You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
In this paper, we propose a deep learning framework based on randomized neural network. In particular, inspired by the principles of Random Vector Functional Link (RVFL) network, we present a deep RVFL network (dRVFL) with stacked layers. The parameters of the hidden layers of the dRVFL are randomly generated within a suitable range and kept fixed while the output weights are computed using the closed form solution as in a standard RVFL network. We also propose an ensemble deep network (edRVFL) that can be regarded as a marriage of ensemble learning with deep learning. Unlike traditional ensembling approaches that require training several models independently from scratch, edRVFL is obtained by training a single dRVFL network once. Both dRVFL and edRVFL frameworks are generic and can be used with any RVFL variant. To illustrate this, we integrate the deep learning networks with a recently proposed sparse-pretrained RVFL (SP-RVFL). Extensive experiments on benchmark datasets from diverse domains show the superior performance of our proposed deep RVFL networks.

Cited Abstract(s):
[1]: A long and uncertain training process is one of the most important problems for a multilayer neural network using the backpropagation algorithm. In this paper, a modified backpropagation algorithm for a certain and fast training process is presented. The modification is based on the solving of the weight matrix for the output layer using theory of equations and least squares techniques. >
Typically, Eq. can be solved via a closed form solution using either ridge regression (i.e. @math ) or Moore-Penrose pseudoinverse (i.e. @math ) [1] . Using Moore-Penrose pseudoinverse, the solution is given by: @math while using the regularized least squares (or ridge regression), the closed form solution is given by: