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The method for maintaining dimensionality monitoring in neuronal networks is known as Principal Component Analysis (PCA). PCA is used to identify the most significant features in the input data and reducing the dimensionality of the input space while preserving the essential information. PCA helps in reducing the number of parameters required for training the neuronal network and also improves its performance by optimizing the learning process. It is an important technique that is widely used for both unsupervised and supervised learning tasks in neuronal networks.