Geometric representations for minimalist grammars

We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in representation space. We also propose harmony, i.e. the distance of an intermediate processing step from the final well-formed state in representation space, as a measure of processing complexity. Finally, we illustrate our findings by means of two particular arithmetic and fractal representations.Comment: 43 pages, 4 figure

Tensorized Self-Attention: Efficiently Modeling Pairwise and Global Dependencies Together

Neural networks equipped with self-attention have parallelizable computation, light-weight structure, and the ability to capture both long-range and local dependencies. Further, their expressive power and performance can be boosted by using a vector to measure pairwise dependency, but this requires to expand the alignment matrix to a tensor, which results in memory and computation bottlenecks. In this paper, we propose a novel attention mechanism called "Multi-mask Tensorized Self-Attention" (MTSA), which is as fast and as memory-efficient as a CNN, but significantly outperforms previous CNN-/RNN-/attention-based models. MTSA 1) captures both pairwise (token2token) and global (source2token) dependencies by a novel compatibility function composed of dot-product and additive attentions, 2) uses a tensor to represent the feature-wise alignment scores for better expressive power but only requires parallelizable matrix multiplications, and 3) combines multi-head with multi-dimensional attentions, and applies a distinct positional mask to each head (subspace), so the memory and computation can be distributed to multiple heads, each with sequential information encoded independently. The experiments show that a CNN/RNN-free model based on MTSA achieves state-of-the-art or competitive performance on nine NLP benchmarks with compelling memory- and time-efficiency

Quantum Aspects of Semantic Analysis and Symbolic Artificial Intelligence

Modern approaches to semanic analysis if reformulated as Hilbert-space problems reveal formal structures known from quantum mechanics. Similar situation is found in distributed representations of cognitive structures developed for the purposes of neural networks. We take a closer look at similarites and differences between the above two fields and quantum information theory.Comment: version accepted in J. Phys. A (Letter to the Editor

Exploiting word embeddings for modeling bilexical relations

There has been an exponential surge of text data in the recent years. As a consequence, unsupervised methods that make use of this data have been steadily growing in the field of natural language processing (NLP). Word embeddings are low-dimensional vectors obtained using unsupervised techniques on the large unlabelled corpora, where words from the vocabulary are mapped to vectors of real numbers. Word embeddings aim to capture syntactic and semantic properties of words. In NLP, many tasks involve computing the compatibility between lexical items under some linguistic relation. We call this type of relation a bilexical relation. Our thesis defines statistical models for bilexical relations that centrally make use of word embeddings. Our principle aim is that the word embeddings will favor generalization to words not seen during the training of the model. The thesis is structured in four parts. In the first part of this thesis, we present a bilinear model over word embeddings that leverages a small supervised dataset for a binary linguistic relation. Our learning algorithm exploits low-rank bilinear forms and induces a low-dimensional embedding tailored for a target linguistic relation. This results in compressed task-specific embeddings. In the second part of our thesis, we extend our bilinear model to a ternary setting and propose a framework for resolving prepositional phrase attachment ambiguity using word embeddings. Our models perform competitively with state-of-the-art models. In addition, our method obtains significant improvements on out-of-domain tests by simply using word-embeddings induced from source and target domains. In the third part of this thesis, we further extend the bilinear models for expanding vocabulary in the context of statistical phrase-based machine translation. Our model obtains a probabilistic list of possible translations of target language words, given a word in the source language. We do this by projecting pre-trained embeddings into a common subspace using a log-bilinear model. We empirically notice a significant improvement on an out-of-domain test set. In the final part of our thesis, we propose a non-linear model that maps initial word embeddings to task-tuned word embeddings, in the context of a neural network dependency parser. We demonstrate its use for improved dependency parsing, especially for sentences with unseen words. We also show downstream improvements on a sentiment analysis task.En els darrers anys hi ha hagut un sorgiment notable de dades en format textual. Conseqüentment, en el camp del Processament del Llenguatge Natural (NLP, de l'anglès "Natural Language Processing") s'han desenvolupat mètodes no supervistats que fan ús d'aquestes dades. Els anomenats "word embeddings", o embeddings de paraules, són vectors de dimensionalitat baixa que s'obtenen mitjançant tècniques no supervisades aplicades a corpus textuals de grans volums. Com a resultat, cada paraula del diccionari es correspon amb un vector de nombres reals, el propòsit del qual és capturar propietats sintàctiques i semàntiques de la paraula corresponent. Moltes tasques de NLP involucren calcular la compatibilitat entre elements lèxics en l'àmbit d'una relació lingüística. D'aquest tipus de relació en diem relació bilèxica. Aquesta tesi proposa models estadístics per a relacions bilèxiques que fan ús central d'embeddings de paraules, amb l'objectiu de millorar la generalització del model lingüístic a paraules no vistes durant l'entrenament. La tesi s'estructura en quatre parts. A la primera part presentem un model bilineal sobre embeddings de paraules que explota un conjunt petit de dades anotades sobre una relaxió bilèxica. L'algorisme d'aprenentatge treballa amb formes bilineals de poc rang, i indueix embeddings de poca dimensionalitat que estan especialitzats per la relació bilèxica per la qual s'han entrenat. Com a resultat, obtenim embeddings de paraules que corresponen a compressions d'embeddings per a una relació determinada. A la segona part de la tesi proposem una extensió del model bilineal a trilineal, i amb això proposem un nou model per a resoldre ambigüitats de sintagmes preposicionals que usa només embeddings de paraules. En una sèrie d'avaluacións, els nostres models funcionen de manera similar a l'estat de l'art. A més, el nostre mètode obté millores significatives en avaluacions en textos de dominis diferents al d'entrenament, simplement usant embeddings induïts amb textos dels dominis d'entrenament i d'avaluació. A la tercera part d'aquesta tesi proposem una altra extensió dels models bilineals per ampliar la cobertura lèxica en el context de models estadístics de traducció automàtica. El nostre model probabilístic obté, donada una paraula en la llengua d'origen, una llista de possibles traduccions en la llengua de destí. Fem això mitjançant una projecció d'embeddings pre-entrenats a un sub-espai comú, usant un model log-bilineal. Empíricament, observem una millora significativa en avaluacions en dominis diferents al d'entrenament. Finalment, a la quarta part de la tesi proposem un model no lineal que indueix una correspondència entre embeddings inicials i embeddings especialitzats, en el context de tasques d'anàlisi sintàctica de dependències amb models neuronals. Mostrem que aquest mètode millora l'analisi de dependències, especialment en oracions amb paraules no vistes durant l'entrenament. També mostrem millores en un tasca d'anàlisi de sentiment

Universal neural field computation

Turing machines and G\"odel numbers are important pillars of the theory of computation. Thus, any computational architecture needs to show how it could relate to Turing machines and how stable implementations of Turing computation are possible. In this chapter, we implement universal Turing computation in a neural field environment. To this end, we employ the canonical symbologram representation of a Turing machine obtained from a G\"odel encoding of its symbolic repertoire and generalized shifts. The resulting nonlinear dynamical automaton (NDA) is a piecewise affine-linear map acting on the unit square that is partitioned into rectangular domains. Instead of looking at point dynamics in phase space, we then consider functional dynamics of probability distributions functions (p.d.f.s) over phase space. This is generally described by a Frobenius-Perron integral transformation that can be regarded as a neural field equation over the unit square as feature space of a dynamic field theory (DFT). Solving the Frobenius-Perron equation yields that uniform p.d.f.s with rectangular support are mapped onto uniform p.d.f.s with rectangular support, again. We call the resulting representation \emph{dynamic field automaton}.Comment: 21 pages; 6 figures. arXiv admin note: text overlap with arXiv:1204.546

Towards Matrix Syntax

Matrix syntax is a model of syntactic relations in language, which grew out of a desire to understand chains. The purpose of this paper is to explain its basic ideas to a linguistics audience, without entering into too many formal details (for which cf. Orús et al. 2017). The resulting mathematical structure resembles some aspects of quantum mechanics and is well-suited to describe linguistic chains. In particular, sentences are naturally modeled as vectors in a Hilbert space with a tensor product structure, built from 2x2 matrices belonging to some specific group. Curiously, the matrices the system employs are simple extensions of customary representations of the major parts of speech, as [±N, ±V] objects.La sintaxi de matrius és un model formal de relacions sintàctiques en el llenguatge que va sorgir del desig de modelar les cadenes. L'objectiu d'aquest treball és explicar les idees bàsiques d'aquest model a un públic lingüístic, sense entrar en gaires detalls formals (vegeu Orús et al. 2017). L'estructura matemàtica resultant s'assembla a alguns aspectes de la mecànica quàntica i s'adapta bé per descriure les cadenes lingüístiques. En particular, les oracions es modelen naturalment com a vectors en un espai de Hilbert amb una estructura de producte tensorial, construïdes a partir de matrius 2 x 2 que pertanyen a un grup específic. Curiosament, les matrius que utilitza el sistema són extensions simples de representacions habituals de les parts principals del discurs com a objectes [± N, ± V]