Device-level analog / mixed-signal computation modelled on biological neural circuits. Canonical substrate elements: leaky-integrate-and-fire (LIF) neurons — Lapicque 1907, Stein 1965 stochastic generalisation; spike-timing-dependent…
neuromorphic-computing
LIF neuron: τ_m·dV/dt = -(V-V_rest) + R·I(t); fire when V≥V_th, reset to V_r
Lapicque 1907 leaky-integrate-and-fire neuron. Membrane potential evolves as a linear first-order ODE τ_m·dV/dt = -(V − V_rest) + R·I(t),…
STDP: Δw = A₊ exp(-Δt/τ₊) for Δt>0 (LTP), -A₋ exp(Δt/τ₋) for Δt<0 (LTD)
Bi-Poo 1998 spike-timing-dependent plasticity: synaptic weight w between a pre-synaptic neuron and a post-synaptic neuron undergoes…
Memristor: V = M(q)·i; HP 2008 model dx/dt = μ_V·R_on·i/D², 0≤x≤1
Chua 1971 theoretical prediction: a fourth passive two-terminal circuit element M(q) — the memristor — links charge q and magnetic flux φ…
LIF firing rate: r(I) = 1/(τ_ref + τ_m·ln((R·I)/(R·I − (V_th-V_rest)))) for suprathreshold
Closed-form firing rate of an LIF neuron under constant suprathreshold input current I > I_th = (V_th − V_rest)/R. Integrate τ_m·dV/dt =…
STDP integral: ∫₀^∞ A₊ exp(-Δt/τ₊) dΔt = A₊·τ₊; ∫_{-∞}^0 A₋ exp(Δt/τ₋) dΔt = A₋·τ₋
Total (integrated) STDP learning contribution across all pre-post timing offsets: for a flat Poisson-paired firing statistic, total LTP per…
HP memristor I-V loop: V(t) = (R_on x + R_off(1-x))·i(t), pinched at origin
HP memristor I-V characteristic: V(t) = M(x(t))·i(t) with memristance M(x) = R_on·x + R_off·(1−x) interpolating linearly between R_on (at…