Space coding for sensorimotor transformations can emerge through unsupervised learning

Michele De Filippo De Grazia, Simone Cutini, Matteo Lisi, Marco Zorzi

The posterior parietal cortex (PPC) is fundamental for sensorimotor transformations because it combines multiple sensory inputs and posture signals into different spatial reference frames that drive motor programming. Here, we present a computational model mimicking the sensorimotor transformations occurring in the PPC. A recurrent neural network with one layer of hidden neurons (restricted Boltzmann machine) learned a stochastic generative model of the sensory data without supervision. After the unsupervised learning phase, the activity of the hidden neurons was used to compute a motor program (a population code on a bidimensional map) through a simple linear projection and delta rule learning. The average motor error, calculated as the difference between the expected and the computed output, was less than 3°. Importantly, analyses of the hidden neurons revealed gain-modulated visual receptive fields, thereby showing that space coding for sensorimotor transformations similar to that observed in the PPC can emerge through unsupervised learning. These results suggest that gain modulation is an efficient coding strategy to integrate visual and postural information toward the generation of motor commands.