Active-absorbing transition in the linear perceptron model

Recently, many studies have been conducted on systems of particles suspended in liquid, since their physics is related to glassy systems. These systems showcase a particular type of out of equilibrium phase transition, called absorbing state phase transition. In order to study this phenomenon, many simple models have been proposed to simulate the dynamics, and they have been characterized through their critical exponents at the transition, suggesting that they belong to the Manna universality class. We focused on simulating a mean field model, the spherical perceptron, using finite learning rate gradient descent on the hinge loss, which reproduces a dynamic with an absorbing phase transition. We conducted extensive numerical simulations to extrapolate the crit- ical exponents of the activity (the number of negative gaps) at the transition point, in order to find if also this system belongs to the same universality class as the other algorithms proposed. We characterize the critical behavior at the transition and find numerically the critical exponents associated to the order parameter, the activity as well as the associated susceptibility.