Ff Ur Mathematik in Den Naturwissenschaften Leipzig Homeokinesis { a New Principle to Back up Evolution with Learning Homeokinesis { a New Principle to Back up Evolution with Learning

Homeokinesis – A new principle to back up evolution with learning

It is well known that individual learning can speed up artificial evolution enormously. However both supervised learning and reinforcement learning require specific learning goals which usually are not available or difficult to find. We introduce a new principle – homeokinesis – which is completely unspecific and yet induces specific, seemingly goal–oriented behaviors of an agent in a complex e...

Ff Ur Mathematik in Den Naturwissenschaften Leipzig Hyperplane Arrangements Separating Arbitrary Vertex Classes in N-cubes Hyperplane Arrangements Separating Arbitrary Vertex Classes in N-cubes

Strictly layered feedforward networks with binary neurons are viewed as maps from the vertex set of an n cube to the vertex set of an l cube With only one output neuron in principle they can realize any Boolean function on n inputs We address the problem of determining the necessary and su cient numbers of hidden units for this task by using separability properties of a ne oriented hyperplane a...

F ¨ Ur Mathematik in Den Naturwissenschaften Leipzig

We provide a new proof of a regularity theorem for systems of nonlinear elliptic equations with the quadratic nonlinearity in dimension two.

F ¨ Ur Mathematik in Den Naturwissenschaften Leipzig Power Series Kernels Power Series Kernels

We introduce a class of analytic positive definite multivariate kernels which includes infinite dot product kernels as sometimes used in machine learning, certain new nonlinearly factorizable kernels and a kernel which is closely related to the Gaussian. Each such kernel reproduces in a certain 'native' Hilbert space of multivariate analytic functions. If functions from this space are interpola...

F Ur Mathematik in Den Naturwissenschaften Leipzig Interacting Quantum Fields on a Curved Background