Network science can offer fundamental insights into the structural and functional properties of complex systems. For example, it is widely known that neuronal circuits tend to organize into basic functional topological modules, called network motifs. In this article we show that network science tools can be successfully applied also to the study of artificial neural networks operating according to selforganizing (learning) principles. In particular, we study the emergence of network motifs in multi-layer perceptrons, whose initial connectivity is defined as a stack of fully-connected, bipartite graphs. Our simulations show that the final network topology is primarily shaped by learning dynamics, but can be strongly biased by choosing appropriate weight initialization schemes. Overall, our results suggest that non-trivial initialization strategies can make learning more effective by promoting the development of useful network motifs, which are often surprisingly consistent with those observed in general transduction networks.Preprint. Under review.

Deep belief networks (DBNs) are stochastic neural networks that can extract rich internal representations of the environment from the sensory data. DBNs had a catalytic effect in triggering the deep learning revolution, demonstrating for the very first time the feasibility of unsupervised learning in networks with many layers of hidden neurons. These hierarchical architectures incorporate plausible biological and cognitive properties, making them particularly appealing as computational models of human perception and cognition. However, learning in DBNs is usually carried out in a greedy, layer-wise fashion, which does not allow to simulate the holistic maturation of cortical circuits and prevents from modeling cognitive development. Here we present iDBN, an iterative learning algorithm for DBNs that allows to jointly update the connection weights across all layers of the model. We evaluate the proposed iterative algorithm on two different sets of visual stimuli, measuring the generative capabilities of the learned model and its potential to support supervised downstream tasks. We also track network development in terms of graph theoretical properties and investigate the potential extension of iDBN to continual learning scenarios. DBNs trained using our iterative approach achieve a final performance comparable to that of the greedy counterparts, at the same time allowing to accurately analyze the gradual development of internal representations in the deep network and the progressive improvement in task performance. Our work paves the way to the use of iDBN for modeling neurocognitive development.

Background: Deep belief networks (DBNs) are stochastic neural networks that can extract rich internal representations of the environment from the sensory data. DBNs had a catalytic effect in triggering the deep learning revolution, demonstrating for the very first time the feasibility of unsupervised learning in networks with many layers of hidden neurons. These hierarchical architectures incorporate plausible biological and cognitive properties, making them particularly appealing as computational models of human perception and cognition. However, learning in DBNs is usually carried out in a greedy, layer-wise fashion, which does not allow to simulate the holistic maturation of cortical circuits and prevents from modeling cognitive development. Method: Here we present iDBN, an iterative learning algorithm for DBNs that allows to jointly update the connection weights across all layers of the model. We evaluate the proposed iterative algorithm on two different sets of visual stimuli, measuring the generative capabilities of the learned model and its potential to support supervised downstream tasks. We also track network development in terms of graph theoretical properties and investigate the potential extension of iDBN to continual learning scenarios. Results: DBNs trained using our iterative approach achieve a final performance comparable to that of the greedy counterparts, at the same time allowing to accurately analyze the gradual development of internal representations in the deep network and the progressive improvement in task performance. Conclusions: Our work paves the way to the use of iDBN for modeling neurocognitive development.

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