الملخص
Modeling spatiotemporal coupling is a key challenge in building physical intelligence across scales, from microscopic to macroscopic. Existing models capture such structure broadly through physics-motivated dynamical formulations or learning-motivated architectures. The former provide stronger priors but may constrain flexibility, whereas the latter are more flexible but leave the spatiotemporal coupling largely implicit. We therefore seek an approach that combines flexible learning with an explicit geometric bias for jointly modeling time and space. To this end, we propose Minkowski Positional Encoding (MinkowskiPE), which uses joint temporal and spatial coordinates to parameterize Lorentz transformations applied to query and key features. With MinkowskiPE, the query-key attention score depends on position only through the relative spacetime displacement between the two tokens and is therefore invariant to global translation of the coordinates. This paradigm retains the standard dot-product attention interface and remains compatible with efficient attention implementations. We evaluate MinkowskiPE on microscopic molecular dynamics and macroscopic video prediction tasks, achieving the best results on all nine multi-trajectory molecular evaluations and reducing KTH video-prediction MSE by 9.9% relative to the best baseline while using roughly one-tenth as many parameters.
الكلمات المفتاحية
الموضوع
بيانات النشر
- المجلة
- غير متاح
- وصول مفتوح
- وصول مفتوح أخضر
اقتبس هذه المقالة
APA 7
Li, Y., Yao, L. H., Shi, T., Cao, H., Hao, H., Zhao, Z., & Liu, S. (2026). MinkowskiPE: Minkowski Positional Encoding for Spatiotemporal Perception. https://omanscience.com/ar/articles/minkowskipe-minkowski-positional-encoding-for-spatiotemporal-perception
MLA 9
Li, Yuhao, et al. "MinkowskiPE: Minkowski Positional Encoding for Spatiotemporal Perception." https://omanscience.com/ar/articles/minkowskipe-minkowski-positional-encoding-for-spatiotemporal-perception.
شيكاغو (المؤلف–التاريخ)
Li, Yuhao, Louie Hong Yao, Tianyi Shi, Hanqun Cao, Hongxia Hao, Zhen Zhao, and Shengchao Liu. 2026. "MinkowskiPE: Minkowski Positional Encoding for Spatiotemporal Perception." https://omanscience.com/ar/articles/minkowskipe-minkowski-positional-encoding-for-spatiotemporal-perception.
هارفارد
Li, Y., Yao, L. H., Shi, T., Cao, H., Hao, H., Zhao, Z. and Liu, S. (2026) 'MinkowskiPE: Minkowski Positional Encoding for Spatiotemporal Perception', Available at: https://omanscience.com/ar/articles/minkowskipe-minkowski-positional-encoding-for-spatiotemporal-perception.
فانكوفر
Li Y, Yao LH, Shi T, Cao H, Hao H, Zhao Z, et al. MinkowskiPE: Minkowski Positional Encoding for Spatiotemporal Perception. https://omanscience.com/ar/articles/minkowskipe-minkowski-positional-encoding-for-spatiotemporal-perception
IEEE
Y. Li, L. H. Yao, T. Shi, H. Cao, H. Hao, Z. Zhao, and S. Liu, "MinkowskiPE: Minkowski Positional Encoding for Spatiotemporal Perception," https://omanscience.com/ar/articles/minkowskipe-minkowski-positional-encoding-for-spatiotemporal-perception.