18,966 research outputs found
Phase transitions in soft-committee machines
Equilibrium statistical physics is applied to layered neural networks with
differentiable activation functions. A first analysis of off-line learning in
soft-committee machines with a finite number (K) of hidden units learning a
perfectly matching rule is performed. Our results are exact in the limit of
high training temperatures. For K=2 we find a second order phase transition
from unspecialized to specialized student configurations at a critical size P
of the training set, whereas for K > 2 the transition is first order. Monte
Carlo simulations indicate that our results are also valid for moderately low
temperatures qualitatively. The limit K to infinity can be performed
analytically, the transition occurs after presenting on the order of N K
examples. However, an unspecialized metastable state persists up to P= O (N
K^2).Comment: 8 pages, 4 figure
Multilayered feed forward Artificial Neural Network model to predict the average summer-monsoon rainfall in India
In the present research, possibility of predicting average summer-monsoon
rainfall over India has been analyzed through Artificial Neural Network models.
In formulating the Artificial Neural Network based predictive model, three
layered networks have been constructed with sigmoid non-linearity. The models
under study are different in the number of hidden neurons. After a thorough
training and test procedure, neural net with three nodes in the hidden layer is
found to be the best predictive model.Comment: 19 pages, 1 table, 3 figure
Equations of States in Statistical Learning for a Nonparametrizable and Regular Case
Many learning machines that have hierarchical structure or hidden variables
are now being used in information science, artificial intelligence, and
bioinformatics. However, several learning machines used in such fields are not
regular but singular statistical models, hence their generalization performance
is still left unknown. To overcome these problems, in the previous papers, we
proved new equations in statistical learning, by which we can estimate the
Bayes generalization loss from the Bayes training loss and the functional
variance, on the condition that the true distribution is a singularity
contained in a learning machine. In this paper, we prove that the same
equations hold even if a true distribution is not contained in a parametric
model. Also we prove that, the proposed equations in a regular case are
asymptotically equivalent to the Takeuchi information criterion. Therefore, the
proposed equations are always applicable without any condition on the unknown
true distribution
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