Machine learning techniques have recently gained prominence in physics, yielding a host of new results and insights. One key concept is that backpropagation, which computes the exact gradient any output program with respect to input. This achieved efficiently within differentiable programming paradigm, utilizes automatic differentiation (AD) each step computer chain rule. A classic application ...

We point out a general problem with the procedures commonly used to obtain improved actions from MCRG decimated configurations. Straightforward measurement of the couplings from the decimated configurations, by one of the known methods, can result into actions that do not correctly reproduce the physics on the undecimated lattice. This is because the decimated configurations are generally not r...

We study the optimization of exact renormalization group ~ERG! flows. We explain why the convergence of approximate solutions towards the physical theory is optimized by appropriate choices of the regularization. We consider specific optimized regulators for bosonic and fermionic fields and compare the optimized ERG flows with generic ones. This is done up to second order in the derivative expa...

In this lecture, we review the derivation of the holographic renormalization group given in hep-th/9912012. Some extra background material is included, and various applications are discussed.

This is a very brief introduction to Wilson’s Renormalization Group with emphasis on mathematical developments.