Abstract

In this talk, I discuss a possible way to perform quantum gravity path integral by using machine learning. Our new model of generative discrete geometry can provide a theoretical ground.  I start with explaining our machine-learning solver of quantum mechanics. Our proposed method computes the wavefunctions in quantum mechanics using machine learning with unstructured deep neural networks (NNs). In the course, we bridge discrete geometry and machine learning through the interpretation of the obtained NN wavefunctions. As an application, we find that a simple NN with ReLU activation generates polyhedra as an approximation of the unit sphere in various dimensions. The type of polyhedron is controlled by the NN architecture. For various activation functions, a generalization of the polyhedra is obtained, which we name the neural polytopes. These are a smooth generalization of polytopes and exhibits geometric duality. As NNs can generate discrete geometries, combining this with the “NN=QFT” idea or the traditional random NN idea, we may formulate quantum gravity by miachine learning.