TY - CONF
TI - Neural Networks, Knowledge and Cognition: A Mathematical Semantic Model Based upon Category Theory
AU - Healy, Michael J.
AU - Caudell, Thomas P.
AB - Category theory can be applied to mathematically model the semantics of cognitive neural systems. We discuss semantics as a hierarchy of concepts, or symbolic descriptions of items sensed and represented in the connection weights distributed throughout a neural network. The hierarchy expresses subconcept relationships, and in a neural network it becomes represented incrementally through a Hebbian-like learning process. The categorical semantic model described here explains the learning process as the derivation of colimits and limits in a concept category. It explains the representation of the concept hierarchy in a neural network at each stage of learning as a system of functors and natural transformations, expressing knowledge coherence across the regions of a multi-regional network equipped with multiple sensors. The model yields design principles that constrain neural network designs capable of the most important aspects of cognitive behavior.
DA - 2004///
PY - 2004
DP - Semantic Scholar
ST - Neural Networks, Knowledge and Cognition
ER -
TY - CONF
TI - Algebraic classifiers: a generic approach to fast cross-validation, online training, and parallel training
AU - Izbicki, Michael
AB - We use abstract algebra to derive new algorithms for fast cross-validation, online learning, and parallel learning. To use these algorithms on a classification model, we must show that the model has appropriate algebraic structure. It is easy to give algebraic structure to some models, and we do this explicitly for Bayesian classifiers and a novel variation of decision stumps called HomStumps. But not all classifiers have an obvious structure, so we introduce the Free HomTrainer. This can be used to give a "generic" algebraic structure to any classifier. We use the Free HomTrainer to give algebraic structure to bagging and boosting. In so doing, we derive novel online and parallel algorithms, and present the first fast cross-validation schemes for these classifiers.
C3 - ICML
DA - 2013///
PY - 2013
DP - Semantic Scholar
ST - Algebraic classifiers
KW - Algebra
KW - Categorical ML
KW - Machine learning
ER -
TY - SLIDE
TI - Linear logic and deep learning
A2 - Murfet, Daniel
A2 - Hu, Huiyi
LA - en
KW - Categorical ML
KW - Linear logic
KW - Machine learning
KW - Semantics
ER -