A Foundation Model for Virtual Sensors

Virtual sensors use machine learning to predict target signals from available measurements, replacing expensive physical sensors in critical applications. Existing virtual sensor approaches require application-specific models with hand-selected inputs for each sensor, cannot leverage task synergies, and lack consistent benchmarks. At the same time, emerging time series foundation models are computationally expensive and limited to predicting their input signals, making them incompatible with virtual sensors. We introduce the first foundation model for virtual sensors addressing both limitations. Our unified model can simultaneously predict diverse virtual sensors exploiting synergies while maintaining computational efficiency. It learns relevant input signals for each virtual sensor, eliminating expert knowledge requirements while adding explainability. In our large-scale evaluation on a standard benchmark and an application-specific dataset with over 18 billion samples, our architecture achieves 415x reduction in computation time and 951x reduction in memory requirements, while maintaining or even improving predictive quality compared to baselines. Our model scales gracefully to hundreds of virtual sensors with nearly constant parameter count, enabling practical deployment in large-scale sensor networks.

Byte Pair Encoding for Efficient Time Series Forecasting

Existing time series tokenization methods predominantly encode a constant number of samples into individual tokens. This inflexible approach can generate excessive tokens for even simple patterns like extended constant values, resulting in substantial computational overhead. Inspired by the success of byte pair encoding, we propose the first pattern-centric tokenization scheme for time series analysis. Based on a discrete vocabulary of frequent motifs, our method merges samples with underlying patterns into tokens, compressing time series adaptively. Exploiting our finite set of motifs and the continuous properties of time series, we further introduce conditional decoding as a lightweight yet powerful post-hoc optimization method, which requires no gradient computation and adds no computational overhead. On recent time series foundation models, our motif-based tokenization improves forecasting performance by 36% and boosts efficiency by 1990% on average. Conditional decoding further reduces MSE by up to 44%. In an extensive analysis, we demonstrate the adaptiveness of our tokenization to diverse temporal patterns, its generalization to unseen data, and its meaningful token representations capturing distinct time series properties, including statistical moments and trends.

Efficient Time Series Processing for Transformers and State-Space Models through Token Merging

Transformer architectures have shown promising results in time series processing. However, despite recent advances in subquadratic attention mechanisms or state-space models, processing very long sequences still imposes significant computational requirements. Token merging, which involves replacing multiple tokens with a single one calculated as their linear combination, has shown to considerably improve the throughput of vision transformer architectures while maintaining accuracy. In this work, we go beyond computer vision and perform the first investigations of token merging in time series analysis on both time series transformers and state-space models. To effectively scale token merging to long sequences, we introduce local merging, a domain-specific token merging algorithm that selectively combines tokens within a local neighborhood, adjusting the computational complexity from linear to quadratic based on the neighborhood size. Our comprehensive empirical evaluation demonstrates that token merging offers substantial computational benefits with minimal impact on accuracy across various models and datasets. On the recently proposed Chronos foundation model, we achieve accelerations up to 5400% with only minor accuracy degradations.