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.

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.

There is strong behavioral and physiological evidence that the brain both represents probability distributions and performs probabilistic inference. Computational neuroscientists have started to shed light on how these probabilistic representations and computations might be implemented in neural circuits. One particularly appealing aspect of these theories is their generality: they can be used to model a wide range of tasks, from sensory processing to high-level cognition. To date, however, these theories have only been applied to very simple tasks. Here we discuss the challenges that will emerge as researchers start focusing their efforts on real-life computations, with a focus on probabilistic learning, structural learning and approximate inference.

When making a decision, one must first accumulate evidence, often over time, and then select the appropriate action. Here, we present a neural model of decision making that can perform both evidence accumulation and action selection optimally. More specifically, we show that, given a Poisson-like distribution of spike counts, biological neural networks can accumulate evidence without loss of information through linear integration of neural activity, and can select the most likely action through attractor dynamics. This holds for arbitrary correlations, any tuning curves, continuous and discrete variables, and sensory evidence whose reliability varies over time. Our model predicts that the neurons in the lateral intraparietal cortex involved in evidence accumulation encode, on every trial, a probability distribution which predicts the animal’s performance. We present experimental evidence consistent with this prediction, and discuss other predictions applicable to more general settings.

Behavior varies from trial to trial even when the stimulus is maintained as constant as possible. In many models, this variability is attributed to noise in the brain. Here, we propose that there is another major source of variability: suboptimal inference. Importantly, we argue that in most tasks of interest, and particularly complex ones, suboptimal inference is likely to be the dominant component of behavioral variability. This perspective explains a variety of intriguing observations, including why variability appears to be larger on the sensory than on the motor side, and why our sensors are sometimes surprisingly unreliable.

A wide range of computations performed by the nervous system involves a type of probabilistic inference known as marginalization. This computation comes up in seemingly unrelated tasks, including causal reasoning, odor recognition, motor control, visual tracking, coordinate transformations, visual search, decision making, and object recognition, to name just a few. The question we address here is: how could neural circuits implement such marginalizations? We show that when spike trains exhibit a particular type of statistics – associated with constant Fano factors and gain-invariant tuning curves, as is often reported in vivo – some of the more common marginalizations can be achieved with networks that implement a quadratic nonlinearity and divisive normalization, the latter being a type of nonlinear lateral inhibition that has been widely reported in neural circuits. Previous studies have implicated divisive normalization in contrast gain control and attentional modulation. Our results raise the possibility that it is involved in yet another, highly critical, computation: near optimal marginalization in a remarkably wide range of tasks.

The ability to search efficiently for a target in a cluttered environment is one of the most remarkable functions of the nervous system. This task is difficult under natural circumstances, as the reliability of sensory information can vary greatly across space and time and is typically a priori unknown to the observer. In contrast, visual-search experiments commonly use stimuli of equal and known reliability. In a target detection task, we randomly assigned high or low reliability to each item on a trial-by-trial basis. An optimal observer would weight the observations by their trial-to-trial reliability and combine them using a specific nonlinear integration rule. We found that humans were near-optimal, regardless of whether distractors were homogeneous or heterogeneous and whether reliability was manipulated through contrast or shape. We present a neural-network implementation of near-optimal visual search based on probabilistic population coding. The network matched human performance.

The anterior cingulate and lateral prefrontal cortices have been implicated in implementing context-appropriate attentional control, but the learning mechanisms underlying our ability to flexibly adapt the control settings to changing environments remain poorly understood. Here we show that human adjustments to varying control demands are captured by a reinforcement learner with a flexible, volatility-driven learning rate. Using model-based functional magnetic resonance imaging, we demonstrate that volatility of control demand is estimated by the anterior insula, which in turn optimizes the prediction of forthcoming demand in the caudate nucleus. The caudate's prediction of control demand subsequently guides the implementation of proactive and reactive attentional control in dorsal anterior cingulate and dorsolateral prefrontal cortices. These data enhance our understanding of the neuro-computational mechanisms of adaptive behaviour by connecting the classic cingulate-prefrontal cognitive control network to a subcortical control-learning mechanism that infers future demands by flexibly integrating remote and recent past experiences.