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Mathematical Aspects of Embodied Intelligence

Tuesday, February 23, 2016
12:00 AM
411 West Hall, 1085 S University Ave

Abstract:

I will propose a causal model of the sensorimotor loop, which allows us to apply various formal tools to the field of embodied intelligence, in particular from information theory, information geometry, and measure theory. I will demonstrate its generality by addressing important subjects of the field and thereby outline corresponding research directions. In particular, I will present recent results on the design of embodied systems with concise control architectures, formalising the notion of "cheap design" within the field of embodied intelligence. This notion highlights the fact that high behavioural complexity, seen from the external observer perspective, does not necessarily imply high control complexity. This complexity gap is a result of two different frames of reference, which is closely related to Uexküll's Umwelt concept. If time allows, I will present a measure-theoretic formalisation of this concept and discuss its implications.   

References:

1. N. Ay. Geometric Design Principles for Brains of Embodied Agents. KI - Künstliche Intelligenz (2015) 29: 389-399. doi: 10.1007/s13218-015-0382-z.

2. N. Ay, W. Löhr. The Umwelt of an Embodied Agent - A Measure-Theoretic Definition. Theory in Biosciences (2015) 134: 105-116. doi: 10.1007/s12064-015-0217-3.

3. G. Montúfar, K. Ghazi-Zahedi, N. Ay. A Theory of Cheap Control in Embodied Systems. PLoS Computational Biology (2015) 11(9): e1004427. doi: 10.1371/journal.pcbi.1004427.

4. G. Montúfar, N. Ay, K. Ghazi-Zahedi. Geometry and Expressive Power of Conditional Restricted Boltzmann Machines. Journal of Machine Learning 16 (2015) 2405-2436.

Link to the project site at the Santa Fe Institute