In this article, the authors consider optimal decision making in two-alternative forced-choice (TAFC) tasks. They begin by analyzing 6 models of TAFC decision making and show that all but one can be reduced to the drift diffusion model, implementing the statistically optimal algorithm (most accurate for a given speed or fastest for a given accuracy). They prove further that there is always an optimal trade-off between speed and accuracy that maximizes various reward functions, including reward rate (percentage of correct responses per unit time), as well as several other objective functions, including ones weighted for accuracy. They use these findings to address empirical data and make novel predictions about performance under optimality.

This review article summarises recently proposed theories on how neural circuits in the brain could approximate the error back-propagation algorithm used by artificial neural networks. Computational models implementing these theories achieve learning as efficient as artificial neural networks, but they use simple synaptic plasticity rules based on activity of presynaptic and postsynaptic neurons. The models have similarities, such as including both feedforward and feedback connections, allowing information about error to propagate throughout the network. Furthermore, they incorporate experimental evidence on neural connectivity, responses, and plasticity. These models provide insights on how brain networks might be organised such that modification of synaptic weights on multiple levels of cortical hierarchy leads to improved performance on tasks.

Neurophysiological studies have identified a number of brain regions critically involved in solving the problem of action selection or decision making. In the case of highly practiced tasks, these regions include cortical areas hypothesized to integrate evidence supporting alternative actions and the basal ganglia, hypothesized to act as a central switch in gating behavioral requests. However, despite our relatively detailed knowledge of basal ganglia biology and its connectivity with the cortex and numerical simulation studies demonstrating selective function, no formal theoretical framework exists that supplies an algorithmic description of these circuits. This article shows how many aspects of the anatomy and physiology of the circuit involving the cortex and basal ganglia are exactly those required to implement the computation defined by an asymptotically optimal statistical test for decision making: the multihypothesis sequential probability ratio test (MSPRT). The resulting model of basal ganglia provides a new framework for understanding the computation in the basal ganglia during decision making in highly practiced tasks. The predictions of the theory concerning the properties of particular neuronal populations are validated in existing experimental data. Further, we show that this neurobiologically grounded implementation of MSPRT outperforms other candidates for neural decision making, that it is structurally and parametrically robust, and that it can accommodate cortical mechanisms for decision making in a way that complements those in basal ganglia.

To efficiently learn from feedback, cortical networks need to update synaptic weights on multiple levels of cortical hierarchy. An effective and well-known algorithm for computing such changes in synaptic weights is the error backpropagation algorithm. However, in this algorithm, the change in synaptic weights is a complex function of weights and activities of neurons not directly connected with the synapse being modified, whereas the changes in biological synapses are determined only by the activity of presynaptic and postsynaptic neurons. Several models have been proposed that approximate the backpropagation algorithm with local synaptic plasticity, but these models require complex external control over the network or relatively complex plasticity rules. Here we show that a network developed in the predictive coding framework can efficiently perform supervised learning fully autonomously, employing only simple local Hebbian plasticity. Furthermore, for certain parameters, the weight change in the predictive coding model converges to that of the backpropagation algorithm. This suggests that it is possible for cortical networks with simple Hebbian synaptic plasticity to implement efficient learning algorithms in which synapses in areas on multiple levels of hierarchy are modified to minimize the error on the output.

This paper provides an easy to follow tutorial on the free-energy framework for modelling perception developed by Friston, which extends the predictive coding model of Rao and Ballard. These models assume that the sensory cortex infers the most likely values of attributes or features of sensory stimuli from the noisy inputs encoding the stimuli. Remarkably, these models describe how this inference could be implemented in a network of very simple computational elements, suggesting that this inference could be performed by biological networks of neurons. Furthermore, learning about the parameters describing the features and their uncertainty is implemented in these models by simple rules of synaptic plasticity based on Hebbian learning. This tutorial introduces the free-energy framework using very simple examples, and provides step-by-step derivations of the model. It also discusses in more detail how the model could be implemented in biological neural circuits. In particular, it presents an extended version of the model in which the neurons only sum their inputs, and synaptic plasticity only depends on activity of pre-synaptic and post-synaptic neurons.