Foundations — Neuromorphic computing

6.5.14 · D1 · Hardware › Advanced & Emerging Architectures › Neuromorphic computing

Yeh page kuch bhi assume nahi karta. Parent page par jo bhi letter, squiggle, ya bold word hai, woh sab neeche explain kiya gaya hai, ek aisi order mein jahan har idea sirf pehle waale ideas par tikaa hai. Upar se neeche ek baar padho aur parent note bilkul plain English jaisa padhega.

1. Voltage $V$ — "charge kitni zyada force se push kar raha hai"

Ek paani ka tank socho. Paani ki height tank ke bottom par pressure hai: zyada bharo toh paani zyada force se niklega. Voltage exactly wahi height hai, lekin paani ki jagah electric charge ke liye.

Yeh topic $V$ isliye chahiye kyunki neuron ka poora kaam voltage ko build up hone dena hai aur phir react karna jab woh kaafi high ho jaye. Parent note mein neuron ki voltage ko membrane potential $V(t)$ kaha jaata hai — chhota $(t)$ bas matlab hai "$V$ ko time $t$ par measure kiya gaya hai", yaani paani ki height abhi, jo time ke saath badlati rehti hai.

2. Current $I$ — "har second kitna charge flow karta hai"

Paani ke tank par wapas jaate hain: current paani ki flow rate hai ek pipe se (litres per second). Voltage pressure hai; current woh actual flow hai jo woh pressure produce karta hai.

Parent note ek neuron ko input current $I(t)$ feed karta hai — doosre neurons se aane wala charge ka stream. Yahi inflow voltage ko raise karta hai.

3. Charge $Q$ — "electricity ki actual quantity"

Charge paani hi hai; current woh speed hai jis par charge move karta hai. Precisely likha jaaye: $I=\frac{dQ}{dt}$ jo padha jaata hai "current charge ki rate of change hai" — exactly parallel "flow rate yeh hai ki paani ki matra kitni tezi se badl rahi hai." Humen yeh relation usi waqt chahiye jab hum poochhen ki capacitor kitni tezi se bharta hai.

4. Resistance $R$ aur leak current $I_{\text{leak}}$

Neuron ki membrane par ion channels hote hain — chhote holes jo charge ko wapas bahar leak hone dete hain. Zyada leak = voltage tezi se girti hai. RC-circuit picture mein yeh leak ek resistor ki tarah draw ki jaati hai.

5. Capacitance $C$ aur capacitor current $C\frac{dV}{dt}$

Neuron ki membrane do thin layers hain jiske dono sides par charge baitha hai: yeh physically ek capacitor hai. Current pour karo aur "water level" (voltage) rise hogi.

Resistor (leak) aur capacitor (storage) ko saath rakho aur tumhare paas ek RC circuit hai. Yeh neuron ka poora electrical skeleton hai, aur isliye parent RC circuits aur Memristors and ReRAM link karta hai — memristors woh hardware hain jo adjustable resistor/synapse ka role play karte hain.

6. Derivative $\frac{dV}{dt}$ — "level kitni tezi se change ho raha hai"

Yahan ek piece of maths aata hai, toh hum ise use karne se pehle earn karte hain.

Humen yeh tool kyun chahiye aur plain algebra kyun nahi? Kyunki neuron ki voltage koi fixed number nahi hai — yeh hamesha move kar rahi hai. Motion describe karne ke liye (rise hona, fall hona, kitni tezi se) tumhe rates of change ki language chahiye, aur woh language derivative hai. "Kya $V$ threshold tak pahunchega?" poochna hai "abhi $V$ kaise move kar raha hai?", jo sirf $\frac{dV}{dt}$ answer kar sakta hai.

Paani ke level ko ek graph par curve socho, time right jaata hai, height upar jaati hai. Kisi bhi moment par:

• level upar ja raha hai → slope positive → $\frac{dV}{dt}>0$,
• level flat → slope zero → $\frac{dV}{dt}=0$,
• level gir raha hai (leaking) → slope negative → $\frac{dV}{dt}<0$.

7. Exponential $e^{-t/\tau }$ — "steady fading", aur charging curve kaise banti hai

Ek aur maths tool. Ise bhi earn karte hain.

Yeh exact shape kyun aur straight line neeche kyun nahi? Kyunki ek leaky bucket tab zyada fast leak karti hai jab zyada bhari hoti hai (zyada pressure) aur jab nearly empty ho toh slow. Ek quantity jiska girna apne size ke proportional ho woh exactly $e^{-t/\tau }$ curve trace karta hai — koi aur function nahi karta. Isliye parent ki leaky voltage $e^{-t/{\tau }_m}$ ki tarah decay karti hai, straight line ki tarah nahi.

Parent mein do mirror-image uses hain:

• Charging up ek target ki taraf: $V(t)=RI\left(1-e^{-t/{\tau }_m}\right)$ — tezi se rise hota hai, phir ease in karta hai.
• Fading learning (baad mein Section 9 mein use hota hai): $e^{-\Delta t/{\tau }_{+}}$ — spikes close the toh bada change, gap badhne par shrink hota hai.

8. Threshold $V_{th}$, reset, spike, aur refractory period

Paani ke tank ko $V_{th}$ height par ek overflow lip ke saath socho. Lip ke upar fill karo aur yeh ek splash dump karta hai (spike) aur neeche drop ho jaata hai. Lip ke neeche sab smooth analog charging hai; lip woh ek nonlinear switch hai jo neuron ko plain analog circuit ki jagah spiking banata hai. Yeh Spiking Neural Networks (SNN) se link karta hai.

9. Spike-Timing-Dependent Plasticity: weight $w$, $\Delta$, aur STDP

Yeh learning ki language hai. $\Delta t$ ka sign decide karta hai ki weight badhega ($\Delta w>0$, potentiation) ya ghategaa ($\Delta w<0$, depression), aur exponential (Section 7) decide karta hai kitna.

10. Big-number notation — $10^{11}$, milli, nano, mega

Parent $10^{11}$ neurons, $\text{M}\Omega$, $\text{nF}$, $\text{mV}$ jaisi values use karta hai. Ek baar decode karo:

Yeh foundations topic ko kaise feed karte hain

Equipment checklist

Right side cover karo aur reveal karne se pehle har ek answer do:

Wapas Neuromorphic computing · prerequisites: RC circuits, Memristors and ReRAM, Spiking Neural Networks (SNN), Hebbian learning, In-memory computing.