Related papers: Symmetries in Sorting
Theorems relating permutations with objects in other fields of mathematics are often stated in terms of avoided patterns. Examples include various classes of Schubert varieties from algebraic geometry (Billey and Abe 2013), commuting…
Curriculum Learning is the presentation of samples to the machine learning model in a meaningful order instead of a random order. The main challenge of Curriculum Learning is determining how to rank these samples. The ranking of the samples…
Several tasks in machine learning are evaluated using non-differentiable metrics such as mean average precision or Spearman correlation. However, their non-differentiability prevents from using them as objective functions in a learning…
The classical Arrow's Theorem answers "how can $n$ voters obtain a collective preference on a set of outcomes, if they have to obey certain constraints?" We give an analogue in the judgment aggregation framework of List and Pettit,…
Abstract convexity generalises classical convexity by considering the suprema of functions taken from an arbitrarily defined set of functions. These are called the abstract linear (abstract affine) functions. The purpose of this paper is to…
In this paper we examine sorting on the assumption that we do not know in advance which way to sort a sequence of numbers and we set at work simple local comparison and swap operators whose repeating application ends up in sorted sequences.…
Sorting an array is a fundamental routine in machine learning, one that is used to compute rank-based statistics, cumulative distribution functions (CDFs), quantiles, or to select closest neighbors and labels. The sorting function is…
We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to…
We generalize several recognizability theorems for free single-sorted algebras to the field of many-sorted algebras and provide, in a uniform way and without using neither regular tree grammars nor tree automata, purely algebraic proofs of…
Analogy-making is at the core of human and artificial intelligence and creativity with applications to such diverse tasks as proving mathematical theorems and building mathematical theories, common sense reasoning, learning, language…
Various decision support systems are available that implement Data Mining and Data Warehousing techniques for diving into the sea of data for getting useful patterns of knowledge (pearls). Classification, regression, clustering, and many…
Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
Algorithmic efficiency is essential to reducing energy and time usage for computational problems. Optimizing efficiency is important for tasks involving multiple resources, for example in stochastic calculations where the size of the random…
This work introduces a new class of symmetric matrix structures, called harmonic structures, which enable the generation of all possible directed transitions $(x_i, x_{i+1})$ over a set of $n$ symbols, without internal repetitions. Unlike…
A well-ordering principle is a principle of the form: If $X$ is well-ordered then $F(X)$ is well-ordered, where $F$ is some natural operator transforming linear orders into linear orders. Many important subsystems of Second-order Arithmetic…
Prolog's ability to return multiple answers on backtracking provides an elegant mechanism to derive reversible encodings of combinatorial objects as Natural Numbers i.e. {\em ranking} and {\em unranking} functions. Starting from a…
Machine learning algorithms play an important role in a variety of important decision-making processes, including targeted advertisement displays, home loan approvals, and criminal behavior predictions. Given the far-reaching impact of…
A novel integer value-sorting technique is proposed replacing bucket sort, distribution counting sort and address calculation sort family of algorithms. It requires only constant amount of additional memory. The technique is inspired from…
We study rewriting for equational theories in the context of symmetric monoidal categories where there is a separable Frobenius monoid on each object. These categories, also called hypergraph categories, are increasingly relevant: Frobenius…