Related papers: Renormalization group-like flows in randomly conne…
Fueled by the expressive power of deep neural networks, normalizing flows have achieved spectacular success in generative modeling, or learning to draw new samples from a distribution given a finite dataset of training samples. Normalizing…
We present recurrent transformer networks (RTNs) for obtaining dense correspondences between semantically similar images. Our networks accomplish this through an iterative process of estimating spatial transformations between the input…
Monotonic renormalization group flows of the "c" and "a" functions are often cited as reasons why cyclic or chaotic coupling trajectories cannot occur. It is argued here, based on simple examples, that this is not necessarily true.…
We study time-changes of unipotent flows on finite volume quotients of semisimple linear groups, generalising previous work by Ratner on time-changes of horocycle flows. Any measurable isomorphism between time-changes of unipotent flows…
We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a novel, quantitative understanding of local correlations in a network. Together with a…
Recurrent Neural Cascades (RNCs) are the recurrent neural networks with no cyclic dependencies among recurrent neurons. This class of recurrent networks has received a lot of attention in practice. Besides training methods for a fixed…
We present the lattice simulation of the renormalization group flow in the $3$-dimensional $O(N)$ linear sigma model. This model possesses a nontrivial infrared fixed point, called Wilson--Fisher fixed point. Arguing that the parameter…
We apply real-space RG methods to study two quantum group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field defined in an open chain with appropiate boundary terms. The quantum group symmetry is…
Recurrent neural networks (RNNs) are known to be universal approximators of dynamic systems under fairly mild and general assumptions. However, RNNs usually suffer from the issues of vanishing and exploding gradients in standard RNN…
Nonequilibrium reaction networks (NRNs) underlie most biological functions. Despite their diverse dynamic properties, NRNs share the signature characteristics of persistent probability fluxes and continuous energy dissipation even in the…
Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories, and to gain insight into the interplay between continuous and discrete rescaling. With minimal assumptions, the methods…
Recurrent neural networks (RNNs) are powerful tools for sequential modeling, but typically require significant overparameterization and regularization to achieve optimal performance. This leads to difficulties in the deployment of large…
We introduce an exceptionally simple gated recurrent neural network (RNN) that achieves performance comparable to well-known gated architectures, such as LSTMs and GRUs, on the word-level language modeling task. We prove that our model has…
We consider relative entropy in Field Theory as a well defined (non-divergent) quantity of interest. We establish a monotonicity property with respect to the couplings in the theory. As a consequence, the relative entropy in a field theory…
We show that in the Gevrey topology, a $d$-torus flow close enough to linear with a unique rotation vector $\omega$ is linearizable as long as $\omega$ satisfies a Brjuno type diophantine condition. The proof is based on the fast…
We show irreversibility of the renormalization group flow in non-unitary but ${\cal PT}$-invariant quantum field theory in two space-time dimensions. In addition to unbroken $\mathcal{PT}$-symmetry and a positive energy spectrum, we assume…
A scalar theory can have many Gaussian (free) fixed points, corresponding to Lagrangians of the form $\phi\,\Box^k\phi$. We use the non-perturbative RG to study examples of flows between such fixed points. We show that the anomalous…
We study the renormalization group evolution up to the fixed point of the lattice topological susceptibility in the 2-d O(3) non-linear sigma-model. We start with a discretization of the continuum topological charge by a local charge…
Lorenz maps are maps of the unit interval with one critical point of order rho>1, and a discontinuity at that point. They appear as return maps of leafs of sections of the geometric Lorenz flow. We construct real a priori bounds for…
Critical transition points between symmetry-broken phases are characterized as fixed points in the renormalization group (RG) theory. We show that, following the standard Wilsonian procedure that traces out the large momentum modes, this…