Related papers: Entropy Bounds for Grammar-Based Tree Compressors
The categorical compositional distributional model of natural language provides a conceptually motivated procedure to compute the meaning of sentences, given grammatical structure and the meanings of its words. This approach has…
We study the notion of sparseness for regular languages over finite trees and infinite words. A language of trees is called sparse if the relative number of $n$-node trees in the language tends to zero, and a language of infinite words is…
Extractive compression is a challenging natural language processing problem. This work contributes by formulating neural extractive compression as a parse tree transduction problem, rather than a sequence transduction task. Motivated by…
We consider in this paper the problem of computing the entropy of a braid. We recall its definition and construct, for each braid, a sequence of real numbers, whose limit is its entropy. We state one conjecture about the convergence speed,…
Entanglement measures based on a logarithmic functional form naturally emerge in any attempt to quantify the degree of entanglement in the state of a multipartite quantum system. These measures can be regarded as generalizations of the…
String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much less…
This paper contains a classification of countable lower 1-transitive linear orders. The notion of lower 1-transitivity generalises that of 1-transitivity for linear orders, and is essential for the structure theory of 1-transitive trees.…
Topologically constrained genome-like polymers often double-fold into tree-like configurations, which can be modelled on the level of folded (ring) polymers or on the level of the underlying random trees. For both descriptions, we have…
XML document markup is highly repetitive and therefore well compressible using grammar-based compression. Downward, navigational XPath can be executed over grammar-compressed trees in PTIME: the query is translated into an automaton which…
Tree transductions are binary relations of finite trees. For tree transductions defined by non-deterministic top-down tree transducers, inclusion, equivalence and synthesis problems are known to be undecidable. Adding origin semantics to…
An alphabetic binary tree formulation applies to problems in which an outcome needs to be determined via alphabetically ordered search prior to the termination of some window of opportunity. Rather than finding a decision tree minimizing…
Identities based on monodromy for integrations in string theory are used to derive relations between different color ordered tree-level amplitudes in both bosonic and supersymmetric string theory. These relations imply that the color…
Distributional semantic models provide vector representations for words by gathering co-occurrence frequencies from corpora of text. Compositional distributional models extend these from words to phrases and sentences. In categorical…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…
Extreme classification problems are multiclass and multilabel classification problems where the number of outputs is so large that straightforward strategies are neither statistically nor computationally viable. One strategy for dealing…
The tree based representation described in this paper, hereditarily binary numbers, applies recursively a run-length compression mechanism that enables computations limited by the structural complexity of their operands rather than by their…
We consider extremal problems related to decks and multidecks of rooted binary trees (a.k.a. rooted phylogenetic tree shapes). Here, the deck (resp. multideck) of a tree $T$ refers to the set (resp. multiset) of leaf induced binary subtrees…
Abstract: In this article, we will analyze in detail the coding limit of an individual sequence by introducing the latest developments brought by the Set Shaping Theory. This new theory made us realize that there is a huge difference…
The main goal of this paper is to develop an estimate for the entropy of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We present here the detailed analytical study of the entropy for the…
Shannon's entropy is a definitive lower bound for statistical compression. Unfortunately, no such clear measure exists for the compressibility of repetitive strings. Thus, ad hoc measures are employed to estimate the repetitiveness of…