Alex Williams^1,2, Fangfang Hong³, Craig Sanders⁴, Michael Shvartsman⁵, Phillip Guan⁴, David Brainard³; ¹Center for Neural Science, New York University, ²Center for Computational Neuroscience, Flatiron Institute, ³Department of Psychology, University of Pennsylvania, ⁴Reality Lab Research, Meta, ⁵FAIR, Meta

Traditional methods for trial selection do not support exhaustive characterization of perceptual thresholds in high-dimensional settings; they require exponentially more data with increasing stimulus dimensionality. Here, we study the efficacy of adaptive sampling for trial selection combined with a Wishart Process model (WPM) for dense characterization of thresholds. Specifically, we simulated color-discrimination performance using the CIELAB color space, which is intended to be perceptually uniform and which coarsely approximates human color sensitivity. We restricted attention to a plane in color space. We generated CIELAB-based 'ground-truth' responses for a forced-choice task in which an observer identifies the odd-colored stimulus (comparison) from two other stimuli that are identical to each other (reference). The reference (R & B calibrated monitor channel intensities) and comparison stimuli (R+ΔR & B+ΔB) were chosen using AEPsych, a non-parametric method that adaptively selects informative trials (Owens et al., 2021). The monitor G intensity was held fixed. We fit the generated responses with a semi-parametric WPM which expresses smoothness of performance over the stimulus space, on the assumption of multivariate-Gaussian performance-limiting internal noise. This approach accurately recovered the ‘ground-truth’ thresholds with 2,800 trials, ~10x fewer trials than required by conventional methods (~30,000 assuming 25 reference stimuli x 8 comparison directions/reference x 150 trials/direction). Evaluation using the Bures-Wasserstein distance showed close agreement between ‘ground-truth’ threshold ellipses and model predictions (mean = 0.009, SD = 0.003; compare to a baseline set by distance between the ‘ground-truth’ ellipses and their inscribed circles: mean = 0.040, SD = 0.010). Crucially, our approach densely characterizes discrimination, interpolating to predict thresholds for any comparison direction around any reference. The approach generalizes to higher stimulus dimensions (full color space) and to any modality where smoothly varying multivariate-Gaussian noise limits performance, for example auditory localization and motor reaching.