Integrating domain knowledge in data-driven AI approaches

Machine Learning (ML) continues to revolutionize various fields, achieving significant advancements across domains such as computer vision, game AI, natural language processing, and speech recognition. However, purely data-driven models face limitations, particularly in scenarios with insufficient data or applications bound by critical constraints, such as regulatory standards or security guidelines. Moreover, there is an increasing demand for interpretable and explainable models in socially sensitive domains like healthcare and education. Integrating prior knowledge into ML models has emerged as a promising approach to address these challenges. Traditionally, this has been achieved through labeling or feature engineering, but recent trends focus on incorporating formal knowledge representations to improve model robustness and performance. In this thesis, we explore the integration of two distinct forms of knowledge representation: logic rules and dynamical systems. First, we examine the advantages of logic-based reasoning for generative tasks by developing the first neuro-symbolic generative model that integrates probabilistic logic programming into variational autoencoders. This approach significantly differs from existing neuro-symbolic methods, which predominantly focus on discriminative tasks. Second, we investigate the integration of dynamical systems into ML models, particularly in the context of automated ranking tasks, by modeling the evolution of fairness and quality metrics as a dynamical system. Additionally, we conduct a comprehensive analysis of an existing framework that combines ML with differential equations. This thesis's contributions are supported by theoretical foundations and validated through experimental results, demonstrating the efficacy of integrating formal knowledge representations into data-driven AI approaches.