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Кліти нні нейро нні мере жі КНМ англ Cellular neural networks CNN схожі за функціонуванням до штучних нейронних мереж ал

Клітинні нейронні мережі

Клітинні нейронні мережі

Кліти́нні нейро́нні мере́жі (КНМ, англ. Cellular neural networks (CNN)) — , схожі за функціонуванням до штучних нейронних мереж, але відрізняються тим, що взаємодії відбуваються лише між сусідніми одиницями. КНМ застосовують для обробки зображень, аналізу 3D поверхонь, обчислення диференційних рівнянь в часткових похідних, приведення негеометричних завдань до геометричних карт, моделювання зору та інших сенсомоторних функцій.

Архітектура КНМ

В зв'язку з великою чисельністю різних архітектур важко дати точне визначення для клітинної нейронної мережі. З точки зору архітектури мереж, КНМ — це система скінченних, чисельно фіксованих, топологічно-фіксованих, локально з'єднаних нелінійних обчислювальних одиниць, що мають багато входів і лише один вихід. Нелінійні обчислювальні одиниці часто називаються нейронами або клітинами.

Математично кожна клітина може бути змодельована як дисипативна, нелінійна динамічна система, в якій інформація закодована через її початковий стан, входи та інші змінні, які визначають її поведінку.

Якщо динаміка станів клітин є неперервною в часі — тоді говорять про Неперервні КНМ (англ. Continuous-Time CNN).

Якщо динаміка є дискретною в часі, то говорять про Дискретні КНМ (англ. Discrete-Time CNN). Кожна клітина має один вихід, за допомогою якого вона передає інформацію про свій стан з іншими клітинами та зовнішніми пристроями. Вихідний сигнал є зазвичай дійсним числом, проте може бути комплексним, або навіть кватерніоном в Багатозмінній КНМ (англ. Multi-Valued CNN).

Зазвичай нейрони (клітини) мережі є однаковим, але в деяких випадках застосовують різні типи (в Неоднорідних КНМ, англ. Non-Uniform Processor CNN). В оригінальній моделі Чуа (англ. Chua) і Янга (англ. Yang) — Chua-Yang CNNстан клітин був ваговою сумою вхідних сигналів, і вихід був кусочно-лінійною функцією. Однак, як і Перцептронні моделі штучних нейронних мереж, ця модель мала обмежені корисні властивості. Наприклад, вона не була здатною моделювати нелінійні функції, наприклад XOR.

Сучасні нелійні КНМ здатні вирішити задачі моделювання нелійних функцій. Клітини зазвичай визначаються в двовимірному просторі з евклідовою геометрією, з розташуванням у вигляді квадратної сітки. Інколи клітини визначаються в багатовимірному просторі з трикутним, гексагональним або іншим просторово-інваріантним розміщенням. Топологічно клітини можуть розміщуватись на кінцевій площині або на тороїдальній площині. Клітини з'єднані локальними зв'язками. Це означає, що усі зв'язки однієї клітини знаходяться в межах певного радіусу (відстань вимірюється топологічно).

Зв'язки також можуть бути із затримкою в часі для того щоб працювати з даними в часі. Більшість архітектур КНМ мають клітини з однаковою коннективністю, однак є приклади застосування нейронних мереж, в яких необхідна просторово варіантна топологія (коннективність різна в різних ділянках КНМ). Можуть також застосовуватись багатошарові КНМ (англ. Multiple-Layer CNN (ML-CNN)), де клітини одного шару є ідентичними, для збільшення обчислювальних можливостей КНМ.

Не зважаючи на локальну коннективність клітинних нейронних мереж, обмін інформацією між віддаленими ділянками нейронної мережі може відбуватись шляхом дифузії. КНМ являють собою набір незалежних, взаємодіючих структур, що формують інтегроване ціле. Складність поведінки КНМ більша, ніж складність поведінки окремих клітин (нейронів). Тобто, клітинні нейронні мережі володіють емерджентними властивостями.

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Kliti nni nejro nni mere zhi KNM angl Cellular neural networks CNN shozhi za funkcionuvannyam do shtuchnih nejronnih merezh ale vidriznyayutsya tim sho vzayemodiyi vidbuvayutsya lishe mizh susidnimi odinicyami KNM zastosovuyut dlya obrobki zobrazhen analizu 3D poverhon obchislennya diferencijnih rivnyan v chastkovih pohidnih privedennya negeometrichnih zavdan do geometrichnih kart modelyuvannya zoru ta inshih sensomotornih funkcij Arhitektura KNMV zv yazku z velikoyu chiselnistyu riznih arhitektur vazhko dati tochne viznachennya dlya klitinnoyi nejronnoyi merezhi Z tochki zoru arhitekturi merezh KNM ce sistema skinchennih chiselno fiksovanih topologichno fiksovanih lokalno z yednanih nelinijnih obchislyuvalnih odinic sho mayut bagato vhodiv i lishe odin vihid Nelinijni obchislyuvalni odinici chasto nazivayutsya nejronami abo klitinami Matematichno kozhna klitina mozhe buti zmodelovana yak disipativna nelinijna dinamichna sistema v yakij informaciya zakodovana cherez yiyi pochatkovij stan vhodi ta inshi zminni yaki viznachayut yiyi povedinku Yaksho dinamika staniv klitin ye neperervnoyu v chasi todi govoryat pro Neperervni KNM angl Continuous Time CNN Yaksho dinamika ye diskretnoyu v chasi to govoryat pro Diskretni KNM angl Discrete Time CNN Kozhna klitina maye odin vihid za dopomogoyu yakogo vona peredaye informaciyu pro svij stan z inshimi klitinami ta zovnishnimi pristroyami Vihidnij signal ye zazvichaj dijsnim chislom prote mozhe buti kompleksnim abo navit kvaternionom v Bagatozminnij KNM angl Multi Valued CNN Zazvichaj nejroni klitini merezhi ye odnakovim ale v deyakih vipadkah zastosovuyut rizni tipi v Neodnoridnih KNM angl Non Uniform Processor CNN V originalnij modeli Chua angl Chua i Yanga angl Yang Chua Yang CNNstan klitin buv vagovoyu sumoyu vhidnih signaliv i vihid buv kusochno linijnoyu funkciyeyu Odnak yak i Perceptronni modeli shtuchnih nejronnih merezh cya model mala obmezheni korisni vlastivosti Napriklad vona ne bula zdatnoyu modelyuvati nelinijni funkciyi napriklad XOR Suchasni nelijni KNM zdatni virishiti zadachi modelyuvannya nelijnih funkcij Klitini zazvichaj viznachayutsya v dvovimirnomu prostori z evklidovoyu geometriyeyu z roztashuvannyam u viglyadi kvadratnoyi sitki Inkoli klitini viznachayutsya v bagatovimirnomu prostori z trikutnim geksagonalnim abo inshim prostorovo invariantnim rozmishennyam Topologichno klitini mozhut rozmishuvatis na kincevij ploshini abo na toroyidalnij ploshini Klitini z yednani lokalnimi zv yazkami Ce oznachaye sho usi zv yazki odniyeyi klitini znahodyatsya v mezhah pevnogo radiusu vidstan vimiryuyetsya topologichno Zv yazki takozh mozhut buti iz zatrimkoyu v chasi dlya togo shob pracyuvati z danimi v chasi Bilshist arhitektur KNM mayut klitini z odnakovoyu konnektivnistyu odnak ye prikladi zastosuvannya nejronnih merezh v yakih neobhidna prostorovo variantna topologiya konnektivnist rizna v riznih dilyankah KNM Mozhut takozh zastosovuvatis bagatosharovi KNM angl Multiple Layer CNN ML CNN de klitini odnogo sharu ye identichnimi dlya zbilshennya obchislyuvalnih mozhlivostej KNM Ne zvazhayuchi na lokalnu konnektivnist klitinnih nejronnih merezh obmin informaciyeyu mizh viddalenimi dilyankami nejronnoyi merezhi mozhe vidbuvatis shlyahom difuziyi KNM yavlyayut soboyu nabir nezalezhnih vzayemodiyuchih struktur sho formuyut integrovane cile Skladnist povedinki KNM bilsha nizh skladnist povedinki okremih klitin nejroniv Tobto klitinni nejronni merezhi volodiyut emerdzhentnimi vlastivostyami LiteraturaL Chua and L Yang Cellular Neural Networks Theory IEEE Trans on Circuits and Systems 35 10 1257 1272 1988 http nonlinear eecs berkeley edu raptor CNNs CellularNeuralNetworks Theory pdf 13 kvitnya 2021 u Wayback Machine L Chua and L Yang Cellular Neural Networks Theory IEEE Trans on Circuits and Systems 35 10 1257 1272 1988 1 13 kvitnya 2021 u Wayback Machine L Chua and L Yang Cellular Neural Networks Applications IEEE Trans on Circuits and Systems 35 10 1273 1290 1988 T Roska L Chua 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