Figure 2. Normalization accounts for the principle of the inverse effectiveness.

(A) The bimodal response of a model unit is plotted as a function of the intensities of Input1 and Input2. Both inputs were located in the center of the receptive field. Diagonal line: inputs with equal intensities. Exponent, n = 2.0. (B) The bimodal response (solid black curve) and the unimodal responses (red and blue curves) are plotted as a function of stimulus intensity (from the diagonal of panel A). The sum of the two unimodal responses is shown as the dashed black curve. Red and blue curves have slightly different amplitudes to improve clarity. (C) Additivity index (AI) is plotted as a function of both input intensities. AI > 1 indicates super-additivity, and AI < 1 indicates sub-additivity. (D) AI values (from the diagonal of panel C) are plotted as a function of intensity for three exponent values: n = 1.0 (blue), 2.0 (black), and 3.0 (magenta). (E) Data from cat superior colliculus, demonstrating inverse effectiveness (replotted from ref ²⁶). The z-scored bimodal response (± SD) is plotted against the predicted sum of the two unimodal responses, both for cross-modal (visual-auditory) inputs (black curve) or pairs of visual inputs (red). Z-score values >1.96 represent significant superadditivity, and values <−1.96 denote significant sub-additivity. (F) Model predictions match the data from cat superior colliculus. For this simulation, model neurons had all 9 combinations of dominance weights from the set (d1, d2 = 0.50, 0.75 or 1.00), and the exponent, n, was 1.5.