تقرير
Fast Tree-Field Integrators: From Low Displacement Rank to Topological Transformers
| العنوان: | Fast Tree-Field Integrators: From Low Displacement Rank to Topological Transformers |
|---|---|
| المؤلفون: | Choromanski, Krzysztof, Sehanobish, Arijit, Chowdhury, Somnath Basu Roy, Lin, Han, Dubey, Avinava, Sarlos, Tamas, Chaturvedi, Snigdha |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science |
| مصطلحات موضوعية: | Computer Science - Machine Learning, Computer Science - Artificial Intelligence |
| الوصف: | We present a new class of fast polylog-linear algorithms based on the theory of structured matrices (in particular low displacement rank) for integrating tensor fields defined on weighted trees. Several applications of the resulting fast tree-field integrators (FTFIs) are presented, including (a) approximation of graph metrics with tree metrics, (b) graph classification, (c) modeling on meshes, and finally (d) Topological Transformers (TTs) (Choromanski et al., 2022) for images. For Topological Transformers, we propose new relative position encoding (RPE) masking mechanisms with as few as three extra learnable parameters per Transformer layer, leading to 1.0-1.5%+ accuracy gains. Importantly, most of FTFIs are exact methods, thus numerically equivalent to their brute-force counterparts. When applied to graphs with thousands of nodes, those exact algorithms provide 5.7-13x speedups. We also provide an extensive theoretical analysis of our methods. Comment: Preprint. Comments welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.15881 |
| رقم الأكسشن: | edsarx.2406.15881 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |