Abstract

In recent years, important new relations between information theory and quantum gravity have been found in the context of generalising the AdS/CFT correspondence. Information measures have been used to describe the quantum nature of black holes. Conversely, concepts such as the renormalisation group and relative entropy are used towards quantifying the learning ability of neural networks, and hyperbolic geometry gives rise to neural networks with improved properties.  I will review these developments based on three examples: 1) Geometric phases and symplectic forms characterise Hilbert spaces and hidden information on both sides of the AdS/CFT duality;  2) The relative entropy or Kullback-Leibler divergence shows similar behaviour for the Ising model under RG transformations and for feedforward neural networks as function of depth; 3) Recent progress towards establishing a holographic duality for regular tilings of hyperbolic space may also have implications for hyperbolic graph neural networks. Based on arXiv 2107.06898,  2205.05693 and 2306.00055