Machine learning algorithms deployed on edge devices must meet certain resource constraints and efficiency requirements. Random Vector Functional Link (RVFL) networks are favored for such applications due to their simple design and training efficiency. We propose a modified RVFL network that avoids computationally expensive matrix operations during training, thus expanding the network's range of potential applications. Our modification replaces the least-squares classifier with the Generalized Learning Vector Quantization (GLVQ) classifier, which only employs simple vector and distance calculations. The GLVQ classifier can also be considered an improvement upon certain classification algorithms popularly used in the area of Hyperdimensional Computing. The proposed approach achieved state-of-the-art accuracy on a collection of datasets from the UCI Machine Learning Repository - higher than previously proposed RVFL networks. We further demonstrate that our approach still achieves high accuracy while severely limited in training iterations (using on average only 21% of the least-squares classifier computational costs).

The learning speed of feed-forward neural networks is notoriously slow and has presented a bottleneck in deep learning applications for several decades. For instance, gradient-based learning algorithms, which are used extensively to train neural networks, tend to work slowly when all of the network parameters must be iteratively tuned. To counter this, both researchers and practitioners have tried introducing randomness to reduce the learning requirement. Based on the original construction of Igelnik and Pao, single layer neural-networks with random input-to-hidden layer weights and biases have seen success in practice, but the necessary theoretical justification is lacking. In this paper, we begin to fill this theoretical gap. We provide a (corrected) rigorous proof that the Igelnik and Pao construction is a universal approximator for continuous functions on compact domains, with approximation error decaying asymptotically like $O(1/\sqrt{n})$ for the number $n$ of network nodes. We then extend this result to the non-asymptotic setting, proving that one can achieve any desired approximation error with high probability provided $n$ is sufficiently large. We further adapt this randomized neural network architecture to approximate functions on smooth, compact submanifolds of Euclidean space, providing theoretical guarantees in both the asymptotic and non-asymptotic forms. Finally, we illustrate our results on manifolds with numerical experiments.

Stochastic configuration networks (SCNs) as a class of randomized learner model have been successfully employed in data analytics due to its universal approximation capability and fast modelling property. The technical essence lies in stochastically configuring hidden nodes (or basis functions) based on a supervisory mechanism rather than data-independent randomization as usually adopted for building randomized neural networks. Given image data modelling tasks, the use of one-dimensional SCNs potentially demolishes the spatial information of images, and may result in undesirable performance. This paper extends the original SCNs to two-dimensional version, termed 2DSCNs, for fast building randomized learners with matrix-inputs. Some theoretical analyses on the goodness of 2DSCNs against SCNs, including the complexity of the random parameter space, and the superiority of generalization, are presented. Empirical results over one regression, four benchmark handwritten digits classification, and two human face recognition datasets demonstrate that the proposed 2DSCNs perform favourably and show good potential for image data analytics.