Related papers: A New Angle on L2 Regularization

Through the lense of multilevel model (MLM) specification and regularization, this is a connect-the-dots introductory summary of Small Area Estimation, e.g. small group prediction informed by a complex sampling design. While a comprehensive…

We investigate the variation of galaxy clustering with luminosity using the recently completed SSRS2 sample. Clustering measurements based on the two-point correlation function and the variance of counts in cells reveal the existence of a…

By a 2-ring we mean a groupoid with a structure analogous to that of a ring, up to coherent isomorphisms. Two different notions of 2-ring appear in the literature: the notion of {\em Ann-category}, due to Quang, and the notion of {\em…

A new approach to the study of the large-scale stellar cluster distribution in the Galaxy based on two-point correlation techniques is presented. The basic formalism for this method is outlined and its applications are then investigated by…

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…

Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a…

We propose a new renormalization scheme in the two Higgs doublet models with a softly-broken $Z_2$ symmetry and CP-conservation in the Higgs sector. In this scheme, counterterms for mixing angles of the Higgs bosons are determined by using…

We build a concrete and natural model for the strict 2-category of orbifolds. In particular we prove that if one localizes the 2-category of proper etale Lie groupoids at a class of 1-arrows that we call "covers", then the strict 2-category…

Quantifying the amount of polarization is crucial for understanding and studying political polarization in political and social systems. Several methods are used commonly to measure polarization in social networks by purely inspecting their…

The Learning to Rank (L2R) research field has experienced a fast paced growth over the last few years, with a wide variety of benchmark datasets and baselines available for experimentation. We here investigate the main assumption behind…

The accurate and automatic extraction of roads from satellite imagery is critical for applications in navigation and urban planning, significantly reducing the need for manual annotation. Many existing methods decompose this task into…

I apply commonly used regularization schemes to a multi-loop calculation to examine the properties of the schemes at higher orders. I find complete consistency between the conventional dimensional regularization scheme and dimensional…

Domain generalization is proposed to address distribution shift, arising from statistical disparities between training source and unseen target domains. The widely used first-order meta-learning algorithms demonstrate strong performance for…

We propose a new loss formulation to further advance the multiclass segmentation of cluttered cells under weakly supervised conditions. We improve the separation of touching and immediate cells, obtaining sharp segmentation boundaries with…

Normalization layers were introduced to stabilize and accelerate training, yet their influence is critical already at initialization, where they shape signal propagation and output statistics before parameters adapt to data. In practice,…

Many results that are difficult can be found more easily by using a generalization in the complex plane of Einstein's addition law of parallel velocities. Such a generalization is a natural way to add quantities that are limited to bounded…

Regularization plays a pivotal role when facing the challenge of solving ill-posed inverse problems, where the number of observations is smaller than the ambient dimension of the object to be estimated. A line of recent work has studied…

This work analyzes the training dynamics of Image Restoration (IR) Transformers and uncovers a critical yet overlooked issue: conventional LayerNorm (LN) drives feature magnitudes to diverge to a million scale and collapses channel-wise…

Contrastive Learning (CL) is a recent representation learning approach, which encourages inter-class separability and intra-class compactness in learned image representations. Since medical images often contain multiple semantic classes in…

A new classification of circular polarization C points in three-dimensional polarization ellipse fields is proposed. The classification type depends on the out-of-plane variation of the polarization ellipse axis, in particular, whether the…