PiTransformer: A Gated Patch-Wise Inverted Transformer for Stochastic Multivariate Time Series Forecasting

Multivariate time series forecasting presents a challenging problem in stochastic modeling, particularly under non-stationary conditions with low signal-to-noise ratios. While recent inverted architectures enhance cross-variable dependency modeling, the conventional point-wise inversion strategy often compromises local temporal patterns. To address this limitation, we propose PiTransformer, a gated patch-wise inverted framework for multivariate time series modeling. Specifically, a Patch-wise Inverted Embedding (PIE) mechanism is introduced to segment temporal sequences into regional patches prior to inversion, enabling the preservation of localized temporal structures. In addition, a Variable–Temporal Gating (VTG) module is incorporated to regulate feature interactions based on the information bottleneck principle, thereby suppressing spurious correlations in noisy environments. Empirical evaluations on diverse benchmarks—including financial and energy datasets—demonstrate that PiTransformer achieves consistent improvements in predictive accuracy and stability over competitive baselines. These results suggest that the proposed framework provides a robust and interpretable approach for modeling high-dimensional stochastic time series under non-stationary conditions.