  This paper is devoted to the features of the practical application of the
Elastic Weight Consolidation (EWC) method for continual learning of neural
networks on several training sets. We will more rigorously compare the
well-known methodologies for calculating the importance of weights used in the
EWC method. These are the Memory Aware Synapses (MAS), Synaptic Intelligence
(SI) methodologies and the calculation of the importance of weights based on
the Fisher information matrix from the original paper on EWC. We will consider
these methodologies as applied to deep neural networks with fully connected and
convolutional layers, find the optimal hyperparameters for each of the
methodologies, and compare the results of continual neural network learning
using these hyperparameters. Next, we will point out the problems that arise
when applying the EWC method to deep neural networks with convolutional layers
and self-attention layers, such as the "gradient explosion" and the loss of
meaningful information in the gradient when using the constraint of its norm
(gradient clipping). Then, we will propose a stabilization approach for the EWC
method that helps to solve these problems, evaluate it in comparison with the
original methodology and show that the proposed stabilization approach performs
on the task of maintaining skills during continual learning no worse than the
original EWC, but does not have its disadvantages. In conclusion, we present an
interesting fact about the use of various types of weight importance in the
problem of neural network pruning.
