Generative Topology for Shape Synthesis

AmazUtah_NLP at SemEval-2024 Task 9: A MultiChoice Question Answering System for Commonsense Defying Reasoning



arXiv:2410.18987v1 Announce Type: new
Abstract: The Euler Characteristic Transform (ECT) is a powerful invariant for assessing geometrical and topological characteristics of a large variety of objects, including graphs and embedded simplicial complexes. Although the ECT is invertible in theory, no explicit algorithm for general data sets exists. In this paper, we address this lack and demonstrate that it is possible to learn the inversion, permitting us to develop a novel framework for shape generation tasks on point clouds. Our model exhibits high quality in reconstruction and generation tasks, affords efficient latent-space interpolation, and is orders of magnitude faster than existing methods.



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