How mechanisms of perceptual decision-making affect the psychometric function

Abstract

Psychometric functions are often interpreted in the context of Signal Detection Theory, which emphasizes a distinction between sensory processing and non-sensory decision rules in the brain. This framework has helped to relate perceptual sensitivity to the "neurometric" sensitivity of sensory-driven neural activity. However, perceptual sensitivity, as interpreted via Signal Detection Theory, is based on not just how the brain represents relevant sensory information, but also how that information is read out to form the decision variable to which the decision rule is applied. Here we discuss recent advances in our understanding of this readout process and describe its effects on the psychometric function. In particular, we show that particular aspects of the readout process can have specific, identifiable effects on the threshold, slope, upper asymptote, time dependence, and choice dependence of psychometric functions. To illustrate these points, we emphasize studies of perceptual learning that have identified changes in the readout process that can lead to changes in these aspects of the psychometric function. We also discuss methods that have been used to distinguish contributions of the sensory representation versus its readout to psychophysical performance.

Figure 1. The decision process

Schematic of a 2AFC perceptual decision (is the stimulus A or B?) decomposed into three processes: 1) the representation of relevant sensory information by populations of neurons with relevant tuning properties and a variety of sensitivities to the two alternatives under consideration; 2) readout of that information to form a decision variable; and 3) application of a rule to the decision variable to generate a choice. The readout scheme illustrated here uses a simple weighted sum of the outputs of sensory neurons. To generate a decision variable whose sign can distinguish between the two alternatives, positive weights are assigned to neurons that encode one alternative, negative weights to the others. To maximize discriminability using this scheme, each weight (indicated by line thickness) is proportional to the relative sensitivity of the associated sensory neuron.

Figure 2. Relationships between the ROC curve, yes-no detection, and 2AFC discrimination according to Signal Detection Theory

The decision variable for yes-no detection (lower left) is compared to a criterion, the value of which (green arrows) determines the proportions of hits and false alarms, plotted as an ROC curve (top). The area under the ROC curve (shaded area) corresponds to the expected percentage of correct responses for a 2AFC discrimination task that uses as a decision variable a difference between the “detect A” and “detect B” yes-no decision variables (lower right). The optimal decision rule in this case is based simply on the sign of the decision variable (in the example shown, positive values correspond to “decide A” and negative values correspond to “decide B”). Psychophysical methods measure the ROC curve directly from behavior and then infer the underlying decision variables (Green & Swets, 1966; Macmillan & Creelman, 2004). Neurometric methods compute ROC curves from neural activity. These methods often assume that 2AFC performance equals the difference in measured activity from a single sensory neuron, corresponding to a “detect A” decision variable, and its presumed “anti-neuron,” corresponding to a “detect B” decision variable (Britten et al., 1992).

Figure 3. Features of 2AFC psychometric functions

Top: An “accuracy” function depicting the fraction of correct responses as a function of stimulus strength, on a logarithmic abscissa in arbitrary units from 0 to 100. The function is a cumulative Weibull function with parameters α (threshold) = 15 and β (shape) = 1.4. Bottom: A “choice” function depicting the fraction of trials in which stimulus “A” was chosen as a function of signed stimulus strength, on a linear abscissa in which positive/negative values correspond to presentation of stimulus A/B. The function is a logistic function with two parameters, θ₀ (bias) = 0 and θ₁ (sensitivity) = 0.099. The functions and parameters used in both panels are similar to those reported for monkeys performing the coarse direction-discrimination task (Britten et al., 1992; Salzman et al., 1992).

Figure 4. Effects of readout on the psychometric function

A. Effects on threshold and lapse rate. The curves are from simulations in which the decision variable is formed as a weighted sum of sensory neurons with a variety of sensitivities to the two alternatives. As the decision variable becomes less dependent on inappropriately tuned neurons, the psychometric function shifts leftward (lower thresholds) and have higher values for the largest stimulus strength (smaller lapse rates). B. Effects on slope. The simulations use a readout scheme with a non-linear pooling operation that compares the maximum absolute value of positively versus negatively weighted sensory signals. As the decision depends on fewer unturned sensory neurons, the psychometric function shifts leftward and becomes shallower. C. Effects on time dependence. The simulations use a readout scheme in which sensory evidence is integrated over time using a leaky integrator. For this log-log plot of discrimination threshold versus stimulus duration, a slope of −0.5 (bottom curve) corresponds to a perfect integrator, with no leak. Increasing the amount of leak causes the relationship to become shallower, indicating smaller improvements in discrimination threshold for increasing stimulus presentation time. D. Effects on choice biases. Simulations use a linear pooling scheme in which the weights corresponding to one alternative are either stronger than, the same as, or weaker than the weights corresponding to the other alternative. Asymmetric weights cause horizontal shifts in the psychometric choice function. Similar effects can result from a fixed offset to the value of the decision variable or asymmetric bounds in an accumulation-to-bound decision process.