Talk page
Title:
Critical Volumes of Toric Sasaki-Einstein Manifolds and Neural Networks Explainability
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Abstract:
The problem of Z-minimisation was introduced and well-studied early this century. For a Kaehler cone over a (compact) Sasaki manifold base it requires finding such a contact structure that minimises the base’s volume, which is equivalent to the Ricci flatness condition on the cone and Einstein condition on the base. The advent of datasets of reflexive polytopes allowed computational studies of the problem in a large class of toric Calabi-Yau varieties leading to new observations, such as the upper bound on the said volumes we proved. After briefly recounting the problem, we will show that the critical volumes and other related quantities can be effectively machine-learned using Neural Networks and easy-to-compute geometric features of the varieties. Furthermore, we will discuss the gradient saliency method, which allows to intuit the relative importance of particular features for the NN. It has recently proved successful in structurally similar problems in knot theory and we will show it can be similarly applied in this toric-geometric case.
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