Modern neural networks obtain information about the problem and calculate the output solely from the input values. We argue that it is not always optimal, and the network's performance can be significantly improved by augmenting it with a query mechanism that allows the network at run time to make several solution trials and get feedback on the loss value on each trial. To demonstrate the capabilities of the query mechanism, we formulate an unsupervised (not depending on labels) loss function for Boolean Satisfiability Problem (SAT) and theoretically show that it allows the network to extract rich information about the problem. We then propose a neural SAT solver with a query mechanism called QuerySAT and show that it outperforms the neural baseline on a wide range of SAT tasks.

Attention is a commonly used mechanism in sequence processing, but it is of O(n^2) complexity which prevents its application to long sequences. The recently introduced neural Shuffle-Exchange network offers a computation-efficient alternative, enabling the modelling of long-range dependencies in O(n log n) time. The model, however, is quite complex, involving a sophisticated gating mechanism derived from the Gated Recurrent Unit. In this paper, we present a simple and lightweight variant of the Shuffle-Exchange network, which is based on a residual network employing GELU and Layer Normalization. The proposed architecture not only scales to longer sequences but also converges faster and provides better accuracy. It surpasses the Shuffle-Exchange network on the LAMBADA language modelling task and achieves state-of-the-art performance on the MusicNet dataset for music transcription while being efficient in the number of parameters. We show how to combine the improved Shuffle-Exchange network with convolutional layers, establishing it as a useful building block in long sequence processing applications.

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 O(log N) layers and O(N ^ 2 log N) total time and O(N^2) space complexity for processing a NxN 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.

A key requirement in sequence to sequence processing is the modeling of long range dependencies. To this end, a vast majority of the state-of-the-art models use attention mechanism which is of O(n^2) complexity that leads to slow execution for long sequences. We introduce a new Shuffle-Exchange neural network model for sequence to sequence tasks which have O(log n) depth and O(n log n) total complexity. We show that this model is powerful enough to infer efficient algorithms for common algorithmic benchmarks including sorting, addition and multiplication. We evaluate our architecture on the challenging LAMBADA question answering dataset and compare it with the state-of-the-art models which use attention. Our model achieves competitive accuracy and scales to sequences with more than a hundred thousand of elements. We are confident that the proposed model has the potential for building more efficient architectures for processing large interrelated data in language modeling, music generation and other application domains.