The role of interpretable neural architectures: from image classification to neural fields

Neural networks have demonstrated outstanding capabilities, surpassing human expertise across diverse tasks. Despite these advances, their widespread adoption is hindered by the complexity of interpreting their decision-making processes. This lack of transparency raises concerns in critical areas such as autonomous mobility, digital security, and healthcare. This thesis addresses the critical need for more interpretable and efficient neural-based technologies, aiming to enhance their transparency and lower their memory footprint. In the first part of this thesis we introduce Agglomerator and Agglomerator++, two frameworks that embody the principles of hierarchical representation to improve the understanding and interpretability of neural networks. These models aim to bridge the cognitive gap between human visual perception and computational models, effectively enhancing the capability of neural networks to dynamically represent complex data. The second part of the manuscript focuses on addressing the lack of spatial coherency and thereby efficiency of the latest fast-training neural field representations. To address this limitation we propose Lagrangian Hashing, a novel method that combines the efficiency of Eulerian grid-based representations with the spatial flexibility of Lagrangian point-based systems. This method extends the foundational work of hierarchical hashing, allowing for an adaptive allocation of the representation budget. In this way we effectively preserve the coherence of the neural structure with respect to the reconstructed 3D space. Within the context of 3D reconstruction we also conduct a comparative evaluation of the NeRF based reconstruction methodologies against traditional photogrammetry, to assess their usability in practical, real-world settings.