Related papers: Equivalence of Dimensional Reduction and Dimension…
We reformulate unsupervised dimension reduction problem (UDR) in the language of tempered distributions, i.e. as a problem of approximating an empirical probability density function by another tempered distribution, supported in a…
Fixed-order perturbative calculations for differential cross sections can suffer from non-physical artifacts: they can be non-positive, non-normalizable, and non-finite, none of which occur in experimental measurements. We propose a…
In the context of Differential Renormalization, using Constrained Differential Renormalization rules at one loop, we show how to obtain concrete results in two loop calculations without making use of Ward identities. In order to do that, we…
We demonstrate that almost all non-parametric dimensionality reduction methods can be expressed by a simple procedure: regularized loss minimization plus singular value truncation. By distinguishing the role of the loss and regularizer in…
High-dimensional prediction is a challenging problem setting for traditional statistical models. Although regularization improves model performance in high dimensions, it does not sufficiently leverage knowledge on feature importances held…
In this article we investigate the connection between regularization theory for inverse problems and dynamic programming theory. This is done by developing two new regularization methods, based on dynamic programming techniques. The aim of…
Dimensional regularization is used to derive the equations of motion of two point masses in harmonic coordinates. At the third post-Newtonian (3PN) approximation, it is found that the dimensionally regularized equations of motion contain a…
In this paper we consider inverse problems that are mathematically ill-posed. That is, given some (noisy) data, there is more than one solution that approximately fits the data. In recent years, deep neural techniques that find the most…
We shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non-analytic perturbation (the latter will be assumed to have continuous derivatives up to a sufficiently large order). We shall…
Data augmentation is one of the most popular techniques for improving the robustness of neural networks. In addition to directly training the model with original samples and augmented samples, a torrent of methods regularizing the distance…
Miscalibration in deep learning refers to there is a discrepancy between the predicted confidence and performance. This problem usually arises due to the overfitting problem, which is characterized by learning everything presented in the…
Sufficient dimension reduction (SDR) methods, which often rely on class precision matrices, are widely used in supervised statistical classification problems. However, when class-specific sample sizes are small relative to the original…
Deep learning based reconstruction methods deliver outstanding results for solving inverse problems and are therefore becoming increasingly important. A recently invented class of learning-based reconstruction methods is the so-called NETT…
We extend an implicit regularization scheme to be applicable in the $n$-dimensional space-time. Within this scheme divergences involving parity violating objects can be consistently treated without recoursing to dimensional continuation.…
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…
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…
In this paper, we study renormalization, that is, the procedure for eliminating singularities, for a special model using both combinatorial techniques in the framework of working with formal series, and using a limit transition in a…
We study the question of whether two frames of a given physical theory are equivalent or not in the presence of quantum corrections. By using field theory arguments we claim that equivalence is broken in the presence of anomalous symmetries…
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…
The controversy concerning the phenomenon of breakdown of dimensional regularization in the problems involving asymptotic expansions of Feynman diagrams in non-Euclidean regimes is discussed with some pertinent bibliographic comments.