← All parts of this equation

Equation 2 · Part 1 · How Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute Actually Works

Symbol V_m

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}
VmV_m

What this part means

VmV_m occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

VmV_m occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

…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 efficient asynchronous implementation nothing is computed downstream, in any cycle where the threshold is not crossed.

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? 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.