Dynamical Mean Field Theory

Dynamical Mean Field Theory (DMFT) is a powerful analytical tool used to understand the collective behavior of complex systems, particularly high-dimensional systems like neural networks. Current research focuses on applying DMFT to analyze the dynamics of various neural network architectures, including transformers and recurrent networks, often employing stochastic gradient descent as the learning algorithm. This allows researchers to gain insights into training dynamics, emergent properties like phase transitions and the "edge of chaos," and the impact of factors such as network width, depth, and the type of optimization algorithm used. The resulting theoretical understanding improves our ability to design and interpret these complex systems, potentially leading to more efficient training methods and a deeper understanding of their learning capabilities.