
Shape Representation Learning with Moments
Alvin Tan * , Kevin Chen , Ryan Li , Nishant Doss , Sophie Shen
* Project Lead
Geospatial shapes vary widely in coordinate complexity, making them incompatible with standard ML models that require fixed-size inputs. Poly2Vec addresses this by encoding shapes into fixed-size vectors via a Fourier transform, but requires Delaunay triangulation as a preprocessing step. This project proposes replacing the Fourier basis with polynomial moments (ie: integrating shapes against Legendre polynomial basis functions) which admits closed-form solutions across all geometry types with no triangulation needed. We evaluate whether this alternative encoding matches or improves on Fourier-based embeddings for downstream spatial reasoning tasks.








