Learning with Slight Forgetting Optimizes Sensorimotor Transformation in Redundant Motor Systems

Recent theoretical studies have proposed that the redundant motor system in humans achieves well-organized stereotypical movements by minimizing motor effort cost and motor error. However, it is unclear how this optimization process is implemented in the brain, presumably because conventional schemes have assumed a priori that the brain somehow constructs the optimal motor command, and largely ignored the underlying trial-by-trial learning process. In contrast, recent studies focusing on the trial-by-trial modification of motor commands based on error information suggested that forgetting (i.e., memory decay), which is usually considered as an inconvenient factor in motor learning, plays an important role in minimizing the motor effort cost. Here, we examine whether trial-by-trial error-feedback learning with slight forgetting could minimize the motor effort and error in a highly redundant neural network for sensorimotor transformation and whether it could predict the stereotypical activation patterns observed in primary motor cortex (M1) neurons. First, using a simple linear neural network model, we theoretically demonstrated that: 1) this algorithm consistently leads the neural network to converge at a unique optimal state; 2) the biomechanical properties of the musculoskeletal system necessarily determine the distribution of the preferred directions (PD; the direction in which the neuron is maximally active) of M1 neurons; and 3) the bias of the PDs is steadily formed during the minimization of the motor effort. Furthermore, using a non-linear network model with realistic musculoskeletal data, we demonstrated numerically that this algorithm could consistently reproduce the PD distribution observed in various motor tasks, including two-dimensional isometric torque production, two-dimensional reaching, and even three-dimensional reaching tasks. These results may suggest that slight forgetting in the sensorimotor transformation network is responsible for solving the redundancy problem in motor control.