Advancing randomized neural networks: interpretability, robustness, expressivity and scalability

Abstract

Can the predictive power of deep learning be achieved without its computational burden and training instability? This thesis addresses this question through the systematic advancement of Randomized Neural Networks (RdNNs), a theoretically grounded learning framework in which hidden-layer parameters are randomly assigned and fixed, reducing the learning problem to a closed-form solution for the output weights alone. This design eliminates iterative gradient-based optimization entirely, yielding fast training, guaranteed global optimality, and freedom from the hardware demands characteristic of conventional deep learning, while retaining universal approximation capability. This thesis advances shallow, broad, deep, and ensemble RdNN architectures along four fundamental and interconnected directions. First, to address the inherent opacity of randomized architectures, interpretability is systematically embedded into the Random Vector Functional Link (RVFL) network and its ensemble deep variants through neuro-fuzzy integrations that encode human-readable IF-THEN fuzzy rules within the learning process, enabling transparent and auditable decision-making without sacrificing predictive performance. Second, robustness is advanced through novel formulations that incorporate intuitionistic fuzzy sample weighting, graph-embedded geometric representations, and the wave loss function, collectively mitigating the adverse effects of noise, outliers, and class imbalance while preserving the intrinsic topological structure of data across diverse and challenging real-world environments. Third, scalability is addressed by overcoming the matrix inversion bottleneck inherent in standard RVFL models through the integration of granular ball computing, which operates on compact granular representations of the training data rather than individual samples, and through ADAM optimization formulations that bypass matrix inversion entirely, enabling efficient learning on large-scale datasets.