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Multilayer Neural Networks and Polyhedral Dichotomies
, 1997
"... We study the number of hidden layers required by a multilayer neural network with threshold units to compute a dichotomy f from R d to f0; 1g, defined by a finite set of hyperplanes. We show that this question is far more intricate than computing Boolean functions, although this wellknown problem ..."
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We study the number of hidden layers required by a multilayer neural network with threshold units to compute a dichotomy f from R d to f0; 1g, defined by a finite set of hyperplanes. We show that this question is far more intricate than computing Boolean functions, although this well
Advances for Exact Resolution of Polyhedral Dichotomies By Multilayer Neural Networks
"... We study the number of hidden layers required by a multilayer neural network with threshold units to compute a dichotomy from R d to f0; 1g, defined by a finite set of hyperplanes. We show that this question is far more intricate than computing Boolean functions, although this wellknown problem i ..."
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We study the number of hidden layers required by a multilayer neural network with threshold units to compute a dichotomy from R d to f0; 1g, defined by a finite set of hyperplanes. We show that this question is far more intricate than computing Boolean functions, although this wellknown problem
Some Remarks on the covolume of Lattices Acting on a Product of Trees.
, 1997
"... this paper show that if \Gamma ! Aut(\Delta) is an irreducible locally primitive lattice and X is covered by a product of two trees. Then one of the following holds: ffl \Gamma = 1 (X; oe 0 ). ffl X is a square. This gives a minimal covolume theorem for a certain subset of all locally primitive ..."
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irreducible lattices acting on a product of two regular trees of prime valence. The minimal volume theorem is stated and proved in section 6. In Sections 2, 3 We develop the technical BassSerre theoretic background used in section 4 to prove the dichotomy theorem mentioned above. I believe that it is true