Ana'urori na Analog Kolmogorov-Arnold don Kuskuren Aiki Mai Inganci a cikin Lantarki Mai Sassauƙa

1. Gabatarwa

Wannan takarda ta gabatar da wata sabuwar dabara ta tsari don kuskuren aiki a cikin Lantarki Mai Sassauƙa (FE) ta amfani da aiwatarwar analog na Cibiyoyin Sadarwa na Kolmogorov-Arnold (KANs). Babban ƙalubalen da aka magance shi ne cinikin halitta a cikin FE tsakanin iyawar lissafi da matsanancin ƙuntatawa akan girman jiki, kasafin wutar lantarki, da farashin masana'antu. Hanyoyin dijital na gargajiya sun zama masu tsada sosai a yanki da wutar lantarki don aikace-aikacen FE kamar na sawa da na'urori masu auna firikwensin IoT. Maganin da aka tsara yana amfani da ɗakin karatu na Tubalan Gina Analog (ABBs) don gina KANs na tushen spline, yana ba da hanyar gama gari kuma mai inganci ta kayan aiki don saka hanyar sarrafa mai hankali, kusa da firikwensin kai tsaye akan kayan aiki masu sassauƙa.

2. Bayanan Baya & Dalili

2.1 Ƙuntatawa na Lantarki Mai Sassauƙa

Lantarki Mai Sassauƙa, sau da yawa bisa kayan kamar Indium Gallium Zinc Oxide (IGZO), suna ba da damar sabbin siffofi don na'urori masu sawa, facin magani, da na'urori masu auna muhalli. Duk da haka, suna fama da manyan girman fasali idan aka kwatanta da silicon CMOS, wanda ke sa da'irori na dijital masu rikitarwa su zama marasa inganci a yanki. Bugu da ƙari, aikace-aikacen suna buƙatar ƙarancin amfani da wutar lantarki don tsawaita rayuwar baturi ko daidaitawar tattara makamashi. Wannan yana haifar da buƙatar gaggawa don tsarin lissafi waɗanda suke da ƙarancin albarkatun kayan aiki a cikin su.

2.2 Cibiyoyin Sadarwa na Kolmogorov-Arnold (KANs)

KANs, wanda Liu da sauransu (2024) suka sake farfado da shi kwanan nan, suna ba da madadin abin burgewa ga Multi-Layer Perceptrons (MLPs) na gargajiya. Maimakon ƙayyadaddun ayyukan kunnawa akan nodes, KANs suna sanya ayyukan univariate masu koyo (yawanci splines) akan gefuna (mafi nauyi) na cibiyar sadarwa. Ka'idar wakilcin Kolmogorov-Arnold ta goyi bayan wannan, tana bayyana cewa kowane aiki na ci gaba na multivariate ana iya wakilta shi azaman ƙayyadaddun abun da ke ciki na ci gaba da ayyuka na maɓalli guda ɗaya da ƙari. Wannan tsarin yana dacewa da aiwatarwar analog mai inganci, kamar yadda ayyuka masu rikitarwa suka rabu zuwa mafi sauƙi, ayyuka masu haɗawa.

3. Tsarin Gine-ginen KAN na Analog da Aka Tsara

3.1 Tubalan Gina Analog (ABBs)

Tushen hanyar shine saitin da'irori na analog masu ƙarancin wutar lantarki waɗanda suka riga sun siffanta, waɗanda ke aiwatar da mahimman ayyukan lissafi: Ƙari, Ninka, da Murabba'i. An tsara waɗannan tubalan laɓɓan la'akari da bambance-bambancen tsarin FE da parasitics. Yanayin su na modular yana ba da damar haɗawa ta tsari.

3.2 Gina Spline tare da ABBs

Kowane aiki na univariate mai koyo a cikin KAN (spline) ana gina shi ta hanyar haɗa ABBs. Spline, wanda aka ayyana ta guntun polynomials tsakanin knots, ana iya aiwatar da shi ta hanyar zaɓin kunna da taƙaita fitar da tubalan ninka da murabba'i waɗanda aka saita tare da haɗin gwiwar polynomial. Wannan spline na analog yana maye gurbin Teburin Nemo (LUT) na dijital ko na'urar lissafi, yana adana yanki mai mahimmanci.

3.3 Haɗa Cibiyar Sadarwar KAN

Ana haɗa cikakken Layer na KAN ta hanyar haɗa masu canjin shigarwa zuwa bankin tubalan spline na analog (ɗaya kowane gefe / nauyi). Ana taƙaita fitar da splines masu haɗuwa akan kumburi ɗaya ta amfani da ƙarin ABBs. Ana maimaita wannan tsari don gina zurfin cibiyar sadarwa. Ana ƙayyade sigogi (haɗin gwiwar spline) a kashe ta hanyar horo sannan a haɗa su cikin da'irar analog biases da riba.

4. Aiwar Fasaha & Cikakkun Bayanai

4.1 Tsarin Lissafi

Tushen Layer na KAN yana canza vector shigarwa $\mathbf{x} \in \mathbb{R}^n$ zuwa vector fitarwa $\mathbf{y} \in \mathbb{R}^m$ ta hanyar ayyukan univariate masu koyo $\Phi_{q,p}$: $$\mathbf{y} = \left( y_1, y_2, ..., y_m \right)$$ $$y_q = \sum_{p=1}^{n} \Phi_{q,p}(x_p), \quad q = 1,...,m$$ A cikin aiwatarwar analog, kowane $\Phi_{q,p}(\cdot)$ da'ira ce ta spline ta jiki. Ana yin taƙaitawar ta hanyar ƙari na yanayin yanzu ko na'urar ƙara ABB.

4.2 Ƙirar Da'ira & Parasitics

ABB mai nawa zai iya zama bisa cell ɗin Gilbert ko ƙa'idar translinear don aiki mai ƙarancin wutar lantarki. Ana iya samun murabba'i daga mai nawa tare da haɗin shigarwa. Manyan abubuwan da ba su dace ba sun haɗa da: rashin daidaiton transistor ($\sigma_V_T$), wanda ke shafar daidaiton haɗin gwiwar; ƙayyadaddun fitarwa mara iyaka, yana haifar da kurakurai masu lodi; da parasitics na capacitance, suna iyakance bandwidth. Waɗannan abubuwan gaba ɗaya suna ba da gudummawa ga kuskuren kuskuren da aka auna.

5. Sakamakon Gwaji & Bincike

5.1 Ma'auni na Ingantaccen Kayan Aiki

An yi gwajin KAN na analog da aka tsara daidai da aiwatarwar spline na dijital mai daidaiton bit 8 a cikin tsarin da ya dace da FE. Sakamakon yana da ban mamaki:

• Yanki: Ragewar 125x. Ƙirar analog tana kawar da manyan rajista na dijital, masu nawa, da ƙwaƙwalwar ajiya don LUTs.
• Wutar Lantarki: Ceton 10.59%. Lissafin analog yana guje wa babban ƙarfin wutar lantarki na agogo da sauyawar da'irori na dijital.

5.2 Binciken Kuskuren Kuskure

Cinikin ingancin kayan aiki shine daidaiton lissafi. Tsarin yana gabatar da matsakaicin kuskuren kuskure na 7.58%. Wannan kuskuren ya samo asali ne daga manyan tushe guda biyu:

1. Kuskuren Ƙira: Kuskuren halitta daga amfani da adadin guntun spline don kuskuren aikin da aka yi niyya.
2. Kuskuren Parasitic: Kurakurai da aka gabatar ta hanyar rashin daidaiton analog (rashin daidaito, amo, parasitics) a cikin ABBs.

6. Nazarin Lamari & Misalin Tsarin

Yanayi: Aiwar mai gano rashin daidaituwa mai sauƙi don na'urar lura da bugun zuciya mai sassauƙa. Na'urar tana buƙatar lissafin ma'aunin lafiya mai sauƙi $H$ daga shigarwa biyu: bambancin bugun zuciya (HRV) $x_1$ da skewness waveform bugun jini $x_2$. An san alaƙar ƙwararru $H = f(x_1, x_2)$ amma ba ta layi daya ba.

Aikace-aikacen Tsarin:

1. Rushewar Aiki: Ta amfani da tsarin da aka tsara, $f(x_1, x_2)$ ana kuskure shi da Layer na KAN mai Layer 2 tare da tsari [2, 3, 1]. Ana horar da cibiyar sadarwa a kashe akan bayanan.
2. Taswirar ABB: Ayyukan univariate da aka horar (splines) akan gefuna 6 na Layer na farko da gefuna 3 na Layer na biyu ana taswirar su zuwa haɗin gwiwar polynomial.
3. Aiwar Da'ira: Ga kowane spline, ana ƙayyade adadin guntun guntun polynomial da ake buƙata. Ana saita ABBs masu nawa da murabba'i da ake buƙata tare da haɗin gwiwar (azaman ƙarfin lantarki / yanzu) kuma an haɗa su tare da ƙarin ABBs bisa ga jadawalin KAN.
4. Mika mulki: Wannan da'irar KAN na analog ana ƙirƙira ta kai tsaye akan facin sassauƙa. Yana ci gaba da cinye microwatts na wutar lantarki, yana sarrafa bayanan firikwensin a ainihin lokaci don alamar rashin daidaituwa ba tare da dijital ko watsa bayanan danye ba.

7. Duban Aikace-aikace & Hanyoyin Gaba

Aikace-aikacen Kusa da Lokaci:

• Faci na Lafiya Mai Hankali: Sarrafa siginar akan faci don ECG, EEG, ko EMG, yana ba da damar hakar fasali na gida (misali, gano QRS) kafin watsa bayanai.
• Cibiyoyin Firikwensin Muhalli: Daidaitawa a cikin wuri da haɗa bayanai don zafin jiki, zafi, da na'urori masu auna iskar gas a cikin nodes na IoT.
• Gane Yanayin Sawa: Sarrafa bayanai masu ƙarancin wutar lantarki daga tsarin firikwensin matsi ko matsi mai sassauƙa.

1. Horo Mai Jurewa Kuskure: Haɓaka algorithms na horo waɗanda ke haɗa ingantaccen sigogin KAN don daidaito da ƙarfi ga rashin daidaiton da'irar analog (kamar horar da cibiyar sadarwa mai sanin kayan aiki).
2. ABB Mai Daidaitawa & Sake Saitawa: Bincika da'irori inda za a iya daidaita haɗin gwiwar spline kaɗan bayan ƙirƙira don rama bambance-bambancen tsari ko don daidaitawa da ayyuka daban-daban.
3. Haɗawa tare da Hankali: Ƙirar ABBs waɗanda ke mu'amala kai tsaye tare da nau'ikan firikwensin takamaiman (misali, photodiodes, abubuwan piezoresistive), suna matsawa zuwa haɗin gwiwar firikwensin-processor na analog na gaskiya.
4. Scalability zuwa Cibiyoyin Sadarwa Masu Zurfi: Bincika dabarun gine-gine da ƙirar da'ira don sarrafa amo da tarin kuskure a cikin KANs na analog masu zurfi don ƙarin ayyuka masu rikitarwa.

8. Nassoshi

1. Z. Liu et al., "KAN: Kolmogorov-Arnold Networks," arXiv:2404.19756, 2024. (Takardar farko da ta farfado da KANs).
2. Y. Chen et al., "Flexible Hybrid Electronics: A Review," Advanced Materials Technologies, vol. 6, no. 2, 2021.
3. M. Payvand et al., "In-Memory Computing with Emerging Memory Technologies: A Review," Proceedings of the IEEE, 2023. (Mahallin kan madadin tsarin lissafi masu inganci).
4. J. Zhu et al., "Analog Neural Networks: An Overview," in IEEE Circuits and Systems Magazine, 2021. (Bayanin baya akan kayan aikin ML na analog).
5. International Roadmap for Devices and Systems (IRDS™), "More than Moore" White Paper, 2022. (Tattauna rawar haɗin gwiwar iri-iri da takamaiman kayan aiki kamar FE).
6. B. Murmann, "Mixed-Signal Computing for Deep Neural Network Inference," IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2021. (Mai dacewa don binciken cinikin daidaito-inganci).

9. Bincike na Asali & Sharhin Kwararre