A general rule for sensory cue summation: evidence from photographic, musical, phonetic and cross-modal stimuli

The Euclidean and MAX metrics have been widely used to model cue summation psychophysically and computationally. Both rules happen to be special cases of a more general Minkowski summation rule (Cue(1)(m) + Cue(2)(m))(1/m), where m = 2 and infinity, respectively. In vision research, Minkowski summation with power m = 3-4 has been shown to be a superior model of how subthreshold components sum to give an overall detection threshold. Recently, we have previously reported that Minkowski summation with power m = 2.84 accurately models summation of suprathreshold visual cues in photographs. In four suprathreshold discrimination experiments, we confirm the previous findings with new visual stimuli and extend the applicability of this rule to cue combination in auditory stimuli (musical sequences and phonetic utterances, where m = 2.95 and 2.54, respectively) and cross-modal stimuli (m = 2.56). In all cases, Minkowski summation with power m = 2.5-3 outperforms the Euclidean and MAX operator models. We propose that this reflects the summation of neuronal responses that are not entirely independent but which show some correlation in their magnitudes. Our findings are consistent with electrophysiological research that demonstrates signal correlations (r = 0.1-0.2) between sensory neurons when these are presented with natural stimuli.