Istituto Nazionale di Fisica Nucleare, Sezione di Lecce

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...

On the geometry of WDVV equations and their Hamiltonian formalism in arbitrary dimension

Abstract It is known that in low dimensions Witten–Dijkgraaf–Verlinde–Verlinde (WDVV) equations can be rewritten as commuting quasilinear bi‐Hamiltonian systems. We extend some of these results to arbitrary dimension and arbitrary scalar product . In particular, we show that suit...