336 citations · 1.6k across the 53 of their papers we have counts for
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Emergent field theories from neural networks
Vitaly Vanchurin
We establish a duality relation between Hamiltonian systems and neural network-based learning systems. We show that the Hamilton's equations for position and momentum variables cor…
Dual Path Integral: a non-perturbative approach to strong coupling
Vitaly Vanchurin
We develop a non-perturbative method for calculating partition functions of strongly coupled quantum mechanical systems with interactions between subsystems described by a path int…
Differential equation for partition functions and a duality pseudo-forest
Vitaly Vanchurin
We consider finite quantum systems defined by a mixed set of commutation and anti-commutation relations between components of the Hamiltonian operator. These relations are represen…
A quantum-classical duality and emergent space-time
Vitaly Vanchurin
We consider the quantum partition function for a system of quantum spinors and then derive an equivalent (or dual) classical partition function for some scalar degrees of freedom.…
Covariant Information Theory and Emergent Gravity
Vitaly Vanchurin
Informational dependence between statistical or quantum subsystems can be described with Fisher matrix or Fubini-Study metric obtained from variations of the sample/configuration s…
Information Graph Flow: a geometric approximation of quantum and statistical systems
Vitaly Vanchurin
Given a quantum (or statistical) system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space (or of a space of distribut…