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Victor Vvedensky, Kurchatov Institute
Direct contact with technical devices
using human speech implies ability of
the computer to understand in some way
the idea of the message. The people feel
semantic similarity of words and can
find the word with close or just opposite
meaning. Can one find mathematical
description of this ability?
Transistors flop millions times faster then
the neurons are spiking, available fast
memory is huge in comparison with the
working memory of the brain, the software
can be sophisticated enough to beat top
chess players, and still, computers fail to
interpret vocal commands of humans.
Special organization of language in the brain is
the probable reason of it’s excellent
performance.
We start our study with the analysis of
compatibility of different elements of
language.
Each verb can be attributed with the set of
properties. The adverbs, which can be readily
used together with this verb in many different
contexts, reflect these properties. One can
смело прыгать to jump bravely
ловко прыгать to jump deftly
возбужденно прыгать to jump excitedly
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уничтожать
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носить
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расходов ать
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приучать
требов ать
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в рать
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призыв ать
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успокаив ать
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покрыв ать
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нарушать
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растягив ать
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пробуждать
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подбив ать
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иметь
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разбив ать
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честв ов ать
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плев ать
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убыв ать
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в ырабатыв ать
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процежив ать
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лишать
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счастливо
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смертельно
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пристально
укладыв ать
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оживленно
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безвольно
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сердечно
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болезненно
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задумчиво
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бить
понятно
следить
развязно
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отчётливо
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скрытно
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ненадежно
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точно
справедливо
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верно
мужественно
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преданно
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тайно
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усердно
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уверенно
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часто
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Compatibility values for representative sets
of 25 verbs and 25 adverbs of Russian language
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2D projections of 900 verbs in first 9 dimensions
of the multidimensional space
Each verb is presented
as a dot. The numbers
indicate the order of
dimensions. Each 2dimensional plane
shows distributions for
the pair of dimensions
with numbers indicated
for rows and columns.
The uppermost square
represents projection on
the plane in dimensions
“one” and “two” or X and
Y. The scale is normalized
to unity
Distributions of verbs and adverbs in first two
dimensions of the multidimensional space
900 verbs and 600 adverbs
of Russian language in first
two dimensions. The
distributions nearly mirror
each other so that the most
compatible verbs and
adverbs are close, while
incompatible pairs are on
the far ends.
Sets of verbs compatible
with three adverbs are
shown as hazel points.
Green points indicate fuzzy
cases.
To cost, to fill over, to throw down, to continue
patiently, industriously, motionlessly
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желать
жертвовать
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дружить
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блуждать
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терзать
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жалеть
владеть
хитрить
губить
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звучать
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врать
любить
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тратить
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крепить
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пробовать
плакать
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делить
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про1 1 1 1 1 1
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пере1 1 1 1 1 1
раз-,рас1 0,5 0,5 1 1
от1 1 1 1
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у0,5 0,5 1
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при1 1 1
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под1
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о1 1 1 1
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пред0,5
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служить
читать
смотреть
чистить
падать
жить
давать
Compatibility of prefixes with word roots
can also be represented as a table for Russian verbs
Distribution of Russian prefixes on the two-dimensional plane,
calculated using compatibility table of word roots and prefixes.
Since the number of prefixes is much smaller then the number of roots (~20
and ~4000) the distribution of prefixes is accurate enough. The opposite is not
true. One needs another approach to analyze the space of roots.
Small cortical patches with a certain function
Brain studies, using special
functional staining techniques, reveal
confined areas performing definite
tasks. These portions of the monkey
cortex extract visual features with
certain orientation. They are about 1
mm x 2 mm large. Rich internal
connections can impart this cortical
patch with properties reflected as
additional dimensions. That is like
blowing up the flat soap film making
the bulb in the space with multiple
dimensions
D.H.Hubel, Eye, Brain, and Vision
The principal central connections of hearing
The principal central connections of speech
The corticobulbar tract is a pathway
connecting the cerebral cortex to the brainstem
The muscles of the face, head and neck are
controlled by the corticobulbar system
Die Liste der 30.000 häufigsten Wortformen aus den Textkorpora
des IDS, absteigend sortiert nach relativer Häufigkeit.
Institut für Deutsche Sprache
Zipf Law for words
Exponential decay for word roots
All the roots can be fit into 2D plot, where they densely fill
the portion of the surface.
Triangles - roots absent in Czech
Triangles - Russian roots compatible with «На» prefix
Russian roots with initial consonants «К» and «П»
Space of qualities
built using frequencies of occurrence of Russian adjectives and adverbs
хорошо - well
хороший - good
прямо - directly
прямой - stright
сильно - strongly
сильный - strong
медленно - slowly
медленный - slow
полный - full
полно - completely
одновременно - simultaneously
одновременный - simultaneous
грязно - dirty
грязный - dirty
поспешно - in hurry
поспешный - hasty
толстый - thick
Positions of
different
qualities,
expressed in
Russian words in
respect to the
positions of
actions and
entities.
Speech
generator should
be in the upper
right corner.
2D distribution of
actions, built using
frequencies of
occurrence of
continuous and
completed forms of
Russian verbs.
понимать-понять
to understand
получать-получить
to get
кричать-крикнуть
to cry
вызывать-вызвать
to call
покупать-купить
to buy
носить-нести
to carry
выполнять-выполнить
to fulfil
выяснять-выяснить
to clear up
избавляться-избавиться
to get rid
Cortical Representation of Sign Language
Cerebral Cortex, Vol. 11, No. 6, 506-512, June 2001
Sketch depicting interactions of cortical patches storing different elements of speech
Аналогично можно построить вмещающее пространство для
конечных согласных корней немецкого языка. А также многих других
языков.