Weber ’ s Law Implies Neural Discharge More Regular than a Poisson Process Running title : Weber ’ s law and neuronal spike train

38 pages, 8 figures, 1 table and 11 equations. The total number of words in: (i) the whole manuscript: 8909. (ii) the Abstract: 164 and (iii) the Introduction: 542. Abstract Weber's law is one of the basic laws in psychophysics, but the link between this psychophysical behavior and the neuronal response has not yet been established. In this paper, we carried out an analysis on the spike train statistics when Weber's law holds, and found that the efferent spike train of a single neuron is less variable than a Poisson process. For population neurons, Weber's law is satisfied only when the population size is small (less than 10 neurons). However, if the population neurons share a weak correlation in their discharges and individual neuronal spike train is more regular than a Poisson process, Weber's law is true without any restriction on the population size. Biased competition attractor network also demonstrates that the coefficient of variation of interspike interval in the winning pool should be less than one for the validity of Weber's law. Our work links Weber's law with neural firing property quantitatively, shedding light on the relation between psychophysical behavior and neuronal responses.