Neural Algorithmic Reasoning with Multiple Correct Solutions

Zeno Kujawa, John Poole, Dobrik Georgiev, Danilo Numeroso, Pietro Liò
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Abstract

Neural Algorithmic Reasoning (NAR) aims to optimize classical algorithms. However, canonical implementations of NAR train neural networks to return only a single solution, even when there are multiple correct solutions to a problem, such as single-source shortest paths. For some applications, it is desirable to recover more than one correct solution. To that end, we give the first method for NAR with multiple solutions. We demonstrate our method on two classical algorithms: Bellman-Ford (BF) and Depth-First Search (DFS), favouring deeper insight into two algorithms over a broader survey of algorithms. This method involves generating appropriate training data as well as sampling and validating solutions from model output. Each step of our method, which can serve as a framework for neural algorithmic reasoning beyond the tasks presented in this paper, might be of independent interest to the field and our results represent the first attempt at this task in the NAR literature.
具有多个正确解决方案的神经算法推理
神经算法推理(NAR)旨在优化经典算法。然而,NAR 的典型实现训练神经网络只返回单一解,即使问题有多个正确解,如单源最短路径。对于某些应用来说,最好能恢复不止一个正确解。为此,我们给出了第一种多解 NAR 方法。我们在两个经典算法上演示了我们的方法:贝尔曼-福德算法(Bellman-Ford,BF)和深度优先搜索算法(Depth-First Search,DFS)。这种方法涉及生成适当的训练数据,以及从模型输出中采样和验证解决方案。我们方法的每一步都可以作为神经算法推理的框架,超越本文提出的任务,可能会引起该领域的独立兴趣,而我们的结果代表了 NAR 文献中对这一任务的首次尝试。
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