相关论文: Characteristic Generators and Dualization for Tail…

We study the ring of characteristic classes with values in the Chow ring for principal $G$-bundles over schemes. If we consider bundles which are locally trivial in the Zariski topology, then we show, for $G$ reductive, that this ring is…

Tensor factorization based models have shown great power in knowledge graph completion (KGC). However, their performance usually suffers from the overfitting problem seriously. This motivates various regularizers -- such as the squared…

Pre-training plays a vital role in various vision tasks, such as object recognition and detection. Commonly used pre-training methods, which typically rely on randomized approaches like uniform or Gaussian distributions to initialize model…

We define a very general class of CHL-models associated with any string theory (bosonic or supersymmetric) compactified on an internal CFT C x T^d. We take the orbifold by a pair (g,\delta), where g is a (possibly non-geometric) symmetry of…

We study a construction of diagrams of dualizable presentable stable $\infty$-categories associated with certain fiber-cofiber sequences over rigid bases, which are sent by localizing invariants, in particular continuous K-theory, to limit…

We present two new algorithms for Householder QR factorization of Block Low-Rank (BLR) matrices: one that performs block-column-wise QR, and another that is based on tiled QR. We show how the block-column-wise algorithm exploits BLR…

We conjecture that the complex of Soergel bimodules associated with the full twist braid is categorically diagonalizable, for any finite Coxeter group. This utilizes the theory of categorical diagonalization introduced earlier by the…

\noindent The algebraic characterization of classes of locally isomorphic aperiodic tilings, being examples of quantum spaces, is conducted for a certain type of tilings in a manner proposed by A. Connes. These $2$-dimensional tilings are…

Gradient compression has surfaced as a key technique to address the challenge of communication efficiency in distributed learning. In distributed deep learning, however, it is observed that gradient distributions are heavy-tailed, with…

This is Part II of our work about random tensor inequalities and tail bounds for bivariate random tensor means. After reviewing basic facts about random tensors, we first consider tail bounds with more general connection functions. Then, a…

This paper considers deep visual recognition on long-tailed data. To be general, we consider two applied scenarios, \ie, deep classification and deep metric learning. Under the long-tailed data distribution, the majority classes (\ie, tail…

This is the sequel paper to arXiv:2108.07185, continuing a study of monogenicity of number rings from a moduli-theoretic perspective. By the results of the first paper in this series, a choice of a generator $\theta$ for an $A$-algebra $B$…

Rate-(n-2)/n unrestricted and CSS-type quantum convolutional codes with up to 4096 states and minimum distances up to 10 are constructed as stabilizer codes from classical self-orthogonal rate-1/n F_4-linear and binary linear convolutional…

Nowadays random number generation plays an essential role in technology with important applications in areas ranging from cryptography, which lies at the core of current communication protocols, to Monte Carlo methods, and other…

In this PhD thesis we discuss methods of recognizing finite groups by the structure of normalizers of certain 3-subgroups. We explain a method for characterizing groups using character theoretic and block theoretic methods and we use these…

Cohomological induction gives an algebraic method for constructing representations of a real reductive Lie group $G$ from irreducible representations of reductive subgroups. Beilinson-Bernstein localization alternatively gives a geometric…

This paper introduces the framework of (local) toric separable geometries, where toric separable K\"ahler geometries come in families, each uniquely determined by an underlying factorization structure. This unifying framework captures all…

Deep long-tailed learning aims to train useful deep networks on practical, real-world imbalanced distributions, wherein most labels of the tail classes are associated with a few samples. There has been a large body of work to train…

We present trellis networks, a new architecture for sequence modeling. On the one hand, a trellis network is a temporal convolutional network with special structure, characterized by weight tying across depth and direct injection of the…

The aim of this work is to develop a systematic manner to close overdetermined systems arising from conformal Killing tensors (CKT). The research performs this action for 1-tensor and 2-tensors. This research makes it possible to develop a…