Learning abstract perceptual notions: The example of space

Abstract

Humans are extremely swift learners. We are able to grasp highly abstract notions, whether they come from art perception or pure mathematics. Current machine learning techniques demonstrate astonishing results in extracting patterns in information. Yet the abstract notions we possess are more than just statistical patterns in the incoming information. Sensorimotor theory suggests that they represent functions, laws, describing how the information can be transformed, or, in other words, they represent the statistics of sensorimotor changes rather than sensory inputs themselves. The aim of our work is to suggest a way for machine learning and sensorimotor theory to benefit from each other so as to pave the way toward new horizons in learning. We show in this study that a highly abstract notion, that of space, can be seen as a collection of laws of transformations of sensory information and that these laws could in theory be learned by a naive agent. As an illustration we do a one-dimensional simulation in which an agent extracts spatial knowledge in the form of internalized ("sensible") rigid displacements. The agent uses them to encode its own displacements in a way which is isometrically related to external space. Though the algorithm allowing acquisition of rigid displacements is designed ad hoc, we believe it can stimulate the development of unsupervised learning techniques leading to similar results.

Acquisition of a space representation by a naive agent from sensorimotor invariance and proprioceptive compensation

“…Making this distinction allows the set of ' T to map specific transformations T unambiguously. Initially, the ' T functions were proposed by Terekhov et al 13,14 They are built from a catalog of all compensable transformations the agent detects. By matching identical sensory inputs before a change and after compensation, ' T functions map proprioception observed before a change to proprioception observed after the compensation.…”

“…For a given displacement T of the environment, the agent will recover the same function ' T for both different initial positions and different environments. As shown by Terekhov and O'Regan, 14 the functions ' T provide the agent with the notion of space.…”

“…That is, how does it determine that they compensate for the same unknown external compensable transformation T ? Terekhov and O'Regan proposed a solution 14 whereby they collected all the agent compensations corresponding to the same external transformation T and repeated for all other values of T . However, as the agent itself does not have access to T , this solution is somewhat artificial.…”

“…Terekov has used a similar model to retrieve the metric. 14 While the agent did not have any a priori knowledge of its body or environment, we made some assumptions about the mathematical functions of the model such as the bijectivity and invertibility of the functions Å and for the retina and foot proprioceptives states. Another assumption that we made was that the foot displacement was unbounded.…”

Unsupervised model-free camera calibration algorithm for robotic applications

“…This method is inspired by work in developmental robotic on the emergence of the concept of space in naïve agents [10], [11]. In particular, two works by Terekhov and O'Regan [12], [13] show how a naïve robot equipped with a simple visual system can be able to measure what physicists commonly call rigid displacements. The key characteristics of Terekhov and O'Regan's algorithm and its main difference from that of Kuipers, is the importance given to camera movements.…”