Using Legendre duality in Machine Learning part3
- Mirror duality of Landau-Ginzburg models via Discrete Legendre Transforms(arXiv)
Author : Helge Ruddat
Abstract : We introduce a duality of Landau-Ginzburg models based on the notion of the discrete Legendre transform given by Gross-Siebert. It generalizes the duality used to construct mirrors of complete intersections in toric varieties in a recent joint work with Gross and Katzarkov. We discuss how it appears as a limit version of the semi-flat Strominger-Yau-Zaslow construction of mirror symmetry with potential given as the obstruction in Floer theor
2. Legendre Duality of Spherical and Gaussian Spin Glasses(arXiv)
Author : Giuseppe Genovese, Daniele Tantari
Abstract : The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work [4], shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model.
