Towards Modular Algorithm Induction

We present a modular neural network architecture Main that learns algorithms given a set of input-output examples. Main consists of a neural controller that interacts with a variable-length input tape and learns to compose modules together with their corresponding argument choices. Unlike previous approaches, Main uses a general domain-agnostic mechanism for selection of modules and their arguments. It uses a general input tape layout together with a parallel history tape to indicate most recently used locations. Finally, it uses a memoryless controller with a length-invariant self-attention based input tape encoding to allow for random access to tape locations. The Main architecture is trained end-to-end using reinforcement learning from a set of input-output examples. We evaluate Main on five algorithmic tasks and show that it can learn policies that generalizes perfectly to inputs of much longer lengths than the ones used for training.Comment: 10 pages, 4 figures, 2 table

Matrix Shuffle-Exchange Networks for Hard 2D Tasks

Convolutional neural networks have become the main tools for processing two-dimensional data. They work well for images, yet convolutions have a limited receptive field that prevents its applications to more complex 2D tasks. We propose a new neural model, called Matrix Shuffle-Exchange network, that can efficiently exploit long-range dependencies in 2D data and has comparable speed to a convolutional neural network. It is derived from Neural Shuffle-Exchange network and has $\mathcal{O}( \log{n})$ layers and $\mathcal{O}( n^2 \log{n})$ total time and space complexity for processing a $n \times n$ data matrix. We show that the Matrix Shuffle-Exchange network is well-suited for algorithmic and logical reasoning tasks on matrices and dense graphs, exceeding convolutional and graph neural network baselines. Its distinct advantage is the capability of retaining full long-range dependency modelling when generalizing to larger instances - much larger than could be processed with models equipped with a dense attention mechanism