Related papers: Yay for Determinants!

The algebra of octonions is non-associative (as well as non-commutative). This makes it very difficult to derive algebraic results, and to perform computation with octonions. Given a product of more than two octonions, in general, the order…

In the last decade, decision diagrams (DDs) have been the basis for a large array of novel approaches for modeling and solving optimization problems. Many techniques now use DDs as a key tool to achieve state-of-the-art performance within…

In a recent work, S. Dowker has shed doubt on a recipe used in computing the partition function for a matrix valued operator. This recipe, advocated by Benson, Bernstein and Dodelson, leads naturally to the so called multiplicative anomaly…

Several enhanced sampling methods such as umbrella sampling or metadynamics rely on the identification of an appropriate set of collective variables. Recently two methods have been proposed to alleviate the task of determining efficient…

We prove an interesting identity for the sum of determinants, which is a generalization of the sum of a geometric progression. The proof is quite long and a number of other identities are proved along the way. Some of the more elementary…

We give a generalization and a short mechanized proof of determinant conjectured by G. Kuperberg and J. Propp. Further generalizations and applications of the method to some q-analogues may be found in http://www.math.temple.edu/~tewodros

This article is a sequel to a recent article by Eric Rowland and Reem Yassawi, presenting yet another approach to the fast determination of congruence properties of `famous' combinatorial sequences. The present approach can be taught to a…

We generalize linear superalgebra to higher gradings and commutation factors, given by arbitrary abelian groups and bicharacters. Our central tool is an extension, to monoidal categories of modules, of the Nekludova-Scheunert faithful…

Recently, decision trees (DT) have been used as an explainable representation of controllers (a.k.a. strategies, policies, schedulers). Although they are often very efficient and produce small and understandable controllers for discrete…

This paper addresses the challenge of selecting explanations for XAI (Explainable AI)-based Intelligent Decision Support Systems (IDSSs). IDSSs have shown promise in improving user decisions through XAI-generated explanations along with AI…

This paper describes our contributions to the Shared Task of the 9th Workshop on Argument Mining (2022). Our approach uses Large Language Models for the task of Argument Quality Prediction. We perform prompt engineering using GPT-3, and…

The development and use of dimension reduction methods is prevalent in modern statistical literature. This paper reviews a class of dimension reduction techniques which aim to simultaneously select relevant predictors and find clusters…

Even though the forecasting literature agrees that aggregating multiple predictions of some future outcome typically outperforms the individual predictions, there is no general consensus about the right way to do this. Most common…

This paper revisits the problem of determinacy inference addressing the problem of how to uniformly handle cut. To this end a new semantics is introduced for cut, which is abstracted to systematically derive a backward analysis that derives…

Expert-level scientific reasoning remains challenging for large language models, particularly on benchmarks such as Humanity's Last Exam (HLE), where rigid tool pipelines, brittle multi-agent coordination, and inefficient test-time scaling…

This paper considers an idempotent and symmetrical algebraic structure as well as some closely related concept. A special notion of determinant is introduced and a Cramer formula is derived for a class of limit systems derived from the…

Causal reasoning is the main learning and explanation tool used by humans. AI systems should possess causal reasoning capabilities to be deployed in the real world with trust and reliability. Introducing the ideas of causality to machine…

Reliable evaluation protocols are of utmost importance for reproducible NLP research. In this work, we show that sometimes neither metric nor conventional human evaluation is sufficient to draw conclusions about system performance. Using…

Data augmentation is one of the most successful techniques to improve the classification accuracy of machine learning models in computer vision. However, applying data augmentation to tabular data is a challenging problem since it is hard…

Understanding why specific items are recommended to users can significantly increase their trust and satisfaction in the system. While neural recommenders have become the state-of-the-art in recent years, the complexity of deep models still…