Related papers: An Empirical Study of Rational Tree Unification fo…

In this paper, we introduce the notion of Cartesian Forest, which generalizes Cartesian Trees, in order to deal with partially ordered sequences. We show that algorithms that solve both exact and approximate Cartesian Tree Matching can be…

The minimum linear arrangement problem on a network consists of finding the minimum sum of edge lengths that can be achieved when the vertices are arranged linearly. Although there are algorithms to solve this problem on trees in polynomial…

Selective rationalization has become a common mechanism to ensure that predictive models reveal how they use any available features. The selection may be soft or hard, and identifies a subset of input features relevant for prediction. The…

Random cost simulations were introduced as a method to investigate optimization problems in systems with conflicting constraints. Here I study the approach in connection with the training of a feed-forward multilayer perceptron, as used in…

Quasi-trees generalize trees in that the unique "path" between two nodes may be infinite and have any countable order type. They are used to define the rank-width of a countable graph in such a way that it is equal to the least upper-bound…

In this paper we introduce a variation on the multidimensional segment tree, formed by unifying different interpretations of the dimensionalities of the data structure. We give some new definitions to previously well-defined concepts that…

In this paper, we define a new kind of weighted tree automata where the weights are only supported by final states. We show that these automata are sequentializable and we study their closures under classical regular and algebraic…

Tree-based machine learning models, such as decision trees and random forests, have been hugely successful in classification tasks primarily because of their predictive power in supervised learning tasks and ease of interpretation. Despite…

Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning approach. Universal logic reasoning…

Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely one cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect…

One considers the behavior of the degree of a rational map under specialization of the coefficients of the defining linear system. The method rests on the classical idea of Kronecker as applied to the context of projective schemes and their…

This paper presents several new tractability results for planning based on macros. We describe an algorithm that optimally solves planning problems in a class that we call inverted tree reducible, and is provably tractable for several…

Recent research has recognized interpretability and robustness as essential properties of trustworthy classification. Curiously, a connection between robustness and interpretability was empirically observed, but the theoretical reasoning…

In this study, we explore a novel approach to demonstrate the countability of rational numbers and illustrate the relationship between the Calkin-Wilf tree and the Stern-Brocot tree in a more intuitive manner. By employing a growth pattern…

With dramatic improvements in optimization software, the solution of large-scale problems that seemed intractable decades ago are now a routine task. This puts even more real-world applications into the reach of optimizers. At the same…

We investigate the spectral properties of rooted trees with the intention of improving the currently existing results that deal with this matter. The concept of an assigned rational function is recursively defined for each vertex of a…

This paper proposes an algebraic view of trees which opens the doors to an alternative computational scheme with respect to classic algorithms. In particular, it is shown that this view is very well-suited for machine learning and…

The purpose of this paper is to build an algebraic framework suited to regularise branched structures emanating from rooted forests and which encodes the locality principle. This is achieved by means of the universal properties in the…

Model interpretability has become an important problem in machine learning (ML) due to the increased effect that algorithmic decisions have on humans. Counterfactual explanations can help users understand not only why ML models make certain…

A soft tree is an actively studied variant of a decision tree that updates splitting rules using the gradient method. Although soft trees can take various architectures, their impact is not theoretically well known. In this paper, we…