Low-rank forward models: A path to the self-organization of visuo-motor systems

Sensorimotor coupling is ubiquitous in living organisms. Sensory and motor systems are utterly useless if left without the presence of the other. One crucial faculty that organisms have developed with tremendous ecological advantages is the ability to discern between the origins of perceptual input as being originated by the environment or the organism itself, provided by resource efficient sensor and motor systems. This ability has been shown to be implemented through a specialized circuit (forward model) receiving a copy of the motor command (corollary discharge). We propose a fast method to derive a resource constrained forward model by framing sensorimotor coupling as a low-rank approximation of an overly detailed forward model. By framing the problem as a factorization approach we can resort to currently available off-the-shelf solvers for matrix factorization. We experimentally show that by solving the problem as a low-rank approximation we obtain more than an order of magnitude speed up relatively to minimizing the objective function with gradient descent methods. The development of resource constrained and ecologically adapted sensorimotor systems is essential for the deployment of low-cost energy efficient autonomous robots for the execution of specific tasks in particular environments.