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Equation 2 · Part 12 · How Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute Actually Works

Starting index or lower bound: i

Vm[t+1]=Vm[t]+∑iwisi[t]−Vm[t]τV_m[t+1] = V_m[t] + \sum_i w_i s_i[t] - \frac{V_m[t]}{\tau}
ii

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

The passage around this formula

At the circuit level, each neuron unit holds a membrane potential, implemented as a charge on a capacitor or a value in a small register, that accumulates incoming weighted spike inputs and simultaneously leaks — decays exponentially — toward a resting value between inputs. A standard discrete-time version of this leaky-integrate-and-fire rule is Vm[t+1]=Vm[t]+∑iwisi[t]−Vm[t]τV_m[t+1] = V_m[t] + \sum_i w_i s_i[t] - \frac{V_m[t]}{\tau}. where the sis_i[t] are the incoming binary spike events, the wiw_i are the corresponding synaptic weights, and τ sets how quickly the leak dissipates unused charge. When VmV_m crosses a fixed threshold, the circuit emits a single digital pulse — a spike — on its output, and its membrane potential resets. Nothing is emitted, and in an…

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Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

Open the illustrated sums and products: repeat an operation over an index guide →

See this notation across published equations →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.