Energy Complexity of Recurrent Neural Networks

Abstrakt

Recently, a new so-called energy complexity measure has been introduced and studied for feedforward perceptron networks. This measure is inspired by the fact that biological neurons require more energy to transmit a spike than not to fire, and the activity of neurons in the brain is quite sparse, with only about 1% of neurons firing. In this paper, we investigate the energy complexity of recurrent networks which counts the number of active neurons at any time instant of a computation. We prove that any deterministic finite automaton with m states can be simulated by a neural network of optimal size s=\Theta(\sqrt{m}) with the time overhead of \tau=O(s/e) per one input bit, using the energy O(e), for any e such that e=\Omega(\log s) and e=O(s), which shows the time-energy tradeoff in recurrent networks. In addition, for the time overhead \tau satisfying \tau^\tau=o(s), we obtain the lower bound of s^{c/\tau} on the energy of such a simulation, for some constant c>0 and for infinitely many s.