Related papers: Diversity-multiplexing Gain Tradeoff: a Tool in Al…

Large data-driven image models are extensively used to support creative and artistic work. Under the currently predominant distribution-fitting paradigm, a dataset is treated as ground truth to be approximated as closely as possible. Yet,…

Data augmentation that introduces diversity into the input data has long been used in training deep learning models. It has demonstrated benefits in improving robustness and generalization, practically aligning well with other…

Complex systems often exhibit multiple levels of organization covering a wide range of physical scales, so the study of the hierarchical decomposition of their structure and function is frequently convenient. To better understand this…

Efficient modeling of uncertain information in real world is still an open issue. Dempster-Shafer evidence theory is one of the most commonly used methods. However, the Dempster-Shafer evidence theory has the assumption that the hypothesis…

In this work, we investigate the diversity-multiplexing tradeoff (DMT) of the multiple-antenna (MIMO) static half-duplex relay channel. A general expression is derived for the DMT upper bound, which can be achieved by a compress-and-forward…

Colors are used as effective tools of representing and transferring information. Number of colors in a palette is the direct arbiter of the information conveying capacity. Yet it should be well elaborated, since increasing the entropy by…

The algebraic intersection type unification problem is an important component in proof search related to several natural decision problems in intersection type systems. It is unknown and remains open whether the algebraic intersection type…

Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.

This is the first paper in a series (of four) designed to show how to use geometric algebras of multivectors and extensors to a novel presentation of some topics of differential geometry which are important for a deeper understanding of…

Multi-modal knowledge graph completion (MMKGC) aims to predict the missing triples in the multi-modal knowledge graphs by incorporating structural, visual, and textual information of entities into the discriminant models. The information…

Use of knowledge-based planning tools can help alleviate the challenges of planning a complex operation by a coalition of diverse parties in an adversarial environment. We explore these challenges and potential contributions of…

We generalize the dual notions of "expansion" and "collapse" so they can be applied to arbitrary metric spaces. We also expand the theory to allow for infinitely many such moves. Those tools are then employed to prove a variety of…

As artificial intelligence is increasingly affecting all parts of society and life, there is growing recognition that human interpretability of machine learning models is important. It is often argued that accuracy or other similar…

Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence…

Deep learning has revolutionized many areas of machine learning, from computer vision to natural language processing, but these high-performance models are generally "black box." Explaining such models would improve transparency and trust…

During the last two decades, concentration of measure has been a subject of various exciting developments in convex geometry, functional analysis, statistical physics, high-dimensional statistics, probability theory, information theory,…

Edge intelligence requires to fast access distributed data samples generated by edge devices. The challenge is using limited radio resource to acquire massive data samples for training machine learning models at edge server. In this…

Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information,…

For massive and heterogeneous modern datasets, it is of fundamental interest to provide guarantees on the accuracy of estimation when computational resources are limited. In the application of learning to rank, we provide a hierarchy of…

In the last quarter of a century, algebraic statistics has established itself as an expanding field which uses multilinear algebra, commutative algebra, computational algebra, geometry, and combinatorics to tackle problems in mathematical…