Andrea E. V. Ferrari

Marianna Marcella Bolognesi, Claudia Collacciani, Andrea Ferrari et al.

Word Ladders is a free mobile application for Android and iOS, developed for collecting linguistic data, specifically lists of words related to each other through semantic relations of categorical inclusion, within the Abstraction project (ERC-2021-STG-101039777). We hereby provide an overview of Word Ladders, explaining its game logic, motivation and expected results and applications to nlp tasks as well as to the investigation of cognitive scientific open questions

Andrea E. V. Ferrari, Prateek Gupta, Nabil Iqbal

The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction of a dual Hamiltonian and a map from the original to the dual observables. By using simple neural networks to parameterize these maps and introducing a loss function that penalises the difference between correlation functions in original and dual models, we formulate the process of duality discovery as an optimization problem. We numerically solve this problem and show that our framework can rediscover the celebrated Kramers-Wannier duality for the 2d Ising model, reconstructing the known mapping of temperatures. We also discuss an alternative approach which uses known features of the mapping of topological lines to reduce the problem to optimizing the couplings in a dual Hamiltonian, and explore next-to-nearest neighbour deformations of the 2d Ising duality. We discuss future directions and prospects for discovering new dualities within this framework.