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Convolutional neural networks have become the main tools for processingtwo-dimensional data. They work well for images, yet convolutions have alimited receptive field that prevents its applications to more complex 2Dtasks. We propose a new neural model, called Matrix Shuffle-Exchange network,that can efficiently exploit long-range dependencies in 2D data and hascomparable speed to a convolutional neural network. It is derived from NeuralShuffle-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 iswell-suited for algorithmic and logical reasoning tasks on matrices and densegraphs, exceeding convolutional and graph neural network baselines. Itsdistinct advantage is the capability of retaining full long-range dependencymodelling when generalizing to larger instances - much larger than could beprocessed with models equipped with a dense attention mechanism.

Matrix Shuffle-Exchange Networks for Hard 2D Tasks