No abstract

Recent psychophysical experiments indicate that humans perform near-optimal Bayesian inference in a wide variety of tasks, ranging from cue integration to decision making to motor control. This implies that neurons both represent probability distributions and combine those distributions according to a close approximation to Bayes' rule. At first sight, it would seem that the high variability in the responses of cortical neurons would make it difficult to implement such optimal statistical inference in cortical circuits. We argue that, in fact, this variability implies that populations of neurons automatically represent probability distributions over the stimulus, a type of code we call probabilistic population codes. Moreover, we demonstrate that the Poisson-like variability observed in cortex reduces a broad class of Bayesian inference to simple linear combinations of populations of neural activity. These results hold for arbitrary probability distributions over the stimulus, for tuning curves of arbitrary shape and for realistic neuronal variability.

How the brain encodes information in population activity, and how it combines and manipulates that activity as it carries out computations, are questions that lie at the heart of systems neuroscience. During the past decade, with the advent of multi-electrode recording and improved theoretical models, these questions have begun to yield answers. However, a complete understanding of neuronal variability, and, in particular, how it affects population codes, is missing. This is because variability in the brain is typically correlated, and although the exact effects of these correlations are not known, it is known that they can be large. Here, we review studies that address the interaction between neuronal noise and population codes, and discuss their implications for population coding in general.

Decision making often involves the accumulation of information over time, but acquiring information typically comes at a cost. Little is known about the cost incurred by animals and humans for acquiring additional information from sensory variables, due, for instance, to attentional efforts. Through a novel integration of diffusion models and dynamic programming, we were able to estimate the cost of making additional observations per unit of time from two monkeys and six humans in a reaction time random dot motion discrimination task. Surprisingly, we find that, the cost is neither zero nor constant over time, but for the animals and humans features a brief period in which it is constant but increases thereafter. In addition, we show that our theory accurately matches the observed reaction time distributions for each stimulus condition, the time-dependent choice accuracy both conditional on stimulus strength and independent of it, and choice accuracy and mean reaction times as a function of stimulus strength. The theory also correctly predicts that urgency signals in the brain should be independent of the difficulty, or stimulus strength, at each trial.

Computational strategies used by the brain strongly depend on the amount of information that can be stored in population activity, which in turn strongly depends on the pattern of noise correlations. In vivo, noise correlations tend to be positive and proportional to the similarity in tuning properties. Such correlations are thought to limit information, which has led to the suggestion that decorrelation increases information. In contrast, we found, analytically and numerically, that decorrelation does not imply an increase in information. Instead, the only information-limiting correlations are what we refer to as differential correlations: correlations proportional to the product of the derivatives of the tuning curves. Unfortunately, differential correlations are likely to be very small and buried under correlations that do not limit information, making them particularly difficult to detect. We found, however, that the effect of differential correlations on information can be detected with relatively simple decoders.