Related papers: A Theoretical Review on Solving Algebra Problems
Artificial Intelligence for Theorem Proving has given rise to a plethora of benchmarks and methodologies, particularly in Interactive Theorem Proving (ITP). Research in the area is fragmented, with a diverse set of approaches being spread…
The algebraic Bethe Ansatz is a prosperous and well-established method for solving one-dimensional quantum models exactly. The solution of the complex eigenvalue problem is thereby reduced to the solution of a set of algebraic equations.…
We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…
In a world of proliferating data, the ability to rapidly summarize text is growing in importance. Automatic summarization of text can be thought of as a sequence to sequence problem. Another area of natural language processing that solves a…
This Ph.D. thesis contains original contributions to several areas within the disciplines of disordered systems, numerical linear algebra, and scientific computing: (1) Theoretical and numerical study of the errors caused by using certain…
Tabular learning transforms raw features into optimized spaces for downstream tasks, but its effectiveness deteriorates under distribution shifts between training and testing data. We formalize this challenge as the Distribution Shift…
Weighted Logic is a powerful tool for the specification of calculations over semirings that depend on qualitative information. Using a novel combination of Weighted Logic and Here-and-There (HT) Logic, in which this dependence is based on…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
It is expected that progress toward true artificial intelligence will be achieved through the emergence of a system that integrates representation learning and complex reasoning (LeCun et al. 2015). In response to this prediction, research…
Coalgebra is a currently quite active field, which aims to look at generic state-based systems (most prominently automata) from a very abstract point of view, mainly using tools from category theory. One of its achievements is to give a…
The paper introduces the notion of off-line justification for Answer Set Programming (ASP). Justifications provide a graph-based explanation of the truth value of an atom w.r.t. a given answer set. The paper extends also this notion to…
The broader goal of this research, on the one hand, is to obtain the State of the Art in Automated Test Production (ATP), to find the open questions and related problems and to track the progress of researchers in the field, and on the…
Answer set programming (ASP) is a paradigm for modeling knowledge intensive domains and solving challenging reasoning problems. In ASP solving, a typical strategy is to preprocess problem instances by rewriting complex rules into simpler…
Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…
State abstraction has been an essential tool for dramatically improving the sample efficiency of reinforcement-learning algorithms. Indeed, by exposing and accentuating various types of latent structure within the environment, different…
Answer Set Programming (ASP) is a well-established formalism for logic programming. Problem solving in ASP requires to write an ASP program whose answers sets correspond to solutions. Albeit the non-existence of answer sets for some ASP…
Building biological models by inferring functional dependencies from experimental data is an im- portant issue in Molecular Biology. To relieve the biologist from this traditionally manual process, various approaches have been proposed to…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
We introduce a new framework called linear algebraic number theory (LANT) that reformulates the number-theoretic problem as a regression model and solves it using matrix algebra. This framework restricts all computations to log space,…
Automated essay scoring is one of the most important problem in Natural Language Processing. It has been explored for a number of years, and it remains partially solved. In addition to its economic and educational usefulness, it presents…