The development of artificial intelligence systems with advanced reasoning capabilities represents a persistent and long-standing research question. Traditionally, the primary strategy to address this challenge involved the adoption of symbolic approaches, where knowledge was explicitly represented by means of symbols and explicitly programmed rules. However, with the advent of machine learning, there has been a paradigm shift towards systems that can autonomously learn from data, requiring minimal human guidance. In light of this shift, in latest years, there has been increasing interest and efforts at endowing neural networks with the ability to reason, bridging the gap between data-driven learning and logical reasoning. Within this context, Neural Algorithmic Reasoning (NAR) stands out as a promising research field, aiming to integrate the structured and rule-based reasoning of algorithms with the adaptive learning capabilities of neural networks, typically by tasking neural models to mimic classical algorithms. In this dissertation, we provide theoretical and practical contributions to this area of research. We explore the connections between neural networks and tropical algebra, deriving powerful architectures that are aligned with algorithm execution. Furthermore, we discuss and show the ability of such neural reasoners to learn and manipulate complex algorithmic and combinatorial optimization concepts, such as the principle of strong duality. Finally, in our empirical efforts, we validate the real-world utility of NAR networks across different practical scenarios. This includes tasks as diverse as planning problems, large-scale edge classification tasks and the learning of polynomial-time approximate algorithms for NP-hard combinatorial problems. Through this exploration, we aim to showcase the potential integrating algorithmic reasoning in machine learning models.

翻译：人工智能系统具备高级推理能力的发展是一个长期且持续的研究课题。传统上，应对这一挑战的主要策略是采用符号方法，即通过符号和显式编程规则来明确表示知识。然而，随着机器学习的兴起，出现了向能够自主从数据中学习、仅需极少量人类指导的系统的范式转变。基于这一转变，近年来，赋予神经网络推理能力的兴趣和努力日益增长，旨在弥合数据驱动学习与逻辑推理之间的鸿沟。在此背景下，神经算法推理（Neural Algorithmic Reasoning, NAR）作为一个前景广阔的研究领域脱颖而出，其目标是将算法的结构化、基于规则的推理与神经网络的自适应学习能力相结合，通常通过让神经模型模仿经典算法来实现。在本论文中，我们对此研究领域做出了理论和实践贡献。我们探索了神经网络与热带代数之间的联系，推导出与算法执行协同的强大架构。此外，我们讨论并展示了这类神经推理器学习与操作复杂算法及组合优化概念（如强对偶原理）的能力。最后，在实证研究中，我们验证了NAR网络在不同实际场景中的实用性，涵盖从规划问题、大规模边分类任务到为NP难组合问题学习多项式时间近似算法等多种任务。通过这一探索，我们旨在展示将算法推理融入机器学习模型的潜力。