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Equation 2 · Part 6 · How Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute Actually Works

Symbol τ

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}
τ\tau

What this part means

τ occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Its job in the formula

τ occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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