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.

Bounded temporal accumulation of evidence is a canonical computation for perceptual decision making (PDM). Previously derived optimal strategies for PDM, however, ignore the fact that focusing on the task of accumulating evidence in time requires cognitive control, which is costly. Here, we derive a theoretical framework for studying how to optimally trade-off performance and control costs in PDM. We describe agents seeking to maximize reward rate in a two-alternative forced choice task, but endowed with default, stimulus-independent response policies which lead to errors and which also bias how speed and accuracy are traded off by the agent. Limitations in the agent's ability to control these default tendencies lead to optimal policies that rely on 'soft' probabilistic decision bounds with characteristic observable behavioral consequences. We show that the axis of control provides an organizing principle for how different task manipulations shape the phenomenology of PDM, including the nature and consequence of decision lapses and sequential dependencies. Our findings provide a path to the study of normative decision strategies in real biological agents.

Encoding and processing sensory information is key to understanding the environment and to guiding behavior accordingly. Characterizing the behavioral and neural correlates of these processes requires the experimenter to have a high degree of control over stimuli presentation. For auditory stimulation in animals with relatively large heads, this can be accomplished by using headphones. However, it has proven more challenging in smaller species, such as rats and mice, and has been only partially solved using closed-field speakers in anesthetized or head-restrained preparations. To overcome the limitations of such preparations and to deliver sound with high precision to freely moving animals, we have developed a set of miniature headphones for rats. The headphones consist of a small, skull-implantable base attached with magnets to a fully adjustable structure that holds the speakers and keeps them in the same position with respect to the ears.