Reproduce “Intrinsic and Triangulation-Agnostic Attention: A Simple and Powerful Approach for Learning on Meshes” on OpenResearch

About this paper

Ashwath Shetty, Zihan Zhu, Soeren Pirk, Noam Aigerman

The authors introduce attention for triangle meshes that treats vertex features as samples of continuous surface signals. Self-attention approximates surface integrals with area-weighted vertex sums, reducing the influence of dense sampling. On a remeshing test, it reaches 33.47 PSNR versus 22.40 for naive attention; on the original triangulation, it reaches 35.2 dB versus PoissonNet’s 29.2. They do not establish invariance.

Key insights

• Endowing attention mechanisms with intrinsicality (accounting for manifold structure) and triangulation-agnosticism (treating signals as continuous discretizations) is crucial for effective mesh-based learning.
• A mass-weighted softmax discretization of the attention mechanism allows it to approximate continuous functions over the manifold, ensuring robustness to varying mesh triangulations.
• The attention layers serve as a powerful conditioning and feature propagation mechanism, capable of enhancing existing mesh network backbones and outperforming non-attention-based state-of-the-art methods.

Summary by alphaXiv.