Cogito, ergo maxplus: ¿es nuestro pensamiento idempotente?
Funded by MINECO (Ministry of Economy and Competitiveness)
TEC2014-61729-EXP (Convocatoria 2014 de Proyectos de I+D del Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia)
Sep. 2015 – Ago. 2017
idempotency, cognition, perception, saliency, cognitive computing, formal concept, biclustering
Philosopher, mathematician and physicist, his transversal thought turned him into the father of modern philosophy and analytic or cartesian geometry. With his most famous statement “I think, therefore I am”, Descartes laid the foundation of European rationalism whereby the ego is the cornerstone on which our certainty of the world we perceive relies.
In this proposal, we dare to hypothesize that cognition does not obey the cartesian geometry and that our knowledge of the world, shaped by human perception, draws a geometry derived from idempotent algebra. Under this perspective, crucial notions as orthogonality or the combination or accumulation of stimuli should be reconsidered. In sum, we question whether for the emulation of human perception we should use a radically different mathematical setting to program machines.
Strong evidence of the unsuitability of conventional algebra for modeling the acquisition and processing of sensory information can be found, for example, in the employment of maximum operations, oftentimes understood as a lossy simplification that could be, in reality, a way of focalizing attention selecting the most relevant or salient stimuli. We also find examples in the well-known Viterbi optimization method, mathematical morphology based preprocessing tools, max-pooling and winner-take-all strategies in artificial vision and neural networks, log-log representations of cognitive phenomena like speech perception, etc.
This paradigm shift will have important consequences in the processing of most signals like speech, image or video as well as on others not that widespread like haptic, smell or taste.
Methodologically, rather than trying to produce exact models of human perception under the idempotent algebra light, we will take a technological viewpoint and assess the improvements on an automatic determination of visual saliency.
- Francisco J. Valverde-Albacete, Carmen Peláez-Moreno, The spectra of irreducible matrices over completed idempotent semifields, Fuzzy Sets and Systems, Volume 271, 15 July 2015, Pages 46-69, ISSN 0165-0114, http://dx.doi.org/10.1016/j.fss.2014.09.022.