Learning Numeracy: Binary Arithmetic with Neural Turing Machines

Computer programs are composed of three fundamental mechanisms: elementary operations, logical flow control and memory usage. In the history of neural networks [19] only the use of elementary operations have been extensively explored since so far, but during the last few years the coupling with an external piece of memory is gaining popularity [24]. Neural Turing Machines (NTMs) were developed in 2014 at Google DeepMind Labs [8] in an attempt to couple a neural network with an external memory component in order to improve long-term dependency learning in sequences prediction. Although recurrent neural networks (RNNs) are Turing-complete on their own [20], the difficulties that arise during their training (like the vanishing or the exploding gradient problems [18, 15]) prevented them from being employed in learning more complex tasks, for example algorithmic ones [27]. NTMs derive their name from the analogy with standard Turing Machines (TMs) [22] in addressing an infinite (or at least large enough to be considered so) portion of memory with an attentional mechanism similar to the read/write head of a TM. In contrast to a standard TM, a NTM is a "differentiable computer" that can be trained using gradient descent methods and can therefore learn its own "program" independently (attempts using Neuroevolution [9] and reinforcement learning [26] have also been made). In human brains, the most similar process to an algorithm is the concept of "working memory" [1]: this mechanism allows the brain to rapidly create "variables" [11] by storing short-term information and manipulating them in a rulebased way [17]. The analogy with an algorithm is evident, and a NTM is similar to this process because it can learn tasks in which it is required to manipulate rapidly-created variables. Also the attention mechanism in a NTM is similar to the way the working memory bounds its information in certain slots of memory in the brain [6], despite the fact that a NTM autonomously learns how to do that.