Functional representation of 3D objects as a method of data generalization in generative machine learning models

Abstract

The article proposes a new method for representing three-dimensional objects through scalar functions of a vector argument. This method of representation allows reducing the function to a series of normalized vectors, which is a key requirement for building machine learning models of Transformer class. The need to develop such a method is based on a general conceptual hypothesis about the possibility of using the currently most successful type of generative neural networks, which is central in the field of large language models (LLM), to generate 3D objects with specific physical properties. This hypothesis follows from the fact that Transformer-like models (in particular, GPT) have already been applied to generate two-dimensional images, therefore, with correct representation of 3D object’s shapes, it is possible to extend their application to 3D modeling. The results of testing the proposed method showed high accuracy in collapsing the “point cloud” of the 3D model surface into a series of vectors (embeddings) and restoring the original figure from this series. The demonstrational implementation of the method has the drawback of inaccuracy in function interpolation, but this is not a limitation of the method itself, but only of its technical implementation. The real limitation of the method is its narrowing down to only one class of topological spaces. Further research will be aimed at generalizing this method to all possible types of topologies