1,018 research outputs found
Mathematical Expression Recognition based on Probabilistic Grammars
[EN] Mathematical notation is well-known and used all over the
world. Humankind has evolved from simple methods representing
countings to current well-defined math notation able to account for
complex problems. Furthermore, mathematical expressions constitute a
universal language in scientific fields, and many information
resources containing mathematics have been created during the last
decades. However, in order to efficiently access all that information,
scientific documents have to be digitized or produced directly in
electronic formats.
Although most people is able to understand and produce mathematical
information, introducing math expressions into electronic devices
requires learning specific notations or using editors. Automatic
recognition of mathematical expressions aims at filling this gap
between the knowledge of a person and the input accepted by
computers. This way, printed documents containing math expressions
could be automatically digitized, and handwriting could be used for
direct input of math notation into electronic devices.
This thesis is devoted to develop an approach for mathematical
expression recognition. In this document we propose an approach for
recognizing any type of mathematical expression (printed or
handwritten) based on probabilistic grammars. In order to do so, we
develop the formal statistical framework such that derives several
probability distributions. Along the document, we deal with the
definition and estimation of all these probabilistic sources of
information. Finally, we define the parsing algorithm that globally
computes the most probable mathematical expression for a given input
according to the statistical framework.
An important point in this study is to provide objective performance
evaluation and report results using public data and standard
metrics. We inspected the problems of automatic evaluation in this
field and looked for the best solutions. We also report several
experiments using public databases and we participated in several
international competitions. Furthermore, we have released most of the
software developed in this thesis as open source.
We also explore some of the applications of mathematical expression
recognition. In addition to the direct applications of transcription
and digitization, we report two important proposals. First, we
developed mucaptcha, a method to tell humans and computers apart by
means of math handwriting input, which represents a novel application
of math expression recognition. Second, we tackled the problem of
layout analysis of structured documents using the statistical
framework developed in this thesis, because both are two-dimensional
problems that can be modeled with probabilistic grammars.
The approach developed in this thesis for mathematical expression
recognition has obtained good results at different levels. It has
produced several scientific publications in international conferences
and journals, and has been awarded in international competitions.[ES] La notación matemática es bien conocida y se utiliza en todo el
mundo. La humanidad ha evolucionado desde simples métodos para
representar cuentas hasta la notación formal actual capaz de modelar
problemas complejos. Además, las expresiones matemáticas constituyen
un idioma universal en el mundo científico, y se han creado muchos
recursos que contienen matemáticas durante las últimas décadas. Sin
embargo, para acceder de forma eficiente a toda esa información, los
documentos científicos han de ser digitalizados o producidos
directamente en formatos electrónicos.
Aunque la mayoría de personas es capaz de entender y producir
información matemática, introducir expresiones matemáticas en
dispositivos electrónicos requiere aprender notaciones especiales o
usar editores. El reconocimiento automático de expresiones matemáticas
tiene como objetivo llenar ese espacio existente entre el conocimiento
de una persona y la entrada que aceptan los ordenadores. De este modo,
documentos impresos que contienen fórmulas podrían digitalizarse
automáticamente, y la escritura se podría utilizar para introducir
directamente notación matemática en dispositivos electrónicos.
Esta tesis está centrada en desarrollar un método para reconocer
expresiones matemáticas. En este documento proponemos un método para
reconocer cualquier tipo de fórmula (impresa o manuscrita) basado en
gramáticas probabilísticas. Para ello, desarrollamos el marco
estadístico formal que deriva varias distribuciones de probabilidad. A
lo largo del documento, abordamos la definición y estimación de todas
estas fuentes de información probabilística. Finalmente, definimos el
algoritmo que, dada cierta entrada, calcula globalmente la expresión
matemática más probable de acuerdo al marco estadístico.
Un aspecto importante de este trabajo es proporcionar una evaluación
objetiva de los resultados y presentarlos usando datos públicos y
medidas estándar. Por ello, estudiamos los problemas de la evaluación
automática en este campo y buscamos las mejores soluciones. Asimismo,
presentamos diversos experimentos usando bases de datos públicas y
hemos participado en varias competiciones internacionales. Además,
hemos publicado como código abierto la mayoría del software
desarrollado en esta tesis.
También hemos explorado algunas de las aplicaciones del reconocimiento
de expresiones matemáticas. Además de las aplicaciones directas de
transcripción y digitalización, presentamos dos propuestas
importantes. En primer lugar, desarrollamos mucaptcha, un método para
discriminar entre humanos y ordenadores mediante la escritura de
expresiones matemáticas, el cual representa una novedosa aplicación
del reconocimiento de fórmulas. En segundo lugar, abordamos el
problema de detectar y segmentar la estructura de documentos
utilizando el marco estadístico formal desarrollado en esta tesis,
dado que ambos son problemas bidimensionales que pueden modelarse con
gramáticas probabilísticas.
El método desarrollado en esta tesis para reconocer expresiones
matemáticas ha obtenido buenos resultados a diferentes niveles. Este
trabajo ha producido varias publicaciones en conferencias
internacionales y revistas, y ha sido premiado en competiciones
internacionales.[CA] La notació matemàtica és ben coneguda i s'utilitza a tot el món. La
humanitat ha evolucionat des de simples mètodes per representar
comptes fins a la notació formal actual capaç de modelar
problemes complexos. A més, les expressions matemàtiques
constitueixen un idioma universal al món científic, i s'han creat
molts recursos que contenen matemàtiques durant les últimes
dècades. No obstant això, per accedir de forma eficient a tota
aquesta informació, els documents científics han de ser
digitalitzats o produïts directament en formats electrònics.
Encara que la majoria de persones és capaç d'entendre i produir
informació matemàtica, introduir expressions matemàtiques en
dispositius electrònics requereix aprendre notacions especials o usar
editors. El reconeixement automàtic d'expressions matemàtiques
té per objectiu omplir aquest espai existent entre el coneixement
d'una persona i l'entrada que accepten els ordinadors. D'aquesta
manera, documents impresos que contenen fórmules podrien
digitalitzar-se automàticament, i l'escriptura es podria utilitzar per
introduir directament notació matemàtica en dispositius electrònics.
Aquesta tesi està centrada en desenvolupar un mètode per reconèixer
expressions matemàtiques. En aquest document proposem un mètode per
reconèixer qualsevol tipus de fórmula (impresa o manuscrita) basat en
gramàtiques probabilístiques. Amb aquesta finalitat, desenvolupem el
marc estadístic formal que deriva diverses distribucions de
probabilitat. Al llarg del document, abordem la definició i estimació
de totes aquestes fonts d'informació probabilística. Finalment,
definim l'algorisme que, donada certa entrada, calcula globalment
l'expressió matemàtica més probable d'acord al marc estadístic.
Un aspecte important d'aquest treball és proporcionar una avaluació
objectiva dels resultats i presentar-los usant dades públiques i
mesures estàndard. Per això, estudiem els problemes de l'avaluació
automàtica en aquest camp i busquem les millors solucions. Així
mateix, presentem diversos experiments usant bases de dades públiques
i hem participat en diverses competicions internacionals. A més, hem
publicat com a codi obert la majoria del software desenvolupat en
aquesta tesi.
També hem explorat algunes de les aplicacions del reconeixement
d'expressions matemàtiques. A més de les aplicacions directes de
transcripció i digitalització, presentem dues propostes
importants. En primer lloc, desenvolupem mucaptcha, un mètode per
discriminar entre humans i ordinadors mitjançant l'escriptura
d'expressions matemàtiques, el qual representa una nova aplicació del
reconeixement de fórmules. En segon lloc, abordem el problema de
detectar i segmentar l'estructura de documents utilitzant el marc
estadístic formal desenvolupat en aquesta tesi, donat que ambdós són
problemes bidimensionals que poden modelar-se amb gramàtiques
probabilístiques.
El mètode desenvolupat en aquesta tesi per reconèixer expressions
matemàtiques ha obtingut bons resultats a diferents nivells. Aquest
treball ha produït diverses publicacions en conferències
internacionals i revistes, i ha sigut premiat en competicions
internacionals.Álvaro Muñoz, F. (2015). Mathematical Expression Recognition based on Probabilistic Grammars [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/51665TESI
Survey on Publicly Available Sinhala Natural Language Processing Tools and Research
Sinhala is the native language of the Sinhalese people who make up the
largest ethnic group of Sri Lanka. The language belongs to the globe-spanning
language tree, Indo-European. However, due to poverty in both linguistic and
economic capital, Sinhala, in the perspective of Natural Language Processing
tools and research, remains a resource-poor language which has neither the
economic drive its cousin English has nor the sheer push of the law of numbers
a language such as Chinese has. A number of research groups from Sri Lanka have
noticed this dearth and the resultant dire need for proper tools and research
for Sinhala natural language processing. However, due to various reasons, these
attempts seem to lack coordination and awareness of each other. The objective
of this paper is to fill that gap of a comprehensive literature survey of the
publicly available Sinhala natural language tools and research so that the
researchers working in this field can better utilize contributions of their
peers. As such, we shall be uploading this paper to arXiv and perpetually
update it periodically to reflect the advances made in the field
Incremental Training of a Recurrent Neural Network Exploiting a Multi-Scale Dynamic Memory
The effectiveness of recurrent neural networks can be largely influenced by
their ability to store into their dynamical memory information extracted from
input sequences at different frequencies and timescales. Such a feature can be
introduced into a neural architecture by an appropriate modularization of the
dynamic memory. In this paper we propose a novel incrementally trained
recurrent architecture targeting explicitly multi-scale learning. First, we
show how to extend the architecture of a simple RNN by separating its hidden
state into different modules, each subsampling the network hidden activations
at different frequencies. Then, we discuss a training algorithm where new
modules are iteratively added to the model to learn progressively longer
dependencies. Each new module works at a slower frequency than the previous
ones and it is initialized to encode the subsampled sequence of hidden
activations. Experimental results on synthetic and real-world datasets on
speech recognition and handwritten characters show that the modular
architecture and the incremental training algorithm improve the ability of
recurrent neural networks to capture long-term dependencies.Comment: accepted @ ECML 2020. arXiv admin note: substantial text overlap with
arXiv:2001.1177
A HINT from Arithmetic: On Systematic Generalization of Perception, Syntax, and Semantics
Inspired by humans' remarkable ability to master arithmetic and generalize to
unseen problems, we present a new dataset, HINT, to study machines' capability
of learning generalizable concepts at three different levels: perception,
syntax, and semantics. In particular, concepts in HINT, including both digits
and operators, are required to learn in a weakly-supervised fashion: Only the
final results of handwriting expressions are provided as supervision. Learning
agents need to reckon how concepts are perceived from raw signals such as
images (i.e., perception), how multiple concepts are structurally combined to
form a valid expression (i.e., syntax), and how concepts are realized to afford
various reasoning tasks (i.e., semantics). With a focus on systematic
generalization, we carefully design a five-fold test set to evaluate both the
interpolation and the extrapolation of learned concepts. To tackle this
challenging problem, we propose a neural-symbolic system by integrating neural
networks with grammar parsing and program synthesis, learned by a novel
deduction--abduction strategy. In experiments, the proposed neural-symbolic
system demonstrates strong generalization capability and significantly
outperforms end-to-end neural methods like RNN and Transformer. The results
also indicate the significance of recursive priors for extrapolation on syntax
and semantics.Comment: Preliminary wor
Building Machines That Learn and Think Like People
Recent progress in artificial intelligence (AI) has renewed interest in
building systems that learn and think like people. Many advances have come from
using deep neural networks trained end-to-end in tasks such as object
recognition, video games, and board games, achieving performance that equals or
even beats humans in some respects. Despite their biological inspiration and
performance achievements, these systems differ from human intelligence in
crucial ways. We review progress in cognitive science suggesting that truly
human-like learning and thinking machines will have to reach beyond current
engineering trends in both what they learn, and how they learn it.
Specifically, we argue that these machines should (a) build causal models of
the world that support explanation and understanding, rather than merely
solving pattern recognition problems; (b) ground learning in intuitive theories
of physics and psychology, to support and enrich the knowledge that is learned;
and (c) harness compositionality and learning-to-learn to rapidly acquire and
generalize knowledge to new tasks and situations. We suggest concrete
challenges and promising routes towards these goals that can combine the
strengths of recent neural network advances with more structured cognitive
models.Comment: In press at Behavioral and Brain Sciences. Open call for commentary
proposals (until Nov. 22, 2016).
https://www.cambridge.org/core/journals/behavioral-and-brain-sciences/information/calls-for-commentary/open-calls-for-commentar
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