Pruning coupled with learning aims to optimize the neural network (NN) structure for solving specific problems. This optimization can be used for various purposes: to prevent overfitting, to save resources for implementation and training, to provide explainability of the trained NN, and many others. The minimal structure that cannot be pruned further is not unique. Ensemble of minimal structures can be used as a committee of intellectual agents that solves problems by voting. Each minimal NN presents an "empirical knowledge" about the problem and can be verbalized. The non-uniqueness of such knowledge extracted from data is an important property of data-driven Artificial Intelligence (AI). In this work, we review an approach to pruning based on the principle: What controls training should control pruning. This principle is expected to work both for artificial NN and for selection and modification of important synaptic contacts in brain. In back-propagation artificial NN learning is controlled by the gradient of loss functions. Therefore, the first order sensitivity indicators are used for pruning and the algorithms based on these indicators are reviewed. The notion of logically transparent NN was introduced. The approach was illustrated on the problem of political forecasting: predicting the results of the US presidential election. Eight minimal NN were produced that give different forecasting algorithms. The non-uniqueness of solution can be utilised by creation of expert panels (committee). Another use of NN pluralism is to identify areas of input signals where further data collection is most useful. In Conclusion, we discuss the possible future of widely advertised XAI program.