Related papers: Two-dimensional Dyck words
Distributed dense word vectors have been shown to be effective at capturing token-level semantic and syntactic regularities in language, while topic models can form interpretable representations over documents. In this work, we describe…
Automata-logic connections are pillars of the theory of regular languages. Such connections are harder to obtain for transducers, but important results have been obtained recently for word-to-word transformations, showing that the three…
In computer science, divide and conquer (D&C) is an algorithm design paradigm based on multi-branched recursion. A D&C algorithm works by recursively and monotonically breaking down a problem into sub problems of the same (or a related)…
A large class of unsupervised algorithms for Word Sense Disambiguation (WSD) is that of dictionary-based methods. Various algorithms have as the root Lesk's algorithm, which exploits the sense definitions in the dictionary directly. Our…
Human language understanding operates at multiple levels of granularity (e.g., words, phrases, and sentences) with increasing levels of abstraction that can be hierarchically combined. However, existing deep models with stacked layers do…
In this work, we leverage the linear algebraic structure of distributed word representations to automatically extend knowledge bases and allow a machine to learn new facts about the world. Our goal is to extract structured facts from…
This article contains a proposal to add coinduction to the computational apparatus of natural language understanding. This, we argue, will provide a basis for more realistic, computationally sound, and scalable models of natural language…
We propose a new algorithm called DK-vec for aligning pairs of Asian/Indo-European noisy parallel texts without sentence boundaries. DK-vec improves on previous alignment algorithms in that it handles better the non-linear nature of noisy…
Analyzing relational languages by their logical expressiveness is well understood. Something not well understood or even formalized is the vague concept of relational query patterns. What are query patterns? And how can we reason about…
In this article, we present a fresh perspective on language, combining ideas from various sources, but mixed in a new synthesis. As in the minimalist program, the question is whether we can formulate an elegant formalism, a universal…
A Lyndon word is a primitive string which is lexicographically smallest among cyclic permutations of its characters. Lyndon words are used for constructing bases in free Lie algebras, constructing de Bruijn sequences, finding the…
Separable, or Kronecker product, dictionaries provide natural decompositions for 2D signals, such as images. In this paper, we describe a highly parallelizable algorithm that learns such dictionaries which reaches sparse representations…
A two-dimensional automaton operates on arrays of symbols. While a standard (four-way) two-dimensional automaton can move its input head in four directions, restricted two-dimensional automata are only permitted to move their input heads in…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
Recent image editing models have achieved strong visual fidelity but often struggle with tasks requiring complex reasoning. To investigate and enhance the reasoning-grounded planning for image editing, we propose DDA-Thinker, a…
Let integer be any C/C++ unsigned integer type up to 64-bits long. Given a Dyck word the following code returns the next Dyck word of the same size, provided it exists. integer next_dyck_word(integer w) { integer const a = w & -w; integer…
A tree-based dictionary learning model is developed for joint analysis of imagery and associated text. The dictionary learning may be applied directly to the imagery from patches, or to general feature vectors extracted from patches or…
A modification of Merino-Mi\v{c}ka-M\"utze's solution to a combinatorial generation problem of Knuth is proposed in this survey. The resulting alternate form to such solution is compatible with a reinterpretation by the author of a proof of…
Distributional semantics provides multi-dimensional, graded, empirically induced word representations that successfully capture many aspects of meaning in natural languages, as shown in a large body of work in computational linguistics;…
A recognizable picture language is defined as the projection of a local picture language defined by a set of two-by-two tiles, i.e. by a strictly-locally-testable (SLT) language of order 2. The family of recognizable picture languages is…