Positive Neural Networks in Discrete Time Implement Monotone-Regular Behaviors
This work provides theoretical insights into neural network expressiveness for researchers in computational theory and machine learning, but it is incremental as it builds on known concepts of monotone-regular behaviors.
The paper tackled the problem of characterizing the expressive power of positive neural networks in discrete time, showing that they capture monotone-regular behaviors based on regular languages, with some behaviors implementable with zero delay and others requiring a delay of one time unit.
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 absence of noise, the class of positive neural networks captures the so-called monotone-regular behaviors, that 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 can not be implemented with zero delay.