.764 0.937 0.880 0.943 0.846 0.492 0.392 0.755 0.647 0.400 0.684 0.795 0.727 0.714 0.869 0.898 0.772 0.898 0.755 0.968 0.769 0.700 0.462 0.872 0.880 0.973 0.946 0.984 0.975 0.695 0.905 0.464 0.609 0.916 0.338 0.928 0.871 0.627 0.956 0.760 0.754 0.712 0.897 0.950 0.713 0.865 0.584 0.845 0.584 0.890 0.819 0.903 0.873 0.909 0.748 0.900 0.780 0.838 0.312 0.660 0.106 0.173 0.120

0.760 0.749 0.586 0.543 0.541 0.777 0.840 0.700 0.850 0.950 0.976 0.767 0.936 0.676 0.740 0.964 0.772 0.667 0.692 0.685 0.672 0.850 0.734 0.775 0.691 0.545 0.787 0.968 0.830 0.934 0.815 0.439 0.301 0.741 0.707 0.352 0.652 0.830 0.713 0.613 0.926 0.900 0.756 0.978 0.945 0.742 0.562 0.485 0.315 0.791 0.785 0.960 0.972 0.972 1.000 0.733 0.892 0.461 0.625 0.866 0.336 1.000 1.000 0.526 0.882 0.760 0.738 0.699 0.850 0.917 0.714 0.925 0.656 0.787 0.552 0.938 0.917 0.942 0.782 0.820 0.798 0.733 0.793 0.784 0.294 0.740 0.389 0.942 0.832

0.830 0.844 0.633 0.677 0.691 0.817 1.000 0.700 0.950 0.900 0.997 0.767 0.950 0.704 0.812 1.000 0.736 0.777 0.790 0.818 0.736 0.843 0.763 0.793 0.712 0.558 0.795 0.952 0.830 0.939 0.930 0.608 0.483 0.748 0.745 0.360 0.719 0.909 0.844 0.719 0.937 0.930 0.800 0.984 0.930 0.930 0.700 0.708 0.400 0.884 0.880 0.980 0.994 1.000 0.997 0.676 0.903 0.497 0.672 0.941 0.467 1.000 1.000 0.603 0.927 0.763 0.721 0.685 0.900 0.933 0.759 0.953 0.591 0.835 0.532 0.948 0.921 0.934 0.862 0.887 0.934 0.833 0.886 0.829 0.371 0.840 0.625 0.933 0.861

0.830 0.829 0.669 0.729 0.697 0.823 1.000 0.900 0.850 0.900 0.999 0.900 0.985 0.609 0.989 1.000 0.656 0.810 0.851 0.841 0.784 0.987 0.791 0.786 0.676 0.649 0.913 0.984 0.920 0.949 0.994 0.635 0.547 0.748 0.609 0.644 0.802 1.000 0.941 0.811 0.926 0.949 0.802 0.998 0.943 0.941 0.785 0.685 0.554 0.860 0.816 0.987 0.991 1.000 1.000 0.686 0.932 0.552 0.578 0.958 0.442 0.964 0.956 0.655 0.961 0.675 0.852 0.849 0.924 0.983 0.796 0.931 0.636 0.852 0.591 0.979 0.955 0.900 0.931 0.942 0.868 0.967 0.844 0.824 0.410 0.780 0.130 0.639 0.731

Table 10: UCR univariate accuracy. Bold = best per dataset. Best variant shown for models with multiple checkpoints. (continued) Dataset

DTW-1NN Catch22 MiniRocket Hydra InceptionTime TS2Vec TICT Chronos-2 TiRex Moment NuTime MantisV2 TimEE

Plane PowerCons ProximalPhalanxOutlineAgeGroup ProximalPhalanxOutlineCorrect ProximalPhalanxTW RefrigerationDevices Rock ScreenType SemgHandGenderCh2 SemgHandMovementCh2 SemgHandSubjectCh2 ShakeGestureWiimoteZ ShapeletSim ShapesAll SmallKitchenAppliances SmoothSubspace SonyAIBORobotSurface1 SonyAIBORobotSurface2 StarLightCurves Strawberry SwedishLeaf Symbols SyntheticControl ToeSegmentation1 ToeSegmentation2 Trace TwoLeadECG TwoPatterns UMD UWaveGestureLibraryAll UWaveGestureLibraryX UWaveGestureLibraryY UWaveGestureLibraryZ Wafer Wine WordSynonyms Worms WormsTwoClass Yoga

1.000 0.922 0.785 0.790 0.756 0.440 0.840 0.411 0.845 0.638 0.800 0.840 0.700 0.802 0.672 0.947 0.696 0.859 0.905 0.946 0.846 0.938 0.983 0.750 0.908 0.990 0.868 0.999 0.972 0.966 0.773 0.699 0.678 0.996 0.611 0.738 0.532 0.584 0.844

1.000 0.917 0.834 0.838 0.766 0.517 0.740 0.533 0.877 0.662 0.807 0.800 0.972 0.777 0.805 0.853 0.845 0.917 0.970 0.927 0.890 0.958 0.987 0.860 0.777 1.000 0.818 0.846 0.896 0.831 0.761 0.707 0.707 0.997 0.463 0.538 0.753 0.857 0.771

1.000 0.989 0.844 0.904 0.815 0.496 0.820 0.475 0.900 0.691 0.860 0.920 1.000 0.922 0.837 0.953 0.894 0.914 0.982 0.981 0.965 0.983 0.987 0.961 0.908 1.000 0.998 0.996 0.993 0.973 0.848 0.776 0.803 0.999 0.852 0.755 0.753 0.766 0.913

1.000 0.978 0.868 0.911 0.810 0.528 0.920 0.493 0.847 0.496 0.771 0.920 0.989 0.928 0.808 0.927 0.920 0.948 0.982 0.973 0.978 0.980 0.957 0.961 0.908 1.000 0.999 0.987 0.993 0.973 0.854 0.792 0.803 1.000 0.907 0.743 0.753 0.766 0.927

1.000 0.994 0.849 0.914 0.771 0.531 0.620 0.589 0.875 0.558 0.682 0.840 0.983 0.925 0.792 0.973 0.869 0.951 0.980 0.984 0.965 0.983 0.997 0.974 0.946 1.000 0.996 1.000 0.993 0.934 0.822 0.762 0.775 0.999 0.685 0.716 0.766 0.766 0.912

0.971 0.961 0.834 0.890 0.795 0.616 0.760 0.413 0.958 0.876 0.951 0.900 0.994 0.903 0.699 0.980 0.913 0.908 0.971 0.968 0.931 0.979 1.000 0.917 0.900 1.000 0.977 1.000 0.986 0.936 0.802 0.720 0.762 0.998 0.926 0.693 0.753 0.792 0.895

1.000 0.917 0.771 0.832 0.776 0.528 0.640 0.544 0.825 0.587 0.820 0.660 0.900 0.698 0.720 0.833 0.894 0.887 0.978 0.911 0.819 0.920 0.977 0.860 0.862 1.000 0.948 0.706 0.972 0.912 0.774 0.720 0.712 0.984 0.889 0.513 0.688 0.818 0.809

1.000 0.922 0.859 0.859 0.805 0.560 0.940 0.507 0.920 0.718 0.844 0.920 1.000 0.883 0.827 0.973 0.709 0.879 0.980 0.959 0.944 0.979 0.997 0.921 0.854 1.000 0.955 0.922 0.986 0.944 0.807 0.738 0.745 0.991 0.889 0.569 0.779 0.805 0.809

1.000 0.978 0.863 0.904 0.820 0.581 0.940 0.541 0.950 0.709 0.867 0.860 0.967 0.857 0.832 0.953 0.902 0.852 0.979 0.957 0.946 0.970 0.987 0.947 0.923 1.000 0.992 0.993 0.965 0.942 0.808 0.748 0.741 0.998 0.759 0.574 0.805 0.844 0.820

0.981 0.856 0.849 0.883 0.805 0.528 0.760 0.429 0.810 0.553 0.724 0.820 0.928 0.830 0.691 0.793 0.779 0.888 0.955 0.946 0.914 0.969 0.990 0.934 0.892 1.000 0.847 0.947 0.965 0.910 0.803 0.725 0.742 0.990 0.833 0.596 0.675 0.727 0.840

1.000 0.933 0.849 0.838 0.795 0.533 0.720 0.507 0.865 0.680 0.733 0.860 0.928 0.842 0.813 0.907 0.772 0.838 0.979 0.935 0.930 0.942 0.973 0.860 0.746 0.990 0.930 0.846 0.951 0.889 0.808 0.742 0.756 0.994 0.796 0.539 0.740 0.792 0.827

1.000 0.972 0.834 0.869 0.824 0.557 0.820 0.485 0.920 0.753 0.831 0.940 0.972 0.875 0.835 0.947 0.802 0.937 0.981 0.965 0.955 0.969 0.990 0.965 0.869 1.000 0.995 0.982 0.986 0.886 0.809 0.759 0.758 0.996 0.889 0.616 0.792 0.857 0.838

1.000 0.989 0.863 0.907 0.805 0.501 0.940 0.448 0.957 0.813 0.940 0.960 0.967 0.900 0.803 0.993 0.923 0.916 0.982 0.976 0.979 0.966 0.983 0.939 0.892 1.000 0.946 0.996 0.965 0.979 0.849 0.793 0.784 0.998 0.778 0.757 0.805 0.870 0.879

Average Mean rank

0.802 10.21

0.815 9.73

0.883 4.37

0.879 4.54

0.863 5.10

0.878 5.94

0.810 10.01

0.864 6.38

0.874 5.71

0.823 9.55

0.830 9.27

0.873 5.69

0.891 4.50

Table 11: UEA multivariate accuracy. Bold = best per dataset. Best variant shown for models with multiple checkpoints. Dataset

DTW-1NN Catch22 MiniRocket Hydra InceptionTime TS2Vec TiCT Chronos-2 TiRex Moment NuTime MantisV2 TimEE (VP) TimEE (PV)

ArticularyWordRecognition AtrialFibrillation BasicMotions CharacterTrajectories Cricket DuckDuckGeese ERing Epilepsy EthanolConcentration FingerMovements HandMovementDirection Handwriting Heartbeat JapaneseVowels LSST Libras MotorImagery NATOPS PEMS-SF RacketSports SelfRegulationSCP1 SelfRegulationSCP2 StandWalkJump UWaveGestureLibrary

0.987 0.200 0.975 0.990 1.000 0.600 0.930 0.964 0.323 0.530 0.231 0.607 0.717 0.949 0.551 0.872 0.500 0.883 0.711 0.803 0.775 0.539 0.200 0.903

0.983 0.200 0.950 0.960 0.986 0.440 0.926 0.949 0.293 0.530 0.189 0.272 0.727 0.759 0.607 0.844 0.510 0.839 1.000 0.803 0.727 0.550 0.400 0.872

0.993 0.133 1.000 0.994 0.986 0.720 0.981 1.000 0.471 0.540 0.365 0.521 0.756 0.981 0.638 0.911 0.520 0.933 0.821 0.882 0.908 0.533 0.400 0.931

0.990 0.133 1.000 0.990 0.986 0.680 0.985 1.000 0.548 0.550 0.216 0.466 0.761 0.978 0.607 0.933 0.500 0.872 0.803 0.914 0.867 0.589 0.400 0.909

0.987 0.200 1.000 0.996 0.986 0.640 0.919 0.964 0.262 0.530 0.392 0.667 0.751 0.992 0.194 0.878 0.550 0.961 0.780 0.895 0.829 0.483 0.400 0.903

0.990 0.200 1.000 0.987 0.986 0.480 0.919 0.978 0.327 0.500 0.270 0.332 0.771 0.946 0.639 0.833 0.490 0.944 0.994 0.888 0.778 0.522 0.133 0.887

0.970 0.267 1.000 0.924 0.931 0.380 0.856 0.964 0.274 0.510 0.351 0.208 0.722 0.641 0.548 0.678 0.530 0.750 0.902 0.783 0.720 0.511 0.400 0.759

0.993 0.333 1.000 0.964 0.986 0.460 0.981 1.000 0.380 0.510 0.297 0.279 0.741 0.805 0.604 0.867 0.550 0.822 0.988 0.836 0.788 0.522 0.667 0.900

0.990 0.267 1.000 0.958 1.000 0.460 0.978 1.000 0.300 0.570 0.270 0.266 0.722 0.819 0.579 0.883 0.540 0.850 1.000 0.849 0.812 0.522 0.467 0.881

0.990 0.267 0.950 0.976 0.944 0.480 0.952 0.978 0.278 0.590 0.378 0.269 0.732 0.786 0.552 0.800 0.530 0.850 1.000 0.796 0.795 0.439 0.600 0.912

0.993 0.267 1.000 0.979 1.000 0.440 0.993 1.000 0.414 0.560 0.324 0.206 0.785 0.957 0.565 0.906 0.580 0.867 1.000 0.908 0.788 0.522 0.467 0.906

0.993 0.200 1.000 0.967 0.986 0.580 0.993 1.000 0.414 0.510 0.311 0.281 0.829 0.954 0.663 0.928 0.490 0.878 0.988 0.914 0.819 0.517 0.467 0.900

0.990 0.133 1.000 0.989 0.972 0.360 0.970 1.000 0.624 0.580 0.324 0.455 0.732 0.824 0.592 0.889 0.480 0.811 0.942 0.882 0.877 0.439 0.400 0.881

0.980 0.333 1.000 0.985 0.972 0.340 0.959 1.000 0.612 0.610 0.324 0.422 0.717 0.784 0.604 0.872 0.570 0.856 0.954 0.895 0.887 0.439 0.400 0.866

Average Mean rank

0.698 8.65

0.680 10.10

0.747 4.79

0.737 5.48

0.715 6.96

0.700 8.04

0.649 11.54

0.720 7.21

0.708 7.40

0.702 8.29

0.726 5.31

0.733 5.83

0.714 7.94

0.724 7.46

30

CD = 2.33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

MiniRocket (4.47)

(13.88) TICT

Hydra (4.87)

(12.79) DTW-1NN

T EE (5.34)

(12.78) Catch22

InceptionTime (5.39)

(12.41) NuTime (Default)

MantisV2 (Tuned) (7.48)

(12.06) NuTime (Tuned)

TS2Vec (7.84)

(11.97) MantisV2 (Default)

TiRex (Tuned) (8.02)

(11.85) Moment (Default)

Chronos-2 (Tuned) (8.36)

(11.60) Moment (Tuned)

TiRex (Default) (8.51)

(11.37) Chronos-2 (Default)

Pairwise Accuracy CD Diagram

Figure 17: Critical difference diagram over ROC AUC across 128 UCR datasets (Wilcoxon–Holm post-hoc test, α = 0.05). Methods connected by a horizontal bar are not significantly different.

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