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<p>Conventional Transformer models for multivariate time series (MTS) rely on fixed-dimension inputs, necessitating explicit masking or pre-filling strategies when handling missing data. These strategies can distort observational distributions, underestimate predictive uncertainty, and introduce bias, particularly in scenarios characterized by dynamic dimensionality and unknown missing patterns. To address these challenges, the authors propose <b>VarDim-Transformer</b>, a novel architecture that natively supports variable input dimensions without requiring padding or channel identifiers, leveraging the Semi-Tensor Product (STP) of matrices. The core mechanism, the <i>PiRegistry</i>, dynamically projects arbitrary-length observation vectors into a unified latent feature space, enabling interaction via VarDim-Attention and VarDim-FFN before inverse projection. The authors evaluate the model under a rigorous “Random Dynamic Two-Level Missingness” protocol, which simulates long-term sensor failure and transient packet loss under privacy constraints. Experiments on the C-MAPSS FD001 remaining-useful-life prediction task demonstrate that VarDim-Transformer significantly outperforms imputation-based baselines. Notably, in a “Top-K” worst-case error analysis, VarDim-Transformer reduces the penalized error score by 21.28% compared to baselines and achieves a 77.1% win rate on the most critical samples. This confirms its superior robustness and generalization capability in extreme, privacy-sensitive missingness scenarios.</p>

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VarDim-Transformer: A Unified Framework for Variable-Dimension Time Series with Unknown Missing Patterns

  • 期刊论文

  • 发表日期：

    2026年4月28日

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  • Shengli Xue,
  • Lijun Zhang

摘要

Conventional Transformer models for multivariate time series (MTS) rely on fixed-dimension inputs, necessitating explicit masking or pre-filling strategies when handling missing data. These strategies can distort observational distributions, underestimate predictive uncertainty, and introduce bias, particularly in scenarios characterized by dynamic dimensionality and unknown missing patterns. To address these challenges, the authors propose VarDim-Transformer, a novel architecture that natively supports variable input dimensions without requiring padding or channel identifiers, leveraging the Semi-Tensor Product (STP) of matrices. The core mechanism, the PiRegistry, dynamically projects arbitrary-length observation vectors into a unified latent feature space, enabling interaction via VarDim-Attention and VarDim-FFN before inverse projection. The authors evaluate the model under a rigorous “Random Dynamic Two-Level Missingness” protocol, which simulates long-term sensor failure and transient packet loss under privacy constraints. Experiments on the C-MAPSS FD001 remaining-useful-life prediction task demonstrate that VarDim-Transformer significantly outperforms imputation-based baselines. Notably, in a “Top-K” worst-case error analysis, VarDim-Transformer reduces the penalized error score by 21.28% compared to baselines and achieves a 77.1% win rate on the most critical samples. This confirms its superior robustness and generalization capability in extreme, privacy-sensitive missingness scenarios.