相关论文: Equivalence Classes in AES -- Part 1

A representation theorem relates different mathematical structures by providing an isomorphism between them: that is, a one-to-one correspondence preserving their original properties. Establishing that the two structures substantially…

An $(m,n,a,b)$-tensor code consists of $m\times n$ matrices whose columns satisfy `$a$' parity checks and rows satisfy `$b$' parity checks (i.e., a tensor code is the tensor product of a column code and row code). Tensor codes are useful in…

Automated essay scoring (AES) is gaining increasing attention in the education sector as it significantly reduces the burden of manual scoring and allows ad hoc feedback for learners. Natural language processing based on machine learning…

We show that the theory of the partial order of computably enumerable equivalence relations (ceers) under computable reduction is 1-equivalent to true arithmetic. We show the same result for the structure comprised of the dark ceers and the…

Distributed representations of words and paragraphs as semantic embeddings in high dimensional data are used across a number of Natural Language Understanding tasks such as retrieval, translation, and classification. In this work, we…

We present bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (2+2)-free posets and a certain class of involutions (or chord diagrams), already appeared in the literature, but were apparently not…

The equivalence test is a main part in any classification problem. It helps to prove bounds for the main parameters of the considered combinatorial structures and to study their properties. In this paper, we present algorithms for…

We consider a large family of equivalence relations on permutations in Sn that generalise those discovered by Knuth in his study of the Robinson-Schensted correspondence. In our most general setting, two permutations are equivalent if one…

Entity resolution (ER), an important and common data cleaning problem, is about detecting data duplicate representations for the same external entities, and merging them into single representations. Relatively recently, declarative rules…

Two factorizations of a permutation into products of cycles are equivalent if one can be obtained from the other by repeatedly interchanging adjacent disjoint factors. This paper studies the enumeration of equivalence classes under this…

We obtain an ESN theorem for a very general class of biunary semigroups with idempotent-valued domain and range operations, representing them in terms of small categories equipped with a suitable biaction of the identities on the category.…

Matchgates are an especially multiflorous class of two-qubit nearest neighbour quantum gates, defined by a set of algebraic constraints. They occur for example in the theory of perfect matchings of graphs, non-interacting fermions, and…

In this paper, we consider ensemble classifiers, that is, machine learning based classifiers that utilize a combination of scoring functions. We provide a framework for categorizing such classifiers, and we outline several ensemble…

In previous work "Betweenness algebras" we introduced and examined the class of betweenness algebras. In the current paper we study a larger class of algebras with binary operators of possibility and sufficiency, the weak mixed algebras.…

Many machine learning tasks such as clustering, classification, and dataset search benefit from embedding data points in a space where distances reflect notions of relative similarity as perceived by humans. A common way to construct such…

Primes in the two complete associative normed division algebras C and H have affinities with structures seen in the standard model of particle physics. On the integers in the two algebras, there are two equivalence relations: a strong one,…

Two pretrained neural networks are deemed equivalent if they yield similar outputs for the same inputs. Equivalence checking of neural networks is of great importance, due to its utility in replacing learning-enabled components with…

In this paper, we present a new comparative study on automatic essay scoring (AES). The current state-of-the-art natural language processing (NLP) neural network architectures are used in this work to achieve above human-level accuracy on…

We study a family of equivalence relations on $S_n$, the group of permutations on $n$ letters, created in a manner similar to that of the Knuth relation and the forgotten relation. For our purposes, two permutations are in the same…

We investigate program equivalence for linear higher-order(sequential) languages endowed with primitives for computational effects. More specifically, we study operationally-based notions of program equivalence for a linear…