Istituto Nazionale di Alta Matematica Francesco Severi

The Infinite Volume Limit of the Hopfield Neural Networks in the Replica-Symmetric Regime

Abstract Despite extensive research over the past five decades, a rigorous determination of the infinite volume limit of the free energy of the Hopfield model with an extensive number of patterns has remained an outstanding open problem as standard methods from spin glass theory...

Spinors Beyond Dirac, Weyl and Majorana: The Flag-Dipoles

Abstract We recall the Lounesto classification of 1/2-spin spinor fields, based on the vanishing of spinorial bilinear quantities: the classes are the regular spinor fields (i.e. the Dirac field), as well as singular spinor fields, also known as flag-dipole spinor fields, admitti...