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Equation 2 · Part 7 · How Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute Actually Works

=

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}
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

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