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Equation 2 · Part 8 · How Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute Actually Works

fraction

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}
fraction

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

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 fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

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