LIF f-I Curve Validation

Validates StochasticLIFNeuron (with noise disabled) against the analytical firing rate for a deterministic leaky integrate-and-fire neuron.

Analytical Solution

For a LIF with membrane equation dv/dt = -(v - v_rest)/tau + R*I:

v_ss = v_rest + R * I * tau
ISI = tau * ln((v_ss - v_reset) / (v_ss - v_threshold))
f = 1 / (ISI + t_ref)

With normalised units (v_rest=0, v_th=1, v_reset=0, R=1, tau=20ms): - Rheobase: I_rh = V_th / (R * tau) = 0.05 - ISI at I=0.1: 20 * ln(2) = 13.863 ms

Reference

Gerstner, W. & Kistler, W.M. (2002). Spiking Neuron Models. Cambridge University Press. Ch. 1.

Measured Results (Kaggle run 2026-03-28, dt=0.1ms)

Current	Analytical (sp/ms)	Simulated	Error
0.06	0.027906	0.027800	0.38%
0.08	0.050977	0.051000	0.04%
0.10	0.072135	0.071800	0.46%
0.15	0.123315	0.123400	0.07%
0.20	0.173803	0.172400	0.81%
0.30	0.274241	0.270200	1.47%
0.50	0.474561	0.454400	4.25%

All within 5% tolerance. Error increases with current because higher firing rates approach the dt=0.1ms discretisation limit.

Additional Validations

• Subthreshold (I < 0.05): zero firing rate confirmed
• Rheobase (I = 0.05): rate < 0.01 confirmed
• Monotonicity: verified across 8 current levels
• Refractory period: reduces rate, matches analytical (<5%)
• Multiple tau (10, 20, 40 ms): all within 5%
• Native StochasticLIFNeuron matches Euler: 0.00% error

Test Files

• tests/test_lif_fi_curve.py — pytest suite (dt=1ms for fast CI)
• benchmarks/results/phase1_validation_results.json — Kaggle measured data (dt=0.1ms)