Weber’s law is the result of exact temporal accumulation of evidence

Abstract

<jats:title>Abstract</jats:title><jats:p>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 mecha-nisms 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.</jats:p>

State-dependent geometry of population activity in rat auditory cortex

“…At the population level, gain modulation in the inactive state is reflected in the overlap between the ILD and the ABL axes ( Figure 5B, D), and in the level-dependence of the accuracy and bias of the decoders of sound lateralization ( Figure 6A, C-F). At the same time, the lack of a consistent pattern of gain modulation across the population in the active state results in the faithful orthogonal stimulus representation shown in Figure 5C, D and in the level-invariant accuracy of our lateralization decoders ( Figure 6B, C-F), similar to what was observed behaviorally (Recanzone and Beckerman, 2004;Stellmack et al, 2004;Nodal et al, 2008;Pardo-Vazquez et al, 2018). Presumably, if tuning curves for ILD were gain modulated in the standard fashion during the active state, the ILD and ABL axes in Figure 5C would still be approximately orthogonal, but the separation between the centroids for each ABL (the three approximately horizontal rows of large points in this figure) would grow with ABL.…”

“…JND ranges from 2.5 to 3.4 which is similar to behavioural values measured in other species (Scott et al, 2007;Keating et al, 2013). We have recently studied ILD discrimination in rats using a subset of stimuli used here with ILDs between ±6 dB (Pardo- Vazquez et al, 2018). The average JND of rats was 2.2 dB, thus just slightly smaller than the decoded JND in the activated recordings.…”

“…For each session, we trained a binary classifier (decoder) predicting the sign of ILD from neural activity. We chose ILD sign because this is the task used in our behavioural experiments (Pardo-Vazquez et al, 2018) and so allows us to compare classification performance with behavioural performance. Furthermore, the neural representation of ILD with tuning curves diplaying high slope, rather than a peak, at the midline Stecker et al (2005); Yao et al (2013) and behavioral studies (Heffner and Heffner, 1988;Recanzone et al, 1998;Recanzone and Beckerman, 2004), all suggest that ILD discrimination with respect to the midline is more relevant than the estimation of any arbitrary ILD.…”

“…The emphasis on difference (as opposed to sum) modes that is apparent in the most active states seems to be well suited for sensory representations supporting a process of discrimination. Decision variables in sensory discrimination tasks are posited to involve differences in activity between oppositely tuned populations of neurons (Gold and Shadlen, 2002;Machens et al, 2005;Brunton et al, 2013;Pardo-Vazquez et al, 2018). Indeed, our decoders for ILD end up subtracting the activity of neurons with coefficients β ILD of different signs (fraction of non-zero decoder weights that have the same sign as β ILD was 0.81 ± 0.08, mean±SD across sessions).…”

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 (Pardo-Vazquez et al, 2018) . The stimulus sequence followed the same pattern as before with repeating and alternating blocks ( Fig.…”