Related papers: The Augmentation Property of Binary Matrices for t…

We associate to a bimonoidal functor, i.e. a bifunctor which is monoidal in each variable, a nonabelian version of a biextension. We show that such a biextension satisfies additional triviality conditions which make it a bilinear analog of…

Matrix-valued polynomials in any finite number of freely noncommuting variables that enjoy certain canonical partial convexity properties are characterized, via an algebraic certificate, in terms of Linear Matrix Inequalities and Bilinear…

Hermitian and unitary matrices are two representatives of the class of normal matrices whose full eigenvalue decomposition can be stably computed in quadratic computing com plexity. Recently, fast and reliable eigensolvers dealing with low…

We consider the problem of determining which matrices are permutable to be supmodular. We show that for small dimensions any matrix is permutable by a universal permutation or by a pair of permutations, while for higher dimensions no…

Binary classification is highly used in credit scoring in the estimation of probability of default. The validation of such predictive models is based both on rank ability, and also on calibration (i.e. how accurately the probabilities…

A banded matrix is a real square matrix where nonzero entries appear around the main diagonal. In this article, we consider linear complementarity properties of (variants) of banded matrices. Focusing on triangular matrices and the newly…

Data augmentations are useful in closing the sim-to-real domain gap when training on synthetic data. This is because they widen the training data distribution, thus encouraging the model to generalize better to other domains. Many image…

General approach to the multiplication or adjoint operation of $2\times 2$ block operator matrices with unbounded entries are founded. Furthermore, criteria for self-adjointness of block operator matrices based on their entry operators are…

Every m by n matrix A with rank r has exactly r independent rows and r independent columns. The fact has become the most fundamental theorem in linear algebra such that we may favor it in an unconscious way. The sole aim of this paper is to…

We consider a school choice matching model where the priorities for schools are represented by binary relations that may not be weak order. We focus on the (total order) extensions of the binary relations. We introduce a class of algorithms…

Model robustness indicates a model's capability to generalize well on unforeseen distributional shifts, including data corruptions and adversarial attacks. Data augmentation is one of the most prevalent and effective ways to enhance…

A matroid has been one of the most important combinatorial structures since it was introduced by Whitney as an abstraction of linear independence. As an important property of a matroid, it can be characterized by several different (but…

Decision tree and random forest classification and regression are some of the most widely used in machine learning approaches. Binary decision tree implementations commonly use conditioning in the form 'feature $\leq$ (or $<$) threshold',…

For a prime $p$ and a matrix $A \in \mathbb{Z}^{n \times n}$, write $A$ as $A = p (A \,\mathrm{quo}\, p) + (A \,\mathrm{rem}\, p)$ where the remainder and quotient operations are applied element-wise. Write the $p$-adic expansion of $A$ as…

We define the notion of an additive model category, and we prove that any additive, stable, combinatorial model category has a natural enrichment over symmetric spectra based on simplicial abelian groups. As a consequence, every object in…

A general result on the structure and dimension of the root subspaces of a matrix or a linear operator under finite rank perturbations is proved: The increase of dimension from the $n$-th power of the kernel of the perturbed operator to the…

Imposing an extensional uniformity condition on a non-uniform circuit complexity class C means simply intersecting C with a uniform class L. By contrast, the usual intensional uniformity conditions require that a resource-bounded machine be…

We propose a novel data augmentation for labeled sentences called contextual augmentation. We assume an invariance that sentences are natural even if the words in the sentences are replaced with other words with paradigmatic relations. We…

There are two approaches for pairwise sentence scoring: Cross-encoders, which perform full-attention over the input pair, and Bi-encoders, which map each input independently to a dense vector space. While cross-encoders often achieve higher…

Data augmentation has emerged as a powerful technique for improving the performance of deep neural networks and led to state-of-the-art results in computer vision. However, state-of-the-art data augmentation strongly distorts training…