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Computer Science and Engineering Faculty Publications

Neural-Symbolic Integration

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10302 Summary - Learning Paradigms In Dynamic Environments, Barbara Hammer, Pascal Hitzler Jul 2010

10302 Summary - Learning Paradigms In Dynamic Environments, Barbara Hammer, Pascal Hitzler

Computer Science and Engineering Faculty Publications

The seminar centered around problems which arise in the context of machine learning in dynamic environments. Particular emphasis was put on a couple of specific questions in this context: how to represent and abstract knowledge appropriately to shape the problem of learning in a partially unknown and complex environment and how to combine statistical inference and abstract symbolic representations; how to infer from few data and how to deal with non i.i.d. data, model revision and life-long learning; how to come up with efficient strategies to control realistic environments for which exploration is costly, the dimensionality is high and data …


Logic Programs, Iterated Function Systems, And Recurrent Radial Basis Function Networks, Sebastian Bader, Pascal Hitzler Sep 2004

Logic Programs, Iterated Function Systems, And Recurrent Radial Basis Function Networks, Sebastian Bader, Pascal Hitzler

Computer Science and Engineering Faculty Publications

Graphs of the single-step operator for first-order logic programs—displayed in the real plane—exhibit self-similar structures known from topological dynamics, i.e., they appear to be fractals, or more precisely, attractors of iterated function systems. We show that this observation can be made mathematically precise. In particular, we give conditions which ensure that those graphs coincide with attractors of suitably chosen iterated function systems, and conditions which allow the approximation of such graphs by iterated function systems or by fractal interpolation. Since iterated function systems can easily be encoded using recurrent radial basis function networks, we eventually obtain connectionist systems which …