Emīls Ozoliņš

Elīza Gaile, Andis Draguns, Emīls Ozoliņš et al.

There has been a growing number of machine learning methods for approximately solving the travelling salesman problem. However, these methods often require solved instances for training or use complex reinforcement learning approaches that need a large amount of tuning. To avoid these problems, we introduce a novel unsupervised learning approach. We use a relaxation of an integer linear program for TSP to construct a loss function that does not require correct instance labels. With variable discretization, its minimum coincides with the optimal or near-optimal solution. Furthermore, this loss function is differentiable and thus can be used to train neural networks directly. We use our loss function with a Graph Neural Network and design controlled experiments on both Euclidean and asymmetric TSP. Our approach has the advantage over supervised learning of not requiring large labelled datasets. In addition, the performance of our approach surpasses reinforcement learning for asymmetric TSP and is comparable to reinforcement learning for Euclidean instances. Our approach is also more stable and easier to train than reinforcement learning.

Karlis Freivalds, Emils Ozolins, Guntis Barzdins

Integer factorization is a famous computational problem unknown whether being solvable in the polynomial time. With the rise of deep neural networks, it is interesting whether they can facilitate faster factorization. We present an approach to factorization utilizing deep neural networks and discrete denoising diffusion that works by iteratively correcting errors in a partially-correct solution. To this end, we develop a new seq2seq neural network architecture, employ relaxed categorical distribution and adapt the reverse diffusion process to cope better with inaccuracies in the denoising step. The approach is able to find factors for integers of up to 56 bits long. Our analysis indicates that investment in training leads to an exponential decrease of sampling steps required at inference to achieve a given success rate, thus counteracting an exponential run-time increase depending on the bit-length.

Ronalds Zakovskis, Andis Draguns, Eliza Gaile et al.

Recurrent neural networks have flourished in many areas. Consequently, we can see new RNN cells being developed continuously, usually by creating or using gates in a new, original way. But what if we told you that gates in RNNs are redundant? In this paper, we propose a new recurrent cell called Residual Recurrent Unit (RRU) which beats traditional cells and does not employ a single gate. It is based on the residual shortcut connection, linear transformations, ReLU, and normalization. To evaluate our cell's effectiveness, we compare its performance against the widely-used GRU and LSTM cells and the recently proposed Mogrifier LSTM on several tasks including, polyphonic music modeling, language modeling, and sentiment analysis. Our experiments show that RRU outperforms the traditional gated units on most of these tasks. Also, it has better robustness to parameter selection, allowing immediate application in new tasks without much tuning. We have implemented the RRU in TensorFlow, and the code is made available at https://github.com/LUMII-Syslab/RRU .

Emils Ozolins, Karlis Freivalds, Andis Draguns et al.

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.

Emīls Ozoliņš, Kārlis Freivalds, Agris Šostaks

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.

Andis Draguns, Emīls Ozoliņš, Agris Šostaks et al.

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.

Kārlis Freivalds, Emīls Ozoliņš, Agris Šostaks

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.