Related papers: The Augmentation Property of Binary Matrices for t…
In this article, we explore the problem of constructing high-dimensional expanders through the study of relations between expansion constants over different rings. We investigate expansion constants of integer matrices regarded as morphisms…
To enhance the performance of the recommender system, side information is extensively explored with various features (e.g., visual features and textual features). However, there are some demerits of side information: (1) the extra data is…
Data-hungry deep neural networks have established themselves as the standard for many NLP tasks including the traditional sequence tagging ones. Despite their state-of-the-art performance on high-resource languages, they still fall behind…
To apportion a complex matrix means to apply a similarity so that all entries of the resulting matrix have the same magnitude. We initiate the study of apportionment, both by unitary matrix similarity and general matrix similarity. There…
Two characteristic-dependent linear rank inequalities are given for eight variables. Specifically, the first inequality holds for all finite fields whose characteristic is not three and does not in general hold over characteristic three.…
Bayesian additive regression trees (BART) are popular Bayesian ensemble models used in regression and classification analysis. Under this modeling framework, the regression function is approximated by an ensemble of decision trees,…
Deep learning models have a large number of freeparameters that need to be calculated by effective trainingof the models on a great deal of training data to improvetheir generalization performance. However, data obtaining andlabeling is…
High-performing predictive models, such as neural nets, usually operate as black boxes, which raises serious concerns about their interpretability. Local feature attribution methods help to explain black box models and are therefore a…
We introduce an exact functor defined on multigraded modules which we call the expansion functor and study its homological properties. The expansion functor applied to a monomial ideal amounts to substitute the variables by monomial prime…
Ryser's max term rank formula with graph theoretic terminology is equivalent to a characterization of degree sequences of simple bipartite graphs with matching number at least $\ell$. In a previous paper by the authors, a generalization was…
Data augmentation is a commonly applied technique with two seemingly related advantages. With this method one can increase the size of the training set generating new samples and also increase the invariance of the network against the…
We study algebraic properties of full rank 1 algebras in a general framework and derive a method to verify if one such matrix polynomial sub-algebra is bispectral. We give two examples illustrating the method. In the first one, we consider…
Ascent sequences and their modified version play a central role in the bijective framework relating several combinatorial structures counted by the Fishburn numbers. Ascent sequences are positive integer sequences defined by imposing a…
Transformation invariances are present in many real-world problems. For example, image classification is usually invariant to rotation and color transformation: a rotated car in a different color is still identified as a car. Data…
We study on what conditions on $B_k,$ \ a linear transformation of rank $r$ \label{form} T(A)=\sum_{k=1}^r\tr(AB_k)U_k where $U_k,\ k=1,2,..., r$ are linear independent and all positive definite; is positive definite preserving. We give…
Modularity has been widely studied as a mechanism to improve the capabilities of neural networks through various techniques such as hand-crafted modular architectures and automatic approaches. While these methods have sometimes shown…
Expansions of abelian categories are introduced. These are certain functors between abelian categories and provide a tool for induction/reduction arguments. Expansions arise naturally in the study of coherent sheaves on weighted projective…
The joint spectral radius of a bounded set of d times d real or complex matrices is defined to be the maximum exponential rate of growth of products of matrices drawn from that set. Under quite mild conditions such a set of matrices admits…
Automatic augmentation methods have recently become a crucial pillar for strong model performance in vision tasks. While existing automatic augmentation methods need to trade off simplicity, cost and performance, we present a most simple…
We consider a multiproduct monopoly pricing model. We provide sufficient conditions under which the optimal mechanism can be implemented via upgrade pricing -- a menu of product bundles that are nested in the strong set order. Our approach…