This internship proposal focuses on studying the dynamical properties of the Hopfield model—a foundational neural network framework that stores and retrieves memories through an energy-based approach similar to spin-glass models. Main objective: Design and implement a computationally efficient parallel Metropolis algorithm using bitwise arithmetics to simulate the Hopfield model's dynamics. Innovation: The method leverages how computers store boolean numbers to simulate multiple system copies simultaneously, all sharing the same random numbers for dynamical steps. Since random number generation is the computational bottleneck, this parallel approach yields significant computational gains. Research focus: The student will explore how the system converges to metastable states from different initial conditions, with emphasis on Monte Carlo dynamics equilibration—aspects less understood than the model's well-known static properties. Skills acquired: Proficiency in C++ programming and familiarity with neural network models. Location: Institut Curie (UMR 168) and occasionally ESPCI Gulliver Laboratory (UMR 7083), Paris. Supervisors: Michele Castellana and David Lacoste