Related papers: Differential Renormalization and Dimensional Reduc…
This paper investigates the double descent phenomenon in two-layer neural networks, focusing on the role of L1 regularization and representation dimensions. It explores an alternative double descent phenomenon, named sparse double descent.…
Shape Dynamics (SD) is a theory dynamically equivalent to vacuum General Relativity (GR), which has a different set of symmetries. It trades refoliation invariance, present in GR, for local 3-dimensional conformal invariance. This…
The holographic correspondence between 2d, N=2 quantum field theories and classical 4d, N=2 supergravity coupled to hypermultiplet matter is proposed. The geometrical constraints on the target space of the 4d, N=2 non-linear sigma-models in…
We construct a new version of the higher covariant derivative regularization for a general ${\cal N}=2$ supersymmetric gauge theory formulated in terms of ${\cal N}=1$ superfields. This regularization preserves both supersymmetries of the…
Dual gradient descent combined with early stopping represents an efficient alternative to the Tikhonov variational approach when the regularizer is strongly convex. However, for many relevant applications, it is crucial to deal with…
In D-dimensional spacetimes which can be foliated by n-dimensional homogeneous subspaces, a quantum field can be decomposed in terms of modes on the subspaces, reducing the system to a collection of (D-n)-dimensional fields. This allows one…
The relation between renormalization and short distance singular divergencies in quantum field theory is studied. As a consequence a finite theory is presented. It is shown that these divergencies are originated by the multiplication of…
Different phenomenological RG transformations based on scaling relations for the derivatives of the inverse correlation length and singular part of the free-energy density are considered. These transformations are tested on the 2D square…
We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of…
Non-minimal renormalisation schemes such as the momentum subtraction scheme (MOM) have frequently been used for physical computations. The consistency of such a scheme relies on the existence of a coupling redefinition linking it to MSbar.…
When using dimensional regularization, the bare couplings are expressed as a power series in (2 - n/2)^{-1} where n is the number of dimensions. It is shown how the renormalization group can be used to sum the leading pole, next to leading…
It is shown that the local coupling of a higher dimensional graviton to a closed degenerate two-form produces dimensional reduction by spontaneous breakdown of extra-dimensional translational symmetry. Four dimensional Poincar\'e invariance…
The exact renormalization group (ERG) is formulated implementing the decimation of degrees of freedom by means of a particular momentum integration measure. The definition of this measure involves a distribution that links this decimation…
A new operator formalism for the reduction of degrees of freedom in the evolution of discrete partial differential equations (PDE) via real space Renormalization Group is introduced, in which cell-overlapping is the key concept.…
The matching between Schrodinger Functional renormalization schemes and conventional perturbative schemes is usually done using an intermediate lattice scheme. We propose to do the matching directly. This requires the perturbative…
The solution to empirical risk minimization with $f$-divergence regularization (ERM-$f$DR) is extended to constrained optimization problems, establishing conditions for equivalence between the solution and constraints. A dual formulation of…
The role of $L^2$ regularization, in the specific case of deep neural networks rather than more traditional machine learning models, is still not fully elucidated. We hypothesize that this complex interplay is due to the combination of…
The causal dynamical triangulations approach aims to construct a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. A renormalization group scheme--in concert with finite size scaling…
We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Kenneth…
A thorough analysis is presented of the class of central fields of force that exhibit: (i) dimensional transmutation and (ii) rotational invariance. Using dimensional regularization, the two-dimensional delta-function potential and the…