The mechanistic foundation of Weber’s law

Abstract

Weber's law states that the discriminability between two stimulus intensities depends only on their ratio. Despite its status as the cornerstone of psychophysics, the mechanisms underlying Weber's law are still debated, as no principled way exists to choose between its many proposed alternative explanations. We studied this problem training rats to discriminate the lateralization of sounds of different overall level. We found that the rats' discrimination accuracy in this task is level-invariant, consistent with Weber's law. Surprisingly, the shape of the reaction time distributions is also level-invariant, implying that the only behavioral effect of changes in the overall level of the sounds is a uniform scaling of time. Furthermore, we demonstrate that Weber's law breaks down if the stimulus duration is capped at values shorter than the typical reaction time. Together, these facts suggest that Weber's law is associated to a process of bounded evidence accumulation. Consistent with this hypothesis, we show that, among a broad class of sequential sampling models, the only robust mechanism consistent with reaction time scale-invariance is based on perfect accumulation of evidence up to a constant bound, Poisson-like statistics, and a power-law encoding of stimulus intensity. Fits of a minimal diffusion model with these characteristics describe the rats performance and reaction time distributions with virtually no error. Various manipulations of motivation were unable to alter the rats' psychometric function, demonstrating the stability of the just-noticeable-difference and suggesting that, at least under some conditions, the bound for evidence accumulation can set a hard limit on discrimination accuracy. Our results establish the mechanistic foundation of the process of intensity discrimination and clarify the factors that limit the precision of sensory systems.

Changes of mind and absolute evidence

“…In particular, we assume that there is an input-dependent noise source in the decision-making process. This assumption accounts for both speed up initial response times and the slight drop in accuracy with the multiplicative stimulus manipulation, and is entirely consistent with a recent mechanistic account of Weber's law (Pardo-Vazquez et al, 2019). As such, whilst Weber's law is a relevant consideration when accounting for our data, it cannot explain why existing models fail to capture the change-of-mind effects we observed.…”

Response outcomes gate the impact of expectations on perceptual decisions

“…To test the extent to which these findings depended on the task design, we trained a new group of rats (Group 2, n = 6) in a different level discrimination 2AFC task, in which noise stimuli had to be classified according to the intensity difference between the two lateral speakers 29 . The stimulus sequence followed the same pattern as before with repeating and alternating blocks (Fig.…”

Sequential Presentation Protects Working Memory From Catastrophic Interference

“…Furthermore, Cicchini, Anobile, and Burr () argued that, outside the domain of number processing, gain control seems to be the usual explanation for Weber signatures. However, as this model is rarely made explicit, and many authors explain Weber ratio signatures based on assumptions about the format and distribution of the mental representations of quantities that are not always independently motivated (e.g., Dehaene, Izard, Spelke, & Pica, ; Feigenson et al., ; Izard & Dehaene, ; Nieder, ; Pardo‐Vazquez et al., ; Piazza, Izard, Pinel, Bihan, & Dehaene, ; Whalen et al., ), we present the gain control model in some detail in its purest and simplest form.…”