A Neural Network Analogue of the Mammalian Local Cortical Circuit Implements Optimal Kalman Prediction and Control

The local cortical circuit (LCC) is a fundamental unit of mammalian neural processing found in neocortical areas subserving diverse sensory, motor, and other functions. A central challenge for neuroscience is to understand what core processing functions the LCC performs. Prediction, the estimation or inference of missing or noisy sensory data, and the goal-driven generation of control signals are important functions of biological brains. Kalman's classical solutions of the optimal estimation and control problems in simple linear systems, and their extensions, have been widely used in engineering for 45 years. It has been speculated that neural circuitry implementing solutions related to Kalman's might be important for enabling sensory processing and motor control, but no neural circuit and algorithm for the general Kalman solution has previously been described. Here we show how optimal Kalman estimation and control are learned and executed by a neural network having simple computational elements. The circuit architecture implied by this algorithm is similar in several ways to recurrent neural circuits in brain, and to LCC architecture in particular. These results suggest that the core functions of the LCC may include those of estimation (including prediction) and control, including more sophisticated nonlinear and context-dependent methods beyond Kalman's solutions, and that LCC studies may be guided by these connections between biological and engineering design. Conversely, further analysis of LCC circuitry and function may lead to advances in nonlinear estimation and control for engineering applications.