Most multilayer Moore-Penrose inverse (MPI)-based neural networks, such as deep random vector functional link (RVFL), are structured with two separate stages: unsupervised feature encoding and supervised pattern classification. Once the unsupervised learning is finished, the latent encoding is fixed without supervised fine-tuning. However, in complex tasks such as handling the ImageNet dataset, there are often many more clues that can be directly encoded, while unsupervised learning, by definition, cannot know exactly what is useful for a certain task. There is a need to retrain the latent space representations in the supervised pattern classification stage to learn some clues that unsupervised learning has not yet been learned. In particular, the residual error in the output layer is pulled back to each hidden layer, and the parameters of the hidden layers are recalculated with MPI for more robust representations. In this article, a recomputation-based multilayer network using Moore-Penrose inverse (RML-MP) is developed. A sparse RML-MP (SRML-MP) model to boost the performance of RML-MP is then proposed. The experimental results with varying training samples (from 3k to 1.8 million) show that the proposed models provide higher Top-1 testing accuracy than most representation learning algorithms. For reproducibility, the source codes are available at https://github.com/W1AE/Retraining.