A generalized Weber’s law reveals behaviorally limiting slow noise in evidence accumulation

Weber’s law concisely describes a mapping between a true change in a physical stimulus and the resulting perceived change. It states that the perceived change governing the behavior is a relative difference, i.e. the true change divided by the magnitude of the two stimuli (Fechner, 1966). This psychophysical phenomenon is observed in domains as varied as time, weight, numerosity, length, brightness, and statistical inference (Dehaene, 2003; Namboodiri et al., 2014). In sequential decision-making, on the other hand, it is usually assumed that behavior reflects the true physical evidence, even when tasks involve comparing magnitudes of accumulated signals supporting competing choice options (Brunton et al., 2013). Here we introduce a novel dynamic, motion-direction discrimination task which allow us to probe Weber’s law during temporal accumulation of evidence. Human participants were asked to report the prevalent direction of motion in a stimulus consisting of a random sequence of motion pulses (left or right) interleaved with static periods. We controlled the difficulty of the task in two ways, by changing the motion strength of each pulse and the difference in number of opposing pulses, neither of which involves injecting external noise. We find that performance is determined by the product of motion strength and the relative difference of opposing pulses, implying a general, “strong” form of Weber’s law. Fits of a large family of 263 stochastic models show that this generalized Weber’s law implies that performance is limited by “slow” neural variability, which varies over trials, but is constant within dynamic motion sequences lasting up to 2s. This finding suggests that the primary cause of Weber’s law, and therefore of behavioral variability, is slow variability arising for instance from suboptimal inference or computation noise (Findling and Wyart, 2021), as opposed to fast neural variability such as Poisson-like noise.