A Systematic Review of Topological Representations for Interpretable Machine Learning Models: Methods, Architectures, and Future Research Directions

Abstract

Interpretable machine learning (IML) has become a critical area of research as complex models such as deep neural networks increasingly influence high-stakes decision-making domains. However, the black-box nature of many machine learning models limits transparency, trust, and regulatory compliance. Topological representations, particularly those derived from Topological Data Analysis (TDA), have emerged as powerful tools for enhancing interpretability by capturing intrinsic geometric and structural properties of data. This paper presents a systematic review of topological representations used in interpretable machine learning models, analysing 30 studies published between 2018 and 2023. The review focuses on key methods such as persistent homology, Mapper algorithms, simplicial complexes, and topological feature extraction techniques. It also examines architectural integrations where topology is combined with machine learning frameworks, including deep learning, graph neural networks, and hybrid interpretable systems. The findings reveal that topological representations provide robust, noise-resistant, and scale-invariant features that improve both interpretability and model generalization. However, challenges remain in computational complexity, scalability to high-dimensional datasets, and integration with modern deep learning pipelines. The study identifies emerging trends such as differentiable topology, explainable AI integration, and real-time topological learning. Future research directions include scalable TDA pipelines, hybrid symbolic-topological models, and domain-specific interpretability frameworks.