Related papers: Rigorous computer-assisted bounds on renormalisati…
It has been observed that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of ${\fR}^2$. A renormalization approach has been used in a "hard" computer-assisted proof of existence…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
Exact numerical minimization of interface energies is used to test the functional renormalization group (FRG) analysis for interfaces pinned by quenched disorder. The fixed-point function R(u) (the correlator of the coarse-grained disorder)…
Physical systems differring in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the…
We present a general framework for understanding and analyzing critical behaviour in gravitational collapse. We adopt the method of renormalization group, which has the following advantages. (1) It provides a natural explanation for various…
In this paper we generalize renormalization theory for analytic critical circle maps with a cubic critical point to the case of maps with an arbitrary odd critical exponent by proving a quasiconformal rigidity statement for renormalizations…
We prove the existence of fixed points of p-tupling renormalization operators for interval and circle mappings having a critical point of arbitrary real degree r > 1. Some properties of the resulting maps are studied: analyticity,…
The complete analysis of a model with three quartic coupling constants associated with an O(2N)--symmetric, a cubic, and a tetragonal interactions is carried out within the three-loop approximation of the renormalization-group (RG) approach…
We use the functional renormalization group and the $\epsilon$-expansion concertedly to explore multicritical universality classes for coupled $\bigoplus_i O(N_i)$ vector-field models in three Euclidean dimensions. Exploiting the…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical…
This paper presents uniform-in-time finite-sample bounds for regularized linear regression with vector-valued outputs and conditionally zero-mean subgaussian noise. By revisiting classical self-normalized martingale arguments, we obtain…
We introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium systems with steady-states: the Dynamically Driven Renormalization Group. We renormalize the time evolution…
We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularisation scheme, parametrised by a general cutoff function and infinitely many higher point…
The optimization foundations of deep linear networks have recently received significant attention. However, due to their inherent non-convexity and hierarchical structure, analyzing the loss functions of deep linear networks remains a…
We study the effective theory of the conformal factor near its infrared stable fixed point.The renormalization group equations for the effective coupling constants are found and their solutions near the critical point are obtained,…
The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our…
We establish new upper bounds for the numerical radius of bounded linear operators on a complex Hilbert space by introducing weighted geometric means of the modulus of an operator and its adjoint. This approach yields a family of…
We construct an approximate renormalization for Hamiltonian systems with two degrees of freedom in order to study the break-up of invariant tori with arbitrary frequency. We derive the equation of the critical surface of the renormalization…
Modern regression problems often involve high-dimensional data and a careful tuning of the regularization hyperparameters is crucial to avoid overly complex models that may overfit the training data while guaranteeing desirable properties…