TU Chemnitz, Fakultät für Mathematik: Fakultät für Mathematik
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Walter Wenzel; Nihat Ay; Frank Pasemann : Hyperplane Arrangements Separating Arbitrary Vertex Classes in n-Cubes
- Author(s) :
- Walter Wenzel; Nihat Ay; Frank Pasemann
- Title :
- Hyperplane Arrangements Separating Arbitrary Vertex Classes in n-Cubes
- Preprint series
- Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 99-6, 1999
- Mathematics Subject Classification :
- 05B25 [ Finite geometries (combinatorics)
]
- 51D20 [ Combinatorial geometries ]
- 52B30 [ Arrangements of hyperplanes (convex geometry) ]
- 54A20 [ Convergence in general topology ]
- 92B20 [ General theory of neural networks ]
- 51D20 [ Combinatorial geometries ]
- Abstract :
- 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;
these maps are induced by hyperplane arrangements
consisting of l hyperplanes and separating
some given vertex set of the n-cube in some sense.
We prove that l grows exponentially with n.
- Keywords :
- Feedforward Networks, Binary Units, Classification Problems, Hypercube, Separability, Affine Oriented Hyperplane Arrangements, Linear Codes
- Language :
- english
- Publication time :
- 5/1999
