The aim of a number of psychophysics tasks is to uncover how mammals make decisions in a world that is in flux. Here we examine the characteristics of ideal and near-ideal observers in a task of this type. We ask when and how performance depends on task parameters and design, and, in turn, what observer performance tells us about their decision-making process. In the dynamic clicks task subjects hear two streams (left and right) of Poisson clicks with different rates. Subjects are rewarded when they correctly identify the side with the higher rate, as this side switches unpredictably. We show that a reduced set of task parameters defines regions in parameter space in which optimal, but not near-optimal observers, maintain constant response accuracy. We also show that for a range of task parameters an approximate normative model must be finely tuned to reach near-optimal performance, illustrating a potential way to distinguish between normative models and their approximations. In addition, we show that using the negative log-likelihood and the 0/1-loss functions to fit these types of models is not equivalent: the 0/1-loss leads to a bias in parameter recovery that increases with sensory noise. These findings suggest ways to tease apart models that are hard to distinguish when tuned exactly, and point to general pitfalls in experimental design, model fitting, and interpretation of the resulting data.
In cat visual cortex, the response of a neural population to the linear combination of two sinusoidal gratings (a plaid) can be well approximated by a weighted sum of the population responses to the individual gratings - a property we refer to as subspace invariance. We tested subspace invariance in mouse primary visual cortex by measuring the angle between the population response to a plaid and the plane spanned by the population responses to its individual components. We found robust violations of subspace invariance arising from a strong, negative correlation between the responses of neurons to individual gratings and their responses to the plaid. Contrast invariance, a special case of subspace invariance, also failed. The responses of some neurons decreased with increasing contrast, while others increased. Altogether the data show that subspace and contrast invariance do not hold in mouse primary visual cortex. These findings rule out some models of population coding, including vector averaging, some versions of normalization and temporal multiplexing.