The recurrent Hopfield mass model: Scalability and optimization

The Recurrent Hopfield Mass Model (RHoMM) is a novel generative model developed for the estimation of large-scale effective connectivity from magnetoencephalography (MEG) Band Limited Power signals. This binary mass model, compared to the other popular generative models, has the advantages of being data-driven and in principle scalable to encode large-scale systems interactions. The aim of this work is to evaluate the scalability of the RHoMM and to optimize it at different network sizes (20-200 nodes). Specifically, using simulated objective networks with different architectures, we analysed the effects of L1 rows' normalization and of the addition of a bias in the training. We obtained that in RHoMM without normalization wider intervals of larger learning rates and convergence speeds, associated with lower errors in the inference of the effective connectivity matrix, can be obtained compared to the implementation with normalization, independently from the objective network architecture. Thus, the selection of the learning rate in this case is less critical than with normalization. To also validate the model on experimental data, we employed a dataset of MEG recordings from 10 subjects and a network size of 155 nodes. The obtained results suggest that the model could be effectively scaled to estimate standard-size MEG connectomes.