*Europhys. Lett.*,

**35**(7), pp. 553-558 (1996)

## Learning in a large committee machine: worst case and average case

Institut für theoretische Physik, Universität Würzburg Am Hubland,
D-97074 Würzburg, Germany

Received:
26
April
1996

Accepted:
5
July
1996

Learning of realizable rules is studied for tree committee machines
with continuous weights. No nontrivial upper bound exists for
the generalization error of consistent students as the number of hidden
units *K* increases. However, numerical considerations show that
consistent students with
a value of the generalization error significantly higher than predicted
by the average-case analysis are extremely hard to find. An on-line
learning algorithm is presented, for which the generalization error scales
with the training set size as in the average-case theory in the limit
of large *K*.

PACS: 87.10.+e – General, theoretical, and mathematical biophysics (including logic of biosystems, quantum biology, and relevant aspects of thermodynamics, information theory, cybernetics, and bionics) / 05.50.+q – Lattice theory and statistics; Ising problems / 64.60.Cn – Order-disorder and statistical mechanics of model systems

*© EDP Sciences, 1996*