Coherent Concepts, Robust Learning

We study learning scenarios in which multiple learners are involved and “nature” imposes some constraints that force the predictions of these learners to behave coherently. This is natural in cognitive learning situations, where multiple learning problems co-exist but their predictions are constrained to produce a valid sentence, image or any other domain representation. Our theory addresses two fundamental issues in computational learning: (1) The apparent ease at which cognitive systems seem to learn concepts, relative to what is predicted by the theoretical models, and (2) The robustness of learnable concepts to noise in their input. This type of robustness is very important in cognitive systems, where multiple concepts are learned and cascaded to produce more and more complex features. Existing models of concept learning are extended by requiring the target concept to cohere with other concepts from the concept class. The coherency is expressed via a (Boolean) constraint that the concepts have to satisfy. We show how coherency can lead to improvements in the complexity of learning and to increased robustness of the learned hypothesis.