Related papers: A New Angle on L2 Regularization
The Second Parameter (2ndP) Problem recognizes the remarkable role played by horizontal branch (HB) morphology in the development of our understanding of globular clusters, and the Galaxy, over the last 50 years. I will describe the…
Ordinal regression is a classification task where classes have an order and prediction error increases the further the predicted class is from the true class. The standard approach for modeling ordinal data involves fitting parallel…
Observations of galaxy clusters (GC's) are a powerful tool to probe the evolution of the Universe at $z<2$. However, the determination of their real shape and structure is not completely understood and the assumption of asphericity is often…
This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within…
We study the angular structure of polarization of light transmitted through a nematic liquid crystal (NLC) cell by theoretically analyzing the polarization state as a function of the incidence angles. For a uniformly aligned NLC cell, the…
The extent to which the arbitrarily selected L2 regularization hyperparameter value affects the outcome of semantic segmentation with deep learning is demonstrated. Demonstrations rely on training U-net on small LGE-MRI datasets using the…
For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie groupoids, furnishing a differential graded-commutative Lie algebra equipped with an adjoint action of the Lie 2-group and a pullback operation…
We study the geometry of the stratification induced by an affine hyperplane arrangement H on the quotient of a complex affine space by the action of a discrete group preserving H. We give conditions ensuring normality or normality in…
In the classification of real singularities by Arnold et al. (1985), normal forms, as representatives of equivalence classes under right equivalence, are not always uniquely determined. We describe the complete structure of the equivalence…
A radiatively-corrected mixing angle has to be independent of the choice of renormalization scale to be a physical observable. At one-loop in MS-bar, this only occurs for a particular value, p*, of the external momentum in the two-point…
Emergent behaviors are in the focus of recent research interest. It is then of considerable importance to investigate what optimizations suit the learning and prediction of chaotic systems, the putative candidates for emergence. We have…
Regularized models are often sensitive to the scales of the features in the data and it has therefore become standard practice to normalize (center and scale) the features before fitting the model. But there are many different ways to…
Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information and is weighted by a regularization parameter.…
In statistical applications, the normal and the Laplace distributions are often contrasted: the former as a standard tool of analysis, the latter as its robust counterpart. I discuss the convolutions of these two popular distributions and…
We introduce a novel statistical way of analyzing the projected mass distribution in galaxy lenses based solely on the angular distribution of images in quads around the lens center. The method requires the knowledge of the lens center…
We consider the 2D $J_1-J_2$ classical XY model on a square lattice. In the frustrated phase corresponding to $J_2>J_1/2$, an Ising order parameter emerges by an ``order due to disorder'' effect. This leads to a discrete symmetry plus the…
Clusters of galaxies acting as gravitational lenses deform the images of background galaxies. For small galaxies the deformation is determined by the local properties of the lens (shear, convergence). Small circular shaped galaxies are seen…
We consider a generalized angle in complex normed vector spaces. Its definition corresponds to the definition of the well known Euclidean angle in real inner product spaces. Not surprisingly it yields complex values as `angles'. This…
Recent empirical and theoretical studies have shown that many learning algorithms -- from linear regression to neural networks -- can have test performance that is non-monotonic in quantities such the sample size and model size. This…
We study the geometry of equiclassical strata of the discriminant in the space of plane curves of a given degree, which are families of curves of given degree, genus and class (degree of the dual curve). Our main observation is that the use…