Related papers: Criticality & Deep Learning II: Momentum Renormali…
Nematic order is an exotic property observed in several strongly correlated systems, such as the iron-based superconductors. Using large-scale density matrix renormalization group (DMRG) techniques, we study at zero-temperature the nematic…
We investigate the analogy between the renormalization group (RG) and deep neural networks, wherein subsequent layers of neurons are analogous to successive steps along the RG. In particular, we quantify the flow of information by…
We propose a new class of deep reinforcement learning (RL) algorithms that model latent representations in hyperbolic space. Sequential decision-making requires reasoning about the possible future consequences of current behavior.…
Flow control is key to maximize energy efficiency in a wide range of applications. However, traditional flow-control methods face significant challenges in addressing non-linear systems and high-dimensional data, limiting their application…
The advantages of using more than one renormalization group (RG) in problems with more than one important length scale are discussed. It is shown that: i) using different RG's can lead to complementary information, i.e. what is very…
Exploring and understanding topological phases in systems with strong distributed disorder requires developing fundamentally new approaches to replace traditional tools such as topological band theory. Here, we present a general real-space…
We explain how to use diffusion models to learn inverse renormalization group flows of statistical and quantum field theories. Diffusion models are a class of machine learning models which have been used to generate samples from complex…
Active matter is not only relevant to living matter and diverse nonequilibrium systems, but also constitutes a fertile ground for novel physics. Indeed, dynamic renormalization group (DRG) analyses have uncovered many new universality…
A catastrophic bifurcation in non-linear dynamical systems, called crisis, often leads to their convergence to an undesirable non-chaotic state after some initial chaotic transients. Preventing such behavior has proved to be quite…
The Kato-Bloch perturbation formalism is used to present a density-matrix renormalization-group (DMRG) method for strongly anisotropic two-dimensional systems. This method is used to study Heisenberg chains weakly coupled by the transverse…
Deep learning is increasingly viewed as a dynamical process in parameter space, yet many existing theories still treat training as a closed optimization system. This view is limited for real-world AI, where models operate under uncertainty,…
In order for autonomous mobile robots to navigate in human spaces, they must abide by our social norms. Reinforcement learning (RL) has emerged as an effective method to train sequential decision-making policies that are able to respect…
Machine Learning (ML) methods and tools have gained great success in many data, signal, image and video processing tasks, such as classification, clustering, object detection, semantic segmentation, language processing, Human-Machine…
The spin 1/2 XXZ chain in a random magnetic field pointing in the Z direction is numerically studied using the Density Matrix Renormalization Group (DMRG) method. The phase diagram as a function of the anisotropy of the XXZ Hamiltonian and…
Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly…
We revisit the renormalisation of models with two U(1) gauge symmetries, in a formulation with non-canonical gauge kinetic terms which is covariant under field reparametrisations among the two gauge bosons. This approach is convenient to…
The susceptibility of deep learning to adversarial attack can be understood in the framework of the Renormalisation Group (RG) and the vulnerability of a specific network may be diagnosed provided the weights in each layer are known. An…
There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…
We compute the two-loop $\beta$-function of scalar and spinorial quantum electrodynamics as well as pure Yang-Mills and quantum chromodynamics using the background field method in a fully quadridimensional setup using Implicit…
Implicit regularization is an important way to interpret neural networks. Recent theory starts to explain implicit regularization with the model of deep matrix factorization (DMF) and analyze the trajectory of discrete gradient dynamics in…