Dual Algorithmic Reasoning

TL;DR

This paper introduces a dual learning approach for neural algorithmic reasoning, leveraging the duality of optimization problems like max-flow and min-cut to improve learning and solution quality, demonstrated on synthetic graphs and a brain vessel classification task.

Contribution

It proposes a novel dual algorithmic reasoning method that jointly learns dual algorithms, enhancing performance on complex problems and real-world applications.

Findings

Joint learning of dual algorithms improves accuracy.

The approach outperforms single-algorithm models on synthetic data.

Demonstrates significant performance gains in brain vessel classification.

Abstract

Neural Algorithmic Reasoning is an emerging area of machine learning which seeks to infuse algorithmic computation in neural networks, typically by training neural models to approximate steps of classical algorithms. In this context, much of the current work has focused on learning reachability and shortest path graph algorithms, showing that joint learning on similar algorithms is beneficial for generalisation. However, when targeting more complex problems, such similar algorithms become more difficult to find. Here, we propose to learn algorithms by exploiting duality of the underlying algorithmic problem. Many algorithms solve optimisation problems. We demonstrate that simultaneously learning the dual definition of these optimisation problems in algorithmic learning allows for better learning and qualitatively better solutions. Specifically, we exploit the max-flow min-cut theorem to simultaneously learn these two algorithms over synthetically generated graphs, demonstrating the effectiveness of the proposed approach. We then validate the real-world utility of our dual algorithmic reasoner by deploying it on a challenging brain vessel classification task, which likely depends on the vessels' flow properties. We demonstrate a clear performance gain when using our model within such a context, and empirically show that learning the max-flow and min-cut algorithms together is critical for achieving such a result.