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6 x 9, illustrated
ISSN
0899-7667
E-ISSN
1530-888X
2014 Impact factor:
2.21

Neural Computation

December 2015, Vol. 27, No. 12, Pages 2623-2660
(doi: 10.1162/NECO_a_00789)
© 2015 Massachusetts Institute of Technology
Positive Neural Networks in Discrete Time Implement Monotone-Regular Behaviors
Article PDF (348.09 KB)
Abstract

We study the expressive power of positive neural networks. The model uses positive connection weights and multiple input neurons. Different behaviors can be expressed by varying the connection weights. We show that in discrete time and in the absence of noise, the class of positive neural networks captures the so-called monotone-regular behaviors, which are based on regular languages. A finer picture emerges if one takes into account the delay by which a monotone-regular behavior is implemented. Each monotone-regular behavior can be implemented by a positive neural network with a delay of one time unit. Some monotone-regular behaviors can be implemented with zero delay. And, interestingly, some simple monotone-regular behaviors cannot be implemented with zero delay.