Related papers: Regularization by Dimensional Reduction: Consisten…

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 prove that Riemannian contraction in a supervised learning setting implies generalization. Specifically, we show that if an optimizer is contracting in some Riemannian metric with rate $\lambda > 0$, it is uniformly algorithmically…

For the special theory of relativity, the normalization problem is formulated as the question how observers in constant relative motion may reach an agreement on space and time scales. As the normalization problem does not receive a…

Explicit analytic expressions for the electron self-energy and the vertex correction in quantum electrodynamics are derived at one loop using the recently proposed regularization scheme known as denominator regularization, assisted by its…

Supervised dimensionality reduction has emerged as an important theme in the last decade. Despite the plethora of models and formulations, there is a lack of a simple model which aims to project the set of patterns into a space defined by…

Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…

A natural and very important development of constrained system theory is a detail study of the relation between the constraint structure in the Hamiltonian formulation with specific features of the theory in the Lagrangian formulation,…

High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…

We consider the problem of nonlinear dimensionality reduction: given a training set of high-dimensional data whose ``intrinsic'' low dimension is assumed known, find a feature extraction map to low-dimensional space, a reconstruction map…

We reduce the dual version of $D=10$, $N=1$ supergravity coupled to $n$ vector fields to four dimensions, and derive the $SL(2,R)\times O(6,6+n)$ transformations which leave the equations of motion invariant. For $n=0$ $SL(2,R)$ is also a…

Tensor decomposition methods allow us to learn the parameters of latent variable models through decomposition of low-order moments of data. A significant limitation of these algorithms is that there exists no general method to regularize…

In the context of the lattice regularization of the four-dimensional $\mathcal{N}=1$ supersymmetric Yang--Mills theory (4D $\mathcal{N}=1$ SYM), we formulate a generalized BRS transformation that treats the gauge, supersymmetry (SUSY),…

Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by…

We reexamine a unitary-transformation method of extracting a physical Hamiltonian from a gauge field theory after quantizing all degrees of freedom including redundant variables. We show that this {\it quantum Hamiltonian reduction} method…

Dimensionally reduced supersymmetric theories retain a great deal of information regarding their higher dimensional origins. In superspace, this "memory" allows us to restore the action governing a reduced theory to that describing its…

We revisit and generalize the geometric procedure of regularizing a sequence of real numbers with respect to a so-called regularizing function. This approach was studied by S. Mandelbrojt and becomes useful and necessary when working with…

We show that formation of crossed products and passage to fixed point algebras by compact group actions with finite Rokhlin dimension preserve the following regularity properties: finite decomposition rank, finite nuclear dimension, and…

Higher-derivative terms in the string and M-theory effective actions are strongly constrained by supersymmetry. Using a mixture of techniques, involving both string amplitude calculations and an analysis of supersymmetry requirements, we…

In a wide class of D-dimensional spacetimes which are direct or semi-direct sums of a (D-n)-dimensional space and an n-dimensional homogeneous ``internal'' space, a field can be decomposed into modes. As a result of this mode decomposition,…

This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…