Federal gosudarstvennoe uchebnoe predpriyatie Chair of the System of Artificial Intelligence

1.1 Biological neurons and neural networks
nekotoroy obuchayushchey vÿborki - "zadachnika", sostoyashchego iz nabora par
otdelnyx neyronov i ix vzaimodeystviya printsipialno vajno dlya
ispolzovaniya protsessov, proisxodyashchix v nervnyx sistemax, dlya vÿrabotki
neural network. I want to work on the human brain is not known
novyx tehnologicheskix resheniy. In bolshinstve sovremennyx neyrosetevyx
study the biological model of the neuron.
obuchayushchuyu
vÿborku. Principles of processing information in modern systems of processing
dannyx i funktsionirovaniya chelovecheskogo mozga sushchestvenno
razlichayutsya. The brain functions on the basis of parallel processing of information in
sozdanii iskusstvennyx neyronnyx setey. Byla sdelana popÿtka
information processing. With this point of view predstavlyaetsya neobxodimÿm
this work. Systems, built on the basis of parallel principles
reshayut zadachi, k vÿpolneniyu kotoryx lish stremyatsya iskusstvennÿe seti. The
nervous system of a person is made up of special nerve cells, called
neurons. The brain has about 1011 neurons, which are formed
architecture byloe sxodstvo stalo sushchestvenno menshe. Tem ne menee,
znakomstvo s estestvennymi neyronnymi setyami polezno, t.k. oni uspeshno
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The neuron is formed from the nucleus and protoplasm. U neyrona
imeetsya telo so standartnÿm naborom organell, nazÿvaemoe somoy, vnutri
kotorogo raspolagaetsya yadro . Ot okrujayushchey sredy neuron otdelen
tonkoy membranoy. Protein molecules, embedded in the membrane, perform
the functions of receptors and ion channels. Neyrony imeyut mnogochislennÿe
otrostki, po kotorym oni poluchayut informatsiyu ot retseptorov i drugix
neyronov i peredayut signalaly neyronnym kletkam ispolnitelnyx organov.
Mojno vydelit dva tipa otrostkov: mnogochislennÿe tonkie, gusto vetvyashchiesya
drevovidnÿe otrostki (dendrity) i bolee tolstÿy, rasshcheplyayushchiysya na
kontse axon. Cherez dendrity neuron poluchaet informatsiyu cherez spetsialnÿe
kontaktÿ - synapsy. Transmission of information from one neuron to the drug
osushchestvlyaetsya rasprostraneniem nervnogo impulsa po nervnomu
voloknu - axon. Vyxodnoy signal otvoditsya axon cherez ego mnogochislennÿe
nervnÿe okonchaniya, nazÿvaemÿe kolateralami. Kolateraly kontaktiruyut s
somoy i dendritami drugix neyronov, obrazuya ocherednye synapsy.
Sinapsÿ otlichayutsya drug ot druga razmerami i vozmojnostyami
kontsentratsii neyromediatora vblizi svoey obolochki. On this prichine impulses
odinakovoy velichiny, postupayushchie na vxody nervnoy kletki cherez
razlichnÿe synapsy, mogut vozbujdat ee v raznoy stepeni. Meroy
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neurons, kajdyy iz kotoryx vÿpolnyaet otnositelno primitivnÿe
The pulse duration is about 1 ms. At the entrance to the nervous system
sluchae lits podderjivaet funktsionirovanie etix uchastkov membrany, a
naturalnymi chislami, prinimayushchimi kak polojitelnÿe, tak i
veshchestva, kotoroe, diffundiruya cherez sinapticheskuyu shchel, dostigaet
«Zapisyvatsya» on the DNA molecule.
drugimi signalami. Takim obrazom, deystvie vozbujdayushchego sinapsa mojet
sravneniya poluchennoy summÿ with porogovÿm znacheniem. Kajdym neuron imeet
tormozyashchego synapse - otritsatelnÿm znacheniem.
tormojeniy mejdu neuronami proisxodit cherez ximicheskie i
chislennÿe koeffitsienty (vesa), proportsionalnÿe kolichestvu
Ogromnoe kolichestvo neyronov i mezhneyronnyx svyazey (do 1000 vxodov v
kajdyy neyron) privodit k tomu, chto oshibka v srabatÿvanii
Otdelnÿy neuron ne yavlyaetsya ÿlementarnoy edinitsey obrabotki
matematicheskoy model neyrona vxodnÿe signalaly doljnÿ umnojatsya na
i vysvobojdeniya sootvetstvuyushchix kolichestv neyromediatora proisxodit
kletok. Neyronnaya set proyavlyaet vÿsokuyu ustoychivost k pomexam - eto
signal to the formation of nerve cells. Sinapsicheskie vesa doljny byt
from summarnogo kolichestva neyromediatora, vÿdelennogo na vsex sinapsax.
mogut vstupat v svyazi s uchastkami membran drugix neyronov, obrazuya seti. These
networks serve information processing systems. The body of the neuron in dannom
chrezvychayno great. Schitaetsya, chto chelovecheskiy mozg soderjit okolo 1011
impulse k sinapticheskomu kontaku proisxodit ximicheskaya reaksiya, sledstviem
chego yavlyaetsya vybros iz axona biologicheski aktivnogo
signals, postupayushchie na vxod po sinapticheskim svyazyam, mogut
otritsatelnÿe znacheniya. In the first sluchae synapse okazÿvaet vozbujdayushchee,
and in the second - tormozyashchee deystvie, prepyatstvuyushchee vozbujdeniyu kletki
funktsii summirovaniya vesovyx koeffitsientov vxodnyx signalov i
modelirovatsya polojitelnÿm znacheniem sinapticheskogo vesa, a deystvie
cells, realizuya sinapticheskuyu peredachu. Peredacha vozbujdeniy i
Iz skazannogo sleduet, chto kajdomu vxodu kletki mojno sopostavit
svoi vesa i svoe porogovoe znachenie.
otdelnogo neyrona ostaetsya nezametnoy v obshchey masse vzaimodeystvuyushchix
electrical synapses. Sushchestvuet mnojestvo razlichnyx tipov neyronov.
neurotransmitter, odnokratno vÿdelyaemogo na sootvetstvuyushchem synapse. V
In the conclusion of postupleniya vxodnyx impulses on specific synapses
informatsii, a vÿpolnyaet funktsii nervnogo tsentra. Dendrity and axons
vozbujdeniya kletki schitaetsya uroven polyarizatsii ee membranÿ, zavisyashchiy
eti koeffitsienty dlya togo, chtoby korrektno uchityvat vliyanie kajdogo
opredelennoe elektricheskoe vozbujdenie nervnoy kletki.
Kolichestvo vzaimodeystvuyushchix drug with drug nervnyx kletok
"stable" set, in which otdelnÿe sboi ne okazÿvayut sushchestvennogo
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srabatÿvaniya kajdoy otdelnoy kletki, izmeryaemÿy in milliseconds. She
ÿÿÿÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿÿ, ÿÿÿÿÿÿÿÿÿ analogichnye characteristics.
soboy popÿtku ispolzovaniya protsessov, proisxodyashchix v nervnyx sistemax,
dlya vÿrabotki novyh tehnologicheskix resheniy.
dostatochno korotkim. Esli udastsya, vzyav za obrazets nervnuyu sisteme, sozdat
ustroystvo s vÿsokoy stepenyu parallelnosti vÿpolneniya
funktsionirovaniya, nesmotrya na otnositelno dlitelnÿy tsikl
srabatÿvaniya otdelnyx ispolnitelnyx ÿlementov SBIS yavlyaetsya
neyronnyx sistem ot obÿchnyx ÿÿÿÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿ, ÿÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿÿ. Sleduet
podcherknut, chto ni odna sovremennaya technology ne pozvolyaet
ogromnym kolichestvom neuronov, soedinennyx mnogochislennymi
sushchestvenno uvelichena i priblijena k urovnyu, nablyudaemomu v protsessax
dostigaetsya blagodarya parallelnoy obrabotke informatsii v mozge
vliyaniya na rezultaty ee funktsionirovaniya. Takovo glavnoe otlichie
nezavisimyx operatsiy, to skorost ego funktsionirovaniya mojet bit
zvukov libo prinyatie resheniy, vÿpolnyayutsya chelovecheskim mozgom za
nervnyx sistem pozvolyayut nadeyatsya na sozdanie novogo pokoleniya
promejutki vremeni, izmeryaemÿe milliseconds. Achieving such
Iskusstvennÿe neyronnye seti voznikli na osnove znaniy o
postroit iskusstvennuyu neyronnuyu set, blizkuyu po masshtabam k
neuron seti mozga. Only study and copying biological
mejneyronnymi svyazyami. Such operations, as the recognition of images in
processing of information on biological objects.
Drugaya vajnaya osobennost nervnyx sistem - vysokaya skorost ix
vyxodit za granitsy sovremennyx tehnicheskix vozmojnostey, hotya tsikl
funktsionirovanii nervnoy sistemy jivyx sushchestv. They predstavlyayut
results when using semiconductor technology VLSI vse eshche
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Uproshchennaya structure of biological nerve cells
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neprerÿvnyx funktsiy veshchestvennyx peremennyx, zamknutÿx otnositelno
slozhnyx nelineynyx system. Kak xorosho izvestno, pryamoy analiz etix
chastnosti, xoroshie rezultaty dostignutÿ in polynomialnoy
bolee pravilnÿm predstavlyaetsya ssylatsya on sleduyushchie theorems ob
prichine chasto gelatelno imet prostuyu approksimatsionnuyu model, kotoraya mojet
bÿt ispolzovana dlya sinteza, analiza i identifikatsii
Veyershtrassa o vozmojnosti ravnomernoy approksimatsii s pomoshchyu
prikladnyx zadach:
1) theorem Veyershtrassa (1885)
2) theorem Stouna M. (1947) 3)
obobshchennaya theorem Stouna (1990-e).
V rabotax A.N. Gorbanya and ego schools proved the theorems about polnote
funktsii neskolkix peremennyx mojno postroit neyronnuyu set, kotoraya
ispolzovana dlya ekstrapolyatsii i upravleniya. Problems of identification
obosnovaniya vozmojnosti approksimatsii s pomoshchyu neyronnyx setey.
dostatochno shirokiy klass analiticheskix modeley, sposobnyx obespechit
Kolmogorova's theorem on the exact representation of functions as a basis for
dostatochno, chtoby klass neyronnyx setey soderjal seti s nelineynoy
neyronnoy seti privodit k ploxim rezultatam testirovaniya. Poetomu
V razlichnyx prilojeniyax chasto voznikaet problema nelineynosti i
sformulirovany osnovnye pologeniya teorii approksimatsii funktsiy. V
neprerÿvnoy funktsiey. Rassmatrivalis linear spaces
sistem mojet byt slozhnÿm, a reshenie mojet byt NP-zadachey. Po etoy
approximations. Klyuchevoe mesto zdes zanimaet xorosho izvestnaya teorema
approksimatsii, pozvolyayushchie ispolzovat neyronnÿe seti dlya resheniya
superposition operations. Dokazano, chto esli takoe prostranstvo soderjit
class functional, vÿchislimyx neyronnymi setyami: dlya lyuboy neprerÿvnoy
source system. Tsel - get model, kotoraya mojet bit
polynomials with lyuboy tochnostyu neprerÿvnoy deystvitelnoy funktsii f, opredelennoy
na diapazone [-1,1]. Poluchennÿe rezultaty ispolzuyutsya dlya
nelineynoy sistemy mojet bÿt reshena udovletvoritelno, esli imeetsya
V mnogochislennyx rabotax zarubejnyx avtorov est ssylki na
vÿchislyaet this function with lyuboy napered zadannoy tochnostyu. For this
xoroshuyu approximation nelineynoy system. In
rabotax on functional analysis and the theory of functions