arXiv:2605.18657v1 [cs.LG] 18 May 2026
K AIROS H OPE : A N EXT-G ENERATION T IME -S ERIES F OUNDATION M ODEL FOR S PECIALIZED C LASSIFICATION VIA D UAL -M EMORY A RCHITECTURE
Luis Balderas
José Alberto Rodríguez
Department of Computer Science and Artificial Intelligence DiCITS, iMUDS, DaSCI University of Granada, Granada, Spain 18071
Department of Computer Science and Artificial Intelligence DiCITS, iMUDS, DaSCI University of Granada, Granada, Spain 18071
Miguel Lastra
Antonio Arauzo-Azofra
Department of Software Engineering DiCITS, iMUDS, DaSCI University of Granada, Granada, Spain 18071
Department of Rural Engineering, DiCITS, iMUDS, University of Córdoba, Córdoba, Spain 14005
[email protected] José M. Benítez
Department of Computer Science and Artificial Intelligence DiCITS, iMUDS, DaSCI University of Granada, Granada, Spain 18071
A BSTRACT Time Series Foundation Models (TSFMs) have demonstrated notable success in generalpurpose forecasting tasks; however, their adaptation to specialized classification problems remains constrained by the computational bottleneck of standard attention and the systematic omission of classical statistical knowledge. This technical report introduces KairosHope, a next-generation TSFM designed to reconcile massive generalization with analytical precision in classification tasks. The core of the proposal is the HOPE Block, an architecture that replaces quadratic attention with a dual-memory system: Titans modules for dynamic shortterm retention and a Continuum Memory System (CMS) for the abstraction of long-term historical context. To enrich the inductive bias, a Hybrid Decision Head is introduced, which fuses deep latent representations with deterministic statistical features extracted via tsfeatures [1]. KairosHope undergoes self-supervised pre-training on the massive Monash archive, combining Masked Time Series Modeling (MTSM) and contrastive learning (InfoNCE). Its subsequent adaptation to the UCR benchmark datasets is conducted through a rigorous Linear Probing and Full 1
KairosHope: A Next-Generation Time-Series Foundation Model for Specialized Classification via Dual-Memory Architecture Fine-Tuning (LP-FT) protocol to prevent catastrophic forgetting. Empirical results demonstrate superior performance in domains characterized by strict temporal causality—such as HAR or Sensor data. Consequently, KairosHope establishes a robust and efficient framework for the adaptation of foundation models to time series analysis. Keywords time series classification, foundation model, HOPE architecture
1
Introduction
Time series analysis and classification represent a central challenge across multiple disciplines, ranging from medical vital sign monitoring [2] to anomaly detection in the Internet of Things (IoT) [3] and financial analysis [4]. Unlike natural language processing (NLP) or computer vision, real-world time series exhibit a highly heterogeneous nature, characterized by variable-length sequences, non-stationary distributions, and complex interactions between local dynamics (short-term volatility) and global dependencies (macro-seasonality). Historically, time series classification was dominated by approaches based on elastic distances, such as Dynamic Time Warping (DTW) [5], as well as dictionary and shapelet-based algorithms [6]. The advent of deep learning radically transformed the field. Architectures such as Fully Convolutional Networks (FCN) [7] and, most prominently, InceptionTime [8], established new performance standards by demonstrating a superior capacity to extract invariant local patterns without the need for manual feature engineering. However, these traditional deep learning models operate under an isolated paradigm: they must be initialized and trained from scratch for each specific dataset, rendering them incapable of transferring structural knowledge across domains. Recently, the success of large language models (LLMs) has catalyzed the development of Time Series Foundation Models (TSFMs). Seminal proposals such as PatchTST [9] demonstrated the efficacy of segmenting series into patches to preserve local semantics and reduce computational complexity. Concurrently, industry models such as TimesFM [10] and MOIRAI [11] scaled pre-training on massive data collections to achieve generalized forecasting capabilities. Throughout the last year, research has vigorously expanded toward general latent understanding and multi-domain classification, highlighting architectures such as UDE [12], which integrate Koopman operators and universal delay projections, or proposals like UniShape [13], which attempt to incorporate geometric interpretability (shapelets) into massive architectures. Despite this rapid evolution, the adaptation of the current generation of TSFMs to specialized classification tasks continues to present critical limitations. The standard attention mechanism suffers from a quadratic memory bottleneck that limits deep historical context, and the vast majority of purely neural architectures completely discard the valuable statistical knowledge inherent in classical time series theory. To address this gap, this paper introduces KairosHope, a next-generation Time Series Foundation Model designed specifically to reconcile massive generalization with analytical precision in specialized classification. KairosHope provides three fundamental contributions. First, the HOPE Block [14] replaces traditional quadratic attention with a dual-memory architecture capable of modeling long-term dependencies with linear computational cost. Second, a dual-objective self-supervised pre-training regime based on the vast and heterogeneous Monash repository [15] forces the model to learn robust and invariant representations. Finally, a Hybrid Decision Head, combined with the LP-FT protocol, fuses deep embeddings with deterministically extracted statistical features, ensuring efficient adaptation to classification domains evaluated on the UCR benchmark [16]. Throughout this document, the underlying architecture, the self-supervised training strategy, and the empirical results on the UCR benchmark datasets are detailed, demonstrating how KairosHope establishes a new paradigm in the adaptation of foundation models for time series classification. 2
KairosHope: A Next-Generation Time-Series Foundation Model for Specialized Classification via Dual-Memory Architecture
Figure 1: KairosHope architecture
2
Our proposal
This section introduces the proposed foundation model for time series classification: KairosHope. The architecture of KairosHope is designed to address the inherent challenges of TSFM, namely variable sequence lengths, non-stationarity, and the necessity of modeling both local semantics and long-term historical dependencies. The following subsections detail both the architecture and the training strategy employed. 2.1
Architecture
KairosHope processes sequences of diverse natures, origins, and types through a meticulously designed architecture comprising a preprocessing module, an HOPE based encoder [14], and a classification head utilizing a hybrid strategy. Figure depicts the KairosHope architecture 2.1.1
Preprocessing: Data Serialization, Patching, and RevIN
Time series data encountered in academic and industrial contexts often exhibit significant variability and distributional shifts. To mitigate these issues and achieve normalization, KairosHope first applies Reversible Instance Normalization (RevIN) [17] to the original input sequence X ∈ RL×C , where L denotes the sequence length and C represents the number of channels. RevIN normalizes the sequence to zero mean and unit variance using trainable affine parameters, effectively removing non-stationary macro-trends temporarily. Once normalized, the sequence is divided into non-overlapping segments, or patches, of length P . This patching mechanism maps the sequence point-wise into a sequence of N tokens, where N = ⌊L/P ⌋. The utilization of patches offers two critical benefits: • Semantic extraction: It captures local temporal semantics, analogous to words in natural language sentences. 3
KairosHope: A Next-Generation Time-Series Foundation Model for Specialized Classification via Dual-Memory Architecture • Computation efficiency: It reduces the computational complexity of subsequent sequence modeling from O(L2 ) to O(N 2 ). Finally, these patches are linearly projected into an embedding space of dimension D, concatenated with a special [CLS] token, and augmented with positional encodings. 2.2
HOPE Encoder
Traditional Transformers [18] rely on static-window self-attention [19], a mechanism that struggles when processing datasets with infinite horizons, primarily due to quadratic memory bottlenecks. To address these limitations, the core of the model replaces standard attention with the HOPE Block, a dual-memory system that integrates two advanced neural memory primitives: • Self-Modifying Titans: This module acts as the model’s short to medium-term working memory. By processing patches in sequential chunks, the Titans [20] module dynamically updates its internal memory state. This enables the network to adapt to sudden volatility and local temporal dynamics without the need to maintain an exhaustive attention matrix over the entire sequence. • Proper Continuum Memory System (CMS): Operating in conjunction with the Titans module, the CMS is responsible for long-term abstraction. It compresses and persists historical representations across hierarchical levels. This mechanism ensures that macro-seasonal trends and distant historical context are preserved, thereby granting KairosHope a substantially extended receptive field. Together, Titans and CMS modules map the input patch embeddings into deep, contextualized representations H ∈ R(N +1)×D . 2.2.1
Hybrid Classification Head
Although deep representations are extremely powerful, completely disregarding certain traditional statistical features often leads to suboptimal performance in highly structured time series. KairosHope introduces a Hybrid Decision Head that integrates deep neural embeddings with deterministic time series features. First, the latent representation is extracted from the encoder. For classification tasks, this corresponds to the state of the [CLS] token, hcls ∈ RD . In parallel, the original time series is processed by a specialized feature extractor, tsfeatures [1], which computes a vector of statistical priors fts ∈ RK that encompasses properties such as autocorrelation, spectral entropy, and seasonal strength, among others. The final representation z is the concatenation of both the deep embedding and the statistical features: z = [ hcls ∥ fts ] This vector z is subsequently passed through a normalization layer, dropout, and finally a linear layer to produce the final classification labels. 2.3
Training Strategy
The training of KairosHope is governed by a two-stage paradigm designed to transform a general-purpose architecture into a high-precision predictor for specific domains. This progression enables the model to first learn the “universal laws” of time series in a self-supervised setting, and subsequently achieve efficient specialization. 4
KairosHope: A Next-Generation Time-Series Foundation Model for Specialized Classification via Dual-Memory Architecture 2.3.1
Pre-training KairosHope
Pre-training is conducted on a massive, heterogeneous corpus using a dual learning objective. This phase does not require external labels and focuses on the structural and relational understanding of the data. 1. Masked Time Series Modeling (MTSM). Drawing on advancements in natural language processing and inspired by [21], a masked patch modeling strategy is implemented. During training, 40% of input patches are randomly masked. The objective is to reconstruct the normalized values of these missing patches. To manage corpus heterogeneity, a dual-masking strategy is employed: a stochastic training mask for learning and a padding mask, which ensures the model ignores the artificial zeros introduced to align sequences of varying lengths. The reconstruction loss is defined by the Mean Squared Error (MSE): LMTSM =
1 X ||P̂i − Pi ||2 M i∈M
where M represents the set of masked patches, P̂i denotes the reconstructed patch, and Pi represents the original patch. 2. Contrastive Learning. To enhance the robustness of global representations, an InfoNCE [22] contrastive loss is integrated. Two augmented views of the same time series are generated by injecting Gaussian noise (2%) and applying random scaling. This technique compels the model to distinguish between different augmented versions of the same time series (positive pairs) and other distinct series within the same batch (negative pairs). By maximizing latent similarity between representations of the same instance using a temperature of τ = 0.1, the model learns invariant features that are robust to perturbations and fundamental for downstream tasks. The loss is formulated as: LNCE = −
X i
exp(sim(zi , zj )/τ log P k exp(sim(zi , zj )/τ
The total pre-training loss function is a weighted combination of both objectives. Ltotal = λ1 LMTSM + λ2 LNCE 2.3.2
Fine-tuning KairosHope
Once the HOPE encoder has developed a universal understanding of temporal dynamics, fine-tuning is conducted on the target dataset utilizing the Linear Probing - Full Fine-tuning (LP-FT) strategy [23]. This approach is vital for ensuring the retention of generalized representations throughout the fine-tuning process. 1. Linear Probing (LP). Initially, the encoder weights are frozen, and only the hybrid decision head is trained. During this phase, the model learns to map rich, pre-trained representations to the specific classes or values of the target domain. Maintaining the encoder intact prevents initial gradient noise from degrading the memory structures learned within the Titans and CMS modules. 2. Full Fine-tuning (FT). Upon initial convergence of the decision head, all model parameters are unlocked for comprehensive training. During this stage, a significantly lower learning rate is employed. This facilitates fine-grained adjustments to the encoder weights, specializing the system’s 5
KairosHope: A Next-Generation Time-Series Foundation Model for Specialized Classification via Dual-Memory Architecture memory toward the nuances and particularities of the target dataset while preserving the underlying generalist knowledge base. This dual LP-FT strategy ensures that KairosHope inherits the stability of the pre-training phase while achieving state-of-the-art precision in the specific target task.
3
Empirical analysis
To validate the efficacy of KairosHope and its generalization capability from a self-supervised environment to specific classification tasks, a thorough experimental framework has been designed. This section details the architectural configuration, optimization hyperparameters, datasets utilized, and the evaluation scheme for the results. 3.1
Metrics
To rigorously assess the performance of KairosHope across its different training phases, both unsupervised and supervised evaluation metrics are employed. During the foundational self-supervised pre-training phase, the model is evaluated using two primary loss-derived metrics: • Masked Time Series Modeling Mean Squared Error (MSEMTSM ): Quantifies the reconstruction accuracy of the masked temporal patches, measuring the backbone’s ability to capture underlying deterministic dynamics and statistical regularities. • InfoNCE Contrastive Loss (LNCE ): Evaluates the quality of the learned latent space by measuring the model’s proficiency in maximizing the similarity of augmented views of the same instance while segregating negative pairs within the batch. With respect to the classification metrics, accuracy and macro-averaged F1-Score have been used. 3.2
Network hyperparameters
The base model architecture was configured with specific structural hyperparameters to balance expressive capacity with computational efficiency. The input sequence length is set to 256 time steps, while the patch size is established at 8 time steps, yielding a sequence of 32 patches per instance. The latent space dimension is fixed at 128, and the encoder depth comprises five HOPE blocks. Regarding the memory architecture, the CMS utilizes four hierarchical levels to facilitate long-term context compression. Finally, to ensure robust regularization, a dropout probability of 0.1 is applied within the backbone HOPE blocks to preserve the retention of underlying features, whereas a dropout rate of 0.4 is employed in the hybrid classifier head to effectively mitigate overfitting. 3.3
Training hyperparameters
The optimization process utilizes AdamW as the primary optimizer, leveraging its efficient decoupling of weight decay. Training follows the progression outlined in Section 3, with distinct configurations applied to each phase. During the pre-training phase, the model is trained for 50 epochs with a learning rate and weight decay of 1 × 10−4 , employing a batch size of 128. For the fine-tuning stage, governed by the LP-FT protocol, a CrossEntropyLoss function mitigated by label smoothing with a factor of 0.1 is used to penalize overconfidence in model predictions. Phase 1, involving 6
KairosHope: A Next-Generation Time-Series Foundation Model for Specialized Classification via Dual-Memory Architecture linear probing, is conducted over 15 epochs with a learning rate and weight decay of 1 × 10−3 . Subsequently, Phase 2, which consists of full fine-tuning, is performed over 30 epochs and employs differentiated, layerwise learning rates of 1 × 10−5 for the backbone and 1 × 10−4 for the classifier. To ensure convergence, a CosineAnnealingLR scheduler gradually decays the learning rate to a lower bound of 1 × 10−6 . Finally, a batch size of 16 is adopted for this stage. 3.4
Datasets
To ensure that the model assimilates a wide variety of temporal dynamics, two distinct data collections are employed for the foundation and specialization phases. The pre-training corpus consists of massive, forecasting-oriented datasets extracted from the Monash Time Series Forecasting Repository [15], specifically m4_hourly, weather, electricity, traffic, and tourism_monthly. This selection exposes the model to patterns ranging from high-frequency and extreme volatility to low-frequency seasonal macro-trends. For the finetuning corpus, the BakeOff classification benchmark [24], based on datasets from the UCR Time Series Classification Archive [16], served as the reference for downstream evaluation. To align this evaluation with typical and pragmatic scenarios in both industrial and academic contexts, the experiment focused on a filtered subset of problems satisfying two conditions: possessing fewer than eight classes and containing sequences with fewer than 400 time steps per instance. 3.5
Results
The following section presents the experimental results for KairosHope. As shown in the appendix, Table 1, the proposed model was evaluated using the datasets containing fewer than eight classes and fewer than 400 time steps per instance from the Bake Off benchmark datasets, achieving a mean test accuracy of 80.11% and an F1-score of 0.786. Table 2, which presents the mean accuracy categorized by dataset type using the aforementioned filter, indicates that HAR datasets yielded the highest performance (91.333%), followed by SENSOR (89.6%) and SPECTRO (83.671%) datasets. Conversely, IMAGE datasets exhibited the lowest performance (66.211%).
4
Discussion
The analysis of the empirical results obtained from the UCR benchmark following the pre-training and fine-tuning (LP-FT) phases provides critical insights into the inductive biases of the model. Generally, the integration of the Titans and CMS modules within the backbone demonstrates a notable superiority in Sensor, Motion, and ECG datasets, where temporal causality and long-term historical dependencies are the determining factors for successful classification. The hybrid decision head successfully capitalizes on the statistical priors of |tsfeatures within these domains. However, the analysis grouped by dataset typology reveals disparate behavior and a margin for improvement in the family of datasets categorized as IMAGE. In these problems, the one-dimensional time series do not represent a dynamic phenomenon over time; rather, they are the result of unwinding or extracting the spatial contour of two-dimensional objects from images. To improve the generalization capability and performance of the model in this specific category, a data augmentation strategy was designed and implemented. Inspired by spatial shape processing literature, the training set was enriched by generating synthetic time series from images with morphological variations, following the contour extraction methodology described in [25]. The objective of this intervention was to provide the fine-tuning phase with a significantly larger volume of data to calibrate the network against rotations, translations, and scale variations intrinsic to spatial contours. 7
KairosHope: A Next-Generation Time-Series Foundation Model for Specialized Classification via Dual-Memory Architecture Despite this robust augmentation strategy, empirical results did not show a significant improvement in Accuracy or F1-Score metrics for IMAGE-type datasets, with performance remaining stagnant relative to the baseline without augmentation. This negative result is highly informative and suggests two primary hypotheses regarding the structural limitations of the approach in this particular niche: • Incompatibility of Temporal Inductive Bias: The HOPE block, particularly through the CMS and the sequential processing of Titans, is heavily optimized to model strict temporal causality (where step t depends on t − 1). In 1D image contours, the starting and ending points are arbitrary and lack a real direction of causal flow, which confounds the long-term memory retention mechanisms designed for genuine time series. • Misalignment of the Hybrid Head: The deterministic statistical feature extractor, which serves as a fundamental pillar in the classification head, computes metrics such as spectral entropy, trend strength, or seasonality. While these concepts possess deep semantic meaning in climatic or financial series, they lack representational utility when applied to the perimeter of a leaf or the silhouette of an insect. Consequently, the performance discrepancy observed in IMAGE-type datasets demonstrates that conventional temporal priors are not directly extrapolatable to problems of geometric invariance, even when employing data augmentation techniques. This contrast underscores that the success of the architecture depends largely on the alignment between the model’s inductive biases and the intrinsic nature of the underlying domain.
5
Conclusions
In this technical report, KairosHope has been presented, a foundation model designed to transform time series classification through a dual-memory architecture and a two-phase training regime. The results obtained validate the central hypothesis that the integration of long-term (CMS) and short-term (Titans) memory mechanisms enables the capture of complex temporal dynamics that conventional models frequently overlook. The primary conclusions derived from this development are summarized as follows: • Efficacy of the HOPE Architecture: The HOPE block has proven to be an efficient alternative to quadratic attention, facilitating linear processing that does not sacrifice the ability to model extensive historical dependencies. • Value of the Hybrid Representation: The fusion of deep neural embeddings with deterministic statistical features (tsfeatures) provides an essential anchor of robustness, which is particularly beneficial when fine-tuning data is limited. • Robustness of the LP-FT Protocol: The Linear Probing strategy followed by Full Fine-Tuning is confirmed as a superior methodology for knowledge transfer from foundation models, achieving precise specialization without degrading the universal representations learned during pre-training. • Limitations of Temporal Biases: Experimentation with IMAGE-type datasets and the utilization of synthetic data augmentation techniques reveal that the geometric nature of spatial contours requires inductive biases distinct from purely causal-temporal ones.
6
Future Work
Building upon these findings, future lines of research for the evolution of KairosHope will focus on the following areas: 8
KairosHope: A Next-Generation Time-Series Foundation Model for Specialized Classification via Dual-Memory Architecture 1. Geometric Invariance: Developing specific feature extraction modules for contour-type data that can be integrated into the hybrid head without compromising performance on dynamic series. 2. Pre-training Scalability: Expanding the pre-training corpus toward even more massive and multimodal domains to observe the emergence point of zero-shot classification capabilities. 3. CMS Optimization: Investigating more aggressive memory compression techniques to enable the processing of ultra-long sequences (comprising millions of time steps) on consumer-grade hardware. 4. Multivariate Extension: Extending the KairosHope architecture to handle multivariate time series classification. This involves researching inter-channel correlation mechanisms and cross-dimensional attention to capture the complex dependencies between multiple variables without compromising the computational efficiency of the HOPE block.
Acknowledgment This research has been partially supported by Proyecto PID2023-151336OB-I00 financiado por MICIU/AEI /10.13039/501100011033 y por FEDER, UE.
Appendix A: Complete Results Dataset
Accuracy
F1-Score
ArrowHead CBF DistalPhalanxTW DistalPhalanxOutlineAgeGroup DistalPhalanxOutlineCorrect Earthquakes ECG200 ECG5000 ECGFiveDays ElectricDevices FaceFour GunPoint ItalyPowerDemand Lightning7 MiddlePhalanxTW MiddlePhalanxOutlineAgeGroup MiddlePhalanxOutlineCorrect MoteStrain NonInvasiveFetalECGThorax1 NonInvasiveFetalECGThorax2 PhalangesOutlinesCorrect Plane ProximalPhalanxTW ProximalPhalanxOutlineAgeGroup
56.571 67.778 69.784 73.381 76.812 75.540 76.000 93.511 66.899 68.551 57.955 91.333 93.586 67.123 58.442 60.390 73.540 87.141 84.784 87.430 78.904 100.000 75.610 84.390
0.564 0.664 0.611 0.735 0.759 0.657 0.749 0.923 0.657 0.678 0.521 0.913 0.936 0.653 0.562 0.567 0.716 0.871 0.846 0.875 0.782 1.000 0.720 0.848
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KairosHope: A Next-Generation Time-Series Foundation Model for Specialized Classification via Dual-Memory Architecture Type Mean Accuracy DEVICE 68.551 ECG 79.252 HAR 91.333 IMAGE 66.211 MOTION 81.609 SENSOR 89.6 SIMULATED 79.469 SPECTRO 83.671 Table 2: KairosHope results by dataset type
Dataset ProximalPhalanxOutlineCorrect SonyAIBORobotSurface1 SonyAIBORobotSurface2 Strawberry SyntheticControl ToeSegmentation1 ToeSegmentation2 Trace TwoLeadECG TwoPatterns UWaveGestureLibraryX UWaveGestureLibraryY UWaveGestureLibraryZ UWaveGestureLibraryAll Wafer Wine Worms WormsTwoClass Yoga
Accuracy
F1-Score
81.443 85.524 85.414 91.622 95.333 85.526 77.692 99.000 80.597 98.725 76.466 65.522 66.974 88.805 99.010 62.963 68.831 77.922 70.900
0.797 0.856 0.856 0.917 0.953 0.855 0.793 0.990 0.804 0.987 0.758 0.645 0.656 0.887 0.990 0.571 0.659 0.780 0.687
Table 1: KairosHope results for UCR and Bake Off benchmark datasets
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