Learning Simple Algorithms from Examples

We present an approach for learning simple algorithms such as copying, multi-digit addition and single digit multiplication directly from examples. Our framework consists of a set of interfaces, accessed by a controller. Typical interfaces are 1-D tapes or 2-D grids that hold the input and output data. For the controller, we explore a range of neural network-based models which vary in their ability to abstract the underlying algorithm from training instances and generalize to test examples with many thousands of digits. The controller is trained using $Q$-learning with several enhancements and we show that the bottleneck is in the capabilities of the controller rather than in the search incurred by $Q$-learning.