Generative Cognitive Representation for Embodied Agents

Symmetry (similarity under transformation) in sensorimotor data streams can be used to derive and represent concepts from percepts, and exploit them in a cognitive framework. This entails finding mechanisms to extract symmetries out of sensorimotor data and convert them into intuitive representations; ”intuitive” implying that the representations created should have a semantic meaning to them. We design these concepts in an object-oriented framework. These concepts, known as wreath product comprise of a control group that acts on a fiber group, and are generative concepts in that they encode not only the symmetry information, but also the process employed to achieve those symmetries. Moreover, probabilistic information can be added to these wreath products in the form of Bayesian networks for quantifying uncertainty in the data and for inference and generalization, which would help the agent achieve tasks requiring cognitive abilities in the real world. In this paper we present the theory behind such a cognitive framework, propose and implement design of concepts from sensor data, and demonstrate this approach on data collected from Kinect. Keywords—Robot Cognition, Symmetry analysis, Wreath Product, Generative Representation.