Population Vector Neural Coding

N neurons with preferred directions θᵢ fire according to cosine tuning curves. The population vector — weighted sum of preferred directions — accurately decodes the stimulus angle. Fisher information quantifies precision.

0°

True angle

0°

Decoded angle

0°

Error

0.0

Fisher Info

Controls

Num neurons N16

Tuning width σ (rad)0.8

Noise level η0.1

Stimulus angle θ (°)90

Theory

Tuning: f_i(θ) = r_max·exp(
−(θ−θ_i)²/2σ²)

Population vector:
v = Σ r_i · (cos θ_i, sin θ_i)
θ_decoded = atan2(v_y, v_x)

Fisher info:
J(θ) = Σ [f'_i(θ)]²/f_i(θ)

Cramér-Rao: Var ≥ 1/J(θ)